‘Solid’ Earth Applications: From the Surface to the Core

Part III - ‘Solid’ Earth Applications: From the Surface to the Core

Published online by Cambridge University Press: 20 June 2023

Edited by

Dylan Jones and

Alik Ismail-Zadeh: Affiliation:
Karlsruhe Institute of Technology, Germany
Fabio Castelli: Affiliation:
Università degli Studi, Florence
Dylan Jones: Affiliation:
University of Toronto
Sabrina Sanchez: Affiliation:
Max Planck Institute for Solar System Research, Germany

Book contents

Get access

Summary

A summary is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'

Type: Chapter
Information: Applications of Data Assimilation and Inverse Problems in the Earth Sciences , pp. 173 - 355

DOI: https://doi.org/10.1017/9781009180412 [Opens in a new window]

Publisher: Cambridge University Press

Print publication year: 2023

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Braun, J., Van der Beek, P., and Batt, G. (2009). Quantitative Thermochronology. Cambridge: Cambridge University Press.Google Scholar

Carlson, W. D., Donelick, R. A., and Ketcham, R. A. (1999). Variability of apatite fission-track annealing kinetics: I. Experimental Results. American Mineralogist, 84, 1213–23Google Scholar

Cros, A., Gautheron, C., Pagel, M. et al. (2014). ⁴He behavior in calcite filling viewed by (U-Th)/He dating, ⁴He diffusion and grainlographic studies. Geochimica et Cosmochimica Acta, 125, 414–32.Google Scholar

Denison, D. G. T., Holmes, C. C., Mallick, B. K., and Smith, A. F. M. (2002). Bayesian Methods for Non-linear Classification and Regression. Chichester: John Wiley and Sons.Google Scholar

Dodson, M. H. (1973). Closure Temperature in Cooling Geochronological and Petrological Systems. Contributions to Mineralogy and Petrology, 40, 259–74.CrossRef Google Scholar

Donelick, R. A., Ketcham, R. A., and Carlson, W. D. (1999). Variability of apatite fission-track annealing kinetics II: Grainlographic orientation effects. American Mineralogist, 84, 1224–34.CrossRef Google Scholar

Ducassou, C. (2009). Age et origine des premiers reliefs de la chaîne hercynienne: le dévonocarbonifère du bassin d’Ancenis. Ph.D. thesis (in French), Université Rennes 1.Google Scholar

Duddy, I. R., Green, P. F., and Laslett, G. M. (1988). Thermal annealing of fission tracks in apatite 3. Variable temperature annealing. Chemical Geology: Isotope Geoscience Section, 73, 25–38.Google Scholar

Duddy, I. R., Green, P. F., Laslett, G. M. et al. (1989). Thermal annealing of fission tracks in apatite 4. Quantitative modelling techniques and extension to geological timescales. Chemical Geology: Isotope Geoscience Section, 79, 155–82.Google Scholar

Everitt, B.S., and Hand, D.J. (1981). Finite Mixture Distributions. New York: Chapman and Hall.CrossRef Google Scholar

Farley, K. A. (2000). Helium diffusion from apatite: General behavior as illustrated by Durango fluorapatite. Journal of Geophysical Research, 105(B2), 2903.CrossRef Google Scholar

Farley, K. A., and McKeon, R. (2015). Radiometric dating and temperature history of banded iron formation–associated hematite, Gogebic iron range, Michigan, USA. Geology 43(12), 1083–6. https://doi.org/10.1130/G37190.1.Google Scholar

Farley, K. A., Wolf, R. A., and Silver, L. T. (1996). The effects of long alpha-stopping distances on (U-Th)/He ages. Geochimica et Cosmochimica Acta, 60, 4223–9.Google Scholar

Flowers, R. M., Ketcham, R. A., Shuster, D. L., and Farley, K. A. (2009). Apatite (U-Th)/He thermochronometry using a radiation damage accumulation and annealing model. Geochimica et Cosmochimica Acta, 73, 2347–65Google Scholar

Friel, N., and Wyse, J. (2012). Estimating the evidence: A review. Statistica Neerlandica, 66, 288–308. https://doi.org/10.1111/j.1467-9574.2011.00515.x.CrossRef Google Scholar

Galbraith, R. (1988). Graphical display of estimates having differing standard errors. Technometrics, 30(3), 271–81. https://doi.org/10.2307/1270081.Google Scholar

Galbraith, R.F. (2005). Statistics for Fission-Track Analysis. New York: Chapman and Hall.CrossRef Google Scholar

Galbraith, R. F., and Green, P. F. (1990). Estimating the component ages in a finite mixture. Nuclear Tracks and Radiation Measurements, 17(3), 197–206.Google Scholar

Gallagher, K. (1995). Evolving thermal histories from fission track data. Earth Planetary Science Letters, 136, 421–35.Google Scholar

Gallagher, K. (2012). Transdimensional inverse thermal history modeling for quantitative thermochronology. Journal of Geophysical Research: Solid Earth, 117, B02408. https://doi.org/10.1029/2011JB00882.Google Scholar

Gallagher, K., Stephenson, J., Brown, R., Holmes, C., and Fitzgerald, P. (2005). Low temperature thermochronology and modelling strategies for multiple samples 1: Vertical profiles. Earth Planetary Science Letters, 237, 193–208.CrossRef Google Scholar

Gautheron, C., Tassan-Got, L., Barbarand, J., and Pagel, M. (2009). Effect of alpha-damage annealing on apatite (U-Th)/He thermochronology. Chemical Geology, 266, 157–70.CrossRef Google Scholar

Ginster, U., Reiners, P. W., Nasdala, L., and Chutimun Chanmuangg, N. (2019). Annealing kinetics of radiation damage in zircon. Geochimica et Cosmochimica Acta, 249, 235–46.Google Scholar

Goswami, J. N., Jha, R., and Lal, D. (1984). Quantitative treatment of annealing of charged particle tracks in common rock minerals. Earth Planetary Science Letters, 71, 120–8.Google Scholar

Green, P. F. (1988). The relationship between track shortening and fission track age reduction in apatite: Combined influences of inherent instability, annealing anisotropy, length bias and system calibration. Earth Planetary Science Letters, 89, 335–52.CrossRef Google Scholar

Green, P. F., Duddy, I. R., Gleadow, A. J. W., Tingate, P. R., and Laslett, G. M. (1986). Thermal annealing of fission tracks in apatite: 1. A qualitative description. Chemical Geology: Isotope Geoscience Section, 59, 237–53CrossRef Google Scholar

Guenthner, W. R., Reiners, P. W., Ketcham, R. A., Nasdala, L., and Giester, G. (2013). Helium diffusion in natural zircon: Radiation damage, anisotropy, and the interpretation of zircon (U- Th)/He thermochronology. American Journal of Science, 313, 145–98.Google Scholar

Herman, F., Seward, D., Valla, P. G. et al. (2013). Worldwide acceleration of mountain erosion under a cooling climate. Nature, 504(7480), 423–6. https://doi.org/10.1038/nature12877.CrossRef Google Scholar

Higson, E., Hadnley, W., Hobson, M, and Lasenby, A. (2019). Dynamic nested sampling: An improved algorithm for parameter estimation and evidence calculation. Statistics and Computing, 29, 891–913Google Scholar

Jasra, A., Stephens, D. A., Gallagher, K., and Holmes, C. C. (2006). Analysis of geochronological data with measurement error using Bayesian mixtures, Mathematical Geology, 38(3), 269-300.Google Scholar

Ketcham, R. A. (2005). Forward and inverse modeling of low-temperature thermochronometry data. In Reiners, P. W. and Ehlers, T. A., eds., Reviews in Mineralogy and Geochemistry. Vol 58: Low-Temperature Thermochronology: Techniques, Interpretations and Applications. Chantilly, VA: Mineralogical Society of America, pp. 275–314.CrossRef Google Scholar

Ketcham, R. A., Carter, A., Donelick, R. A., Barbarand, J., and Hurford, A. J. (2007). Improved modeling of fission-track annealing in apatite. American Mineralogist, 92, 799–810.Google Scholar

Ketcham, R. A., Donelick, R. A., and Carlson, W. D. (1999). Variability of apatite fission-track annealing kinetics. III. Extrapolation to geological timescales. American Mineralogist, 84, 1235–55.Google Scholar

Ketcham, R. A., Guenthner, W. R., and Reiners, P. W. (2013). Geometric analysis of radiation damage connectivity in zircon, and its implications for helium diffusion. American Mineralogist, 98, 350–60CrossRef Google Scholar

Lartillot, N., and Philippe, H. (2006). Computing Bayes factors using thermodynamic integration. Systematic Biology, 55, 195–207.Google Scholar

Laslett, G. M., Green, P. F., Duddy, I. R., and Gleadow, A. J. W. (1987). Thermal annealing of fission tracks, 2. A quantitative analysis. Chemical Geology: Isotope Geoscience Section, 65, 1–13.Google Scholar

Li, W., Wang, L., Lang, M., Trautmann, C., and Ewing, R. C. (2011). Thermal annealing mechanisms of latent fission tracks: Apatite vs. zircon. Earth and Planetary Science Letters, 203, 227–35.Google Scholar

Licciardi, A., Gallagher, K., and Clark, S. A. (2020). A Bayesian approach for thermal history reconstruction in basin modelling, Journal of Geophysical Research: Solid Earth, 125(7), e2020JB019384. https://doi.org/10.1029/2020JB019384.Google Scholar

Liu, P., Elshall, A. S., Ye, M. et al. (2016). Evaluating marginal likelihood with thermodynamic integration method and comparison with several other numerical methods. Water Resources Research, 52(2), 734–58. https://doi.org/10.1002/2014WR016718.Google Scholar

Lovera, O. M., Richter, F. M, and Harrison, T. M. (1989). 40Ar/39Ar geothermometry for slowly cooled samples having a distribution of domain sizes. Journal of Geophysical Research, 94, 17917–35.Google Scholar

Malusa, M., and Fitzgerald, P. F. (2019). Fission-Track Thermochronology and its Application to Geology, Springer Textbooks in Earth Sciences. Cham: Springer International Publishing.Google Scholar

McDannell, K. T., and Issler, D. R. (2021). Simulating sedimentary burial cycles. Part 1: Investigating the role of apatite fission track annealing kinetics using synthetic data. Geochronology, 3, 321–35. https://doi.org/10.5194/gchron-3-321-2021.CrossRef Google Scholar

McDougall, I., and Harrison, T. M. (1988). Geochronology and Thermochronology by the 40Ar/39Ar method, 2nd ed. New York: Oxford University Press.Google Scholar

Meesters, A. G., and Dunai, T. J (2002a). Solving the production-diffusion equation for finite diffusion domains of various shapes. Part I: Implications for low-temperature (U-Th)/He-thermochronology. Chemical Geology, 186, 333–44Google Scholar

Meesters, A. G., and Dunai, T. J. (2002b). Solving the production-diffusion equation for finite diffusion domains of various shapes. Part II: Application to cases with -ejection and non-homogenous distribution of the source. Chemical Geology, 186, 347–63Google Scholar

Pooley, C. M., and Marion, G. (2018). Bayesian model evidence as a practical alternative to deviance information criterion. Royal Society Open Science, 5(3), 171519. http://dx.doi.org/10.1098/rsos.171519.Google Scholar

Recanati, A., Gautheron, C., Barbarand, J. et al. (2017). Helium trapping in apatite damage: Insights from (U-Th-Sm)/He dating of different granitoid lithologies. Chemical Geology 470, 116–31Google Scholar

Reiners, P. W., Carlson, R.W., Renne, P.R. et al. (2018). Geochronology and Thermochronology. Hoboken, NJ: Wiley.Google Scholar

Reiners, P. W., and Ehlers, T. A., eds. (2005). Reviews in Mineralogy and Geochemistry. Vol. 58: Low-Temperature Thermochronology: Techniques, Interpretations and Applications. Chantilly, VA: Mineralogical Society of America.Google Scholar

Richardson, S., and Green, P. J. (1997). On Bayesian analysis of mixture models with an unknown number of components. Journal of the Royal Statistical Society Series B, 59(4), 731–92.Google Scholar

Richardson, S., Leblond, L., Jaussent, I., and Green, P. J. (2002). Mixture models in measurement error problems, with reference to epidemiological studies. Journal of the Royal Statistical Society Series A, 165(3), 549–66.Google Scholar

Sambridge, M. (2014). A parallel tempering algorithm for probabilistic sampling and multimodal optimization. Geophysical Journal International, 196, 357–74. https://doi.org/10.1093/gji/ggt342.Google Scholar

Sambridge, M. S., and Compston, W. (1994). Mixture modelling of multi-component data sets with application to ion-probe zircon ages. Earth Planetary Science Letters, 128, 373–90.CrossRef Google Scholar

Sambridge, M., Gallagher, K., Jackson, A., and Rickwood, P. (2006). Trans-dimensional inverse problems, Model Comparison and the Evidence. Geophysical Journal International, 167, 528–42.Google Scholar

Schildgen, T. F., van der Beek, P. A., Sinclair, H. D., and Thiede, R. C. (2018). Spatial correlation bias in late-Cenozoic erosion histories derived from thermochronology. Nature, 559(7712), 89–93. https://doi.org/10.1038/s41586-018-0260-6.Google Scholar

Schoene, B. (2014). U-Th-Pb Geochronology. In Holland, H. D. and Turekian, K. K., eds., Treatise on Geochemistry, 2nd ed. Amsterdam: Elsevier, pp. 341–78.Google Scholar

Shuster, D. L, Flowers, R. M., and Farley, K. A. (2006). The influence of natural radiation damage on helium diffusion kinetics in apatite. Earth and Planetary Science Letters. https://doi.org/10.1016/J.EPSL.2006.07.028.CrossRef Google Scholar

Stephenson, J., Gallagher, K., and Holmes, C. (2006). Low temperature thermochronology and modelling strategies for multiple samples 2: Partition modeling for 2D and 3D distributions with discontinuities. Earth and Planetary Science Letters, 241, 557–70.Google Scholar

Tagami, T., Galbraith, R., Yamada, R., and Laslett, G. (1998). Revised annealing kinetics of fission tracks in zircon and geological implications. In Van den Haute, P. and De Corte, F., eds., Advances in Fission-Track Geochronology. Dordrecht: Kluwer, pp. 99–112.Google Scholar

Titterington, D. M., Smith, A. F. M., and Makov, H. E. (1985). Statistical Analysis of Finite Mixture Distributions. Chichester: Wiley.Google Scholar

Trotta, R. (2008). Bayes in the sky: Bayesian inference and model selection in cosmology. Contemporary Physics, 49, 71–104Google Scholar

Willett, C. D., Fox, M., and Shuster, D.L. (2017). A helium-based model for the effects of radiation damage annealing on helium diffusion kinetics in apatite. Earth Planetary Science Letters, 477, 195–204Google Scholar

Willett, S. D., Herman, F., Fox, M. et al. (2021). Bias and error in modelling thermochronometric data: Resolving a potential increase in Plio-Pleistocene erosion rate. Earth Surface Dynamics, 9, 1153–221. https://doi.org/10.5194/esurf-9-1153-2021.Google Scholar

Yamada, R., Murakami, M., and Tagami, T. (2007). Statistical modelling of annealing kinetics of fission tracks in zircon; Reassessment of laboratory experiments. Chemical Geology 236, 75–91.Google Scholar

References

Branca, S., De Beni, E., and Proietti, C. (2013). The large and destructive 1669 AD eruption at Etna volcano: Reconstruction of the lava flow field evolution and effusion rate trend. Bulletin of Volcanology, 75, 694. https://doi.org/10.1007/s00445-013-0694-5.CrossRef Google Scholar

Bryant, E. (2005). Natural Hazards. Cambridge: Cambridge University Press.Google Scholar

Buttner, R., Zimanowski, B., Blumm, J., and Hagemann, L. (1998). Thermal conductivity of a volcanic rock material (olivine-melilinite) in the temperature range between 288 and 1470 K. Journal of Volcanology and Geothermal Research, 80, 293–302.CrossRef Google Scholar

Calder, E. S., Lavallée, Y., Kendrick, J. E., and Bernstein, M. (2015). Lava dome eruptions. In Sigurdsson, H., Houghton, B, Rymer, H, Stix, J, and McNutt, S, eds., Encyclopedia of Volcanoes, 2nd ed. San Diego, CA: Academic Press, pp. 343–62.CrossRef Google Scholar

Calvari, S., Spampinato, L., Lodato, L. et al. (2005). Chronology and complex volcanic processes during the 2002–2003 flank eruption at Stromboli volcano (Italy) reconstructed from direct observations and surveys with a handheld thermal camera. Journal of Geophysical Research, 110, B02201. https://doi.org/10.1029/2004JB003129.Google Scholar

Castruccio, A., and Contreras, M. A. (2016). The influence of effusion rate and rheology on lava flow dynamics and morphology: A case study from the 1971 and 1988–1990 eruptions at Villarrica and Lonquimay volcanoes, Southern Andes of Chile. Journal of Volcanology and Geothermal Research, 327, 469–83.Google Scholar

Chandrasekhar, S. (1961). Hydrodynamic and Hydromagnetic Stability. Oxford: Oxford University Press.Google Scholar

Chevrel, M. O., Platz, T., Hauber, E., Baratoux, D., Lavallée, Y., and Dingwell, D. B. (2013). Lava flow rheology: A comparison of morphological and petrological methods. Earth and Planetary Science Letters, 384, 109–20.Google Scholar

Christensen, U. R. (1992). An Eulerian technique for thermomechanical modeling of lithospheric extension. Journal of Geophysical Research, 97, 2015–36.Google Scholar

Cordonnier, B., Lev, E., and Garel, F. (2015). Benchmarking lava-flow models. In Harris, A. J. L., De Groeve, T., Garel, F., and Carn, S. A., eds., Detecting, Modelling and Responding to Effusive Eruptions, Special Publications, 426. London: Geological Society, pp. 425–45.Google Scholar

Costa, A., and Macedonio, G. (2005). Computational modeling of lava flows: A review. In Manga, M. and Ventura, G., eds., Kinematics and Dynamics of Lava Flows, Special Paper 396, Boulder, CO: Geological Society of America, pp. 209–18.Google Scholar

Costa, A., Caricchi, L., and Bagdassarov, N. (2009). A model for the rheology of particle-bearing suspensions and partially molten rocks. Geochemistry, Geophysics, Geosystems, 10, Q03010. https://doi.org/10.1029/2008Gc002138.Google Scholar

Cutter, S., Ismail-Zadeh, A., Alcántara-Ayala, I. et al. (2015). Global risk: Pool knowledge to stem losses from disasters. Nature, 522, 277–9.Google Scholar

Daag, A. S., Dolan, M. T., Laguerta, E. et al. (1996). Growth of a postclimactic lava dome at Pinatubo Volcano, July‒October 1992. In Newhall, C. and Punongbayan, R., eds., Fire and Mud: Eruptions and Lahars of Mount Pinatubo, Philippines. Seattle: University of Washington Press, pp. 647–64.Google Scholar

Dragoni, M. A. (1989). A dynamical model of lava flows cooling by radiation. Bulletin of Volcanology, 51, 88–95.Google Scholar

Flynn, L. P., Harris, A. J. L., and Wright, R. (2001). Improved identification of volcanic features using Landsat 7 ETM+. Remote Sensing of Environment, 78, 180–93.Google Scholar

Giordano, D., and Dingwell, D. B. (2003). Viscosity of hydrous Etna basalt: Implications for Plinian-style basaltic eruptions. Bulletin of Volcanology, 65, 8–14.Google Scholar

Griffiths, R. W. (2000). The dynamics of lava flows. Annual Review of Fluid Mechanics, 32, 477–518.Google Scholar

Harris, A. J. L., Flynn, L. P., Keszthelyi, L. et al. (1998). Calculation of lava effusion rates from Landsat TM data. Bulletin of Volcanology, 60, 52–71.Google Scholar

Harris, A. J. L., Flynn, L. P., Matias, O., Rose, W. I., and Cornejo, J. (2004). The evolution of an active silicic lava flow field: An ETM+ perspective. Journal of Volcanology and Geothermal Research, 135, 147–68.Google Scholar

Harris, A. J. L., Rose, W. I., and Flynn, L. P. (2003). Temporal trends in lava dome extrusion at Santiaguito 1922–2000. Bulletin of Volcanology, 65, 77–89.Google Scholar

Heap, M. J., Troll, V., Kushnir, A. R. L. et al. (2019). Hydrothermal alteration of andesitic lava domes can lead to explosive volcanic behaviour. Nature Communications, 10, 5063. https://doi.org/10.1038/s41467-019-13102-8.Google Scholar

Hidaka, M., Goto, A., Umino, S., and Fujita, E. (2005). VTFS project: Development of the lava flow simulation code LavaSIM with a model for three-dimensional convection, spreading, and solidification. Geochemistry, Geophysics, Geosystems, 6, Q07008. https://doi.org/10.1029/2004GC000869.Google Scholar

Ismail-Zadeh, A., and Tackley, P. (2010). Computational Methods for Geodynamics. Cambridge: Cambridge University Press.Google Scholar

Ismail-Zadeh, A., and Takeuchi, K. (2007). Preventive disaster management of extreme natural events. Natural Hazards, 42, 459–67.Google Scholar

Ismail-Zadeh, A., Korotkii, A., Schubert, G., and Tsepelev, I. (2007). Quasi-reversibility method for data assimilation in models of mantle dynamics. Geophysical Journal International, 170, 1381–98.Google Scholar

Ismail-Zadeh, A., Korotkii, A., and Tsepelev, I. (2016). Data-Driven Numerical Modeling in Geodynamics: Methods and Applications. Heidelberg: Springer.Google Scholar

Jeffrey, D., and Acrivos, A. (1976). The rheological properties of suspensions of rigid particles. AIChE Journal, 22, 417–32.Google Scholar

Kabanikhin, S. I. (2011). Inverse and Ill-Posed Problems: Theory and Applications. Berlin: De Gruyter.Google Scholar

Kelfoun, K., and Vargas, S. V. (2015). VolcFlow capabilities and potential development for the simulation of lava flows. In Harris, A. J. L., De Groeve, T., Farel, F., and Carn, S. A., eds., Detecting, Modelling and Responding to Effusive Eruptions, Special Publications 426. London: Geological Society, pp. 337–43.Google Scholar

Kelfoun, K., Santoso, A. B., Latchimy, T. et al. (2021). Growth and collapse of the 2018–2019 lava dome of Merapi volcano. Bulletin of Volcanology, 83, 8. https://doi.org/10.1007/s00445-020-01428-x.Google Scholar

Kilburn, C. R. J. (2000). Lava flow and flow fields. In Sigurdsson, H., ed., Encyclopedia of Volcanoes. San Diego, CA: Academic Press, pp.291–305.Google Scholar

Korotkii, A. I., and Kovtunov, D. A. (2006). Reconstruction of boundary regimes in an inverse problem of thermal convection of a high viscous fluid. Proceedings of the Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, 12(2), 88–97.Google Scholar

Korotkii, A. I., and Starodubtseva, Y. V. (2014). Direct and inverse problems for models of stationary reactive-convective-diffusive flow. Proceedings of the Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, 20(3), 98–113.Google Scholar

Korotkii, A., Kovtunov, D., Ismail-Zadeh, A., Tsepelev, I., and Melnik, O. (2016). Quantitative reconstruction of thermal and dynamic characteristics of lava from surface thermal measurements. Geophysical Journal International, 205, 1767–79.Google Scholar

Ladyzhenskaya, O. A. (1969). The Mathematical Theory of Viscous Incompressible Flow. New York: Gordon and Breach.Google Scholar

Lavallée, Y., Varley, N. R., Alatorre-Ibarguengoitia, M. A. et al. (2012). Magmatic architecture of dome building eruptions at Volcán de Colima, Mexico. Bulletin of Volcanology, 74, 249–60.Google Scholar

Lejeune, A., and Richet, P. (1995). Rheology of crystal-bearing silicate melts: An experimental study at high viscosity. Journal of Geophysical Research, 100, 4215–29.Google Scholar

Lions, J. L. (1971). Optimal Control of Systems Governed by Partial Differential Equations. Berlin: Springer.Google Scholar

Lombardo, V., Musacchio, M., and Buongiorno, M. F. (2012). Error analysis of subpixel lava temperature measurements using infrared remotely sensed data. Geophysical Journal International, 191, 112–25.Google Scholar

Loughlin, S. C., Sparks, S., Brown, S. K., Jenkins, S. F., and Vye-Brown, C., eds. (2015). Global Volcanic Hazards and Risk. Cambridge: Cambridge University Press.Google Scholar

Mardles, E. (1940). Viscosity of suspensions and the Einstein equation. Nature, 145, 970. https://doi.org/10.1038/145970a0.Google Scholar

Marsh, B. D. (1981). On the crystallinity, probability of occurrence, and rheology of lava and magma. Contributions to Mineralogy and Petrology, 78, 85–98.Google Scholar

Melnik, O., and Sparks, R. S. J. (1999). Nonlinear dynamics of lava dome extrusion. Nature, 402, 37–41.Google Scholar

Naimark, B. M., and Ismail-Zadeh, A. T. (1995). Numerical models of subsidence mechanism in intracratonic basin: Application to North American basins. Geophysical Journal International, 123, 149–60.Google Scholar

Naimark, B. M., Ismail-Zadeh, A. T., and Jacoby, W. R. (1998). Numerical approach to problems of gravitational instability of geostructures with advected material boundaries. Geophysical Journal International, 134, 473–83.Google Scholar

Nakada, S., Shimizu, H., and Ohta, K. (1999). Overview of the 1990‒1995 eruption at Unzen Volcano. Journal of Volcanology and Geothermal Research, 89, 1–22.Google Scholar

Nakada, S., Zaennudin, A., Yoshimoto, M. et al. (2019). Growth process of the lava dome/flow complex at Sinabung volcano during 2013‒2016. Journal of Volcanology and Geothermal Research, 382, 120–36.Google Scholar

Navon, I. M., Zou, X., Derber, J. and Sela, J. (1992). Variational data assimilation with an adiabatic version of the NMC spectral model. Monthly Weather Review, 120, 1433–46.Google Scholar

Papale, P., ed. (2014). Volcanic Hazards, Risks and Disasters. Amsterdam: Elsevier.Google Scholar

Patankar, S. V., and Spalding, D. B. (1972). A calculation procedure for heat and mass transfer in three-dimensional parabolic flows. International Journal of Heat and Mass Transfer, 15, 1787–806.Google Scholar

Poland, M. P., and Anderson, K. R. (2020). Partly cloudy with a chance of lava flows: Forecasting volcanic eruptions in the twenty‐first century. Journal of Geophysical Research, 125, e2018JB016974. https://doi.org/10.1029/2018JB016974.Google Scholar

Polak, E., and Ribière, G. (1969). Note on the convergence of methods of conjugate directions. Revue Francaise d’Informatique et de Recherche Operationnelle, 3(16), 35–43.Google Scholar

Rumpf, M. E., Lev, E. and Wysocki, R. (2018). The influence of topographic roughness on lava flow emplacement. Bulletin of Volcanology, 80, 63. https://doi.org/10.1007/s00445-018-1238-9.Google Scholar

Salomon, D. (2007). Data Compression: The Complete Reference. London: Springer.Google Scholar

Sheldrake, T. E., Sparks, R. S. J., Cashman, K. V., Wadge, G., and Aspinall, W. P. (2016). Similarities and differences in the historical records of lava dome-building volcanoes: Implications for understanding magmatic processes and eruption forecasting. Earth-Science Reviews, 160, 240–63.Google Scholar

Short, N. M., and Stuart, L. M. (1983). The Heat Capacity Mapping Mission (HCMM) Anthology. Washington, DC: NASA Scientific and Technical Information Branch.Google Scholar

Starodubtseva, Y., Starodubtsev, I., Ismail-Zadeh, A. et al. (2021). A method for magma viscosity assessment by lava dome morphology. Journal of Volcanology and Seismology, 15, 159–68. https://doi.org/10.1134/S0742046321030064.Google Scholar

