Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-27T08:56:55.284Z Has data issue: false hasContentIssue false

14 - Global Seismic Tomography Using Time Domain Waveform Inversion

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

Published online by Cambridge University Press:  20 June 2023

By
Barbara Romanowicz
Edited by
Alik Ismail-Zadeh ,
Fabio Castelli ,
Dylan Jones  and
Sabrina Sanchez
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
Get access

Summary

Abstract: In this chapter, I present an overview of waveform tomography, in the context of imaging of the Earth‘s whole mantle at the global scale. In this context, waveform tomography is defined utilising entire wide-band filtered records of the seismic wavefield, generated by natural earthquakes and observed at broadband receivers located at teleseismic distances. This is in contrast to imaging methodologies that first extract secondary observables, such as, most commonly, travel times of the most prominent energy arrivals (i.e. seismic phases), that can be easily identified and isolated in the records. Waveform tomography is a non-linear process that requires the ability to compute the predicted wavefield in a given three-dimensional Earth model and compare it to the observed wavefield. One of its main challenges, is the computational cost involved. I first review the history of methodological developments, specifically focusing on the global, whole mantle Earth imaging problem. I then discuss and contrast the two recent methodologies that have led to the development of the first three-dimensional elastic global shear velocity models that have been published to-date using numerical integration of the wave equation, specifically, using the spectral element method. I discuss how the forward problem is addressed, the data selection approaches, definitions of the misfit function, and computation of kernels for the inverse step of the imaging procedure, as well as the choice of the optimisation method. I also discuss model parametrisation, and, in particular, the important topic of how the strongly heterogeneous crust is modelled. In the final parts of this chapter, I discuss efforts towards resolving the difficult problem of model evaluation and present my views on promising directions and remaining challenges in this rapidly evolving field, aiming at further improving resolution of deep mantle elastic structure with the goal of informing our understanding of the dynamics of our planet.

Keywords

computational seismologyEarth structurefull waveform inversiongeophysicsglobal seismic imagingseismic tomographyseismology
Type
Chapter
Information
Applications of Data Assimilation and Inverse Problems in the Earth Sciences , pp. 220 - 238
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

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.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle 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/ggy078CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle Scholar
Dziewonski, A., and Anderson, D. (1981). Preliminary reference Earth model. Physics of the Earth and Planetary Interiors, 25, 297–356.CrossRefGoogle Scholar
Dziewonski, A., Hager, B., and O’Connell, R. (1977). Large-scale heterogeneities in the lower mantle. Journal of Geophysical Research, 82, 239–55.CrossRefGoogle Scholar
Efron, B., and Stein, C. (1981). The jackknife estimate of variance. Annals of Statistics, 9(3), 586–96.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle ScholarPubMed
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), 1225–36CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle 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

Save book to Kindle

To save this book to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×