Swanson, D. A., Dzurisin, D., Holcomb, R. T. et al. (1987). Growth of the lava dome at Mount St Helens, Washington, (USA) 1981‒1983. In Fink, J. H., ed., The Emplacement of Silicic Domes and Lava Flows, Special Paper 212. Boulder, CO: Geological Society of America, pp. 1–16.Google Scholar

Takeuchi, S. (2011). Preeruptive magma viscosity: An important measure of magma eruptibility. Journal of Geophysical Research, 116, B10201. https://doi.org/10.1029/2011JB008243.Google Scholar

Temam, R. (1977). Navier–Stokes Equations: Theory and Numerical Analysis. Amsterdam: North-Holland.Google Scholar

Tikhonov, A. N. (1963). Solution of incorrectly formulated problems and the regularization method, Soviet Mathematics Doklady 4, 1035–8.Google Scholar

Tikhonov, A. N., and Arsenin, V. Y. (1977). Solution of Ill-Posed Problems. Washington, DC: Winston.Google Scholar

Tikhonov, A. N., and Samarskii, A. A. (1990). Equations of Mathematical Physics. New York: Dover Publications.Google Scholar

Tsepelev, I., Ismail-Zadeh, A., Melnik, O., and Korotkii, A. (2016). Numerical modelling of fluid flow with rafts: An application to lava flows. Journal of Geodynamics, 97, 31–41.Google Scholar

Tsepelev, I., Ismail-Zadeh, A., Starodubtseva, Y., Korotkii, A., and Melnik, O. (2019). Crust development inferred from numerical models of lava flow and its surface thermal measurements. Annals of Geophysics, 62(2), VO226. https://doi.org/10.4401/ag-7745.Google Scholar

Tsepelev, I., Ismail-Zadeh, A., and Melnik, O. (2020). Lava dome morphology inferred from numerical modelling. Geophysical Journal International, 223(3), 1597–609.Google Scholar

Tsepelev, I., Ismail-Zadeh, A., and Melnik, O. (2021). Lava dome evolution at Volcán de Colima, México during 2013: Insights from numerical modeling. Journal of Volcanology and Seismology, 15, 491–501. https://doi.org/10.1134/S0742046321060117.Google Scholar

Turcotte, D. L., and Schubert, G. (2002). Geodynamics, 2nd ed. Cambridge: Cambridge University Press.Google Scholar

Voight, B., and Elsworth, D. (2000). Instability and collapse of hazardous gas-pressurized lava domes. Geophysical Research Letters, 27(1), 1–4.Google Scholar

Wadge, G., Robertson, R. E. A., and Voight, B., eds. (2014). The Eruption of Soufrière Hills Volcano, Montserrat, from 2000 to 2010. GSL Memoirs, vol. 39. London: Geological Society. https://doi.org/10.1144/M39.Google Scholar

Wang, Z., Bovik, A. C., Sheikh, H. R., and Simoncelli, E. P. (2004). Image quality assessment: From error visibility to structural similarity. IEEE Transactions on Image Processing, 13(4), 600–12.Google Scholar

Walker, G. P. L. (1973). Lengths of lava flows. Philosophical Transactions of the Royal Society, 274, 107–18.Google Scholar

Watts, R. B., Herd, R. A., Sparks, R. S. J., and Young, S. R. (2002). Growth patterns and emplacement of the andesitic lava dome at Soufrière Hills Volcano, Montserrat. In Druitt, T. H., and Kokelaar, B. P., eds., The Eruption of Soufrière Hills Volcano, Montserrat, from 1995 to 1999. GLS Memoirs, vol. 21. London: Geological Society, pp. 115–52.Google Scholar

Wright, R., Garbeil, H., and Davies, A. G. (2010). Cooling rate of some active lavas determined using an orbital imaging spectrometer. Journal of Geophysical Research, 115, B06205. https://doi.org/10.1029/2009JB006536.Google Scholar

Wright, T. L., and Okamura, R. T. (1977). Cooling and crystallization of tholeiitic basalt, 1965 Makaopuhi lava lake, Hawaii. US Geological Survey Professional Paper 1004.Google Scholar

Zakšek, K., Hort, M., and Lorenz, E. (2015). Satellite and ground based thermal observation of the 2014 effusive eruption at Stromboli volcano. Remote Sensing, 7, 17190–211.Google Scholar

Zeinalova, N., Ismail-Zadeh, A., Melnik, O. E., Tsepelev, I., and Zobin, V. M. (2021). Lava dome morphology and viscosity inferred from data-driven numerical modeling of dome growth at Volcán de Colima, Mexico during 2007–2009. Frontiers in Earth Science, 9, 735914. https://doi.org/10.3389/feart.2021.735914.Google Scholar

Zobin, V. M., Arámbula, R., Bretón, M. et al. (2015). Dynamics of the January 2013–June 2014 explosive-effusive episode in the eruption of Volcán de Colima, México: Insights from seismic and video monitoring. Bulletin of Volcanology, 77, 31. https://doi.org/10.1007/s00445-015-0917-z.Google Scholar

References

Asano, K., and Iwata, T. (2012). Source model for strong ground motion generation in the frequency range 0.1–10 Hz during the 2011 Tohoku earthquake. Earth Planets Space, 64, 1111–23. https://doi.org/10.5047/eps.2012.05.003.Google Scholar

Awaji, T., Kamachi, M., Ikeda, M., and Ishikawa, Y. (2009). Data Assimilation: Innovation Combining Observation and Model (in Japanese). Kyoto: Kyoto University Press.Google Scholar

Böse, M., Smith, D. E., Felizardo, C. et al. (2018). FinDer v.2: Improved real-time ground-motion predictions forM2–M9 with seismic finite-source characterization. Geophysical Journal International, 212, 725–42. https://doi.org/10.1093/gji/ggx430.Google Scholar

Chen, D. Y., Hsiao, N. C., and Wu, Y. M. (2015). The earthworm-based earthquake alarm reporting system in Taiwan. Bulletin of the Seismological Society of America, 105, 568–79. https://doi.org/10.1785/0120140147.Google Scholar

Cochran, E. S., Bunn, J., Minson, S. E. et al. (2019). Event detection performance of the PLUM earthquake early warning algorithm in southern California. Bulletin of the Seismological Society of America, 109, 1524–41. https://doi.org/10.1785/0120180326.Google Scholar

Cuellar, A., Espinosa-Aranda, J. M., Suárez, G. (2014). The Mexican Seismic Alert System (SASMEX): Its alert signals, broadcast results and performance during the M 7.4 Punta Maldonado earthquake of March 20th, 2012. In Wenzel, F. and Zschau, J., eds., Early Warning for Geological Disasters. Berlin: Springer, pp. 71–87.Google Scholar

Erdik, M., Fahjan, Y., Ozel, O. et al. (2003). Istanbul earthquake rapid response and the early warning system, Bulletin of Earthquake Engineering, 1, 157–63. https://doi.org/10.1023/A:1024813612271.Google Scholar

Furumura, T., and Maeda, T. (2021). High-resolution source imaging based on time-reversal wave propagation simulations using assimilated dense seismic records. Geophysical Journal International, 225, 140–57. https://doi.org/10.1093/gji/ggaa586.Google Scholar

Furumura, T., Maeda, T., and Oba, A. (2019). Early forecast of long‐period ground motions via data assimilation of observed ground motions and wave propagation simulations. Geophysical Research Letters, 46(1), 139–47. https://doi.org/10.1029/2018GL081163.Google Scholar

Gasparini, P., and Manfredi, G. (2014). Development of earthquake early warning systems in the European Union. In Zschau, J. and Wenzel, F., eds., Early Warning for Geological Disasters: Scientific Methods and Current Practice, Berlin: Springer, pp. 89–101. https://doi.org/10.1007/978-3-642-12233-0_5.Google Scholar

Gusev, A. A., and Abubakirov, I. R. (1987). Monte-Carlo simulation of record envelope of a near earthquake. Physics of the Earth and Planetary Interiors, 49, 30–6.Google Scholar

Hoshiba, M. (1991). Simulation of multiple scattered coda wave excitation based on the energy conservation law. Physics of the Earth and Planetary Interiors, 67, 123–6.Google Scholar

Hoshiba, M. (2013a). Real-time prediction of ground motion by Kirchhoff–Fresnel boundary integral equation method: Extended front detection method for earthquake early warning. Journal of Geophysical Research: Solid Earth, 118, 1038–50. https://doi.org/10.1002/jgrb.50119.Google Scholar

Hoshiba, M. (2013b). Real-time correction of frequency-dependent site amplification factors for application to earthquake early warning. Bulletin of the Seismological Society of America, 103, 3179–88. https://doi.org/10.1785/0120130060.Google Scholar

Hoshiba, M. (2020). Too-late warnings by estimating Mw: earthquake early warning in the near-fault region. Bulletin of the Seismological Society of America, 110, 1276–88. https://doi.org/10.1785/0120190306.Google Scholar

Hoshiba, M. (2021), Real-time prediction of impending ground shaking: Review of wavefield-based (ground-motion-based) method for earthquake early warning. Frontier in Earth Sciences, 22. https://doi.org/10.3389/feart.2021.722784.Google Scholar

Hoshiba, M., and Aoki, S. (2015). Numerical shake prediction for earthquake early warning: Data assimilation, real‐time shake mapping, and simulation of wave propagation. Bulletin of the Seismological Society of America, 105, 1324–38. https://doi.org/10.1785/0120140280.Google Scholar

Hoshiba, M., and Ozaki, T. (2014). Earthquake early warning and tsunami warning of the Japan Meteorological Agency, and their performance in the 2011 off the Pacific Coast of Tohoku Earthquake (Mw9.0). In Wenzel, F. and Zschau, J., eds., Early Warning for Geological Disasters: Scientific Methods and Current Practice. Berlin: Springer, pp. 1–28. https://doi.org/10.1007/978-3-642-12233-0_1.Google Scholar

Hoshiba, M., Iwakiri, K., Hayashimoto, N. et al. (2011). Outline of the 2011 off the Pacific Coast of Tohoku Earthquake (Mw 9.0): Earthquake Early Warning and observed seismic intensity. Earth Planets Space, 63, 547–51. https://doi.org/10.5047/eps.2011.05.031.Google Scholar

Hoshiba, M., Kamigaichi, O., Saito, M., Tsukada, S. Y., and Hamada, N. (2008). Earthquake early warning starts nationwide in Japan. Eos, Transactions, American Geophysical Union, 89, 73–4. https://doi.org/10.1029/2008EO080001.Google Scholar

Japan Meteorological Agency. (2012). Report of the 2011 off the Pacific Coast of Tohoku earthquake by Japan Meteorological Agency (in Japanese), Japan Meteorological Agency.Google Scholar

Kalnay, E. (2003). Atmospheric Modeling, Data Assimilation and Predictability. Cambridge: Cambridge University Press.Google Scholar

Kurahashi, S. and Irikura, K. (2013). Short-period source model of the 2011 Mw 9.0 Off the Pacific Coast of Tohoku earthquake. Bulletin of the Seismological Society of America, 103, 1373–93. https://doi.org/10.1785/0120120157.Google Scholar

Kurzon, I., Nof, R. N., Laporte, M. et al. (2020). The ‘TRUAA’ seismic network: Upgrading the Israel seismic network – Toward national earthquake early warning system. Seismological Research Letters, 91, 3236–3255. https://doi.org/10.1785/0220200169.Google Scholar

Oba, A., Furumura, T., and Maeda, T. (2020). Data assimilation‐based early forecasting of long‐period ground motions for large earthquakes along the Nankai Trough. Journal of Geophysical Research: Solid Earth, 125(6), e2019JB019047. https://doi.org/10.1029/2019JB019047.Google Scholar

Ogiso, M., Aoki, S., and Hoshiba, M. (2016). Real-time seismic intensity prediction using frequency-dependent site amplification factors. Earth Planets Space 68, 83. https://doi.org/10.1186/s40623-016-0467-4.Google Scholar

Ogiso, M., Hoshiba, M., Shito, A., and Matsumoto, S.(2018). Numerical shake prediction for earthquake early warning incorporating heterogeneous attenuation structure: The case of the 2016 Kumamoto earthquake. Bulletin of the Seismological Society of America, 108, 3457–68. https://doi.org/10.1785/0120180063.Google Scholar

Peng, H., Wu, Z., Wu, Y. M. et al. (2011). Developing a prototype earthquake early warning system in the Beijing Capital Region. Seismological Research Letters, 82, 394–403. https://doi.org/10.1785/gssrl.82.3.394.Google Scholar

Sato, H., Fehler, M. C., and Maeda, T. (2012). Seismic Wave Propagation and Scattering in the Heterogeneous Earth, 2nd ed. Berlin: Springer. https://doi.org/10.1007/978-3-642-23029-5.Google Scholar

Sheen, D. H., Park, J. H., Chi, H. C. et al. (2017). The first stage of an earthquake early warning system in South Korea. Seismological Research Letters, 88, 1491–98. https://doi.org/10.1785/0220170062 Google Scholar

Suzuki, W., Aoi, S., Kunugi, T. et al. (2017). Strong motions observed by K-NET and KiK-net during the 2016 Kumamoto earthquake sequence. Earth Planets Space, 69, 19. https://doi.org/10.1186/s40623-017-0604-8.Google Scholar

Tamaribuchi, K., Yamada, M., and Wu, S. (2014). A new approach to identify multiple concurrent events for improvements of earthquake early warning. Zisin, 67(2), 41–55. https://doi.org/10.4294/zisin67.41 (in Japanese with English abstract).Google Scholar

Wald, D. J., Worden, B. C., Quitoriano, V., and Pankow, K. L. (2005). ShakeMap manual: Technical manual, user’s guide, and software guide, Techniques and Methods 12-A1. https://doi.org/10.3133/tm12A1.Google Scholar

Wang, T., Jin, X., Wei, Y. and Huang, Y. (2017a). Real-time numerical shake prediction and updating for earthquake early warning. Earthquake Science, 30, 251–67. https://doi.org/10.1007/s11589-017-0195-2 Google Scholar

Wang, T., Jin, X., Huang, Y. and Wei, Y. (2017b). Real-time three-dimensional space numerical shake prediction for earthquake early warning. Earthquake Science, 30, 269–81. https://doi.org/10.1007/s11589-017-0196-1.Google Scholar

Wessel, P., and Smith, W. H. F. (1995). New version of the generic mapping tool released. Eos, Transactions, American Geophysical Union, 76, 329.Google Scholar

Yoshimoto, K. (2000). Monte Carlo simulation of seismogram envelopes in scattering medium. Journal of Geophysical Research: Solid Earth, 105, 6153–61. https://doi.org/10.1029/1999JB900437.Google Scholar

Specific Terms

EEW: Earthquake early warning. Warning of strong shaking before its arrival.Google Scholar

GMPE: Ground-motion prediction equation. Strength of ground motion is empirically estimated from the equation, in which earthquake magnitude and distance (hypocentral distance, epicentral distance, or fault distance) are usually used.Google Scholar

JMA: Japan Meteorological Agency. A national governmental organization in Japan.Google Scholar

K-NET, KiK-net: Observation networks of strong ground motion operated by National Research Institute for Earth Science and Disaster Resilience (NIED) in Japan.Google Scholar

RTT: Radiative transfer theory. A model of wave propagation based on ray theoretical approach, in which scattering and attenuation are included.Google Scholar

References

Adourian, S., Lyu, C., Masson, Y., Munch, F., and Romanowicz, B. (2023). Combining different 3-D global and regional seismic wave propagation solvers towards box tomography in the deep Earth. Geophysical Journal International, 232(2), 1340–56.Google Scholar

Aki, K., Christofferson, A., and Husebye, E. S. (1977). Determination of the three-dimensional seismic structure of the lithosphere. Journal of Geophysical Research, 82, 277–96.Google Scholar

Al-Attar, D., Woodhouse, J. H., and Deuss, A. (2012). Calculation of normal mode spectra in laterally heterogeneous earth models using an iterative direct solution method. Geophysical Journal International, 189, 1038–46.Google Scholar

Backus, G. (1962). Long-wave elastic anisotropy produced by horizontal layering. Journal of Geophysical Research, 67(11), 4427–40.Google Scholar

Bassin, C., Laske, G., and Masters, G. (2000). The current limits of resolution for surface wave tomography in North America. EOS Transactions American Geophysical Union, 81, 1351–75.Google Scholar

Borgeaud, A. F. E., Kawai, K., and Geller, R. J. (2019). Three-dimensional S velocity structure of the mantle transition zone beneath Central America and the Gulf of Mexico inferred using waveform inversion. Journal of Geophysical Research: Solid Earth, 124, 9664–81.Google Scholar

Boschi, L., Becker, T. W., Soldati, G., and Dziewonski, A. M. (2006). On the relevance of Born theory in global seismic tomography. Geophysical Research Letters, 33, L06302.Google Scholar

Bozdag, E., and Trampert, J. (2008). On crustal corrections in surface wave tomography. Geophysical Journal International, 172, 1066–82.Google Scholar

Bozdag, E., Trampert, J., and Tromp, J. (2011). Misfit functions for full waveform inversion based on instantaneous phase and envelope measurements. Geophysical Journal International, 185, 845–70.Google Scholar

Bozdag, E., Peter, D., Lefebvre, M., et al. (2016). Global adjoint tomography: First generation model. Geophysical Journal International, 207(3), 1739–66.Google Scholar

Bozdag, E., Orsvuran, R., Ciardelli, C., Peter, D., and Wang, Y. (2021). Upper mantle anisotropy from global adjoint tomography. AGU Fall Meeting 2021, New Orleans, LA, 13–17 December 2021, abstract DI42A-08.Google Scholar

Capdeville, Y., and Marigo, J. J. (2007). Second order homogenization of the elastic wave equation for non-periodic layered media. Geophysical Journal International, 170, 823–38.Google Scholar

Capdeville, Y., Chaljub, E., Vilotte, J. P., and Montagner, J. P. (2003a). Coupling the spectral element method with a modal solution for elastic wave propagation in global Earth models. Geophysical Journal International, 152, 34–66.Google Scholar

Capdeville, Y., Gung, Y., and Romanowicz, B. (2005). Towards global Earth tomography using the spectral element method: A technique based on source stacking. Geophysical Journal International, 162, 541–54.Google Scholar

Capdeville, Y., To, A., and Romanowicz, B. A. (2003b). Coupling spectral elements and modes in a spherical Earth: An extension to the ‘sandwich’ case. Geophysical Journal International, 154, 44–57.Google Scholar

Chaljub, E., and Valette, B., B. (2004). Spectral element modelling of three-dimensional wave propagation in a self-gravitating Earth with an arbitrarily stratified outer core, Geophysical Journal International, 158, 131–41.Google Scholar

Chang, S.-J., Ferreira, A. M., Ritsema, J., van Heijst, H. J., and Woodhouse, J. H. (2014). Global radially anisotropic mantle structure from multiple datasets: a review, current challenges, and outlook. Tectonophysics, 617, 1–19.Google Scholar

Chen, P., Zhao, L., and Jordan, T. H. (2007). Full three-dimensional tomography: A comparison between the scattering-integral and adjoint-wavefield methods. Bulletin of the Seismological Society of America, 97, 1094–120.Google Scholar

Clévédé, E., and Lognonné, P. (1996). Fréchet derivatives of coupled seismograms with respect to an anelastic rotating Earth. Geophysical Journal International, 124, 456–82.Google Scholar

Clouzet, P., Masson, Y., and Romanowicz, B. (2018). Box tomography: First application to the imaging of upper mantle shear velocity and radial anisotropy structure beneath the North American continent. Geophysical Journal International, 213, 1849–75. doi: 10.1093/gji/ggy078Google Scholar

COSOD-II (1987). Report of the Second Conference on Scientific Ocean Drilling (Cosod II): Strasbourg, 6–8 July, 1987, Joint Oceanographic Institutions for Deep Earth Sampling. https://archives.eui.eu/en/fonds/476326?item=ESF-1224.Google Scholar

Cupillard, P., Delavaud, E., Burgos, G. et al. (2012). RegSEM: a versatile code based on the spectral element method to compute seismic wave propagation at the regional scale. Geophysical Journal International, 188, 1203–20.Google Scholar

Dahlen, F. A., Hung, S.-H., and Nolet, G. (2000). Fréchet kernels for finite-frequency traveltimes – I. Theory. Geophysical Journal International, 141, 157–74.Google Scholar

Davaille, A., and Romanowicz, B. (2020). Deflating the LLSVPs: Bundles of mantle thermochemical plumes, rather than thick ‘stagnant’ piles. Tectonics, 39, e2020TC006265. https://doi.org/10.1029/2020TC006265.Google Scholar

Durek, J. J., and Ekström, G. (1996). A radial model of anelasticity consistent with long-period surface-wave attenuation. Bulletin of the Seismological Society of America, 86, 144–58.Google Scholar

Dziewonski, A., and Anderson, D. (1981). Preliminary reference Earth model. Physics of the Earth and Planetary Interiors, 25, 297–356.Google Scholar

Dziewonski, A., Hager, B., and O’Connell, R. (1977). Large-scale heterogeneities in the lower mantle. Journal of Geophysical Research, 82, 239–55.Google Scholar

Efron, B., and Stein, C. (1981). The jackknife estimate of variance. Annals of Statistics, 9(3), 586–96.Google Scholar

Efron, B., and Tibishirani, R. J. (1991). An Introduction to the Bootstrap. Boca Raton, FL: Chapman and Hall.Google Scholar

Ferreira, A. M., Woodhouse, J. H., Visser, K., and Trampert, J. (2010). On the robustness of global radially anisotropic surface wave tomography. Journal of Geophysical Research, 115, B04313. https://doi.org/:10.1029/2009JB006716.Google Scholar

Fichtner, A. (2011). Full Seismic Waveform Modelling and Inversion. Cham: Springer.Google Scholar

Fichtner, A., and Igel, H. (2008). Efficient numerical surface wave propagation through the optimization of discrete crustal models: A technique based on non-linear dispersion curve matching (DCM). Geophysical Journal International, 173, 519–33.Google Scholar

Fichtner, A., and Trampert, J. (2011a). Hessian kernels of seismic data functionals based upon adjoint techniques. Geophysical Journal International, 185, 775–98.Google Scholar

Fichtner, A., and Trampert, J. (2011b). Resolution analysis in full waveform inversion. Geophysical Journal International, 187, 1604–24. https://doi.org/10.1111/j.1365-246X.2011.05218.x.Google Scholar

Fichtner, A., Kennett, B. L. N., Igel, H., and Bunge, H.-P. (2008). Theoretical background for continental- and global-scale full-waveform inversion in the time-frequency domain. Geophysical Journal International, 175, 665–85.Google Scholar

Fichtner, A., Kennett, B. L. N., Igel, H., and Bunge, H. P. (2009). Full seismic waveform tomography for upper-mantle structure in the Australasian region using adjoint methods. Geophysical Journal International, 179, 1703–25.Google Scholar

Fichtner, A., Kennett, B. L. N., Igel, H., and Bunge, H.-P. (2010). Full waveform tomography for radially anisotropic structure: New insights into present and past states of the Australasian upper mantle. Earth and Planetary Science Letters, 290, 270–80.Google Scholar

French, S., Lekic, V., and Romanowicz, B. (2013). Waveform tomography reveals channeled flow at the base of the oceanic asthenosphere. Science, 342, 227–30.Google Scholar

French, S. W. & Romanowicz, B. (2014). Whole-mantle radially anisotropic shear velocity structure from spectral-element waveform tomography. Geophysical Journal International, 199(3), 1303–27.Google Scholar

French, S. W., Zheng, Y., Romanowicz, B., and Yelick, K. (2015). Parallel Hessian assembly for Seismic Waveform inversion using Global updates, Proceedings of the 29th IEEE International Parallel and Distributed Processing Symposium (2015). https://doi.org/10.1109/IPDPS.2015.58.Google Scholar

Fukao, Y., and Obayashi, M. (2013). Subducted slabs stagnant above, penetrating through, and trapped below the 660 km discontinuity. Journal of Geophysical Research, 118(11), 5920–38.Google Scholar

Gharti, H. N., Tromp, J., and Zampini, S. (2018). Spectral-infinite-element simulations of gravity anomalies, Geophysical Journal International, 215, 1098–117. https://doi.org/10.1093/gji/ggy324.Google Scholar

Geller, R. J., and Ohminato, T (1994). Computation of synthetic seismograms and their partial derivatives for heterogeneous media with arbitrary natural boundary conditions using the direct solution method. Geophysical Journal International, 116, 421–46.Google Scholar

Gung, Y., and Romanowicz, B. (2004). Q tomography of the upper mantle using three-component long-period waveforms. Geophysical Journal International, 157(2), 813–30.Google Scholar

Gung, Y., Panning, M., and Romanowicz, B. (2003). Global anisotropy and the thickness of continents. Nature, 422(6933), 707–11.Google Scholar

Hello, Y., Ogé, A. Sukhovich, , A., and Nolet, G. (2011). Modern mermaids: New floats image the Deep Earth. EOS Transactions American Geophysical Union, 92, 337–48.Google Scholar

Houser, C., Masters, G., Shearer, P., and Laske, G. (2008). Shear and compressional velocity models of the mantle from cluster analysis of long period waveforms. Geophysical Journal International, 174, 195–212.Google Scholar

Karaoglu, H., and Romanowicz, B. (2017). Global seismic attenuation imaging using full-waveform inversion: a comparative assessment of different choices of misfit functionals. Geophysical Journal International, 212, 807–26.Google Scholar

Karaoglu, H., and Romanowicz, B. (2018). Inferring global upper-mantle shear attenuation structure by waveform tomography using the spectral element method. Geophysical Journal International, 213, 1536–58.Google Scholar

Kawai, K., Konishi, K., Geller, R. J., and Fuji, N. (2014). Methods for inversion of body‐wave waveforms for localized three‐dimensional seismic structure and an application to D″ structure beneath Central America. Geophysical Journal International, 197(1), 495–524. https://doi.org/10.1093/gji/ggt520.Google Scholar

Komatitsch, D., and Tromp, J. (2002a). Spectral-element simulations of global seismic wave propagation – I. Validation. Geophysical Journal International, 149, 390–412.Google Scholar

Komatitsch, D., and Tromp, J. (2002b). Spectral-element simulations of global seismic wave propagation – II. Three-dimensional models, oceans, rotation and self-gravitation. Geophysical Journal International, 150, 303–18.Google Scholar

Komatitsch, D., and Vilotte, J. P. (1998).The spectral element method: an efficient tool to simulate the seismic response of 2D and 3D geological structures. Bulletin of the Seismological Society of America, 88, 368–92.Google Scholar

Koroni, M., and Trampert, J. (2021). Imaging global mantle discontinuities: a test using full-waveforms and adjoint kernels. Geophysical Journal International, 226, 1498–15.Google Scholar

Krebs, J., Anderson, J., Hinkley, D. et al. (2009). Fast full-wavefield seismic inversion using encoded sources. Geophysics, 74, WCC177–WCC188.Google Scholar

Kustowski, B., Ekström, G., and Dziewonski, A.M. (2008). Anisotropic shear-wave velocity structure of the Earth’s mantle: A global model. Journal of Geophysical Research: Solid Earth, 113(B6), 2156–202.Google Scholar

Laske, G., Collins, J. A., Wolfe, C. J. et al. (2009). Probing the Hawaiian hotspot with new broadband ocean bottom instruments, Eos, Transactions, American Geophysical. Union, 90(41), 362–636.Google Scholar

Lee, E.-J., Chen, P., Jordan, T. H. et al. (2014). Full‐3‐D tomography for crustal structure in southern California based on the scattering‐integral and the adjoint‐wavefield methods. Journal of Geophysical Research, 119, 6421–51.Google Scholar

Lei, W., Ruan, Y., Bozdag, E. et al. (2020). Global adjoint tomography: model GLAD-M25. Geophysical Journal International 223, 1–21.Google Scholar

Lekic, V., and Romanowicz, B. (2011). Inferring upper-mantle structure by full waveform tomography with the spectral element method. Geophysical Journal International, 185, 799–831.Google Scholar

Lekic, V., Panning, M., and Romanowicz, B. (2010). A simple method for improving crustal corrections in waveform tomography. Geophysical Journal International, 182, 265–78.Google Scholar

Lerner-Lam, A.L., and, Jordan, T. H. (1983). Earth structure from fundamental and higher mode waveform analysis. Geophysical Journal of the Royal Astronomical Society, 75(3), 759–97.Google Scholar

Lévêque, J. J., Rivera, L., and Wittlinger, G. (1993). On the use o the checker-board test to assess the resolution of tomographic inversions. Geophysical Journal International, 115, 313–18Google Scholar

Li, X.-D., and Romanowicz, B. (1995). Comparison of global waveform inversions with and without considering cross-branch modal coupling. Geophysical Journal International, 121(3), 695–709.Google Scholar

Li, X.-D., and Romanowicz, B. (1996). Global mantle shear velocity model developed using non-linear asymptotic coupling theory. Journal of Geophysical Research, 101, 22245–72.Google Scholar

Li, X.-D., and Tanimoto, T. (1993). Waveforms of long-period body waves in a slightly aspherical Earth model. Geophysical Journal International, 112, 92–102.Google Scholar

Lin, C., Monteiller, V., Wang, K., Liu, T., Tong, P., and Liu, Q. (2019). High-frequency seismic wave modelling of the Deep Earth based on hybrid methods and spectral-element simulations: a conceptual study. Geophysical Journal International, 219, 1948–69.Google Scholar

Liu, Q., Beller, S., Lei, W., Peter, D., and Tromp, J. (2022). Pre-conditioned BFGS-based uncertainty quantification in elastic full-waveform inversion. Geophysical Journal International, 228(2), 796–815.Google Scholar

Maggi, A., Tape, C., Chen, M., Chao, D., and Tromp, J. (2009). An automated time-window selection algorithm for seismic tomography. Geophysical Journal International, 178, 257–81.Google Scholar

Marquering, H., Nolet, G., and Dahlen, F. A. (1998). Three-dimensional waveform sensitivity kernels. Geophysical Journal International, 132, 521–34.Google Scholar

Marone, F., and Romanowicz, B. (2007). Non-linear crustal corrections in high-resolution regional waveform seismic tomography. Geophysical Journal International, 170, 460–67.Google Scholar

Masson, Y. (2023). Distributed finited difference modelling of seismic waves, Geophysical Journal International , 233, 264–96.Google Scholar

Masson, Y., Cupillard, P., Capdeville, Y., and Romanowicz, B. (2014). On the numerical implementation of time reversal mirrors for tomographic imaging. Geophysical Journal International, 196, 1580–99. https://doi.org/10.1093/gji/ggt459.Google Scholar

Masson, Y., and Romanowicz, B. (2017a). Fast computation of synthetic seismograms within a medium containing remote localized perturbations: a numerical solution to the scattering problem. Geophysical Journal International, 208(2), 674–92.Google Scholar

Masson, Y., and Romanowicz, B. (2017b). Box tomography: localized imaging of remote targets buried in an unknown medium, a step forward for understanding key structures in the deep Earth. Geophysical Journal International, 211(1), 141–63.Google Scholar

Mégnin, C., and Romanowicz, B. (2000). The three-dimensional shear velocity structure of the mantle from the inversion of body, surface and highermode waveforms. Geophysical Journal International, 143, 709–28.Google Scholar

Meier, U., Curtis, A., and Trampert, J. (2007). Fully nonlinear inversion of fundamental mode surface waves for a global crustal model. Geophysical Research Letters, 34, L16304. https://doi.org/10.1029/2007GL030989.Google Scholar

Mochizuki, E. (1986). Free oscillations and surface waves of an aspherical Earth. Geophysical Research Letters, 13, 1478–81.Google Scholar

Moczo, P., Kristek, J., and Halada, L. (2004). The Finite-Difference Method for Seismologists. Bratislava: Comenius University. www.spice-rtn.org.Google Scholar

Modrak, R., and Tromp, J. (2016). Seismic waveform inversion best practices: Regional, global and exploration test cases. Geophysical Journal International, 206, 1864–89.Google Scholar

Montagner, J., and Anderson, D. (1989). Petrological constraints on seismic anisotropy. Physics of the Earth and Planetary Interiors, 54, 82–105.Google Scholar

Monteiller, V., Chevrot, S., Komatitsch, D., and Wang, Y. (2015). Three-dimensional full waveform inversion of short period teleseismic wavefields based upon the SEM-DSM hybrid method. Geophysical Journal International, 202, 811–27.Google Scholar

Montelli, R., Nolet, G., Dahlen, F.A. et al. (2004a). Finite-frequency tomography reveals a variety of plumes in the mantle. Science, 303(5656), 338–43.Google Scholar

Nocedal, J., and Wright, S. J. (2017). Numerical Optimization, 2nd ed. New York: Springer.Google Scholar

Nolet, G. (1990). Partitioned waveform inversion and two-dimensional structure under the network of autonomously recording seismograph. Journal of Geophysical Research, 95, 8499–8512.Google Scholar

Nolet, G., and Dahlen, F. A. (2000). Wave front healing and the evolution of seismic delay times. Journal of Geophysical Research, 105, 19043–54.Google Scholar

Nolet, G., Hello, Y., van der Lee, S. et al. (2019). Imaging the Galapagos mantle plume with an unconventional application of floating seismometers. Scientific Reports, 9, 1326.Google Scholar

Panning, M., and Romanowicz, B. (2006). A three-dimensional radially anisotropic model of shear velocity in the whole mantle. Geophysical Journal International, 167, 361–79.Google Scholar

Park, J. (1987). Asymptotic coupled-mode expressions for multiplet amplitude anomalies and frequency shifts on an aspherical earth. Geophysical Journal of the Royal Astronomical Society, 90(1), 129–69.Google Scholar

Pasyanos, M., and Nyblade, A. (2007). A top to bottom lithospheric study of Africa and Arabia. Tectonophysics, 444(1–4), 27–44.Google Scholar

Pienkowska, M., Monteiller, V., and Nissen-Meyer, T. (2020). High-frequency global wavefields for local 3-D structures by wavefield injection and extrapolation. Geophysical Journal International, 225, 1782–98.Google Scholar

Pipatprathanporn, P., and Simons, F. J. (2022). One year of sound recorded by a MERMAID float in the Pacific: hydroacoustic earthquake signals and infrasonic ambient noise. Geophysical Journal International, 228(1), 193–212.Google Scholar

Obayashi, M., Yoshimitsu, J., Sugioka, H. et al. (2016). Mantle plumes beneath the South Pacific Superswell revealed by finite frequency P tomography using regional seafloor and island data. Geophysical Research Letters, 43(11), 628–11634.Google Scholar

Rawlinson, N., Fichtner, A., Sambridge, M., and Young, M. K. (2014). Seismic tomography and the assessment of uncertainty. Advances in Geophysics, 55, 1–76.Google Scholar

Replumaz, A., Karason, H., van der Hilst, R. D., Besse, J., and Tapponnier, P. (2004). 4-D evolution of SE Asia’s mantle from geological reconstructions and seismic tomography. Earth and Planetary Science Letters, 221, 103–15.Google Scholar

Richards, M. A., and Engebretson, D. C. (1992). Large scale mantle convection and the history of subduction. Nature, 355, 437–40.Google Scholar

Rickers, F., Fichtner, A., and Trampert, J. (2013). The Iceland–Jan Mayen plume system and its impact on mantle dynamics in the North Atlantic region: Evidence from full-waveform inversion. Earth and Planetary Science Letters, 367, 39–51.Google Scholar

Ritsema, J., and Lekic, V. (2020). Heterogeneity of seismic wave velocity in Earth’s mantle. Annual Review of Earth and Planetary Sciences, 48, 377–401Google Scholar

Ritsema, J., Deuss, A., van Heijst, H. J., and Woodhouse, J. H. (2011). S40RTS: A degree-40 shear-velocity model for the mantle from new Rayleigh wave dispersion, teleseismic traveltime and normal-mode splitting function measurements. Geophysical Journal International, 184(3), 1223–36.Google Scholar

Ritsema, J., van Heijst, H. J., and Woodhouse, J. H. (1999). Complex shear velocity structure imaged beneath Africa and Iceland. Science, 286, 1925–8.Google Scholar

Ritsema, J., van Heijst, H.J., and Woodhouse, J.H. (2004). Global transition zone tomography. Journal of Geophysical Research, 109. https://doi.org/10.1029/2003JB002610.Google Scholar

Romanowicz, B. (1987). Multiplet-multiplet coupling due to lateral heterogeneity: Asymptotic effects on the amplitude and frequency of the Earth’s normal modes. Geophysical Journal of the Royal Astronomical Society, 90(1), 75–100.Google Scholar

Romanowicz, B. (2003). Global mantle tomography: Progress status in the last 10 years. Annual Review of Earth and Planetary Sciences, 31(1), 303–28.Google Scholar

Romanowicz, B. (2020). Seismic tomography of the Earth’s mantle. In Alderton, D. and Elias, S. A., eds., Encyclopedia of Geology, vol. 1, 2nd ed. Cambridge, MA: Academic Press, pp. 587–609.Google Scholar

Romanowicz, B., and Suyehiro, K. (2001). History of the International Ocean Network. http://eri-ndc.eri.u-tokyo.ac.jp/OHP-sympo2/report/index.html.Google Scholar

Romanowicz, B., and Wenk, R. (2017). Anisotropy in the Deep Earth. Physics of the Earth and Planetary Interiors, 269, 58–90. https://doiorg/10.1016/j.pepi.2017.05.005.Google Scholar

Romanowicz, B., Chen, L.-W., and French, S. W. (2019). Accelerating full waveform inversion via source stacking and cross-correlations. Geophysical Journal International, 220(1), 308–22.Google Scholar

Romanowicz, B., Panning, M., Gung, Y., and Capdeville, Y. (2008). On the computation of long period seismograms in a 3-D Earth using normal mode based approximations. Geophysical Journal International, 175, 520–36.Google Scholar

Romanowicz, B. A., French, S. W., Rickers, F., and Yuan, H. (2013). Source stacking for numerical wavefield computations: Application to continental and global scale seismic mantle tomography, in American Geophysical Union, Fall Meeting 2013, abstract S21E-05.Google Scholar

Ruan, Y., Lei, W., Modrak, R. et al. (2019). Balancing unevenly distributed data in seismic tomography: a global adjoint tomography example. Geophysical Journal International, 219(2), 1225–36Google Scholar

Schaeffer, A. J., and Lebedev, S. (2013). Global shear speed structure of the upper mantle and transition zone. Geophysical Journal International, 194(1), 417–49.Google Scholar

Schaeffer, A. J., and Lebedev, S. (2014). Imaging the North American continent using waveform inversion of global and USArray data. Earth and Planetary Science Letters, 402, 26–41.Google Scholar

Shapiro, N., and Ritzwoller, M. (2002). Monte-Carlo inversion for a global shear-velocity model of the crust and upper mantle. Geophysical Journal International, 151, 88–105.Google Scholar

Sigloch, K., McQuarrie, N., and Nolet, G. (2008). Two-stage subduction history under North America inferred from multiple-frequency tomography. Nature Geoscience, 1, 458–63.Google Scholar

Su, W.-J., Woodward, R. L., and Dziewonski, A. M. (1994). Degree-12 model of shear velocity heterogeneity in the mantle. Journal of Geophysical Research, 99(4), 4945–80.Google Scholar

Suetsugu, D., Isse, T., Tanaka, S. et al. (2009). South Pacific mantle plumes imaged by seismic observation on islands and seafloor. G-Cubed, 10, Q11014.Google Scholar

Sukhovich, A., Bonnieux, S., Hello, Y. et al. (2015). Seismic monitoring in the oceans by autonomous floats. Nature Communications, 6, 8027–33.Google Scholar

Suzuki, Y., Kawai, K., Geller, R. J., Borgeaud, A. F. E., and Konishi, K. (2016). Waveform inversion for 3‐D S‐velocity structure of D″ beneath the Northern Pacific: Possible evidence for a remnant slab and a passive plume. Earth, Planets and Space, 68(1). https://doi.org/10.1186/s40623‐016‐0576‐0.Google Scholar

Suzuki, Y., Kawai, K., Geller, R. J. et al. (2020). High-resolution 3-D S-velocity structure in the D’ region at the western margin of the Pacific LLSVP: Evidence for small-scale plumes and paleoslabs. Physics of the Earth and Planetary Interiors, 307, 106544.Google Scholar

Tanimoto, T. (1987). The three-dimensional shear wave structure in the mantle by overtone waveform inversion – I. Radial seismogram inversion. Geophysical Journal of the Royal Astronomical Society, 89(2), 713–40.Google Scholar

Tape, C., Liu, Q., Maggi, A., and Tromp, J. (2010). Seismic tomography of the southern California crust based upon spectral-element and adjoint methods. Geophysical Journal International, 180, 433–62.Google Scholar

Tarantola, A. (1984). Inversion of seismic reflection data in the acoustic approximation. Geophysics, 49, 1259–66.Google Scholar

Tarantola, A. (2005). Inverse Problem Theory and Methods for Model Parameter Estimation. Philadelphia, PA: Society for Industrial and Applied Mathematics.Google Scholar

Tarantola, A., and Valette, B. (1982). Generalized nonlinear inverse problems solved using the least squares criterion. Reviews of Geophysics, 20(2), 219–232.Google Scholar

Thrastarson, S., van Driel, M., Krischer, L. et al. (2020). Accelerating numerical wave propagation by wavefield adapted meshes. Part II: Full-waveform inversion. Geophysical Journal International, 221, 1591–604.Google Scholar

Thurber, C., and Ritsema, J. (2015). Theory and Observations- Seismic Tomography and Inverse Methods. In Schubert, G., ed., Treatise on Geophysics, vol. 1. Amsterdam: Elsevier, pp. 307–37.Google Scholar

Tromp, J. (2015). 1.07 – Theory and Observations: Forward Modeling and Synthetic Seismograms, 3D Numerical Methods. In Schubert, G., ed., Treatise on Geophysics. Amsterdam: Elsevier, pp. 231–51.Google Scholar

Tromp, J. (2020). Seismic wavefield imaging of earth’s interior across scales. Nature Reviews Earth and Environment, 1, 40–53.Google Scholar

Tromp, J., and Bachmann, E. (2019). Source encoding for adjoint tomography. Geophysical Journal International, 218, 2019–44.Google Scholar

Tromp, J., Tape, C. & Liu, Q. Y. (2005). Seismic tomography, adjoint methods, time reversal and banana-doughnut kernels. Geophysical Journal International, 160, 195–216.Google Scholar

Tromp, J., Komatitsch, D., Hjörleifsdóttir, V. et al. (2010). Near real-time simulations of global CMT earthquakes. Geophysical Journal International, 183(1), 381–9.Google Scholar

Valentine, A. P., and Trampert, J. (2016). The impact of approximations and arbitrary choices on geophysical images. Geophysical Journal International, 204, 59–73.Google Scholar

van der Hilst, R., and de Hoop, M. V. (2005). Banana-doughnut kernels and mantle tomography. Geophysical Journal International, 163, 956–61.Google Scholar

van der Lee, S., and Nolet, G. (1997). Upper mantle S velocity structure of North America. Journal of Geophysical Research: Solid Earth, 102, 22815–38.Google Scholar

van der Meer, D. G., Spakman, W., van Hinsbergen, D. J. J, Amaru, M. L., and Torsvik, T. H. (2010). Towards absolute plate motions constrained by lower-mantle slab remnants. Nature Geoscience, 3, 36–40.Google Scholar

van Driel, M., Krischer, L., Stähler, S. C., Hosseini, K., and Nissen-Meyer, T. (2015). Instaseis: instant global seismograms based on a broadband waveform database. Solid Earth, 6(2), 701–17.Google Scholar

van Driel, M., Kemper, J., and Boehm, C. (2021). On the modelling of self-gravitation for full 3-D global seismic wave propagation. Geophysical Journal International, 227, 632–43.Google Scholar

van Herwaarden, D. P., Boehm, C., Afanasiev, M. et al. (2020). Accelerated full-waveform inversion using dynamic mini-batches. Geophysical Journal International, 221, 1427–38.Google Scholar

Virieux, J., and Operto, S. (2009). An overview of full-waveform inversion in exploration geophysics. Geophysics, 74, WCC127–WCC152.Google Scholar

Virieux, J., Asnaashari, A., Brossier, R. et al. (2014). 6. An introduction to full waveform inversion. In Encyclopedia of Exploration Geophysics, Geophysical References Series: R1-1-R1-40. Tulsa, OK: Society of Exploration Geophysicists.Google Scholar

Wang, Z., and Dahlen, F.A. (1995). Spherical-spline parameterization of three-dimensional Earth models. Geophysical Research Letters, 22, 3099–102.Google Scholar

Wen, L., and Helmberger, D.V. (1998). A two-dimensional P-SV hybrid method and its application to modeling localized structures near the core-mantle boundary. Journal of Geophysical Research, 103, 17901–18.Google Scholar

Woodhouse, J. H., and Dziewonski, A. M. (1984). Mapping the upper mantle: Three dimensional modeling of Earth structure by inversion of seismic waveforms. Journal of Geophysical Research, 89, 5953–86.Google Scholar

Woodhouse, J. H., and Deuss, A. (2015). 1.03 – Theory and Observations: Earth’s Free Oscillations. In Schubert, G., ed., Treatise on Geophysics. Amsterdam: Elsevier, pp. 31–65.Google Scholar

Yang, H., and Tromp, J. (2015). Synthetic free-oscillation spectra: an appraisal of various mode-coupling methods. Geophysical Journal International, 203, 1179–92.Google Scholar

Zhang, Q., Mao, W., Zhou, H., Zhang, H., and Chen, Y. (2018). Hybrid-domain simultaneous-source full waveform inversion without crosstalk noise. Geophysical Journal International, 215(3), 1659–81.Google Scholar

Zhu, H., Bozdag, E., and Tromp, J. (2015). Seismic structure of the European upper mantle based on adjoint tomography. Geophysical Journal International, 201(1), 18–52.Google Scholar

References

Afanasiev, M., Boehm, C., van Driel, M. et al. (2019). Modular and flexible spectral-element waveform modelling in two and three dimensions. Geophysical Journal International, 216, 1675–92.Google Scholar

Afanasiev, M. V., Pratt, R. G., Kamei, R., and McDowell, G. (2014). Waveform-based simulated annealing of crosshole transmission data: A semi-global method for estimating seismic anisotropy. Geophysical Journal International, 199, 1586–607.Google Scholar

Ajo-Franklin, J. B. (2009). Optimal experiment design for time-lapse traveltime tomography. Geophysics, 74, Q27–Q40.Google Scholar

Backus, G. E., and Gilbert, F. (1968). The resolving power of gross Earth data. Geophysical Journal of the Royal Astronomical Society, 16, 169–205.Google Scholar

Backus, G. E., and Gilbert, F. (1970). Uniqueness in the inversion of inaccurate gross Earth data. Philosophical Transactions of the Royal Society A, 266(1173), 123–92.Google Scholar

Bamberger, A., Chavent, G., and Lailly, P. (1977). Une application de la théorie du contrôle à un problème inverse sismique. Annales Geophysicae, 33, 183–200.Google Scholar

Bamberger, A., Chavent, G., Hemons, C., and Lailly, P. (1982). Inversion of normal incidence seismograms. Geophysics, 47, 757–70.Google Scholar

Bayes, T. (1764). An essay toward solving a problem in the doctrine of chances. Philosophical Transactions of the Royal Society of London, 53, 370-418.Google Scholar

Bernauer, M., Fichtner, A., and Igel, H. (2014). Optimal observables for multi-parameter seismic tomography. Geophysical Journal International, 198, 1241–54.Google Scholar

Betancourt, M. (2017). A conceptual introduction to Hamiltonian Monte Carlo. arXiv:1701.02434 [stat.ME].Google Scholar

Blom, N., Boehm, C., and Fichtner, A. (2017). Synthetic inversion for density using seismic and gravity data. Geophysical Journal International, 209, 1204–20.Google Scholar

Bodin, T., Sambridge, M., Rawlinson, N., and Arroucau, P. (2012). Transdimensional tomography with unknown data noise. Geophysical Journal International, 189, 1536–56.Google Scholar

Bozdag, E., Peter, D., Lefebvre, M. et al. (2016). Global adjoint tomography: First-generation model. Geophysical Journal International, 207, 1739–66.Google Scholar

Bui-Thanh, T., Ghattas, O., Martin, J., and Stadler, G. (2013). A computational framework for infinite-dimensional Bayesian inverse problems. Part I: The linearized case, with application to global seismic inversion. SIAM Journal on Scientific Computing, 35, A2494–A2523.Google Scholar

Calvetti, D., and Somersalo, E. (2017). Inverse problems: From regularization to Bayesian inference. Computational Statistics, 10(3). http://doi.org/10.1002/wics.1427.Google Scholar

Capdeville, Y., Guillot, L., and Marigo, J. J. (2010). 2-D non-periodic homogenization to upscale elastic media for P–SV waves. Geophysical Journal International, 182, 903–22.Google Scholar

Chen, P., Jordan, T. H., and Zhao, L. (2007a). Full 3D waveform tomography: A comparison between the scattering-integral and adjoint-wavefield methods. Geophysical Journal International, 170, 175–81.Google Scholar

Chen, P., Zhao, L., and Jordan, T. H. (2007b). Full 3D tomography for the crustal structure of the Los Angeles region. Bulletin of the Seismological Society of America, 97, 1094–120.Google Scholar

Chib, S., and Greenberg, E. (1995). Understanding the Metropolis-Hastings algorithm. American Statistician, 49, 327–35.Google Scholar

Choi, Y., and Alkhalifah, T. (2011). Source-independent time-domain waveform inversion using convolved wavefields: Application to the encoded multisource waveform inversion. Geophysics, 76, R125–R134.Google Scholar

Clouzet, P., Masson, Y., and Romanowicz, B. (2018). Box tomography: First application to the imaging of upper mantle shear velocity and radial anisotropy structure beneath the north American continent. Geophysical Journal International, 213, 1849–75.Google Scholar

Curtis, A. (1999). Optimal experiment design: Cross-borehole tomographic examples. Geophysical Journal International, 136, 637–50.Google Scholar

de la Puente, J., Dumbser, M., Käser, M., and Igel, H. (2007). An arbitrary high-order discontinuous Galerkin method for elastic waves on unstructured methods. IV. Anisotropy. Geophysical Journal International, 169, 1210–28.Google Scholar

Djikpesse, H. A., Khodja, M. R., Prange, M. D., Duchenne, S., and Menkiti, H. (2012). Bayesian survey design to optimize resolution in waveform inversion. Geophysics, 77, R81–R93.Google Scholar

Duane, S., Kennedy, A. D., Pendleton, B. J., and Roweth, D. (1987). Hybrid Monte Carlo. Physics Letters B, 195, 216–22.Google Scholar

Dziewonski, A. M., and Anderson, D. L. (1981). Preliminary reference Earth model. Physics of the Earth and Planetary Interiors, 25, 297–356.Google Scholar

Fichtner, A., Bunge, H.-P., and Igel, H. (2006). The adjoint method in seismology – I. Theory. Physics of the Earth and Planetary Interiors, 157, 105–23.Google Scholar

Fichtner, A., Kennett, B. L. N., Igel, H., and Bunge, H.-P. (2009). Full seismic waveform tomography for upper-mantle structure in the Australasian region using adjoint methods. Geophysical Journal International, 179, 1703–25.Google Scholar

Fichtner, A. (2010). Full seismic waveform modeling and inversion. Heidelberg: Springer.Google Scholar

Fichtner, A., and Trampert, J. (2011). Resolution analysis in full waveform inversion. Geophysical Journal International, 187, 1604–24.Google Scholar

Fichtner, A. (2021). Lecture Notes on Inverse Theory. Cambridge: Cambridge Open Engage, http://doi.org/10.33774/coe-2021-qpq2j.Google Scholar

Fichtner, A., van Herwaarden, D.-P., Afanasiev, M. et al. (2018). The Collaborative Seismic Earth Model: Generation I. Geophysical Research Letters, 45, 4007–16.Google Scholar

Fichtner, A., and van Leeuwen, T. (2015). Resolution analysis by random probing. Journal of Geophysical Research: Solid Earth, 120, 5549–73.Google Scholar

Gebraad, L., Boehm, C., and Fichtner, A. (2020). Bayesian elastic full‐waveform inversion using Hamiltonian Monte Carlo. Journal of Geophysical Research: Solid Earth, 125, e2019JB018428.Google Scholar

Green, P. J. (1995). Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika, 82, 711–32.Google Scholar

Hardt, M., and Scherbaum, F. (1994). The design of optimum networks for aftershock recordings. Geophysical Journal International, 117, 716–26.Google Scholar

Huang, Y., and Schuster, G. T. (2018). Full‐waveform inversion with multisource frequency selection of marine streamer data. Geophysical Prospecting, 66, 1243–57.Google Scholar

Hunziker, J., Laloy, E., and Linde, N. (2019). Bayesian full-waveform tomography with application to crosshole ground penetrating radar data. Geophysical Journal International, 218, 913–31.Google Scholar

Igel, H. (2016). Computational Seismology: A Practical Introduction. Cambridge: Cambridge University Press.Google Scholar

Kijko, A. (1977). An algorithm for the optimum distribution of a regional seismic network – I. Pure and Applied Geophysics, 115, 999–1009.Google Scholar

Komatitsch, D., and Vilotte, J.-P. (1998). The spectral element method: An effective tool to simulate the seismic response of 2D and 3D geological structures. Bulletin of the Seismological Society of America, 88, 368–92.Google Scholar

Käufl, P., Fichtner, A., and Igel, H. (2013). Probabilistic full waveform inversion based on tectonic regionalisation: Development and application to the Australian upper mantle. Geophysical Journal International, 193, 437–51.Google Scholar

Kotsi, P., Malcolm, A., and Ely, G. (2020). Time-lapse full-waveform inversion using Hamiltonian Monte Carlo: A proof of concept. SEG Technical Program Expanded Abstracts, 845–49.Google Scholar

Krampe, V., Edme, P., and Maurer, H. (2021). Optimized experimental design for seismic full waveform inversion: A computationally efficient method including a flexible implementation of acquisition costs. Geophysical Prospecting, 69, 152–66.Google Scholar

Krebs, J. R., Anderson, J. E., Hinkley, D. et al. (2009). Fast full-wavefield seismic inversion using encoded sources. Geophysics, 74, WCC177–WCC188.Google Scholar

Krebs, J. R., Cha, Y. H., Lee, S. et al. ExxonMobil Upstream Research Co (2018). Orthogonal Source and Receiver Encoding. U.S. Patent 10,012,745.Google Scholar

Kullback, S., and Leibler, R. A. (1951). On information and sufficiency. Annals of Mathematical Statistics, 22, 79–86.Google Scholar

Kuo, C., and Romanowicz, B. (2002). On the resolution of density anomalies in the Earth’s mantle using spectral fitting of normal mode data. Geophysical Journal International, 150, 162–79.Google Scholar

Leng, K., Nissen-Meyer, T., and van Driel, M. (2016). Efficient global wave propagation adapted to 3-D structural complexity: A pseudospectral/spectral-element approach. Geophysical Journal International, 207, 1700–21.Google Scholar

Liu, Q., and Gu, Y. (2012). Seismic imaging: From classical to adjoint tomography. Tectonophysics, 566–567, 31–66.Google Scholar

Liu, Q., and Peter, D. (2019). Square-root variable metric based elastic full-waveform inversion. Part 2: Uncertainty estimation. Geophysical Journal International, 218(2), 1100–20.Google Scholar

Liu, Q., and Wang, D. (2016). Stein variational gradient descent: A general purpose Bayesian inference algorithm. Advances in Neural Information Processing Systems, 2378–86. arXiv:1608.04471.Google Scholar

Liu, Q., Peter, D., and Tape, C. (2019). Square-root variable metric based elastic full-waveform inversion. Part 1: Theory and validation. Geophysical Journal International, 218(2), 1121–35.Google Scholar

Masson, Y., and Romanowicz, B. (2017). Fast computation of synthetic seismograms within a medium containing remote localized perturbations: A numerical solution to the scattering problem. Geophysical Journal International, 218, 674–92.Google Scholar

Maurer, H., Nuber, A., Martiartu, N. K. et al. (2017). Optimized experimental design in the context of seismic full waveform inversion and seismic waveform imaging. In Nielsen, L., ed., Advances in Geophysics, vol. 58. Cambridge, MA: Academic Press, pp. 1–45.Google Scholar

Malinverno, A. (2002). Parsimonious Bayesian Markov chain Monte Carlo inversion in a nonlinear geophysical problem. Geophysical Journal International, 151, 675–88.Google Scholar

Moczo, P., Kristek, J., Vavrycuk, V., Archuleta, R., and Halada, L. (2002). 3D heterogeneous staggered-grid finite-difference modeling of seismic motion with volume harmonic and arithmetic averaging of elastic moduli. Bulletin of the Seismological Society of America, 92, 3042–66.Google Scholar

Mosegaard, K. (2012). Limits to nonlinear inversion. In Jónasson, K., ed., Applied Parallel and Scientific Computing, Berlin: Springer, pp. 11–21.Google Scholar

Neal, R. M. (2011). MCMC using Hamiltonian dynamics. In Brooks, S., Gelman, A., Jones, G., and Meng, X.-L., eds., Handbook of Markov chain Monte Carlo. New York: Chapman and Hall, pp. 113–62.Google Scholar

Plessix, R.-E. (2006). A review of the adjoint-state method for computing the gradient of a functional with geophysical applications. Geophysical Journal International, 167, 495–503.Google Scholar

Rabinowitz, N., and Steinberg, D. M. (1990). Optimal configuration of a seismographic network: A statistical approach. Bulletin of the Seismological Society of America, 80, 187–96.Google Scholar

Resovsky, J., and Trampert, J. (2002). Reliable mantle density error bars: An application of the Neighbourhood Algorithm to normal-mode and surface wave data. Geophysical Journal International, 150, 665–72.Google Scholar

Romero, L. A., Ghiglia, D. C., Ober, C. C., and Morton, S. A. (2000). Phase encoding of shot records in prestack migration. Geophysics, 65, 426–36.Google Scholar

Ronchi, C., Iacono, R., and Paolucci, P. S. (1996). The ‘cubed sphere’: A new method for the solution of partial differential equations in spherical geometry. Journal of Computational Physics, 124, 93–114.Google Scholar

Sambridge, M. S., Bodin, T., Gallagher, K., and Tkalcic, H. (2013). Transdimensional inference in the geosciences. Philosophical Transactions of the Royal Society A, 371, 20110547.Google Scholar

Sambridge, M. S., Gallagher, K., Jackson, A., and Rickwood, P. (2006). Trans-dimensional inverse problems, model comparison, and the evidence. Geophysical Journal International, 167, 528–42.Google Scholar

Schiemenz, A., and Igel, H. (2013). Accelerated 3-D full-waveform inversion using simultaneously encoded sources in the time domain: Application to Valhall ocean-bottom cable data. Geophysical Journal International, 195, 1970–88.Google Scholar

Sieminski, A., Trampert, J., and Tromp, J. (2009). Principal component analysis of anisotropic finite-frequency kernels. Geophysical Journal International, 179, 1186-98.Google Scholar

Sirgue, L., and Pratt, R. G. (2004). Efficient waveform inversion and imaging: A strategy for selecting temporal frequencies. Geophysics, 69, 231–48.Google Scholar

Sirgue, L., Barkved, O. I., Dellinger, J. et al, (2010). Full-waveform inversion: The next leap forward in imaging at Valhall. First Break, 28, 65–70.Google Scholar

Tarantola, A. (1988). Theoretical background for the inversion of seismic waveforms, including elasticity and attenuation. Pure and Applied Geophysics, 128, 365–99.Google Scholar

Tarantola, A. (2005). Inverse Problem Theory and Methods for Model Parameter Estimation, 2nd ed. Philadelphia, PA: Society for Industrial and Applied Mathematics.Google Scholar

Thrastarson, S., van Driel, M., Krischer, L. et al. (2020). Accelerating numerical wave propagation by wavefield adapted meshes. Part II: full-waveform inversion. Geophysical Journal International, 221, 1591–604.Google Scholar

Thrastarson, S., van Herwaarden, D.-P. and Fichtner, A. (2021). Inversionson: Fully Automated Seismic Waveform Inversions. EarthArXiv, http://doi.org/10.31223/X5F31V.Google Scholar

Thrastarson, S., van Herwaarden, D.-P., Krischer, L. et al. (2022). Data-adaptive global full-waveform inversion. Geophysical Journal International, 230, 1374–93, https://doi.org/10.1093/gji/ggac122.Google Scholar

Tromp, J., Tape, C., and Liu, Q. (2005). Seismic tomography, adjoint methods, time reversal and banana-doughnut kernels. Geophysical Journal International, 160, 195–216.Google Scholar

Tromp, J., and Bachmann, E. (2019). Source encoding for adjoint tomography. Geophysical Journal International, 218, 2019–44.Google Scholar

van Driel, M., Boehm, C., Krischer, L., and Afanasiev, M. (2020). Accelerating numerical wave propagation using wavefield adapted meshes. Part I: forward and adjoint modelling. Geophysical Journal International, 221, 1580–90.Google Scholar

van Herwaarden, D.-P., Boehm, C., Afanasiev, M. et al. (2020). Accelerated full-waveform inversion using dynamic mini-batches. Geophysical Journal International, 221, 1427–38.Google Scholar

van Herwaarden, D.-P., Afanasiev, M., Thrastarson, S., and Fichtner, A. (2021). Evolutionary full-waveform inversion. Geophysical Journal International, 224, 306–11.Google Scholar

van Leeuwen, T., and Herrmann, F. J. (2013). Fast waveform inversion without source‐encoding. Geophysical Prospecting, 61, 10–19.Google Scholar

Virieux, J. (1986). P-SV wave propagation in heterogeneous media: Velocity-stress finite difference method. Geophysics, 51, 889–901.Google Scholar

Virieux, J., and Operto, S. (2009). An overview of full waveform inversion in exploration geophysics. Geophysics, 74, WCC127–WCC152.Google Scholar

Visser, G., Guo, P., and Saygin, E. (2019). Bayesian transdimensional seismic full-waveform inversion with a dipping layer parameterization. Geophysical Journal International, 84(6), R845–R858.Google Scholar

Woodhouse, J. H., and Dziewonski, A. M. (1984). Mapping the upper mantle: Three-dimensional modeling of Earth structure by inversion of seismic waveforms. Journal of Geophysical Research: Solid Earth, 89, 5953–86.Google Scholar

Wolpert, D. H., and Macready, W. G. (1997). No Free Lunch theorems for optimization. IEEE Transactions on Evolutionary Computation, 1, 67–88.Google Scholar

Zhang, X., and Curtis, A. (2020). Variational full-waveform inversion. Geophysical Journal International, 222, 406–11.Google Scholar

Bibliography

Afonso, J. C., Moorkamp, M., and Fullea, J. (2016). Imaging the lithosphere and upper mantle: Where we are at and where we are go. In Moorkamp, M., Lelièvre, P. G., Linde, N., and Khan, A. (eds.) Integrated Imaging of the Earth: Theory and Applications, AGU Geophysical Monograph 218. Hoboken, NJ: John Wiley & Sons, pp. 191–218.Google Scholar

Afonso, J. C., Salajegheh, F., Szwillus, W., Ebbing, J., and Gaina, C. (2019). A global reference model of the lithosphere and upper mantle from joint inversion and analysis of multiple data sets. Geophysical Journal International, 217(3), 1602–28.Google Scholar

Astic, T., and Oldenburg, D. W. (2019). A framework for petrophysically and geologically guided geophysical inversion using a dynamic Gaussian mixture model prior. Geophysical Journal International, 219(3), 1989–2012.Google Scholar

Astic, T., Heagy, L. J., and Oldenburg, D. W. (2021). Petrophysically and geologically guided multi-physics inversion using a dynamic Gaussian mixture model. Geophysical Journal International, 224(1), 40–68.Google Scholar

Bankey, V., Cuevas, A., Daniels, D. et al. (2002). Digital data grids for the magnetic anomaly map of North America. USGS Open-File Report 02-414. https://pubs.usgs.gov/of/2002/ofr-02-414/.Google Scholar

Barton, P. J. (1986). The relationship between seismic velocity and density in the continental crust: A useful constraint? Geophysical Journal International, 87(1), 195–208.Google Scholar

Bedrosian, P. A., and Feucht, D. W. (2014). Structure and tectonics of the northwestern United States from EarthScope USArray magnetotelluric data. Earth and Planetary Science Letters, 402, 275–89.Google Scholar

Bennington, N. L., Zhang, H., Thurber, C. H., and Bedrosian, P. A. (2015). Joint inversion of seismic and magnetotelluric data in the Parkfield region of California using the normalized cross-gradient constraint. Pure and Applied Geophysics, 172(5), 1033–52.Google Scholar

Birch, F. (1961). The velocity of compressional waves in rocks to 10 kilobars: Part 2. Journal of Geophysical Research, 66(7), 2199–224.Google Scholar

Blom, N., Boehm, C., and Fichtner, A. (2017). Synthetic inversions for density using seismic and gravity data. Geophysical Journal International, 209(2), 1204–20.Google Scholar

Bosch, M. (2016). Inference networks in Earth models with multiple components and data. In Moorkamp, M., Lelièvre, P. G., Linde, N., and Khan, A. (eds.) Integrated Imaging of the Earth: Theory and Applications, AGU Geophysical Monograph 218. Hoboken, NJ: John Wiley & Sons, pp. 29–47.Google Scholar

Bosch, M., and McGaughey, J. (2001). Joint inversion of gravity and magnetic data under lithologic constraints. The Leading Edge, 20(8), 877–81.Google Scholar

Bouligand, C., Glen, J. M. G., and Blakely, R. J. (2009). Mapping Curie temperature depth in the western United States with a fractal model for crustal magnetization. Journal of Geophysical Research: Solid Earth, 114(B11).Google Scholar

Bouligand, C., Glen, J. M. G., and Blakely, R. J. (2014). Distribution of buried hydrothermal alteration deduced from high-resolution magnetic surveys in Yellowstone National Park. Journal of Geophysical Research: Solid Earth, 119(4), 2595–630.Google Scholar

Carter-McAuslan, A., Leliévre, P. G. and Farquharson, C. G. (2015). A study of fuzzy c-means coupling for joint inversion, using seismic tomography and gravity data test scenarios. GEOPHYSICS, 80(1), W1–W15.Google Scholar

Chen, C. W., Rondenay, S., Weeraratne, D. S., and Snyder, D. B. (2007).New constraints on the upper mantle structure of the Slave Craton from Rayleigh wave inversion. Geophysical Research Letters, 34, L10301. https://doi.org/10.1029/2007GL029535 Google Scholar

Chulliat, A., Brown, W., Alken, P. et al. (2020). The US/UK world magnetic model for 2020–2025: Technical Report. National Centers for Environmental Information (U.S.); British Geological Survey. https://doi.org/10.25923/ytk1-yx35 Google Scholar

Colombo, D., and Rovetta, D. (2018). Coupling strategies in multiparameter geophysical joint inversion. Geophysical Journal International, 215(2), 1171–84.Google Scholar

Darijani, M., Farquharson, C. G., and Lelièvre, P. G. (2021). Joint and constrained inversion of magnetic and gravity data: A case history from the McArthur River area, Canada. Geophysics, 86(2), B79–B95.Google Scholar

de Groot-Hedlin, C., Constable, S., and Weitemeyer, K. (2003–4).Transfer functions for deep magnetotelluric sounding along the Yellowstone-Snake River hotspot track. https://doi.org/10.17611/DP/EMTF/YSRP/2004.Google Scholar

Elsasser, W. M. (1950). The Earth’s interior and geomagnetism. Reviews of Modern Physics, 22(1), 1–35.Google Scholar

Finn, C. A., and Morgan, L. A. (2002). High-resolution aeromagnetic mapping of volcanic terrain, Yellowstone National Park. Journal of Volcanology and Geothermal Research, 115(1-2), 207–31.Google Scholar

Fishwick, S. (2010). Surface wave tomography: Imaging of the lithosphere-asthenosphere boundary beneath central and southern Africa? Lithos, 120(1–2), 63–73.Google Scholar

Franz, G., Moorkamp, M., Jegen, M., Berndt, C., and Rabbel, W. (2021). Comparison of different coupling methods for joint inversion of geophysical data: A case study for the Namibian continental margin. Journal of Geophysical Research: Solid Earth, 126 (12), e2021JB022092.Google Scholar

Fullagar, P. K., and Oldenburg, D. W. (1984). Inversion of horizontal loop electromagnetic frequency soundings. Geophysics, 49(2), 150–64.Google Scholar

Gallardo, L. A., and Meju, M. A. (2003). Characterization of heterogeneous near-surface materials by joint 2D inversion of dc resistivity and seismic data. Geophysical Research Letters, 30(13), 1658.Google Scholar

Gallardo, L. A., and Meju, M. A. (2007). Joint two-dimensional cross-gradient imaging of magnetotelluric and seismic traveltime data for structural and lithological classification. Geophysical Journal International, 169, 1261–72.Google Scholar

Gallardo, L. A., and Meju, M. A. (2011). Structure-coupled multiphysics imaging in geophysical sciences. Reviews of Geophysics, 49(1).Google Scholar

Gao, H., and Shen, Y. (2014). Upper mantle structure of the Cascades from full-wave ambient noise tomography: Evidence for 3D mantle upwelling in the back-arc. Earth and Planetary Science Letters, 390, 222–33.Google Scholar

Gardner, G. H. F., Gardner, L. W., and Gregory, A. R. (1974). Formation velocity and density: The diagnostic basics for stratigraphic traps. Geophysics, 39(6), 770–80.Google Scholar

Ghalenoei, E., Dettmer, J., Ali, M. Y., and Kim, J. W. (2021). Gravity and magnetic joint inversion for basement and salt structures with the reversible-jump algorithm. Geophysical Journal International, 227(2), 746–58.Google Scholar

Giraud, J., Pakyuz-Charrier, E., Jessell, M. et al. (2017). Uncertainty reduction through geologically conditioned petrophysical constraints in joint inversion. Geophysics, 82(6), ID19–ID34.Google Scholar

Gross, L. (2019). Weighted cross-gradient function for joint inversion with the application to regional 3-D gravity and magnetic anomalies. Geophysical Journal International, 217(3), 2035–46.Google Scholar

Haber, E., and Holtzman Gazit, M. (2013). Model fusion and joint inversion. Surveys in Geophysics, 34(5), 675–95.Google Scholar

Haber, E., and Oldenburg, D. W. (1997). Joint inversion: A structural approach. Inverse Problems, 13(1), 63–77.Google Scholar

Harmon, N., Wang, S., Rychert, C. A. Constable, S., and Kendall, J. M. (2021). Shear velocity inversion guided by resistivity structure from the pi-lab experiment for integrated estimates of partial melt in the mantle. Journal of Geophysical Research: Solid Earth, e2021JB022202.Google Scholar

Heincke, B., Jegen, M., Moorkamp, M., Hobbs, R. W., and Chen, J. (2017). An adaptive coupling strategy for joint inversions that use petrophysical information as constraints. Journal of Applied Geophysics, 136, 279–97.Google Scholar

Hinze, W. J., Von Frese, R. R. B., and Saad, A. H. (2013). Gravity and magnetic exploration: Principles, practices, and applications. Cambridge: Cambridge University Press.Google Scholar

Hong, T., and Sen, M. K. (2009). A new MCMC algorithm for seismic waveform inversion and corresponding uncertainty analysis. Geophysical Journal International, 177 (1), 14–32.Google Scholar

IRIS. USArray Transportable Array. (2003). https://doi.org/10.7914/SN/TA.Google Scholar

Julia, J., Ammon, C. J., Herrmann, R. B,. and Correig, A. M. (2000). Joint inversion of receiver function and surface wave dispersion observations. Geophysical Journal International,143(1), 99–112.Google Scholar

Kamm, J., Lundin, I. A., Bastani, M., Sadeghi, M., and Pedersen, L. B. (2015). Joint inversion of gravity, magnetic, and petrophysical data: A case study from a gabbro intrusion in Boden, Sweden. Geophysics, 80(5), B131–B152.Google Scholar

Kelbert, A., Egbert, G. D., and Schultz, A. (2011). IRIS DMC data services products: EMTF, the magnetotelluric transfer functions. https://doi.org/10.17611/DP/EMTF.1.Google Scholar

Kelbert, A., Egbert, G. D., and deGroot-Hedlin, C. (2012). Crust and upper mantle electrical conductivity beneath the Yellowstone Hotspot Track. Geology, 40(5), 447–50.Google Scholar

Konstantinou, A., Strickland, A., Miller, E. L., and Wooden, J. P. (2012). Multistage Cenozoic extension of the Albion–Raft River–Grouse Creek metamorphic core complex: Geochronologic and stratigraphic constraints. Geosphere, 8(6), 1429–66.Google Scholar

Lelièvre, P. G., Bijani, R., and Farquharson, C. G. (2016). Joint inversion using multi-objective global optimization methods. In 78th EAGE Conference and Exhibition 2016. Houten: European Association of Geoscientists & Engineers. https://doi.org/10.3997/2214-4609.201601655.Google Scholar

Li, X., and Sun, J. (2022). Towards a better understanding of the recoverability of physical property relationships from geophysical inversions of multiple potential-field data sets.Geophysical Journal International, 230(3), 1489–507.Google Scholar

Linde, N., Binley, A., Tryggvason, A., Pedersen, L. B., and Revil, A. (2006). Improved hydrogeophysical characterization using joint inversion of cross-hole electrical resistance and ground-penetrating radar traveltime data. Water Resources Research, 42: 12404.Google Scholar

Linde, N., and Doetsch, J. (2016). Joint Inversion in Hydrogeophysics and Near-Surface Geophysics. In Moorkamp, M., Lelièvre, P. G., Linde, N., and Khan, A., eds., Integrated Imaging of the Earth: Theory and Applications. Hoboken, NJ: John Wiley & Sons, pp. 117–35.Google Scholar

Lines, L. R., Schultz, A. K., and Treitel, S. (1986). Cooperative inversion of geophysical data. Geophysics, 53(1), 8–20.Google Scholar

Liu, L., and Gao, S. S. (2018). Lithospheric layering beneath the contiguous United States constrained by S-to-P receiver functions. Earth and Planetary Science Letters, 495, 79–86.Google Scholar

Maceira, M., and Ammon, C. J. (2009). Joint inversion of surface wave velocity and gravity observations and its application to central Asian basins shear velocity structure. Journal of Geophysical Research: Solid Earth, 114(B2), B02314.Google Scholar

Mackie, R. L., Meju, M. A., Miorelli, F. et al. (2020). Seismic image-guided 3D inversion of marine controlled-source electromagnetic and magnetotelluric data. Interpretation, 8(4), SS1–SS13.Google Scholar

Manassero, M. C., Afonso, J. C., Zyserman, F I. et al. (2021). A reduced order approach for probabilistic inversions of 3D magnetotelluric data II: Joint inversion of MT and surface-wave data. Journal of Geophysical Research: Solid Earth, 126 (12), e2021JB021962.Google Scholar

Mandolesi, E., and Jones, A. G. (2014). Magnetotelluric inversion based on mutual information. Geophysical Journal International, 199(1), 242–52.Google Scholar

Martin, R., Giraud, J., Ogarko, V. et al. (2021). Three-dimensional gravity anomaly data inversion in the Pyrenees using compressional seismic velocity model as structural similarity constraints. Geophysical Journal International, 225(2), 1063–85.Google Scholar

Meilă, M. (2003). Comparing clusterings by the variation of information. In Schölkopf, B. and Warmuth, M. K., eds., Learning Theory and Kernel Machines: Lecture Notes in Computer Science, vol. 2777. Berlin: Springer, pp. 173–87. https://doi.org/10.1007/978-3-540-45167-9_14.Google Scholar

Meju, M., and Gallardo, L. A. (2016). Structural Coupling Approaches in Integrated Geophysical Imaging. In Moorkamp, M., Lelièvre, P. G., Linde, N., and Khan, A., eds., Integrated Imaging of the Earth: Theory and Applications. Hoboken, NJ: . John Wiley & Sons, pp. 49–67.Google Scholar

Meju, M., Saleh, A. S., Mackie, R. L. et al. (2018). Workflow for improvement of 3D anisotropic CSEM resistivity inversion and integration with seismic using cross-gradient constraint to reduce exploration risk in a complex fold-thrust belt in offshore northwest Borneo. Interpretation, 6(3), SG49–SG57.Google Scholar

Meqbel, N. M., Egbert, G. D., Wannamaker, P. E., Kelbert, A., and Schultz, A. (2014). Deep electrical resistivity structure of the northwestern US derived from 3-D inversion of USArray magnetotelluric data. Earth and Planetary Science Letters, 402,290–304.Google Scholar

Moorkamp, M. (2007). Joint inversion of MT and receiver-function data. PhD thesis, National University of Ireland, Galway.Google Scholar

Moorkamp, M. (2017). Integrating electromagnetic data with other geophysical observations for enhanced imaging of the Earth: A tutorial and review. Surveys in Geophysics, 38(5), 935–62.Google Scholar

Moorkamp, M. (2021). Joint inversion of gravity and magnetotelluric data from the Ernest Henry IOCG deposit with a variation of information constraint. In Swinford, B. and Abubakar, A. First International Meeting for Applied Geoscience & Energy. Houston, TX: Society of Exploration Geophysicists, pp. 1711–15.Google Scholar

Moorkamp, M. (2022). Deciphering the state of the lower crust and upper mantle with multi-physics inversion. Geophysical Research Letters, 49 (9), e2021GL096336.Google Scholar

Moorkamp, M., Jones, A. G., and Eaton, D. W. (2007). Joint inversion of teleseismic receiver functions and magnetotelluric data using a genetic algorithm: Are seismic velocities and electrical conductivities compatible? Geophysical Research Letters, 34(16), L16311.Google Scholar

Moorkamp, M., Roberts, A. W., Jegen, M., Heincke, B., and Hobbs, R. W. (2013). Verification of velocity-resistivity relationships derived from structural joint inversion with borehole data. Geophysical Research Letters, 40(14), 3596–601.Google Scholar

Moorkamp, M., Heincke, B., Jegen, M., Roberts, A. W., and Hobbs, R. W. (2011). A framework for 3-D joint inversion of MT, gravity and seismic refraction data. Geophysical Journal International, 184, 477–93.Google Scholar

Moorkamp, M., Heincke, B., Jegen, M., Roberts, A. W., and Hobbs, R. W. (2016a). Joint Inversion in Hydrocarbon Exploration. In Moorkamp, M., Lelièvre, P. G., Linde, N., and Khan, A., eds., Integrated Imaging of the Earth: Theory and Applications. Hoboken, NJ: John Wiley & Sons, pp. 167–189.Google Scholar

Moorkamp, M., Lelièvre, P. G., Linde, N., and Khan, A., eds. (2016b). Integrated Imaging of the Earth. Hoboken, NJ: John Wiley & Sons.Google Scholar

Nafe, J. E., and Drake, C. L. (1957). Variation with depth in shallow and deep water marine sediments of porosity, density and the velocities of compressional and shear waves. Geophysics, 22(3), 523–52.Google Scholar

O’Donnell, J. P., Daly, E., Tiberi, C. et al. (2011). Lithosphere-asthenosphere interaction beneath Ireland from joint inversion of teleseismic p-wave delay times and grace gravity. Geophysical Journal International, 184(3), 1379–96.Google Scholar

Pail, R., Fecher, T., Barnes, D. et al. (2018). Short note: The experimental geopotential model XGM2016. Journal of Geodesy, 92(4), 443–51.Google Scholar

Panzner, M., Morten, J. P., Weibull, W. W., and Arntsen, B. (2016). Integrated seismic and electromagnetic model building applied to improve subbasalt depth imaging in the Faroe-Shetland basin. Geophysics, 81(1), E57–E68.Google Scholar

Pasquale, V. (2011). Curie temperature. In Gupta, H. K., ed., Encyclopedia of Solid Earth Geophysics. Dordrecht: Springer, pp. 89–90. https://doi.org/10.1007/978-90-481-8702-7_109.Google Scholar

Paulatto, M., Moorkamp, M., Hautmann, S. et al. (2019). Vertically extensive magma reservoir revealed from joint inversion and quantitative interpretation of seismic and gravity data. Journal of Geophysical Research: Solid Earth, 124(11), 11170–91.Google Scholar

Pluim, J. P. W. Maintz, J. B. A. and Viergever, M. A. (2003). Mutual-information-based registration of medical images: A survey. IEEE Transactions on Medical Imaging, 22(8), 986–1004.Google Scholar

Schmandt, B., and Humphreys, E. (2011). Seismically imaged relict slab from the 55 Ma Siletzia accretion to the northwest United States. Geology, 39(2), 175–8.Google Scholar

Schultz, A., Egbert, G. D., Kelbert, A. et al., and staff of the National Geoelectromagnetic Facility and their contractors. (2006–8). USArray TA magnetotelluric transfer functions. https://doi.org/10.17611/DP/EMTF/USARRAY/TA.Google Scholar

Shi, Z., Hobbs, R. W., Moorkamp, M., Tian, G., and Jiang, L. (2017). 3-D cross-gradient joint inversion of seismic refraction and dc resistivity data. Journal of Applied Geophysics, 141, 54–67.Google Scholar

Spichak, V. V. (2020). Modern methods for joint analysis and inversion of geophysical data. Russian Geology and Geophysics, 61(3), 341–57.Google Scholar

Sun, J., and Li, Y. (2015a). Advancing the understanding of petrophysical data through joint clustering inversion: A sulfide deposit example from Bathurst mining camp. In Schneider, R. V., ed., SEG Technical Program Expanded Abstracts 2015. Houston, TX: Society of Exploration Geophysicists, pp. 2017–21.Google Scholar

Sun, J., and Li, Y. (2015b). Multidomain petrophysically constrained inversion and geology differentiation using guided fuzzy c-means clustering. Geophysics, 80(4), ID1–ID18.Google Scholar

Sun, J., and Li, Y. (2016). Joint inversion of multiple geophysical data using guided fuzzy c-means clustering. Geophysics, 81(3), ID37–ID57.Google Scholar

Sun, J., Melo, A. T., Kim, J. D., and Wei, X. (2017). Unveiling the 3D undercover structure of a Precambrian intrusive complex by integrating airborne magnetic and gravity gradient data into 3D quasi-geology model building. Interpretation, 8(4), SS15–SS29.Google Scholar

Tauxe, L., Luskin, C., Selkin, P., Gans, P., and Calvert, A. (2004). Paleomagnetic results from the Snake River Plain: Contribution to the time-averaged field global database. Geochemistry, Geophysics, Geosystems, 5(8), Q08H13. https://doi.org/10.1029/2003GC000661.Google Scholar

Tiberi, C., Diament, M., Déverchère, J. et al. (2003). Deep structure of the Baikal rift zone revealed by joint inversion of gravity and seismology. Journal of Geophysical Research: Solid Earth, 108(B3), 2133. https://doi.org/10.1029/2002JB001880.Google Scholar

Tu, X., and Zhdanov, M. S. (2021). Joint Gramian inversion of geophysical data with different resolution capabilities: Case study in Yellowstone. Geophysical Journal International, 226(2), 1058–85.Google Scholar

Wagner, F. M., Mollaret, C., Günther, T., Kemna, A., and Hauck, C. (2019). Quantitative imaging of water, ice and air in permafrost systems through petrophysical joint inversion of seismic refraction and electrical resistivity data. Geophysical Journal International 219(3), 1866–75.Google Scholar

Weise, B. (2021). Joint Inversion of magnetotelluric, seismic and gravity data. PhD thesis, University of Leicester.Google Scholar

Zhao, Y., Guo, L., Guo, Z. et al. (2020). High resolution crustal model of SE Tibet from joint inversion of seismic p-wave travel times and Bouguer gravity anomalies and its implication for the crustal channel flow. Tectonophysics, 792, 228580.Google Scholar

Zhdanov, M. S., Gribenko, A., and Wilson, G. (2012). Generalized joint inversion of multimodal geophysical data using Gramian constraints. Geophysical Research Letters, 39(9).Google Scholar

Zhou, J. Revil, A. Karaoulis, M. et al. (2014). Image-guided inversion of electrical resistivity data. Geophysical Journal International, 197 (1), 292–309.Google Scholar

Zingerle, P., Pail, R., Gruber, T., and Oikonomidou, X. (2020). The combined global gravity field model xgm2019e. Journal of Geodesy, 94(7), 1–12.Google Scholar

References

Bagherbandi, M. (2012). A comparison of three gravity inversion methods for crustal thickness modelling in Tibet plateau. Journal of Asian Earth Sciences, 43(1), 89–97.Google Scholar

Bai, Z. M., Zhang, S. F., and Braitenberg, C. (2013). Crustal density structure from 3D gravity modeling beneath Himalaya and Lhasa blocks, Tibet. Journal of Asian Earth Sciences, 78, 301–17.Google Scholar

Bao, X. W., Song, X. D., and Li, J. T. (2015). High-resolution lithospheric structure beneath Mainland China from ambient noise and earthquake surface-wave tomography. Earth and Planetary Science Letters, 417, 132–41.Google Scholar

Barnoud, A., Coutant, O., Bouligand, C., Gunawan, H., and Deroussi, S. (2016). 3-D linear inversion of gravity data: Method and application to Basse-Terre volcanic island, Guadeloupe, Lesser Antilles. Geophysical Journal International, 205(1), 562–74.Google Scholar

Basuyau, C., Diament, M., Tiberi, C. et al. (2013). Joint inversion of teleseismic and GOCE gravity data: Application to the Himalayas. Geophysical Journal International, 193(1), 149–60.Google Scholar

Braitenberg, C., Zadro, M., Fang, J., Wang, Y., and Hsu, H. T. (2000). Gravity inversion in Qinghai-Tibet plateau. Physics and Chemistry of the Earth Part A: Solid Earth and Geodesy, 25(4), 381–36.Google Scholar

Brocher, T. A. (2005). Empirical relations between elastic wavespeeds and density in the earth’s crust. Bulletin of the Seismological Society of America, 95(6), 2081–92.Google Scholar

Chen, L., Wang, X., Liang, X. F., Wan, B., and Liu, L. J. (2020). Subduction tectonics vs. Plume tectonics: Discussion on driving forces for plate motion. Science China Earth Sciences, 63(3), 315–28.Google Scholar

Chen, W. J. (2017). Determination of crustal thickness under Tibet from gravity-gradient data. Journal of Asian Earth Sciences, 143, 315–25.Google Scholar

Chen, W. J., and Tenzer, R. (2017). Moho modeling in spatial domain: A case study under Tibet. Advances in Space Research, 59(12), 2855–69.Google Scholar

Clark, M. K., and Royden, L. H. (2000). Topographic ooze: Building the eastern margin of Tibet by lower crustal flow. Geology, 28, 703–6.Google Scholar

Conrad, C. P., and Lithgow-Bertelloni, C. (2004). The temporal evolution of plate driving forces: Importance of ‘slab suction’ versus ‘slab pull’ during the Cenozoic. Journal of Geophysical Research: Solid Earth, 109 (B10407). https://doi.rog/10.1029/2004jb002991.Google Scholar

Fu, G. Y., and She, Y. W. (2017). Gravity anomalies and isostasy deduced from new dense gravimetry around the Tsangpo Gorge, Tibet. Geophysical Research Letters, 44(20), 10233–9.Google Scholar

He, R. Z., Zhao, D. P., Gao, R., and Zheng, H.W. (2010). Tracing the Indian lithospheric mantle beneath central Tibetan Plateau using teleseismic tomography. Tectonophysics, 491(1–4), 230–43.Google Scholar

Hetényi, G., Cattin, R., Brunet, F. et al. (2007). Density distribution of the India plate beneath the Tibetan plateau: Geophysical and petrological constraints on the kinetics of lower-crustal eclogitization. Earth and Planetary Science Letters, 264(1-2), 226–44.Google Scholar

Houseman, G., and England, P. (1986). Finite strain calculations of continental deformation 1. Method and general results for convergent zones. Journal of Geophysical Research, 91(B3), 3651–63.Google Scholar

Huang, J. L., and Zhao, D. P. (2006). High-resolution mantle tomography of China and surrounding regions. Journal of Geophysical Research: Solid Earth, 111, B09305. https://doi.org/10.1029/2005JB004066.Google Scholar

Jiang, W. L., Zhang, J. F., Tian, T., and Wang, X. (2012). Crustal structure of Chuan-Dian region derived from gravity data and its tectonic implications. Physics of the Earth and Planetary Interiors, 212, 76–87.Google Scholar

Jiménez-Munt, I., Fernàndez, M., Vergés, J., and Platt, J. P. (2008). Lithosphere structure underneath the Tibetan Plateau inferred from elevation, gravity and geoid anomalies. Earth and Planetary Science Letters, 267, 276–89.Google Scholar

Jin, S. G., and Park, P. (2006). Strain accumulation in South Korea inferred from GPS measurements. Earth Planets Space, 58(5), 529–34.Google Scholar

Jin, S. G., Park, P., and Zhu, W. (2007). Micro-plate tectonics and kinematics in northeast Asia inferred from a dense set of GPS observations. Earth and Planetary Science Letters, 257(3–4), 486–96.Google Scholar

Kumar, P., Yuan, X. H., Kind, R., and Ni, J. (2006). Imaging the colliding Indian and Asian lithospheric plates beneath Tibet. Journal of Geophysical Research: Solid Earth, 111, B06308. https://doi.org/10.1029/2005JB003930.Google Scholar

Laske, G., Masters., G., Ma, Z., and Pasyanos, M. (2013). Update on CRUST1.0: A 1-degree global model of Earth’s crust. Geophysical Research Abstracts, 15, EGU2013-2658.Google Scholar

Li, C., Van der Hilst, R .D., Meltzer, A. S., and Engdahl, E. R. (2008). Subduction of the Indian lithosphere beneath the Tibetan Plateau and Burma. Earth and Planetary Science Letters, 274(1–2), 157–68.Google Scholar

Li, S. L., Mooney, W. D., and Fan, J. C. (2006). Crustal structure of mainland China from deep seismic sounding data. Tectonophysics, 420(1–2), 239–52.Google Scholar

Li, Y. H., Gao, M. T., and Wu, Q. J. (2014). Crustal thickness map of the Chinese mainland from teleseismic receiver functions. Tectonophysics, 611, 51–60.Google Scholar

Liang, X. F., Chen, Y., Tian, X. B. et al. (2016). 3D imaging of subducting and fragmenting Indian continental lithosphere beneath southern and central Tibet using body-wave finite-frequency tomography. Earth and Planetary Science Letters, 443, 162–75.Google Scholar

Molnar, P., and Tapponnier, P. (1975). Cenozoic tectonics of Asia: Effects of a continental collision. Science, 189, 419–26.Google Scholar

Monsalve, G., Sheehan, A., Rowe, C., and Rajaure, S. (2008). Seismic structure of the crust and the upper mantle beneath the Himalayas: Evidence for eclogitization of lower crustal rocks in the Indian Plate. Journal of Geophysical Research: Solid Earth, 113(B8). https://doi.rog/10.1029/2007jb005424.Google Scholar

Nábělek, J., Hetényi, G., Vergne, J. et al. (2009). Underplating in the Himalaya-Tibet collision zone revealed by the Hi-CLIMB experiment. Science, 325, 1371–74.Google Scholar

Oldenburg, D. W. (1974). The inversion and interpretation of gravity anomalies. Geophysics, 39(4), 526–36.Google Scholar

Owens, T. J., and Zandt, G. (1997). Implications of crustal property variations for models of Tibetan plateau evolution. Nature, 387, 37–43.Google Scholar

Parker, R. L. (1973). The rapid calculation of potential anomalies. Geophysical Journal of the Royal Astronomical Society, 31, 447–55.Google Scholar

Pavlis, N. K., Holmes, S. A., Kenyon, S. C., and Factor, J. K. (2008). An Earth gravitational model to degree 2160: EGM2008, EGU General Assembly. Vienna: European Geosciences Union.Google Scholar

Royden, L. H., Burchfiel, B. C., King, R. W. et al. (1997). Surface deformation and lower crustal flow in eastern Tibet. Science, 276(5313), 788–90.Google Scholar

Searle, M. P., Elliott, J. R., Phillips, R. J., and Chung, S. L. (2011). Crustal-lithospheric structure and continental extrusion of Tibet. Journal of the Geological Society, 168(3), 633–72.Google Scholar

Shin, Y. H., Xu, H., Braitenberg, C., Fang, J., and Wang, Y. (2007). Moho undulations beneath Tibet from GRACE-integrated gravity data. Geophysical Journal International, 170(3), 971–85.Google Scholar

Shin, Y. H., Shum, C. K., Braitenberg, C. et al. (2009. Three-dimensional fold structure of the Tibetan Moho from GRACE gravity data. Geophysical Research Letters, 36. https://doi.rog/10.1029/2008gl036068.Google Scholar

Shin, Y. H., Shum, C. K., Braitenberg, C. et al. (2015). Moho topography, ranges and folds of Tibet by analysis of global gravity models and GOCE data. Scientific Reports, 5. https://doi.rog/10.1038/srep11681.Google Scholar

Sjöberg, L .E. (2013). On the isostatic gravity anomaly and disturbance and their applications to Vening Meinesz-Moritz gravimetric inverse problem. Geophysical Journal International, 193(3), 1277–82.Google Scholar

Socquet, A., and Pubellier, M. (2005). Cenozoic deformation in western Yunnan (China–Myanmar border). Journal of Asian Earth Sciences, 24(4), 495–515.Google Scholar

Steffen, R., Steffen, H., and Jentzsch, G. (2011). A three-dimensional Moho depth model for the Tien Shan from EGM2008 gravity data. Tectonics, 30(TC5019). https://doi.rog/10.1029/2011tc002886.Google Scholar

Stern, R. J. (2007). When and how did plate tectonics begin? Theoretical and empirical considerations. Chinese Science Bulletin, 52(5), 578–1.Google Scholar

Tapponnier, P., Peltzer, G., Le Dain, A. Y., Armijo, R., and Cobbold, P. (1982). Propagating extrusion tectonics in Asia: New insights from simple experiments with plasticine. Geology, 10: 611–16.Google Scholar

Teng, J. W., Zhang, Z. J., Zhang, X. K. et al. (2013). Investigation of the Moho discontinuity beneath the Chinese mainland using deep seismic sounding profiles. Tectonophysics, 609, 202–16.Google Scholar

Teng, J. W., Yang, D. H., Tian, X. B. et al. (2020). Geophysical investigation progresses of the Qinghai-Tibetan Plateau in the past 70 years. Scientia Sinica Terrae, 49, 1546–64.Google Scholar

Tenzer, R., and Bagherbandi, M. (2012). Reformulation of the Vening-Meinesz Moritz inverse problem of isostasy for isostatic gravity disturbances. International Journal of Geosciences, 3: 918–29.Google Scholar

Tenzer, R., Chen, W., and Jin, S. G. (2015). Effect of the upper mantle density structure on the Moho geometry. Pure and Applied Geophysics, 172(6), 1563–83.Google Scholar

Tilmann, F., Ni, J., and Team, I. I. S. (2003). Seismic imaging of the downwelling Indian lithosphere beneath central Tibet. Science, 300(5624), 1424–7.Google Scholar

Tiwari, V. M., Rao, M. B. S. V., and Singh, M. B. (2006). Crustal structure across Sikkim, NE Himalaya from new gravity and magnetic data. Earth and Planetary Science Letters, 247, 61–9.Google Scholar

Vaníček, P., Tenzer, R., Sjöberg, L. E., Martinec, Z., and Featherstone, W. E. (2004). New views of the spherical Bouguer gravity anomaly. Geophysical Journal International, 159, 460–72.Google Scholar

Wang, C. Y., Chan, W. W., and Mooney, W. D. (2003). Three-dimensional velocity structure of crust and upper mantle in southwestern China and its tectonic implications. Journal of Geophysical Research: Solid Earth, 108(B9). https://doi.org/10.1029/2002JB001973.Google Scholar

Wang, C. Y., Han, W. B., Wu, J. P., Lou, H., and Chan, W. W. (2007). Crustal structure beneath the eastern margin of the Tibetan Plateau and its tectonic implications. Journal of Geophysical Research: Solid Earth, 112(B7). https://doi.rog/10.1029/2005jb003873.Google Scholar

Wang, C. Y., Lou, H., Lue, Z. Y. et al. (2008). S-wave crustal and upper mantle’s velocity structure in the eastern Tibetan Plateau: Deep environment of lower crustal flow. Science in China Series D: Earth Sciences, 51(2), 263–74.Google Scholar

Wang, Z. W., Zhao, D. P., Gao, R., and Hua, Y. Y. (2019). Complex subduction beneath the Tibetan plateau: A slab warping model. Physics of the Earth and Planetary Interiors, 292, 42–54.Google Scholar

Xu, C., Liu, Z. W., Luo, Z.C ., Wu, Y. H., and Wang, H. H. (2017). Moho topography of the Tibetan Plateau using multi-scale gravity analysis and its tectonic implications. Journal of Asian Earth Sciences, 138: 378–86.Google Scholar

Xuan, S., Shen, C. Y., Li, H., and Tan, H. B. (2016). Structural interpretation of the Chuan-Dian block and surrounding regions using discrete wavelet transform. International Journal of Earth Sciences, 105(5), 1591–602.Google Scholar

Xuan, S., Shen, C. Y., Tan, H. B., and Li, H. (2015). Inversion of Moho depth in China mainland from EGM2008 gravity data. Journal of Geodesy and Geodynamics, 35 (2), 309–11, 317.Google Scholar

Yin, A., and Harrison, T. M. (2000). Geologic Evolution of the Himalayan-Tibetan Orogen. Annual Review of Earth and Planetary Sciences, 28: 211–80.Google Scholar

Zhang, Z. J., Deng, Y. F., Teng, J. W. et al. (2011). An overview of the crustal structure of the Tibetan plateau after 35 years of deep seismic soundings. Journal of Asian Earth Sciences, 40(4), 977–89.Google Scholar

Zhang, Z. J., Teng, J. W., Romanelli, F. (2014). Geophysical constraints on the link between cratonization and orogeny: Evidence from the Tibetan Plateau and the North China Craton. Earth-Science Reviews, 130, 1–48.Google Scholar

Zhang, C., Huang, D. N., Wu, G. C. et al. (2015). Calculation of Moho depth by gravity anomalies in Qinghai-Tibet plateau based on an improved iteration of Parker-Oldenburg inversion. Pure and Applied Geophysics, 172(10), 2657–68.Google Scholar

Zhao, G. D., Liu, J. X., Chen, B., Kaban, M. K., and Zheng, X. Y. (2020). Moho beneath Tibet based on a joint analysis of gravity and seismic data. Geochemistry, Geophysics, Geosystem, 21(2), e2019GC008849.Google Scholar

Zhao, L. F., Xie, X. B., He, J. K., Tian, X. B., and Yao, Z. X. (2013). Crustal flow pattern beneath the Tibetan plateau constrained by regional Lg-wave Q tomography. Earth and Planetary Science Letters, 383, 113–22.Google Scholar

Zheng, H. W., Li, T. D., Gao, R., Zhao, D. P., and He, R. Z. (2007). Teleseismic P-wave tomography evidence for the Indian lithospheric mantle subducting northward beneath the Qiangtang terrane. Chinese Journal of Geophysics, 50(5), 1223–32.Google Scholar

References

Argus, D. F., and Gordon, R. G. (1991). No-net-rotation model of current plate velocities incorporating plate motion model NUVEL-1. Geophysical Research Letters, 18(11), 2039–2042. https://doi.org/10.1029/91GL01532.Google Scholar

Argus, D. F., and Heflin, M. (1995). Plate motion and crustal deformation estimated with geode-tic data from the Global Positioning System. Geophysical Research Letters, 22(15), 1973–6. https://doi.org/10.1029/95GL02006.Google Scholar

Barbot, S., and Fialko, Y. (2010). Fourier-domain Green’s function for an elastic semi-infinite solid under gravity, with applications to earthquake and volcano deformation. Geophysical Journal International, 182, 568–82.Google Scholar

Bourgeois, J., Pinegina, T., Razhegaeva, N. et al. (2007). Tsunami runup in the middle Kuril Islands from the great earthquake of 15 Nov 2006. Eos Transactions of the American Geophysical Union, 88(52), Abstract S51C-02.Google Scholar

Bürgmann, R., Kogan, M. G., Levin, V. E. et al. (2001). Rapid aseismic moment release following the 5 December 1997 Kronotsky, Kamchatka, Earthquake. Geophysical Research Letters, 28, 1331–4. https://doi.org/10.1029/2000GL012350.Google Scholar

Bürgmann, R., Kogan, M. G., Steblov, G. M. et al. (2005). Interseismic coupling and asperity distribution along the Kamchatka subduction zone. Journal of Geophysical Research, 110, B07405. https://doi.org/10.1029/2005JB003648.Google Scholar

Das, S., and Henry, C. (2003). Spatial relation between main earthquake slip and its aftershock distribution. Reviews of Geophysics, 41(3), 1–26.Google Scholar

DeMets, C., Gordon, R. G., Argus, D. F., and Stein, S. (1994). Effect of recent revisions to the geomagnetic reversal time scale on estimates of current plate motions. Geophysical Research Letters, 21(20), 2191–4.Google Scholar

DeMets, C., Gordon, R. G., and Argus, D. F. (2010). Geologically current plate motions. Geophysical Research Letters, 181, 1–80.Google Scholar

Dixon, T. H. (1991). An introduction to the Global Positioning System and some geological applications. Reviews of Geophysics 29(2), 249–76.Google Scholar

Dziewoński, A. M., and Anderson, D. L. (1981). Preliminary reference earth model, Physics of the Earth and Planetary Interiors 25, 297–356. https://doi.org/10.1016/0031-9201(81)90046-7.Google Scholar

Engdahl, E. R., and Villaseñor, A. (2002). Global Seismicity: 1900–1999. In Lee, W. H. K. et al., eds., International Handbook of Earthquake Engineering and Seismology. Amsterdam: Academic Press, pp. 665–90.Google Scholar

Fedotov, S. A. (1965). Regularities of distribution of large earthquakes of Kamchatka, Kuril Islands and North-Eastern Japan. Seismic microzoning. Transactions of the Institute of Physics of the Earth of the USSR Academy of Sciences, 36, 66–93 (in Russian).Google Scholar

Freed, A. M., Bürgmann, R., and Herring, T. (2007). Far-reaching transient motions after Mojave earthquakes require broad mantle flow beneath a strong crust. Geophysical Research Letters, 34. https://doi.org/10.1029/2007GL030959.Google Scholar

Freymueller, J. T., and Beavan, J. (1999). Absence of strain accumulation in the western Shumagin segment of the Alaska subduction zone. Geophysical Research Letters, 26, 3233–6.Google Scholar

Gill, P. E., Murray, W., Saunders, M. A., and Wright, M.H. (1986). User’s Guide for NPSOL (Version 4.0): A Fortran Package for Nonlinear Programming, Report SOL 86–2, Department of Operations Research, Stanford University.Google Scholar

Govers, R., Furlong, K. P., van de Wiel, L., Herman, M. W., and Broerse, T. (2018). The geodetic signature of the earthquake cycle at subduction zones: Model constraints on the deep processes. Reviews of Geophysics, 56, 6–49. https://doi.org/10.1002/2017RG000586.Google Scholar

He, Y.-M., Wang, W.-M., and Yao, Z.-X. (2003). Static deformation due to shear and tensile faults in a layered half-space. Bulletin of the Seismological Society of America, 93, 2253–63.Google Scholar

Helmstetter, A., and Shaw, B. E. (2009). Afterslip and aftershocks in the rate-and-state friction law. Journal of Geophysical Research, 114(B01308), 1−24.Google Scholar

International Seismological Centre (2022). On-line Bulletin. https://doi.org/10.31905/D808B830.Google Scholar

Ismail-Zadeh, A., and Tackley, P. (2010). Computational Methods for Geodynamics. Cambridge: Cambridge University Press.Google Scholar

Kogan, M. G., and Steblov, G. M. (2008). Current global plate kinematics from GPS (1995–2007) with the plate-consistent reference frame. Journal of Geophysical Research, 113(B04416). https://doi.org/10.1029/2007JB005353.Google Scholar

Kogan, M. G., Bürgmann, R., Vasilenko, N. F. et al. (2003). The 2000 Mw 6.8 Uglegorsk earthquake and regional plate boundary deformation of Sakhalin from geodetic data. Geophysical Research Letters, 30(3), 1102. https://doi.org/10.1029/2002GL016399.Google Scholar

Kuchay, O. A. (1982). Spatial Regularities of Aftershock Deformation of the Source Region of a Strong Earthquake. Izv., Physics of the Solid Earth, 10, 62–7. (in Russian)Google Scholar

Lay, T., and Kanamori, H. (1981). An asperity model of large earthquake sequences. In Simpson, D. W. and Richards, P.G., eds., Earthquake Prediction, vol. 4. Washington, DC: American Geophysical Union, pp. 579–92. https://doi.org/10.1029/ME004p0579.Google Scholar

Lay, T., Kanamori, H., Ammon, C. J. et al. (2009). The 2006–2007 Kuril Islands great earthquake sequence. Journal of Geophysical Research, 114(B11308), 1–31.Google Scholar

Lay, T., Ammon, С. J., Kanamori, H., Kim, M. J., and Xue, L. (2011). Possible large near-trench slip during the 2011 Mw 9.0 off the Pacific coast of Tohoku Earthquake. Earth, Planets and Space, 63, 713–18.Google Scholar

Lévêque, J.-J., Rivera, L., and Wittlinger, G. (1993). On the use of the checker-board test to assess the resolution of tomographic inversions. Geophysical Journal International, 115, 313–18.Google Scholar

Lundgren, P., Protti, M., Donnellan, A. et al. (1999). Seismic cycle and plate margin deformation in Costa Rica: GPS observations from 1994 to 1997. Journal of Geophysical Research, 104(28), 915–26.Google Scholar

Marone, C. J., Scholz, C. H., and Bilham, R. G. (1991). On the mechanics of earthquake afterslip. Journal of Geophysical Research, 96(B5), 8441–52.Google Scholar

Masse, R. P., and Needham, R. E. (1989). NEIC – the National Earthquake Information Center. Earthquakes & Volcanoes (USGS), 21(1), 4–44.Google Scholar

Mavrommatis, A. P., Segall, P., Uchida, N., and Johnson, K. M. (2015). Long-term acceleration of aseismic slip preceding the Mw 9 Tohoku-oki earthquake: Constraints from repeating earthquakes. Geophysical Research Letters, 42, 9717–25. https://doi.org/10.1002/2015GL066069.Google Scholar

Mazzotti, S., Le Pichon, X., and Henry, P. (2000). Full interseismic locking of the Nankai and Japan-west Kurile subduction zones: An analysis of uniform elastic strain accumulation in Japan constrained by permanent GPS. Journal of Geophysical Research, 105, 13159–77.Google Scholar

Molchan, G. M., and Dmitrieva, O. E. (1992). Aftershock identification: Methods and new approaches. Geophysical Journal International, 109, 501–16. https://doi.org/10.1111/j.1365-246X.1992.tb00113.x.Google Scholar

Muto, J., Moore, J. D. P., Barbot, S. et al. (2019). Coupled afterslip and transient mantle flow after the 2011 Tohoku earthquake. Science Advances, 5(9), eaaw1164. https://doi.org/10.1126/sciadv.aaw1164.PMID:31579819;PMCID:PMC6760927.Google Scholar

Namegaya, Y., and Satake, K. (2014). Reexamination of the A.D. 869 Jogan earthquake size from tsunami deposit distribution, simulated flow depth, and velocity. Geophysical Research Letters, 41, 2297–303.Google Scholar

Okada, Y. (1985). Surface deformation due to shear and tensile faults in a half-space. Bulletin of the Seismological Society of America, 75(4), 1135–54.Google Scholar

Okada, Y. (1992). Internal deformation due to shear and tensile faults in a half-space. Bulletin of the Seismological Society of America, 82(2), 1018–40.Google Scholar

Oleskevich, D., Hyndman, R. D., and Wang, K. (1999). The updip and downdip limits of subduction earthquakes: Thermal and structural models of Cascadia, south Alaska, S.W. Japan, and Chile. Journal of Geophysical Research, 104(14), 965–91.Google Scholar

Pacheco, J. F., Sykes, L. R., and Scholz, C. H. (1993). Nature of seismic coupling along simple plate boundaries of the subduction type. Journal of Geophysical Research, 98, 14,133–59.Google Scholar

Peacock, S. M. (1996). Thermal and petrologic structure of subduction zones. In Bebout, G. E., Scholl, D. W., Kirby, S. H., and Platt, J. P., eds., Subduction: Top to Bottom. Geophysical Monograph 96. Washington, DC: American Geophysical Union, pp.119–33. https://doi.org/10.1029/GM096p0119.Google Scholar

Peltzer, G., Rosen, P. A., Rogez, P., and Hudnut, K. (1996). Postseismic rebound in fault step-overs caused by pore fluid flow. Science, 273, 1202–4. https://doi.org/10.1126/science.273.5279.1202.Google Scholar

Perfettini, H., and Avouac, J.-P. (2004). Stress transfer and strain rate variations during the seismic cycle. Journal of Geophysical Research, 109, B06402. https://doi.org/10.1029/2003JB002917.Google Scholar

Perfettini, H., Avouac, J.-P., and Ruegg, J.-C. (2005). Geodetic displacements and aftershocks following the 2001 Mw = 8.4 Peru earthquake: Implications for the mechanics of the earthquake cycle along subduction zones. Journal of Geophysical Research, 110, B09404. https://doi.org/10.1029/2004JB003522.Google Scholar

Piersanti, A., Spada, G., Sabadini, R., and Bonafede, M. (1995). Global postseismic deformation. Geophysical Journal International, 120, 544–66.Google Scholar

Pollitz, F. F. (1996). Coseismic deformation from earthquake faulting on a layered spherical Earth. Geophysical Journal International, 125, 1–14.Google Scholar

Pollitz, F. F. (1997). Gravitational viscoelastic postseismic relaxation on a layered spherical Earth. Journal of Geophysical Research, 102, 17921–41.Google Scholar

Pollitz, F.F. (2019). Lithosphere and shallow asthenosphere rheology from observations of post-earthquake relaxation. Physics of the Earth and Planetary Interiors, 293. https://doi.org/10.1016/j.pepi.2019.106271.Google Scholar

Pollitz, F., Banerjee, P., Grijalva, K., Nagarajan, B., and Bürgmann, R. (2008). Effect of 3-D viscoelastic structure on post-seismic relaxation from the 2004 M = 9.2 Sumatra earthquake. Geophysical Journal International, 173, 189–204. https://doi.org/10.1111/j.1365-246X.2007.03666.x.Google Scholar

Press, W. H., Teukolsky, S. A., Wetterling, W. T., and Flannery, B. P. (2007). Numerical Recipes: The Art of Scientific Computing, 3rd ed. New York: Cambridge University Press.Google Scholar

Pritchard, M. E., and Simons, M. (2006). An aseismic slip pulse in northern Chile and along-strike variations in seismogenic behavior. Journal of Geophysical Research, 111, 1–14.Google Scholar

Riznichenko, Y. V. (1985). Problems of Seismology: Selected Works. Moscow: Nauka (in Russian).Google Scholar

Rundle, J. B. (1980). Static elastic-gravitational deformation of a layered half-space by point couple sources. Journal of Geophysical Research, 85, 5354–63.Google Scholar

Savage, J. C. (1983). A dislocation model of strain accumulation and release at a subduction zone. Journal of Geophysical Research, 88, 4984–96. https://doi.org/10.1029/JB088IB06P04984.Google Scholar

Savage, J. C., Svarc, J. L., and Yu, S.-B. (2005). Postseismic relaxation and transient creep. Journal of Geophysical Research, 110, B11402. https://doi.org/10.1029/2005JB003687.Google Scholar

Scholz, C. H. (1998). Earthquakes and friction laws. Nature, 391, 37−42.Google Scholar

Scholz, C. H. (1988). The brittle-plastic transition and the depth of seismic faulting. Geologische Rundschau, 77, 319–28.Google Scholar

Scholz, C. H. (2019). The Mechanics of Earthquakes and Faulting, 3rd ed. Cambridge: Cambridge University Press.Google Scholar

Song, T.-R. A., and Simons, M. (2003). Large trench-parallel gravity variations predict seismogenic behaviour in subduction zones. Science, 301, 630–3.Google Scholar

Sun, Т., Wang, К., Iinuma, T. et al. (2014). Prevalence of viscoelastic relaxation after the 2011 Tohoku-oki earthquake. Nature, 514(7520), 84–87.Google Scholar

Sun, T., and Wang, K. (2015). Viscoelastic relaxation following subduction earthquakes and its effects on afterslip determination. Journal of Geophysical Research: Solid Earth, 120(2), 1329–44.Google Scholar

Tanaka, Y. (2013). Theoretical computation of long-term postseismic relaxation due to a great earthquake using a spherically symmetric viscoelastic Earth model. Journal of the Geodetic Society of Japan, 59, 1–10.Google Scholar

Tichelaar, B. W., and Ruff, L. J. (1993). Depth of seismic coupling along subduction zones. Journal of Geophysical Research, 98, 2017–37.Google Scholar

Turcotte, D. L., and Schubert, D. (2001). Geodynamics, 2nd ed. Cambridge: Cambridge University Press.Google Scholar

Vladimirova, I. S., Lobkovsky, L. I., Gabsatarov, Y. V. et al. (2019). Source data for Vladimirova et al. (2020). Patterns of seismic cycle in the Kuril Island arc from GPS observations. Pure and Applied Geophysics, figshare, Dataset. https://doi.org/10.6084/m9.figshare.10028582.v2.Google Scholar

Wang, K., and Dixon, T. H. (2004). Coupling semantics and science in earthquake research. EOS Transactions of the American Geophysical Union, 85, 180–1.Google Scholar

Wang, K., Hu, Y., and He, J. (2012). Deformation cycles of subduction earthquakes in a viscoelastic Earth. Nature, 484, 327–32.Google Scholar

Wang, L. (2010). Analysis of Postseismic Processes: Afterslip, Viscoelastic Relaxation and Aftershocks. Ph.D. thesis, Institute of Geology, Mineralogy and Geophysics. Ruhr University Bochum, Germany.Google Scholar

Wang, R., Martin, F. L., and Roth, F. (2003). Computation of deformation induced by earthquakes in a multi-layered elastic crust: FORTRAN programs EDGRN/EDCMP. Computers & Geosciences, 29(2), 195–207.Google Scholar

Wells, R. E., Blakely, R. J., Sugiyama, Y., Scholl, D. W., and Dinterman, P. A. (2003). Basin-centered asperities in great subduction zone earthquakes: A link between slip, subsidence, and subduction erosion? Journal of Geophysical Research, 108(B10), 2507. https://doi.org/10.1029/2002JB002072.Google Scholar

Wessel, P., Luis, J. F., Uieda, L. et al. (2019). The generic mapping tools, version 6. Geochemistry, Geophysics, Geosystems, 20, 5556–64. https://doi.org/10.1029/2019GC008515 Google Scholar

Zhou, X., Cambiotti, G., Sun, W. K., and Sabadini, R. (2018). Co-seismic slip distribution of the 2011 Tohoku (M_W 9.0) earthquake inverted from GPS and space-borne gravimetric data. Earth and Planetary Physics, 2, 120–38. http://doi.org/10.26464/epp2018013.Google Scholar

Yamanaka, Y., and Kikuchi, M. (2004). Asperity map along the subduction zone in northeastern Japan inferred from regional seismic data. Journal of Geophysical Research, 109, B07307. https://doi.org/10.1029/2003JB002683.Google Scholar

Yamazaki, Y., Cheung, K. F., and Lay, T. (2018). A self-consistent fault slip model for the 2011 Tohoku earthquake and tsunami. Journal of Geophysical Research: Solid Earth, 123, 1435–8. https://doi.org/10.1002/2017JB014749.Google Scholar

Yokota, Y., Koketsu, K., Fujii, Y. et al. (2011). Joint inversion of strong motion, teleseismic, geodetic, and tsunami datasets for the rupture process of the 2011 Tohoku earthquake. Geophysical Research Letters, 38, L00G21. https://doi.org/10.1029/2011GL050098.Google Scholar

Zelt, C. A., Azaria, A., and Levander, A. (2006). 3D seismic refraction traveltime tomography at a ground water contamination site. Geophysics, 71(5), H67–H78.Google Scholar

References

Alekseev, A. K., and Navon, I. M. (2001). The analysis of an ill-posed problem using multiscale resolution and second order adjoint techniques. Computer Methods in Applied Mechanics and Engineering, 190, 1937–53.Google Scholar

Bennett, A. F. (1992). Inverse Methods in Physical Oceanography. Cambridge: Cambridge University Press.Google Scholar

Billen, M. I. (2008). Modeling the dynamics of subducting slabs. Annual Review of Earth and Planetary Sciences, 36, 325–56.Google Scholar

Bird, P. (2003). An updated digital model of plate boundaries. Geochemistry, Geophysics, Geosystems, 4, 1027. https://doi.org/10.1029/2001GC000252.Google Scholar

Boussinesq, J. (1903). Theorie Analytique de la Chaleur, vol. 2. Paris: Gauthier-Villars.Google Scholar

Bubnov, V. A. (1976). Wave concepts in the theory of heat. International Journal of Heat and Mass Transfer, 19, 175–84.Google Scholar

Bubnov, V. A. (1981). Remarks on wave solutions of the nonlinear heat-conduction equation. Journal of Engineering Physics and Thermophysics, 40(5), 565–71.Google Scholar

Bunge, H.-P., Richards, M. A., and Baumgardner, J. R. (2002). Mantle circulation models with sequential data-assimilation: Inferring present-day mantle structure from plate motion histories. Philosophical Transactions of the Royal Society A, 360, 2545–67.Google Scholar

Bunge, H.-P., Hagelberg, C. R., and Travis, B. J. (2003). Mantle circulation models with variational data assimilation: Inferring past mantle flow and structure from plate motion histories and seismic tomography. Geophysical Journal International, 152, 280–301.Google Scholar

Busse, F. H., Christensen, U., Clever, R. et al. (1993). 3D convection at infinite Prandtl number in Cartesian geometry: A benchmark comparison. Geophysical and Astrophysical Fluid Dynamics, 75, 39–59.Google Scholar

Cattaneo, C. (1958). Sur une forme de l’equation de la chaleur elinant le paradox d’une propagation instantance. Comptes Rendus de l’Académie des Sciences, 247, 431–33.Google Scholar

Chandrasekhar, S. (1961). Hydrodynamic and Hydromagnetic Stability. Oxford: Oxford University Press.Google Scholar

Christensen, U. R., and Yuen, D. A. (1985). Layered convection induced by phase transitions. Journal of Geophysical Research, 90, 10291–300.Google Scholar

Coltice, N., Husson, L., Faccenna, C., and Arnould, M. (2019). What drives tectonic plates? Science Advances, 5, eaax4295.Google Scholar

Conrad, C. P., and Gurnis, M. (2003). Seismic tomography, surface uplift, and the breakup of Gondwanaland: Integrating mantle convection backwards in time. Geochemistry, Geophysics, Geosystems, 4(3). https://doi.org/10.1029/2001GC000299.Google Scholar

Davaille, A., and Vatteville, J. (2005). On the transient nature of mantle plumes. Geophysical Research Letters, 32, L14309. https://doi.org/10.1029/2005GL023029.Google Scholar

Doglioni, C., Ismail-Zadeh, A., Panza, G., and Riguzzi, F. (2011). Lithosphere-asthenosphere viscosity contrast and decoupling. Physics of the Earth and Planetary Interiors, 189, 1–8.Google Scholar

Drewes, H. (2009). The Actual Plate Kinematic and Crustal Deformation Model APKIM2005 as basis for a non-rotating ITRF. In Drewes, H., ed., Geodetic Reference Frames, IAG Symposia series 134. Berlin: Springer, pp. 95–99.Google Scholar

Forte, A. M., and Mitrovica, J. X. (1997). A resonance in the Earth’s obliquity and precession over the past 20 Myr driven by mantle convection. Nature, 390, 676–80.Google Scholar

Fukao, Y., Widiyantoro, S., and Obayashi, M. (2001). Stagnant slabs in the upper and lower mantle transition region. Reviews of Geophysics, 39, 291–323.Google Scholar

Furumura, T., and Kennett, B. L. N. (2005). Subduction zone guided waves and the heterogeneity structure of the subducted plate: Intensity anomalies in northern Japan. Journal of Geophysical Research, 110, B10302. https://doi.org/10.1029/2004JB003486.Google Scholar

Ghelichkhan, S., and Bunge, H.-P. (2016). The compressible adjoint equations in geodynamics: derivation and numerical assessment. International Journal on Geomathematics, 7, 1–30.Google Scholar

Ghelichkhan, S., and Bunge, H.-P. (2018). The adjoint equations for thermochemical compressible mantle convection: derivation and verification by twin experiments. Proceedings of the Royal Society A, 474, 20180329.Google Scholar

Glišović, P., and Forte, A. M. (2014). Reconstructing the Cenozoic evolution of the mantle: Implications for mantle plume dynamics under the Pacific and Indian plates. Earth and Planetary Science Letters, 390, 146–156.Google Scholar

Glišović, P., and Forte, A. M. (2016). A new back-and-forth iterative method for time-reversed convection modeling: Implications for the Cenozoic evolution of 3-D structure and dynamics of the mantle. Journal of Geophysical Research, 121, 4067–84.Google Scholar

Glišović, P., and Forte, A. M. (2017). On the deep-mantle origin of the Deccan Traps. Science, 355(6325), 613–16.Google Scholar

Glišović, P., and Forte, A M. (2019). Two deep-mantle sources for Paleocene doming and volcanism in the North Atlantic. Proceedings of the National Academy of Sciences USA, 116(27), 13227–32.Google Scholar

Hall, R. (2002). Cenozoic geological and plate tectonic evolution of SE Asia and the SW Pacific: computer-based reconstructions, model and animations. Journal of Asian Earth Sciences, 20, 353–431.Google Scholar

Hansen, U., Yuen, D. A., and Kroening, S. E. (1990). Transition to hard turbulence in thermal convection at infinite Prandtl number. Physics of Fluids, A2(12), 2157–63.Google Scholar

Hier-Majumder, C. A., Belanger, E., DeRosier, S., Yuen, D. A., and Vincent, A. P. (2005). Data assimilation for plume models. Nonlinear Processes in Geophysics, 12, 257–67.Google Scholar

Honda, S., Yuen, D. A., Balachandar, S., and Reuteler, D. (1993). Three-dimensional instabilities of mantle convection with multiple phase transitions. Science, 259, 1308–11.Google Scholar

Horbach, A., Bunge, H.-P., and Oeser, J. (2014). The adjoint method in geodynamics: derivation from a general operator formulation and application to the initial condition problem in a high resolution mantle circulation model. International Journal on Geomathematics, 5, 163–94.Google Scholar

Howard, L. N. (1966). Convection at high Rayleigh number. In Goertler, H., and Sorger, P., eds., Applied Mechanics, Proc. of the 11th Intl Congress of Applied Mechanics, Munich, Germany 1964. New York: Springer-Verlag, pp. 1109–15.Google Scholar

Ismail-Zadeh, A., and Tackley, P. (2010). Computational Methods for Geodynamics. Cambridge: Cambridge University Press.Google Scholar

Ismail-Zadeh, A. T., Talbot, C. J., and Volozh, Y. A. (2001a). Dynamic restoration of profiles across diapiric salt structures: Numerical approach and its applications. Tectonophysics, 337, 21–36.Google Scholar

Ismail-Zadeh, A. T., Korotkii, A. I., Naimark, B. M., and Tsepelev, I. A. (2001b). Numerical modelling of three-dimensional viscous flow with gravitational and thermal effects. Computational Mathematics and Mathematical Physics, 41(9), 1331–45.Google Scholar

Ismail-Zadeh, A. T., Korotkii, A. I., and Tsepelev, I. A. (2003a). Numerical approach to solving problems of slow viscous flow backwards in time. In Bathe, K. J., ed., Computational Fluid and Solid Mechanics. Amsterdam: Elsevier Science, pp. 938–41.Google Scholar

Ismail-Zadeh, A. T., Korotkii, A. I., Naimark, B. M., and Tsepelev, I. A. (2003b). Three-dimensional numerical simulation of the inverse problem of thermal convection. Computational Mathematics and Mathematical Physics, 43(4), 587–99.Google Scholar

Ismail-Zadeh, A., Schubert, G., Tsepelev, I., and Korotkii, A. (2004a). Inverse problem of thermal convection: Numerical approach and application to mantle plume restoration. Physics of the Earth and Planetary Interiors, 145, 99–114.Google Scholar

Ismail-Zadeh, A. T., Tsepelev, I. A., Talbot, C. J., and Korotkii, A. I. (2004b). Three-dimensional forward and backward modelling of diapirism: Numerical approach and its applicability to the evolution of salt structures in the Pricaspian basin. Tectonophysics, 387, 81–103.Google Scholar

Ismail-Zadeh, A., Mueller, B., and Schubert, G. (2005). Three-dimensional modeling of present-day tectonic stress beneath the earthquake-prone southeastern Carpathians based on integrated analysis of seismic, heat flow, and gravity observations. Physics of the Earth and Planetary Interiors, 149, 81–98.Google Scholar

Ismail-Zadeh, A., Schubert, G., Tsepelev, I., and Korotkii, A. (2006). Three-dimensional forward and backward numerical modeling of mantle plume evolution: Effects of thermal diffusion. Journal of Geophysical Research, 111, B06401. https://doi.org/10.1029/2005JB003782.Google Scholar

Ismail-Zadeh, A., Schubert, G., Tsepelev, I., and Korotkii, A. (2008). Thermal evolution and geometry of the descending lithosphere beneath the SE-Carpathians: An insight from the past. Earth and Planetary Science Letters, 273, 68–79.Google Scholar

Ismail-Zadeh, A., Honda, S., and Tsepelev, I. (2013). Linking mantle upwelling with the lithosphere descent and the Japan Sea evolution: a hypothesis. Scientific Reports, 3, 1137. https://doi.org/10.1038/srep01137.Google Scholar

Ismail-Zadeh, A., Korotkii, A., and Tsepelev, I. (2016). Data-Driven Numerical Modeling in Geodynamics: Methods and Applications. Heidelberg: Springer.Google Scholar

Jolivet, L., Tamaki, K., and Fournier, M. (1994). Japan Sea, opening history and mechanism: A synthesis. Journal of Geophysical Research, 99, 22232–59.Google Scholar

Kalnay, E. (2003). Atmospheric Modeling, Data Assimilation and Predictability. Cambridge: Cambridge University Press.Google Scholar

Karato, S. (2010). Rheology of the Earth’s mantle: A historical review. Gondwana Research, 18, 17–45.Google Scholar

Kaus, B. J. P., and Podladchikov, Y. Y. (2001). Forward and reverse modeling of the three-dimensional viscous Rayleigh–Taylor instability. Geophysical Research Letters, 28, 1095–8.Google Scholar

Kirsch, A. (1996). An Introduction to the Mathematical Theory of Inverse Problems, New York: Springer-Verlag.Google Scholar

Lattes, R., and Lions, J. L. (1969). The Method of Quasi-Reversibility: Applications to Partial Differential Equations. New York: Elsevier.Google Scholar

Li, D., Gurnis, M., and Stadler, G. (2017). Towards adjoint-based inversion of time-dependent mantle convection with nonlinear viscosity. Geophysical Journal International, 209(1), 86–105.Google Scholar

Liu, D. C., and Nocedal, J. (1989). On the limited memory BFGS method for large scale optimization. Mathematical Programming, 45, 503–28.Google Scholar

Liu, L., and Gurnis, M. (2008). Simultaneous inversion of mantle properties and initial conditions using an adjoint of mantle convection. Journal of Geophysical Research, 113, B08405. https://doi.org/10.1029/2008JB005594.Google Scholar

Liu, L., Spasojevic, S., and Gurnis, M. (2008). Reconstructing Farallon plate subduction beneath North America back to the Late Cretaceous. Science, 322, 934–38.Google Scholar

Liu, L., Gurnis, M., Seton, M. et al. (2010). The role of oceanic plateau subduction in the Laramide orogeny. Nature Geoscience, 3, 353–7.Google Scholar

Liu, M., Yuen, D. A., Zhao, W., and Honda, S. (1991). Development of diapiric structures in the upper mantle due to phase transitions. Science, 252, 1836–9.Google Scholar

Malevsky, A. V., and Yuen, D. A. (1993). Plume structures in the hard-turbulent regime of three-dimensional infinite Prandtl number convection. Geophysical Research Letters, 20, 383–6.Google Scholar

Maruyama, S., Isozaki, Y., Kimura, G., and Terabayashi, M. (1997). Paleogeographic maps of the Japanese Islands: Plate tectonic synthesis from 750 Ma to the present. The Island Arc, 6, 121–42.Google Scholar

Massimi, P., Quarteroni, A., Saleri, F., and Scrofani, G. (2007). Modeling of salt tectonics. Computational Methods in Applied Mathematics, 197, 281–93.Google Scholar

McLaughlin, D. (2002). An integrated approach to hydrologic data assimilation: Interpolation, smoothing, and forecasting. Advances in Water Resources, 25, 1275–86.Google Scholar

Moore, W. B., Schubert, G., and Tackley, P. (1998). Three-dimensional simulations of plume–lithosphere interaction at the Hawaiian Swell. Science, 279, 1008–11.Google Scholar

Morse, P. M., and Feshbach, H. (1953). Methods of Theoretical Physics. New York: McGraw-Hill.Google Scholar

Moucha, R., and Forte, A. M. (2011). Changes in African topography driven by mantle convection. Nature Geoscience, 4, 707–12.Google Scholar

Northrup, C. J., Royden, L. H., and Burchfiel, B. C. (1995). Motion of the Pacific plate relative to Eurasia and its potential relation to Cenozoic extension along the eastern margin of Eurasia. Geology, 23, 719–22.Google Scholar

Obayashi, M., Sugioka, H., Yoshimitsu, J., and Fukao, Y. (2006). High temperature anomalies oceanward of subducting slabs at the 410-km discontinuity. Earth and Planetary Science Letters, 243, 149–58.Google Scholar

Obayashi, M., Yoshimitsu, J., and Fukao, Y. (2009). Tearing of stagnant slab. Science, 324, 1173–5.Google Scholar

Olson, P., and Singer, H. (1985). Creeping plumes. Journal of Fluid Mechanics, 158, 511–31.Google Scholar

Peng, D., and Liu, L. (2022). Quantifying slab sinking rates using global geodynamic models with data-assimilation, Earth-Science Reviews, 230, 104039.Google Scholar

Ratnaswamy, V., Stadler, G., and Gurnis, M. (2015). Adjoint-based estimation of plate coupling in a non-linear mantle flow model: Theory and examples. Geophysical Journal International, 202, 768–86.Google Scholar

Ribe, N. M., and Christensen, U. (1994). Three-dimensional modeling of plume–lithosphere interaction. Journal of Geophysical Research, 99, 669–82.Google Scholar

Rowley, D. B. (2008). Extrapolating oceanic age distributions: Lessons from the Pacific region. Journal of Geology, 116, 587–98.Google Scholar

Samarskii, A. A., and Vabishchevich, P. N. (2007). Numerical Methods for Solving Inverse Problems of Mathematical Physics. Berlin: De Gruyter.Google Scholar

Samarskii, A. A., Vabishchevich, P. N., and Vasiliev, V. I. (1997). Iterative solution of a retrospective inverse problem of heat conduction. Mathematical Modeling, 9, 119–27.Google Scholar

Schubert, G., Turcotte, D. L., and Olson, P. (2001). Mantle Convection in the Earth and Planets. Cambridge: Cambridge University Press.Google Scholar

Schuh-Senlis, M., Thieulot, C., Cupillard, P., and Caumon, G. (2020). Towards the application of Stokes flow equations to structural restoration simulations. Solid Earth, 11, 1909–30.Google Scholar

Seno, T., and Maruyama, S. (1984). Paleogeographic reconstruction and origin of the Philippine Sea. Tectonophysics, 102, 53–84.Google Scholar

Shephard, G., Müller, R., Liu, L. et al. (2010). Miocene drainage reversal of the Amazon River driven by plate–mantle interaction. Nature Geoscience, 3, 870–75.Google Scholar

Spasojevic, S., Liu, L., and Gurnis, M. (2009). Adjoint models of mantle convection with seismic, plate motion, and stratigraphic constraints: North America since the Late Cretaceous. Geochemistry, Geophysics, Geosystems, 10, Q05W02. https://doi.org/10.1029/2008GC002345.Google Scholar

Steinberger, B., and O’Connell, R.J. (1997). Changes of the Earth’s rotation axis owing to advection of mantle density heterogeneities. Nature, 387, 169–73.Google Scholar

Steinberger, B., and O’Connell, R. J. (1998). Advection of plumes in mantle flow: implications for hotspot motion, mantle viscosity and plume distribution. Geophysical Journal International, 132, 412–34.Google Scholar

Tikhonov, A. N. (1963). Solution of incorrectly formulated problems and the regularization method. Soviet Mathematics Doklady, 4, 1035–8.Google Scholar

Tikhonov, A. N., and Arsenin, V. Y. (1977). Solution of Ill-Posed Problems. New York: Halsted Press.Google Scholar

Tikhonov, A. N., and Samarskii, A. A. (1990). Equations of Mathematical Physics. New York: Dover Publications.Google Scholar

Trompert, R. A., and Hansen, U. (1998). On the Rayleigh number dependence of convection with a strongly temperature-dependent viscosity. Physics of Fluids, 10, 351–60.Google Scholar

Tsepelev, I. A. (2011). Iterative algorithm for solving the retrospective problem of thermal convection in a viscous fluid. Fluid Dynamics, 46, 835–42.Google Scholar

Turcotte, D. L., and Schubert, G. (2002). Geodynamics, 2nd ed. Cambridge: Cambridge University Press.Google Scholar

Vasiliev, F. P. (2002). Methody optimizatsii. Moscow: Factorial Press.Google Scholar

Vernotte, P. (1958). Les paradoxes de la theorie continue de l’equation de la chaleur. Comptes Rendus de l’Académie des Sciences, 246, 3154–5.Google Scholar

Wang, K., Hyndman, R. D., and Yamano, M. (1995). Thermal regime of the Southwest Japan subduction zone: Effects of age history of the subducting plate. Tectonophysics, 248, 53–69.Google Scholar

Worthen, J., Stadler, G., Petra, N., Gurnis, M., and Ghattas, O. (2014). Towards an adjoint-based inversion for rheological parameters in nonlinear viscous mantle flow. Physics of the Earth and Planetary Interiors, 234, 23–34.Google Scholar

Yamano, M., Kinoshita, M., Goto, S., and Matsubayashi, O. (2003). Extremely high heat flow anomaly in the middle part of the Nankai Trough. Physics and Chemistry of the Earth, 28, 487–97.Google Scholar

Yamazaki, T., Takahashi, M., Iryu, Y. et al. (2010). Philippine Sea Plate motion since the Eocene estimated from paleomagnetism of seafloor drill cores and gravity cores. Earth Planets Space, 62, 495–502.Google Scholar

Yu, N., Imatani, S., and Inoue, T. (2004). Characteristics of temperature field due to pulsed heat input calculated by non-Fourier heat conduction hypothesis. JSME International Journal Series A, 47(4), 574–80.Google Scholar

Zhong, S. (2005). Dynamics of thermal plumes in three-dimensional isoviscous thermal convection. Geophysical Journal International, 162, 289–300.Google Scholar

Zou, X., Navon, I. M., Berger, M. et al. (1993). Numerical experience with limited-memory quasi-Newton and truncated Newton methods. SIAM Journal of Optimization, 3(3), 582–608.Google Scholar

References

Bauer, S., Huber, M., Ghelichkhan, S. et al. (2019). Large-scale simulation of mantle convection based on a new matrix-free approach. Journal of Computational Science, 31, 60–76.Google Scholar

Baumgardner, J. R. (1985). Three-dimensional treatment of convective flow in the Earth’s mantle. Journal of Statistical Physics, 39(5/6).Google Scholar

Becker, T. W., and Boschi, L. (2002). A comparison of tomographic and geodynamic mantle models. Geochemistry, Geophysics, Geosystems, 3(1).Google Scholar

Bello, L., Coltice, N., Rolf, T., and Tackley, P. J. (2014). On the predictability limit of convection models of the Earth’s mantle. Geochemistry, Geophysics, Geosystems, 15, 2319–28.Google Scholar

Braun, J. (2010). The many surface expressions of mantle dynamics. Nature Geoscience, 3(12), 825–33.Google Scholar

Bunge, H.-P. (2005). Low plume excess temperature and high core heat flux inferred from non-adiabatic geotherms in internally heated mantle circulation models. Physics of the Earth and Planetary Interiors, 153(1–3), 3–10.Google Scholar

Bunge, H.-P., and Davies, J. H. (2001). Tomographic images of a mantle circulation model. Geophysical Research Letters, 28(1), 77–80.Google Scholar

Bunge, H.-P., and Glasmacher, U. (2018). Models and observations of vertical motion (MoveOn) associated with rifting to passive margins: Preface. Gondwana Research, 53, 1–8.Google Scholar

Bunge, H. P., Hagelberg, C. R., and Travis, B. J. (2003). Mantle circulation models with variational data assimilation: Inferring past mantle flow and structure from plate motion histories and seismic tomography. Geophysical Journal International, 152(2), 280–301.Google Scholar

Bunge, H.-P., and Richards, M. A. (1992). The backward-problem of plate tectonics and mantle convection (abstract). Eos, Transactions, American Geophysical Union, 73(14), 281.Google Scholar

Bunge, H.-P., Richards, M. A., and Baumgardner, J. R. (2002). Mantle-circulation models with sequential data assimilation: Inferring present-day mantle structure from plate-motion histories. Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences, 360(1800), 2545–67.Google Scholar

Bunge, H.-P., Richards, M. A., Lithgow-Bertelloni, C. et al. (1998). Time scales and heterogeneous structure in geodynamic Earth models. Science, 280(5360), 91–5.Google Scholar

Burgess, P. M., Gurnis, M., and Moresi, L. (1997). Formation of sequences in the cratonic interior of North America by interaction between mantle, eustatic, and stratigraphic processes. Geological Society of America Bulletin, 109(12), 1515–35.Google Scholar

Burstedde, C., Stadler, G., Alisic, L. et al. (2013). Large-scale adaptive mantle convection simulation. Geophysical Journal International, 192(3), 889–906.Google Scholar

Carena, S., Bunge, H.-P., and Friedrich, A. M. (2019). Analysis of geological hiatus surfaces across Africa in the Cenozoic and implications for the timescales of convectively-maintained topography. Canadian Journal of Earth Sciences, 56(12), 1333–46.Google Scholar

Carrassi, A., and Vannitsem, S. (2010). Accounting for model error in variational data assimilation: A deterministic formulation. Monthly Weather Review, 138(9), 3369–86.Google Scholar

Chust, T. C., Steinle-Neumann, G., Dolejš, D., Schuberth, B. S. A., and Bunge, H. P. (2017). MMA-EoS: A computational framework for mineralogical thermodynamics. Journal of Geophysical Research: Solid Earth, 122(12), 9881–920.Google Scholar

Cohen, K. M., Finney, S., Gibbard, P. L., and Fan, J.-X. (2013). The ICS International Chronostratigraphic Chart. Episodes, 36(3), 199–204.Google Scholar

Colli, L., Bunge, H.-P., and Oeser, J. (2020). Impact of model inconsistencies on reconstructions of past mantle flow obtained using the adjoint method. Geophysical Journal International, 221(1), 617–39.Google Scholar

Colli, L., Bunge, H.-P., and Schuberth, B. S. A. (2015). On retrodictions of global mantle flow with assimilated surface velocities. Geophysical Research Letters, 42(20), 8341–8.Google Scholar

Colli, L., Fichtner, A., and Bunge, H.-P. (2013). Full waveform tomography of the upper mantle in the South Atlantic region: Imaging a westward fluxing shallow asthenosphere? Tectonophysics, 604, 26–40.Google Scholar

Colli, L., Ghelichkhan, S., and Bunge, H.-P. (2016). On the ratio of dynamic topography and gravity anomalies in a dynamic Earth. Geophysical Research Letters, 43(6), 2510–16.Google Scholar

Colli, L., Ghelichkhan, S., Bunge, H.-P., and Oeser, J. (2018). Retrodictions of Mid Paleogene mantle flow and dynamic topography in the Atlantic region from compressible high resolution adjoint mantle convection models: Sensitivity to deep mantle viscosity and tomographic input model. Gondwana Research, 53, 252–72.Google Scholar

Colton, D., and Kress, R. (1992). Inverse Acoustic and Electromagnetic Scattering Theory. Berlin: Springer Verlag.Google Scholar

Czarnota, K., Hoggard, M., White, N., and Winterbourne, J. (2013). Spatial and temporal patterns of Cenozoic dynamic topography around Australia. Geochemistry, Geophysics, Geosystems, 14(3), 634–58.Google Scholar

Davies, D. R., Goes, S., Davies, J. H. et al. (2012). Reconciling dynamic and seismic models of Earth’s lower mantle: The dominant role of thermal heterogeneity. Earth and Planetary Science Letters, 353–4(0), 253–69.Google Scholar

DiCaprio, L., Gurnis, M., and Müller, R. D. (2009). Long-wavelength tilting of the Australian continent since the Late Cretaceous. Earth and Planetary Science Letters, 278(3–4), 175–85.Google Scholar

Dziewonski, A. M., and Anderson, D. L. (1981). Preliminary reference Earth model. Physics of the Earth and Planetary Interiors, 25(4), 297–356.Google Scholar

Fernandes, V. M., and Roberts, G. G. (2020). Cretaceous to recent net continental uplift from paleobiological data: Insights into sub-plate support. GSA Bulletin, 133(5–6), 1217–36.Google Scholar

Fichtner, A., Kennett, B. L. N., Igel, H., and Bunge, H.-P. (2009). Full seismic wave-form tomography for upper-mantle structure in the Australasian region using adjoint methods. Geophysical Journal International, 179(3), 1703–25.Google Scholar

Fichtner, A., van Herwaarden, D.-P., Afanasiev, M. et al. (2018). The collaborative seismic Earth model: Generation 1. Geophysical Research Letters, 45(9), 4007–16.Google Scholar

Flowers, R., Wernicke, B., and Farley, K. (2008). Unroofing, incision, and uplift history of the southwestern Colorado Plateau from apatite (U-Th)/He thermochronometry. GSA Bulletin, 120(5–6), 571–87.Google Scholar

Freissler, R., Zaroli, C., Lambotte, S., and Schuberth, B. S. (2020). Tomographic filtering via the generalized inverse: A way to account for seismic data uncertainty. Geophysical Journal International, 223(1), 254–69.Google Scholar

French, S. W., and Romanowicz, B. A. (2014). Whole-mantle radially anisotropic shear velocity structure from spectral-element waveform tomography. Geophysical Journal International, 199(3), 1303–27.Google Scholar

Friedrich, A. M. (2019). Palaeogeological hiatus surface mapping: A tool to visualize vertical motion of the continents. Geological Magazine, 156(2), 308–19.Google Scholar

Friedrich, A. M., Bunge, H.-P., Rieger, S. M. et al. (2018). Stratigraphic framework for the plume mode of mantle convection and the analysis of interregional unconformities on geological maps. Gondwana Research, 53, 159–88.Google Scholar

Ghelichkhan, S., and Bunge, H.-P. (2016). The compressible adjoint equations in geodynamics: Derivation and numerical assessment. GEM – International Journal on Geomathematics, 7(1), 1–30.Google Scholar

Ghelichkhan, S., and Bunge, H.-P. (2018). The adjoint equations for thermochemical compressible mantle convection: Derivation and verification by twin experiments. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 474(2220), 20180329.Google Scholar

Ghelichkhan, S., Bunge, H.-P., and Oeser, J. (2021), Global mantle flow retrodictions for the early Cenozoic using an adjoint method: Evolving dynamic topographies, deep mantle structures, flow trajectories and sublithospheric stresses. Geophysical Journal International, 226(2), 1432–60.Google Scholar

Guillocheau, F., Rouby, D., Robin, C. et al. (2012). Quantification and causes of the terrigeneous sediment budget at the scale of a continental margin: A new method applied to the Namibia-South Africa margin. Basin Research, 24(1), 3–30.Google Scholar

Guillocheau, F., Simon, B., Baby, G. et al. (2018). Planation surfaces as a record of mantle dynamics: The case example of Africa. Gondwana Research, 53, 82–98.Google Scholar

Hager, B. H., Clayton, R. W., Richards, M. A., Comer, R. P., and Dziewonski, A. M. (1985). Lower mantle heterogeneity, dynamic topography and the geoid. Nature, 313(6003), 541–5.Google Scholar

Hartley, R. A., Roberts, G. G., White, N. J., and Richardson, C. (2011). Transient convective uplift of an ancient buried landscape. Nature Geoscience, 4(8), 562–5.Google Scholar

Hayek, J. N., Vilacís, B., Bunge, H.-P. et al. (2020). Continent-scale hiatus maps for the Atlantic Realm and Australia since the Upper Jurassic and links to mantle flow induced dynamic topography. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 476(2242), 20200390.Google Scholar

Hayek, J. N., Vilac´ıs, B., Bunge, H.-P. et al. (2021). Correction: Continent-scale hiatus maps for the Atlantic Realm and Australia since the Upper Jurassic and links to mantle flow-induced dynamic topography. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 477(2251), 20210437.Google Scholar

Heister, T., Dannberg, J., Gassmöller, R., and Bangerth, W. (2017). High accuracy mantle convection simulation through modern numerical methods. II: Realistic models and problems. Geophysical Journal International, 210(2), 833–51.Google Scholar

Hoggard, M. J., Austerman, J., Randel, C., and Stephenson, S. (2021). Observational estimates of dynamic topography through space and time. In Marquardt, H., Ballmer, S., adn Cottaar, M., and Konter, J., eds., Mantle Convection and Surface Expressions. Washington DC: American Geophysical Union (AGU), pp. 371–411.Google Scholar

Hoggard, M. J., Winterbourne, J., Czarnota, K., and White, N. (2017). Oceanic residual depth measurements, the plate cooling model, and global dynamic topography. Journal of Geophysical Research: Solid Earth, 122(3), 2328–72.Google Scholar

Horbach, A., Bunge, H. P., and Oeser, J. (2014). The adjoint method in geodynamics: Derivation from a general operator formulation and application to the initial condition problem in a high resolution mantle circulation model. GEM – International Journal on Geomathematics, 5(2), 163–94.Google Scholar

Iaffaldano, G., and Bunge, H.-P. (2015). Rapid plate motion variations through geological time: Observations serving geodynamic interpretation. Annual Review of Earth and Planetary Sciences 43, 571–92.Google Scholar

Ismail-Zadeh, A., Schubert, G., Tsepelev, I., and Korotkii, A. (2004). Inverse problem of thermal convection: numerical approach and application to mantle plume restoration. Physics of the Earth and Planetary Interiors, 145(1–4), 99–114.Google Scholar

Japsen, P. (2018). Sonic velocity of chalk, sandstone and marine shale controlled by effective stress: Velocity-depth anomalies as a proxy for vertical movements. Gondwana Research, 53, 145–58.Google Scholar

Jarvis, G. T., and Mckenzie, D. P. (1980). Convection in a compressible fluid with infinite Prandtl number. Journal of Fluid Mechanics, 96(03), 515–83.Google Scholar

Kronbichler, M., Heister, T., and Bangerth, W. (2012). High accuracy mantle convection simulation through modern numerical methods. Geophysical Journal International, 191, 12–29.Google Scholar

McNamara, A. K. (2019). A review of large low shear velocity provinces and ultra low velocity zones. Tectonophysics, 760, 199–220.Google Scholar

McNamara, A. K., and Zhong, S. (2005). Thermochemical structures beneath Africa and the Pacific Ocean. Nature, 437(7062), 1136–9.Google Scholar

Mégnin, C., Bunge, H.-P., Romanowicz, B., and Richards, M. A. (1997). Imaging 3-D spherical convection models: What can seismic tomography tell us about mantle dynamics? Geophysical Research Letters, 24(11), 1299–302.Google Scholar

Meinhold, G. (2010). Rutile and its applications in Earth sciences. Earth–Science Reviews, 102(1), 1–28.Google Scholar

Miall, A. D. (2016). The valuation of unconformities. Earth-Science Reviews, 163, 22–71.Google Scholar

Mitrovica, J. X. (1996). Haskell [1935] revisited. Journal of Geophysical Research, 101(B1), 555.Google Scholar

Mitrovica, J. X., Beaumont, C., and Jarvis, G. T. (1989). Tilting of continental interiors by the dynamical effects of subduction. Tectonics, 8(5), 1079–94.Google Scholar

Mosca, I., Cobden, L., Deuss, A., Ritsema, J., and Trampert, J. (2012). Seismic and mineralogical structures of the lower mantle from probabilistic tomography. Journal of Geophysical Research, 117(B6).Google Scholar

Moulik, P., Lekic, V., Romanowicz, B. et al. (2021). Global reference seismological datasets: Multi-mode surface wave dispersion. Geophysical Journal International, 228(3).Google Scholar

Müller, R. D., Seton, M., Zahirovic, S. et al. (2016). Ocean basin evolution and global-scale plate reorganization events since Pangea breakup. Annual Review of Earth and Planetary Sciences, 44, 107–38.Google Scholar

Nelson, P. L., and Grand, S. P. (2018). Lower-mantle plume beneath the Yellowstone hotspot revealed by core waves. Nature Geoscience, 11(4), 280–4.Google Scholar

Ogg, J. G., Ogg, G. M., and Gradstein, F. M. eds. (2016). Introduction. In Ogg, J. G., Ogg, G. M., and Gradstein, F. M., eds., A Concise Geologic Time Scale. Amsterdam: Elsevier, pp. 1–8.Google Scholar

Paulson, A., and Richards, M. A. (2009). On the resolution of radial viscosity structure in modelling long-wavelength postglacial rebound data. Geophysical Journal International, 179(3), 1516–26.Google Scholar

Pekeris, C. L. (1935). Thermal convection in the interior of the Earth. Geophysical Journal International, 3(8), 343–67.Google Scholar

Piazzoni, A. S., Steinle-Neumann, G., Bunge, H., and Dolejš, D. (2007). A mineralogical model for density and elasticity of the Earth’s mantle. Geochemistry, Geophysics, Geosystems, 8(11).Google Scholar

Price, M. G., and Davies, J. H. (2018). Profiling the robustness, efficiency and limits of the forward-adjoint method for 3D mantle convection modelling. Geophysical Journal International, 212(2), 1450–62.Google Scholar

Reiners, P. W., and Brandon, M. T. (2006). Using thermochronology to understand orogenic erosion. Annual Review of Earth and Planetary Sciences, 34(1), 419–66.Google Scholar

Reuber, G. S., and Simons, F. J. (2020). Multi-physics adjoint modeling of Earth structure: Combining gravimetric, seismic, and geodynamic inversions. GEM – International Journal on Geomathematics, 11, 30. https://doi.org/10.1007/s13137-020-00166-8.Google Scholar

Richards, M. A., and Hager, B. H. (1984). Geoid anomalies in a dynamic Earth. Journal of Geophysical Research, 89(B7), 5987–6002.Google Scholar

Ritsema, J., Deuss, A., Van Heijst, H.-J., and Woodhouse, J. H. (2011). S40RTS: A degree-40 shear-velocity model for the mantle from new Rayleigh wave dispersion, teleseismic traveltime and normal-mode splitting function measurements. Geophysical Journal International, 184(3), 1223–36.Google Scholar

Roberts, G. G., and White, N. (2010). Estimating uplift rate histories from river profiles using African examples. Journal of Geophysical Research: Solid Earth 115(B2), B02406.Google Scholar

Said, A., Moder, C., Clark, S., and Abdelmalak, M. M. (2015). Sedimentary budgets of the Tanzania coastal basin and implications for uplift history of the East African rift system. Journal of African Earth Sciences, 111, 288–95.Google Scholar

Said, A., Moder, C., Clark, S., and Ghorbal, B. (2015). Cretaceous-Cenozoic sedimentary budgets of the Southern Mozambique Basin: Implications for uplift history of the South African Plateau. Journal of African Earth Sciences, 109, 1–10.Google Scholar

Sandiford, M. (2007). The tilting continent: A new constraint on the dynamic topographic field from Australia. Earth and Planetary Science Letters, 261(1-2), 152–63.Google Scholar

Schaber, K., Bunge, H.-P., Schuberth, B., Malservisi, R., and Horbach, A. (2009). Stability of the rotation axis in high-resolution mantle circulation models: Weak polar wander despite strong core heating. Geochemistry, Geophysics, Geosystems, 10, Q11W04. https://doi.org/10.1029/2009GC002541.Google Scholar

Schaeffer, A. J., and Lebedev, S. (2013). Global shear speed structure of the upper mantle and transition zone. Geophysical Journal International, 194(1), 417–49.Google Scholar

Schuberth, B. S. A., Bunge, H.-P., and Ritsema, J. (2009). Tomographic filtering of high-resolution mantle circulation models: Can seismic heterogeneity be explained by temperature alone? Geochemistry, Geophysics, Geosystems, 10(5).Google Scholar

Schuberth, B. S. A., Bunge, H.-P., Steinle-Neumann, G., Moder, C., and Oeser, J. (2009). Thermal versus elastic heterogeneity in high-resolution mantle circulation models with pyrolite composition: High plume excess temperatures in the lowermost mantle. Geochemistry, Geophysics, Geosystems, 10(1).Google Scholar

Schuberth, B. S. A., Zaroli, C., and Nolet, G. (2012). Synthetic seismograms for a synthetic Earth: Long-period Pand S-wave traveltime variations can be explained by temperature alone. Geophysical Journal International, 188(3), 1393–412.Google Scholar

Sengör, A. M. C. (2001). Elevation as indicator of mantle-plume activity. Mantle Plumes: Their identification through Time, 352, 183–245.Google Scholar

Seton, M., Müller, R. D., Zahirovic, S. et al. (2012). Global continental and ocean basin reconstructions since 200 Ma. Earth-Science Reviews, 113(3–4), 212–70.Google Scholar

Simmons, N. A., Myers, S. C., Johannesson, G., and Matzel, E. (2012). LLNL-G3Dv3: Global P-wave tomography model for improved regional and teleseismic travel time prediction. Journal of Geophysical Research: Solid Earth, 117(10), 1–28.Google Scholar

Simmons, N. A., Myers, S. C., Johannesson, G., Matzel, E., and Grand, S. P. (2015). Evidence for long-lived subduction of an ancient tectonic plate beneath the southern Indian Ocean. Geophysical Research Letters, 42(21), 9270–8.Google Scholar

Smith, A., Smith, D., and Funnel, B. (1994). Atlas of Mesozoic and Cenozoic landmasses. Cambridge: Cambridge University Press.Google Scholar

Spasojevic, S., Liu, L., Gurnis, M., and Müller, R. D. (2008). The case for dynamic subsidence of the U.S. east coast since the Eocene. Geophysical Research Letters, 35(8).Google Scholar

Steinberger, B., and O’Connell, R. J. (1997). Changes of the Earth’s rotation axis owing to advection of mantle density heterogeneities. Nature, 387(6629), 169–73.Google Scholar

Stixrude, L., and Lithgow-Bertelloni, C. (2011). Thermodynamics of mantle minerals II. Phase equilibria. Geophysical Journal International, 184(3), 1180–213Google Scholar

Stotz, I. L., Tassara, A., and Iaffaldano, G. (2021). Pressure-driven Poiseuille flow inherited from Mesozoic mantle circulation led to the Eocene separation of Australia and Antarctica. Journal of Geophysical Research: Solid Earth, 126(4), e2020JB019945.Google Scholar

Torsvik, T. H., Müller, R. D., Van Der Voo, R., Steinberger, B., and Gaina, C. (2008). Global plate motion frames: Toward a unified model. Reviews of Geophysics, 46(3), RG3004.Google Scholar

Vibe, Y., Friedrich, A. M., Bunge, H.-P., and Clark, S. R. (2018). Correlations of oceanic spreading rates and hiatus surface area in the North Atlantic realm. Lithosphere, 10(5), 677–84.Google Scholar

Vynnytska, L., and Bunge, H. (2014). Restoring past mantle convection structure through fluid dynamic inverse theory: Regularisation through surface velocity boundary conditions. GEM – International Journal on Geomathematics, 6(1), 83–100.Google Scholar

Young, A., Flament, N., Maloney, K. et al. (2019). Global kinematics of tectonic plates and subduction zones since the late Paleozoic Era. Geoscience Frontiers, 10(3), 989–1013.Google Scholar

Zahirovic, S., Flament, N., Dietmar Müller, R., Seton, M., and Gurnis, M. (2016). Large fluctuations of shallow seas in low-lying Southeast Asia driven by mantle flow. Geochemistry, Geophysics, Geosystems, 17(9), 3589–607.Google Scholar

Zaroli, C. (2016). Global seismic tomography using Backus-Gilbert inversion. Geophysical Journal International, 207(2), 876–88.Google Scholar

Zaroli, C., Sambridge, M., Le´veˆque, J.-J., Debayle, E., and Nolet, G. (2013). An objective rationale for the choice of regularisation parameter with application to global multiple-frequency S-wave tomography. Solid Earth, 4(2), 357–71.Google Scholar

Zhong, S. J., Yuen, D. A., Moresi, L. N., and Knepley, M. G. (2015). Numerical methods for mantle convection, in Bercovici, D., ed., Treatise on Geophysics. Vol. 7: Mantle Dynamics, 2nd ed. Amsterdam: Elsevier, pp. 197–222.Google Scholar

Zhou, Q., and Liu, L. (2017). A hybrid approach to data assimilation for reconstructing the evolution of mantle dynamics. Geochemistry, Geophysics, Geosystems, 18(11), 3854–68.Google Scholar

References

Alken, P., Thébault, E., Beggan, C. D. et al. (2021a). International Geomagnetic Reference Field: The thirteenth generation. Earth, Planets and Space, 73, 49. https://doi.org/10.1186/s40623-020-01288-x.Google Scholar

Alken, P., Chulliat, A., and Nair, M. (2021b). NOAA/NCEI and University of Colorado candidate models for IGRF-13. Earth, Planets and Space, 73, 44. https://doi.org/10.1186/s40623–020–01313–z.Google Scholar

Amit, H., Korte, M., Aubert, J., Constable, C., and Hulot, G. (2011). The time-dependence of intense archeomagnetic flux patches. Journal of Geophysical Research: Solid Earth, 116, B12106. https://doi.org/10.1029/2011JB008538.Google Scholar

Aubert, J. (2014). Earth’s core internal dynamics 1840–2010 imaged by inverse geodynamo modelling. Geophysical Journal International, 197, 1321–34.Google Scholar

Aubert, J. (2015). Geomagnetic forecasts driven by thermal wind dynamics in the Earth’s core. Geophysical Journal International, 203(3), 1738–51.Google Scholar

Aubert, J., and Finlay, C. C. (2019). Geomagnetic jerks and rapid hydromagnetic waves focusing at Earth’s core surface. Nature Geoscience, 12, 393–8.Google Scholar

Aubert, J., and Fournier, A. (2011). Inferring internal properties of Earth’s core dynamics and their evolution from surface observations and a numerical geodynamo model. Nonlinear Processes in Geophysics, 18, 657–74.Google Scholar

Aubert, J., and Gillet, N. (2021). The interplay of fast waves and slow convection in geodynamo simulations nearing Earth’s core conditions. Geophysical Journal International, 225(3), 1854–73.Google Scholar

Aubert, J., Gastine, T., and Fournier, A. (2017). Spherical convective dynamos in the rapidly rotating asymptotic regime. Journal of Fluid Mechanics, 813, 558–93.Google Scholar

Bärenzung, J., Holschneider, M., Wicht, J., Lesur, V., and Sanchez, S. (2020). The Kalmag model as a candidate for IGRF-13. Earth, Planets and Space, 72(163).Google Scholar

Bärenzung, J., Holschneider, M., Wicht, J. Sanchez, S., and Lesur, V. (2018). Modeling and predicting the short-term evolution of the geomagnetic field. Journal of Geophysical Research: Solid Earth, 123(6), 4539–60.Google Scholar

Barrois, O., Hammer, M. D., Finlay, C. C., Martin, Y., and Gillet, N. (2018). Assimilation of ground and satellite magnetic measurements: inference of core surface magnetic and velocity field changes. Geophysical Journal International, 215(1), 695–712.Google Scholar

Beggan, C. D., and Whaler, K. A. (2009). Forecasting change of the magnetic field using core surface flows and ensemble Kalman filtering. Geophysical Research Letters, 36, L18303. https://doi.org/10.1029/2009GL039927.Google Scholar

Beggan, C. D., and Whaler, K. A. (2010). Forecasting secular variation using core flows. Earth, Planets and Space, 62, 821–28.Google Scholar

Bloxham, J, Zatman, S., and Dumburry, M. (2002). The origin of geomagnetic jerks. Nature, 420, 65–68.Google Scholar

Bonavita, M., Isaksen, L., and Hólm, E. (2012). On the use of EDA background error variances in the ECMWF 4D-Var. Quarterly Journal of the Royal Meteorological Society, 138(667), 1540–59.Google Scholar

Braginsky, S. I. (1970). Torsional magnetohydrodynamic vibrations in the Earth’s core and variation in day length. Geomagnetism and Aeronomy, 10, 1–8.Google Scholar

Braginsky, S. I., and Roberts, P. H. (1995). Equations governing convection in Earth’s core and the geodynamo. Geophysical and Astrophysical Fluid Dynamics, 79, 1–97.Google Scholar

Brown, M., Korte, M., Holme, R., Wardinski, I., and Gunnarson, S. (2018). Earth’s magnetic field is probably not reversing. PNAS, 115, 5111–16.Google Scholar

Brown, W. J., Beggan, C. D., Cox, G. A., and Macmillan, S. (2021). The BGS candidate models for IGRF-13 with a retrospective analysis of IGRF-12 secular variation forecasts. Earth, Planets and Space, 73 (42). https://doi.org/10.1186/s40623–020–01301–3.Google Scholar

Buehner, M., McTaggart-Cowan, R., and Heilliette, S. (2017). An Ensemble Kalman filter for numerical weather prediction based on variational data assimilation: VarEnKF. Monthly Weather Review, 145(2), 617–35.Google Scholar

Cande, S. C., and Kent, D. V. (1995). Revised calibration of the geomagnetic polarity timescale for the late Cretaceous and Cenozoic. Journal of Geophysical Research, 100, 6093–6095.Google Scholar

Canet, E., Fournier, A., and Jault, D. (2009). Forward and adjoint quasigeostrophyic models of geomagnetic secular variations. Journal of Geophysical Research, 114, B11101.Google Scholar

Chorin, A. J., and Morzfeld, M. (2013). Conditions for successful data assimilation. Journal of Geophysical Research: Atmospheres, 118(20), 11522–33.Google Scholar

Christensen, U. R. (2010). Dynamo scaling laws and applications to the planets. Space, Science, Reviews, 152, 565–90.Google Scholar

Christensen, U.R., Aubert, J., Cardin, P. et al. (2001). A numerical dynamo benchmark. Physics of the Earth and Planetary Interiors, 128(1), 25–34.Google Scholar

Chulliat, A., and Maus, S. (2014). Geomagnetic secular acceleration, jerks, and localized standing wave at the core surface from 2000 to 2010. Journal of Geophysical Research: Solid Earth, 119, 1531–43.Google Scholar

Constable, C., Korte, M., and Panovska, S. (2016). Persistent high paleosecular variation activity in southern hemisphere for at least 10000 years. Earth and Planetary Science Letters, 453, 78–86.Google Scholar

Courtier, P. (1997). Variational methods. Journal of the Meteorological Society of Japan, 75(1B), 211–18.Google Scholar

Cox, G. A., Livermore, P. W., and Mound, J. E. (2016). The observational signature of modelled torsional waves and comparison to geomagnetic jerks. Physics of the Earth and Planetary Interiors, 255, 50–65.Google Scholar

Deuss, A. (2014). Heterogeneity and anisotropy of Earth’s inner core. Annual Review of Earth and Planetary Sciences, 42, 103–26.Google Scholar

Doglioni, C., Pignatti, J., and Coleman, M. (2016). Why did life develop on the surface of the Earth in the Cambrian? Geoscience Frontiers, 7, 865–75.Google Scholar

Evensen, G. (2006). Data assimilation: The ensemble Kalman filter. Springer.Google Scholar

Finlay, C. C., and Jackson, A. (2003). Equatorially dominated magnetic field change at the surface of the Earth’s core. Science, 300, 2084–6.Google Scholar

Finlay, C. C., Maus, S., Beggan, C. D. et al. (2010). International Geomagnetic Reference Field: The eleventh generation. Geophysical Journal International, 183(3), 1216–30.Google Scholar

Finlay, C. C., Kloss, C., Olsen, N. et al. (2020). The CHAOS-7 geomagnetic field model and observed changes in the South Atlantic Anomaly. Earth, Planets and Space, 72, 156. https://doi.org/10.1186/s40623-020-01252-9.Google Scholar

Fournier, A., Eymin, C., and Alboussier, T. (2007). A case for variational geomagnetic data assimilation: Insights from a one-dimensional, nonlinear, and sparsely observed MHD system. Nonlinear Processes in Geophysics, 14, 163–80.Google Scholar

Fournier, A., Aubert, J., and Thébault, E. (2011). Inference on core surface flow from observations and 3-D dynamo modelling. Geophysical Journal International, 186, 118–36.Google Scholar

Fournier, A., Nerger, L., and Aubert, J. (2013). An ensemble Kalman filter for the time-dependent analysis of the geomagnetic field. Geochemistry, Geophysics, Geosystems, 14(10), 4035–43. https://doi.org/10.1002/ggge.20252.Google Scholar

Fournier, A., Aubert, J., and Thébaut, E. (2015). A candidate secular variation model for IGRF-12 based on Swarm data and inverse geodynamo modeling. Earth, Planets and Space, 67. https://doi.org/10.1186/s40623–015–0245–8.Google Scholar

Fournier, A., Aubert, J., Lesur, V., and Thébault, E. (2021a). Physics-based secular variation candidate models for the IGRF. Earth, Planets and Space. https://doi.org/10.1186/s40623–021–01507–z.Google Scholar

Fournier, A., Aubert, J., Lesur, V., and Ropp, G. (2021b). A secular variation candidate model for IGRF-13 based on Swarm data and ensemble inverse geodynamo modeling. Earth, Planets and Space. https://doi.org/10.1186/s40623–020–01309–9.Google Scholar

Fournier, A. G., Hulot, G., Jault, D. et al. (2010). An introduction to data assimilation and predictability in geomagnetism. Space Science Reviews. https://doi.org/10.1007/s11214–010–9669–4.Google Scholar

Garnero, E. J. (2000). Heterogeneity of the lowermost mantle. Annual Review of Earth and Planetary Sciences, 28, 509–37.Google Scholar

Gissinger, C. (2012). A new deterministic model for chaotic reversals. European Physical Journal B, 85, 137.Google Scholar

Glatzmaier, G. A., and Roberts, P. H. (1995). A three-dimensional convective dynamo solution with rotating and finitely conducting inner core and mantle. Physics of the Earth and Planetary Interiors, 91, 63–75.Google Scholar

Gwirtz, K, Morzfeld, M, Fournier, A, and Hulot, G. (2020). Can one use Earth’s magnetic axial dipole field intensity to predict reversals? Geophysical Journal International, 225(1), 277–97.Google Scholar

Gwirtz, K., Morzfeld, M., Kuang, W., and Tangborn, A. (2021). A testbed for geomagnetic data assimilation. Geophysical Journal International, 227, 2180–203.Google Scholar

Heirtzler, J. R., Allen, J. H., and Wilkinson, D. C. (2002). Everpresent South Atlantic Anomaly damages spacecraft. Eos, Transactions American Geophysical Union, 83(15), 165–9.Google Scholar

Hirose, K., Labrosse, S., and Hernlund, J. (2013). Composition and state of the core. Annual Review of Earth and Planetary Sciences, 41(1), 657–91.Google Scholar

Holme, R. (2007). Large-scale flow in the core. In Olson, P, ed., Treatise on Geophysics: Vol. 8. Core Dynamics. Amsterdam: Elsevier, pp. 107–30.Google Scholar

Huder, L., Gillet, N., Finlay, C. C., Hammer, M. D., and Tchoungui, H. (2020). COV-OBS.x2: 180 years of geomagnetic field evolution from ground-based and satellite observations. Earth, Planets and Space, 72(160). https://doi.org/10.1186/s40623–020–01194–2.Google Scholar

Hulot, G., Eymin, C., Langlais, B., Mandea, M., and Olsen, N. (2002). Smallscale structure of the geodynamo inferred from Oested and Magsat satellite data. Nature, 416, 620–3. https://doi.org/10.1038/416620a.Google Scholar

Hulot, G., Lhuillier, F., and Aubert, J. (2010). Earth’s dynamo limit of predictability. Geophysical Research Letters, 37(6). https://doi.org/10.1029/2009GL041869.Google Scholar

Hunt, B. R., Kostelich, E. J., and Szunyogh, I. (2007). Efficient data assimilation for spatiotemporal chaos: A local ensemble transform Kalman filter. Physica D, 230(1), 112–26.Google Scholar

Jackson, A. (2003). Intense equatorial flux spots on the surface of the Earth’s core. Nature, 424, 760–63.Google Scholar

Jackson, A., Jonkers, A. R. T., and Walker, M. R. (2000). Four centuries of geomagnetic secular variation from historical records. Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 358(1768), 957–90.Google Scholar

Jault, D., Gire, C., and LeMouёl, J.-L. (1988). Westward drift, core motions and exchanges of angular momentum between core and mantle. Nature, 333, 353–6.Google Scholar

Jiang, W., and Kuang, W. (2008). An MPI-based MoSST core dynamics model. Physics of the Earth and Planetary Interiors, 170(1), 46–51.Google Scholar

Jones, C. A., Boronski, P., Brun, A. et al. (2011). Anelastic convection-driven dynamo benchmarks. Icarus, 216, 120–35.Google Scholar

Kageyama, A., and Sato, T. (1997). Generation mechanism of a dipole field by a magnetohydrodynamic dynamo. Physical Review E, 55, 4617–26.Google Scholar

Kaji, C. V., Hoover, R. C., and Ragi, S. (2019). Underwater navigation using geomagnetic field variations. 2019 IEEE International Conference on Electro Information Technology. https://doi.org/10.1109/EIT.2019.8834192 of:Google Scholar

Kloss, C, and Finlay, C. C. (2019). Time-dependent low-latitude core flow and geomagnetic field acceleration pulses. Geophysical Journal International, 217(1), 140–68.Google Scholar

Kotsuki, S., Ota, Y., and Miyoshi, T. (2017). Adaptive covariance relaxation methods for ensemble data assimilation: experiments in the real atmosphere. Quarterly Journal of the Royal Meteorological Society, 143(705), 2001–15.Google Scholar

Kuang, W., and Bloxham, J. (1997). An Earth-like numerical dynamo model. Nature, 389, 371–4.Google Scholar

Kuang, W., and Bloxham, J. (1999). Numerical Modeling of Magnetohydrodynamic Convection in a Rapidly Rotating Spherical Shell: Weak and Strong Field Dynamo Action. J. Comput. Phys., 153(1), 51–81.Google Scholar

Kuang, W., and Chao, B. F. (2003). Geodynamo Modeling and Core-Mantle Interactions. In Dehant, V., Creager, K., Karato, S., and Zatman, S., eds., Earth’s Core: Dynamics, Structure, Rotation, Geodynamics Series 31. Washington, DC: American Geophysical Union (AGU), pp. 193–212.Google Scholar

Kuang, W., and Tangborn, A. (2015). Dynamic responses of the Earth’s outer core to assimilation of observed geomagnetic secular variation. Progress in Earth and Planetary Science, 2. https://doi.org/10.1186/s40645–015–0071–4.Google Scholar

Kuang, W., Tangborn, A., Jiang, W. (2008). MoSST− DAS: The first generation geomagnetic data assimilation framework. Communications in Computational Physics, 3, 85–108.Google Scholar

Kuang, W., Tangborn, A., Wei, Z., and Sabaka, T. J. (2009). Constraining a numerical geodynamo model with 100 years of surface observations. Geophysical Journal International, 179(3), 1458–68, https://doi.org/10.1111/j.1365–246X.2009.04376.x.Google Scholar

Kuang, W., Wei, Z., Holme, R., and Tangborn, A. (2010). Prediction of geomagnetic field with data assimilation: a candidate secular variation model for IGRF-11. Earth, Planets and Space, 62, 775–85.Google Scholar

Kuang, W., Chao, B. F., and Chen, J. (2017). Decadal polar motion of the Earth excited by the convective outer core from geodynamo simulations. Journal of Geophysical Research: Solid Earth, 122(10), 8459–73.Google Scholar

Langel, R. A., and Estes, R. H. (1982). A geomagnetic field spectrum. Geophysical Research Letters, 9, 250–3.Google Scholar

Larmor, J. (1919). How could a rotating body such as the Sun become a magnet? Reports of the British Association, 87, 159–60.Google Scholar

Lesur, V., Wardinski, I., Hamoudi, M., and Rother, M. (2010). The second generation of the GFZ internal magnetic model: GRIMM-2. Earth, Planets and Space, 62, 765–73.Google Scholar

Li, K., Jackson, A., and Livermore, P. W. (2011). Variational data assimilation for the initial-value dynamo problem. Physical Review E, 84. https://doi.org/10.1103/PhysRevE.84.056321.Google Scholar

Li, K., Jackson, A., and Livermore, P. W. (2014). Variational data assimilation for a forced, inertia-free magnetohydrodynamic dynamo model. Geophysical Journal International, 199, 1662–76.Google Scholar

Liu, D., Tangborn, A., and Kuang, W. (2007). Observing system simulation experiments in geomagnetic data assimilation. Journal of Geophysical Research, 112. https://doi.org/10.1029/2006JB004691.Google Scholar

Lowrie, W., and Kent, D. V. (2004). Geomagnetic polarity time scale and reversal frequency regimes. Timescales of the paleomagnetic field, 145, 117–29.Google Scholar

Mandea, M., and Korte, M., eds. (2011). Geomagnetic Observations and Models. Dordrecht: Springer.Google Scholar

Mandea, M., Holme, R., Pais, A. et al. (2010). Geomagnetic jerks: Rapid core field variations and core dynamics. Space Science Reviews, 155, 147–75.Google Scholar

Matsui, H., Heien, E., Aubert, J. (2016). Performance benchmarks for a next generation numerical dynamo model. Geochemistry, Geophysics, Geosystems, 17(5), 1586–607.Google Scholar

Maus, S., Silva, L., and Hulot, G. (2008). Can core-surface flow models be used to improve the forecast of the Earth’s main magnetic field? Journal of Geophysical Research, 113, B08102. https://doi.org/10.1029/2007JB005199.Google Scholar

Minami, T., Nakano, S., Lesur, V. et al. (2020). A candidate secular variation model for IGRF-13 based on MHD dynamo simulation and 4DEnVar data assimilation. Earth, Planets and Space, 72, 136. https://doi.org/10.1186/s40623–020–01253–8.Google Scholar

Morzfeld, M., and Buffett, B. A. (2019). A comprehensive model for the kyr and Myr timescales of Earth’s axial magnetic dipole field. Nonlinear Processes in Geophysics, 26(3), 123–42.Google Scholar

Morzfeld, M., and Chorin, A. J. (2012). Implicit particle filtering for models with partial noise, and an application to geomagnetic data assimilation. Nonlinear Processes in Geophysics, 19(3), 365–82.Google Scholar

Morzfeld, M., Fournier, A., and Hulot, G. (2017). Coarse predictions of dipole reversals by low-dimensional modeling and data assimilation. Physics of the Earth and Planetary Interiors, 262, 8–27.Google Scholar

Nakagawa, T. (2020). A coupled core-mantle evolution: review and future prospects. Progress in Earth and Planetary Science, 7. https://doi.org/10.1186/s40645–020–00374–8.Google Scholar

Nilsson, A., Suttie, N., Korte, M., Holme, R., and Hill, M. (2020). Persistent westward drift of the geomagnetic field at the core-mantle boundary linked to recurrent high-latitude weak/reverse flux patches. Geophysical Journal International, 222, 1423–32.Google Scholar

Nimmo, F. (2007). Energetics of the core. In Olson, P, ed., Treatise on Geophysics: Vol. 8. Core Dynamics. Amsterdam: Elsevier, pp. 31–66.Google Scholar

Ogg, J. G. (2012). Geomagnetic polarity time scale. In Gradstein, F. M., Ogg, J. G., Schmitz, M., and Ogg, G., eds., The Geologic Time Scale 2012. Amsterdam: Elsevier Science, pp. 85–113.Google Scholar

Olsen, N., and Mandea, M. (2008). Rapidly changing flows in the Earth’s core. Nature Geoscience, 1, 390–94.Google Scholar

Pais, M. A., and Jault, D. (2008). Quasi-geostrophyic flows responsible for the secular variation of the Earth’s magnetic field. Geophysical Journal International, 173, 421–43.Google Scholar

Panovska, S., Korte, M., and Constable, C. G. (2019). One hundred thousand years of geomagnetic field evolution. Reviews of Geophysics, 57(4), 1289–337.Google Scholar

Petitdemange, L. (2018). Systematic parameter study of dynamo bifurcations in geodynamo simulations. Physics of the Earth and Planetary Interiors, 277, 113–32.Google Scholar

Pétrélis, F., Fauve, S., Dormy, E., and Valet, J.-P. (2009). Simple mechanism for reversals of Earth’s magnetic field. Physical Review Letters, 102, 144503.Google Scholar

Roberts, P. H., and Scott, S. (1965). On analysis of the secular variation. Journal of Geomagnetism and Geoelectricity, 17, 137–51.Google Scholar

Roberts, P. H, and King, E. M. (2013). On the genesis of the Earth’s magnetism. Reports on Progress in Physics, 76(9), 096801.Google Scholar

Sabaka, T. J., Tøffner-Clausen, L., Olsen, N., and Finlay, C. C. (2020). CM6: A comprehensive geomagnetic field model derived from both CHAMP and Swarm satellite observations. Earth, Planets and Space, 72, 80.Google Scholar

Sanchez, S., Fournier, A., Aubert, J., Cosme, E., and Gallet, Y. (2016). Modeling the archaeomagnetic field under spatial constraints from dynamo simulations: A resolution analysis. Geophysical Journal International, 207, 983–1002.Google Scholar

Sanchez, S., Wicht, J., Bärenzung, J., and Holschneider, M. (2019). Sequential assimilation of geomagnetic observations: Perspectives for the reconstruction and prediction of core dynamics. Geophysical Journal International, 217, 1434–50.Google Scholar

Sanchez, S., Wicht, J., Bärenzung, J., and Holschneider, M. (2020). Predictions of the geomagnetic secular variation based on the ensemble sequential assimilation of geomagnetic field models by dynamo simulations. Earth, Planets and Space, 72, 157. https://doi.org/10.1186/s40623–020–01279–y.Google Scholar

Schaeffer, N., Lora Silva, E., and Pais, M. A. (2016). Can core flows inferred from geomagnetic field models explain the Earth’s dynamo? Geophysical Journal International, 204(2), 868–77.Google Scholar

Shlyaeva, A., Whitaker, J. S., and Snyder, C. (2019). Model-space localization in serial ensemble filters. Journal of Advances in Modeling Earth Systems, 11(6), 1627–36.Google Scholar

Sun, Z., and Kuang, W. (2015). An ensemble algorithm based component for geomagnetic data assimilation. Terrestrial Atmospheric and Oceanic Sciences, 26, 53–61.Google Scholar

Sun, Z., Tangborn, A., and Kuang, W. (2007). Data assimilation in a sparsely observed one-dimensional modeled MHD system. Nonlinear Processes in Geophysics, 14, 181–92.Google Scholar

Talagrand, O., and Courtier, P. (1987). Variational assimilation of meteorological observations with the adjoint vorticity equation. I: Theory. Quarterly Journal of the Royal Meteorological Society, 113(478), 1311–28.Google Scholar

Tangborn, A., and Kuang, W. (2015). Geodynamo model and error parameter estimation using geomagnetic data assimilation. Geophysical Journal International, 200, 664–75.Google Scholar

Tangborn, A., and Kuang, W. (2018). Impact of archeomagnetic field model data on modern era geomagnetic forecasts. Physics of the Earth and Planetary Interiors, 276, 2–9.Google Scholar

Tangborn, A., Kuang, W., Sabaka, T. J., and Yi, C. (2021). Geomagnetic secular variation forecast using the NASA GEMS ensemble Kalman filter: A candidate SV model for IGRF-13. Earth, Planets and Space, 73, 47. https://doi.org/10.1186/s40623–020–01324–w.Google Scholar

Tippett, M. K., Anderson, J. L., Bishop, C. H., Hamill, T. M., and Whitaker, J. S. (2003). Ensemble square root filters. Monthly Weather Review, 131, 1485–90.Google Scholar

Wicht, J., and Christensen, U. R. (2010). Torsional oscillations in dynamo simulations. Geophysical Journal International, 181, 1367–80.Google Scholar

Wicht, J., and Sanchez, S. (2019). Advances in geodynamo modelling. Geophysical & Astrophysical Fluid Dynamics, 113(1–2), 2–50.Google Scholar

Yadav, R. K., Gastine, T., and Christensen, U. R. (2013). Scaling laws in spherical shell dynamos with free-slip boundaries. Icarus, 225, 185–93.Google Scholar

Zhang, M., and Zhang, F. (2012). E4DVar: Coupling an ensemble Kalman filter with four-dimensional variational data assimilation in a limited-area weather prediction model. Monthly Weather Review, 140(2), 587–600.Google Scholar

References

Amit, H., Leonhardt, R., and Wicht, J. (2010). Polarity reversals from paleomagnetic observations and numerical dynamo simulations. Space Science Reviews, 155(1), 293–335.Google Scholar

Amit, H., Terra-Nova, F., Lézin, M., and Trindade, R. I. (2021). Non-monotonic growth and motion of the south Atlantic anomaly. Earth, Planets and Space, 73(1), 1–10.Google Scholar

Anderson, J. L., and Anderson, S. L. (1999). A Monte Carlo implementation of the nonlinear filtering problem to produce ensemble assimilations and forecasts. Monthly Weather Review, 127(12), 2741–58.Google Scholar

Arneitz, P., Leonhardt, R., Schnepp, E. et al. (2017). The HISTMAG database: Combining historical, archaeomagnetic and volcanic data. Geophysical Journal International, 210(3), 1347–59.Google Scholar

Aubert, J. (2015). Geomagnetic forecasts driven by thermal wind dynamics in the Earth’s core. Geophysical Journal International, 203(3), 1738–51.Google Scholar

Aubert, J., and Finlay, C. C. (2019). Geomagnetic jerks and rapid hydromagnetic waves focusing at Earth’s core surface. Nature Geoscience, 12(5), 393–8.Google Scholar

Aubert, J., Finlay, C. C., and Fournier, A. (2013). Bottom-up control of geomagnetic secular variation by the Earth’s inner core. Nature, 502(7470), 219–23.Google Scholar

Aubert, J., Gastine, T., and Fournier, A. (2017). Spherical convective dynamos in the rapidly rotating asymptotic regime. Journal of Fluid Mechanics, 813, 558–93.Google Scholar

Aubert, J., Labrosse, S., and Poitou, C. (2009). Modelling the palaeo-evolution of the geodynamo. Geophysical Journal International, 179(3), 1414–28.Google Scholar

Baerenzung, J., Holschneider, M., Wicht, J., Lesur, V., and Sanchez, S. (2020). The Kalmag model as a candidate for IGRF-13. Earth, Planets and Space, 72(1), 1–13.Google Scholar

Barrois, O., Hammer, M., Finlay, C., Martin, Y., and Gillet, N. (2018). Assimilation of ground and satellite magnetic measurements: Inference of core surface magnetic and velocity field changes. Geophysical Journal International, 215(1), 695–712.Google Scholar

Braginsky, S. I., and Roberts, P. H. (1995). Equations governing convection in Earth’s core and the geodynamo. Geophysical & Astrophysical Fluid Dynamics, 79(1–4), 1–97.Google Scholar

Brown, M. C., Donadini, F., Korte, M. et al. (2015). Geomagia50. v3: 1. General structure and modifications to the archeological and volcanic database. Earth, Planets and Space, 67(1), 1–31.Google Scholar

Bullard, E. C., and Gellman, H. (1954). Homogeneous dynamos and terrestrial magnetism. Philosophical Transactions of the Royal Society of London A, 247(928), 213–78.Google Scholar

Burgers, G., Jan van Leeuwen, P., and Evensen, G. (1998). Analysis scheme in the Ensemble Kalman Filter. Monthly Weather Review, 126(6), 1719–24.Google Scholar

Christensen, U., and Wicht, J. (2015). Numerical dynamo simulations. In Schubert, G., ed., Treatise on Geophysics, 2nd ed. Oxford: Elsevier, pp. 245–77.Google Scholar

Christensen, U. R., Aubert, J., and Hulot, G. (2010). Conditions for Earth-like geodynamo models. Earth and Planetary Science Letters, 296(3), 487–96.Google Scholar

Constable, C. G., Parker, R. L., and Stark, P. B. (1993). Geomagnetic field models incorporating frozen-flux constraints. Geophysical Journal International, 113(2), 419–33.Google Scholar

Evensen, G. (1994). Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics. Journal of Geophysical Research: Oceans, 99(C5), 10143–62.Google Scholar

Finlay, C. C. (2008). Historical variation of the geomagnetic axial dipole. Physics of the Earth and Planetary Interiors, 170(1–2), 1–14.Google Scholar

Finlay, C. C., Kloss, C., Olsen, N. et al. (2020). The CHAOS-7 geomagnetic field model and observed changes in the South Atlantic anomaly. Earth, Planets and Space, 72(1), 1–31.Google Scholar

Fournier, A., Hulot, G., Jault, D. et al. (2010). An introduction to data assimilation and predictability in geomagnetism. Space Science Reviews, 155(1–4), 247–91.Google Scholar

Fournier, A., Nerger, L., and Aubert, J. (2013). An ensemble Kalman filter for the time dependent analysis of the geomagnetic field. Geochemistry, Geophysics, Geosystems, 14(10), 4035–43.Google Scholar

Fratter, I., Léger, J.-M., Bertrand, F. et al. (2016). Swarm absolute scalar magnetometers first in-orbit results. Acta Astronautica, 121, 76–87.Google Scholar

Friis-Christensen, E., Lühr, H., and Hulot, G. (2006). Swarm: A constellation to study the earth’s magnetic field. Earth, Planets and Space, 58(4), 351–8.Google Scholar

Gillet, N., Gerick, F., Angappan, R., and Jault, D. (2021). A dynamical prospective on interannual geomagnetic field changes. Surveys in Geophysics, 43, 71–105.Google Scholar

Gottwald, G. A., and Majda, A. (2013). A mechanism for catastrophic filter divergence in data assimilation for sparse observation networks. Nonlinear Processes in Geophysics, 20(5), 705–12.Google Scholar

Gubbins, D., and Zhang, K. (1993). Symmetry properties of the dynamo equations for palaeomagnetism and geomagnetism. Physics of the Earth and Planetary Interiors, 75(4), 225–41.Google Scholar

Gwirtz, K., Morzfeld, M., Kuang, W., and Tangborn, A. (2021). A testbed for geomagnetic data assimilation. Geophysical Journal International, 227(3), 2180–203.Google Scholar

Hamill, T. M., Whitaker, J. S., and Snyder, C. (2001). Distance-dependent filtering of background error covariance estimates in an ensemble Kalman filter. Monthly Weather Review, 129(11), 2776–90.Google Scholar

Huder, L., Gillet, N., Finlay, C. C., Hammer, M. D., and Tchoungui, H. (2020). Cov-obs. x2: 180 years of geomagnetic field evolution from ground-based and satellite observations. Earth, Planets and Space, 72(1), 1–18.Google Scholar

Jackson, A., Jonkers, A. R., and Walker, M. R. (2000). Four centuries of geomagnetic secular variation from historical records. Philosophical Transactions of the Royal Society of London A: Mathematical. Physical and Engineering Sciences, 358(1768), 957–90.Google Scholar

Johnson, C. L., and Constable, C. G. (1997). The time-averaged geomagnetic field: global and regional biases for 0–5 Ma. Geophysical Journal International, 131(3), 643–66.Google Scholar

Jonkers, A. R. T. (2003). Earth’s Magnetism in the Age of Sail. Baltimore, MD: John Hopkins University Press.Google Scholar

Kalman, R. E. (1960). A new approach to linear filtering and prediction problems. Journal of basic Engineering, 82(1), 35–45.Google Scholar

Korte, M., and Constable, C. (2008). Spatial and temporal resolution of millennial scale geomagnetic field models. Advances in Space Research, 41(1), 57–69.Google Scholar

Korte, M., Donadini, F., and Constable, C. (2009). Geomagnetic field for 0–3 ka: 2. A new series of time-varying global models. Geochemistry, Geophysics, Geosystems, 10 (6).Google Scholar

Korte, M., Constable, C., Donadini, F., and Holme, R. (2011). Reconstructing the Holocene geomagnetic field. Earth and Planetary Science Letters, 312(3–4), 497–505.Google Scholar

Kuang, W., Tangborn, A., Wei, Z., and Sabaka, T. (2009). Constraining a numerical geodynamo model with 100 years of surface observations. Geophysical Journal International, 179(3), 1458–68.Google Scholar

Kuang, W., Wei, Z., Holme, R., and Tangborn, A. (2010). Prediction of geomagnetic field with data assimilation: a candidate secular variation model for igrf-11. Earth, Planets and Space, 62(10), 775–85.Google Scholar

Lhuillier, F., Fournier, A., Hulot, G., and Aubert, J. (2011). The geomagnetic secular-variation timescale in observations and numerical dynamo models. Geophysical Research Letters, 38, L09306.Google Scholar

Licht, A., Hulot, G., Gallet, Y., and Thébault, E. (2013). Ensembles of low degree archeomagnetic field models for the past three millennia. Physics of the Earth and Planetary Interiors, 224, 38–67.Google Scholar

Liu, D., Tangborn, A., and Kuang, W. (2007). Observing system simulation experiments in geomagnetic data assimilation. Journal of Geophysical Research: Solid Earth, 112, B08103.Google Scholar

Livermore, P. W., Finlay, C. C., and Bayliff, M. (2020). Recent north magnetic pole acceleration towards Siberia caused by flux lobe elongation. Nature Geoscience, 13(5), 387–91.Google Scholar

Mandea, M., and Chambodut, A. (2020). Geomagnetic field processes and their implications for space weather. Surveys in Geophysics, 41(6), 1611–27.Google Scholar

Matzka, J., Chulliat, A., Mandea, M., Finlay, C., and Qamili, E. (2010). Geomagnetic observations for main field studies: from ground to space. Space Science Reviews, 155(1), 29–64.Google Scholar

Merril, R. T., McElhinny, M., and McFadden, P. L., eds. (1996). The Magnetic Field of the Earth, vol. 63. Cambridge, MA: Academic Press.Google Scholar

Morzfeld, M., Fournier, A., and Hulot, G. (2017). Coarse predictions of dipole reversals by lowdimensional modeling and data assimilation. Physics of the Earth and Planetary Interiors, 262, 8–27.Google Scholar

Panovska, S., Korte, M., and Constable, C. (2019). One hundred thousand years of geomagnetic field evolution. Reviews of Geophysics, 57(4), 1289–337.Google Scholar

Reda, J., Fouassier, D., Isac, A. et al. (2011). Improvements in geomagnetic observatory data quality. In Mandea, M. and Korte, M., eds., Geomagnetic Observations and Models. Dordrecht: Springer, pp. 127–48.Google Scholar

Roberts, P. H., and King, E. M. (2013). On the genesis of the Earth’s magnetism. Reports on Progress in Physics, 76(9), 096801.Google Scholar

Ropp, G., Lesur, V., Baerenzung, J., and Holschneider, M. (2020). Sequential modelling of the earth’s core magnetic field. Earth, Planets and Space, 72(1), 1–15.Google Scholar

Sanchez, S. (2016). Assimilation of geomagnetic data into dynamo models, an archeomagnetic study. PhD thesis, Institut de Physique du Globe de Paris (IPGP), France.Google Scholar

Sanchez, S., Fournier, A., Aubert, J., Cosme, E., and Gallet, Y. (2016). Modelling the archaeomagnetic field under spatial constraints from dynamo simulations: a resolution analysis. Geophysical Journal International, 207, 983–1002.Google Scholar

Sanchez, S., Wicht, J., and Bärenzung, J. (2020). Predictions of the geomagnetic secular variation based on the ensemble sequential assimilation of geomagnetic field models by dynamo simulations. Earth, Planets and Space, 72(1), 1–20.Google Scholar

Sanchez, S., Wicht, J., Bärenzung, J., and Holschneider, M. (2019). Sequential assimilation of geomagnetic observations: perspectives for the reconstruction and prediction of core dynamics. Geophysical Journal International, 217(2), 1434–50.Google Scholar

Schaeffer, N., Jault, D., Nataf, H.-C., and Fournier, A. (2017). Turbulent geodynamo simulations: a leap towards Earth’s core. Geophysical Journal International, 211(1), 1–29.Google Scholar

Tangborn, A., and Kuang, W. (2015). Geodynamo model and error parameter estimation using geomagnetic data assimilation. Geophysical Journal International, 200(1), 664–75.Google Scholar

Tangborn, A., and Kuang, W. (2018). Impact of archeomagnetic field model data on modern era geomagnetic forecasts. Physics of the Earth and Planetary Interiors, 276, 2–9.Google Scholar

Valet, J.-P., and Fournier, A. (2016). Deciphering records of geomagnetic reversals. Reviews of Geophysics, 54(2), 410–46.Google Scholar

Book contents

Part III - ‘Solid’ Earth Applications: From the Surface to the Core

Summary

Access options

References

References

References

References

Specific Terms

References

References

Bibliography

References

References

References

References

References

References

Save book to Kindle

Save book to Dropbox

Save book to Google Drive