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9 - Spatial and Temporal Changes of the Geomagnetic Field

Insights from Forward and Inverse Core Field Models

from Part III - Spatial and Temporal Variations of the Geomagnetic Field

Published online by Cambridge University Press:  25 October 2019

By
Nicolas Gillet
Edited by
Mioara Mandea ,
Monika Korte ,
Andrew Yau  and
Eduard Petrovsky
Mioara Mandea
Affiliation:
Centre National d'études Spatiales, France
Monika Korte
Affiliation:
GeoforschungsZentrum, Helmholtz-Zentrum, Potsdam
Andrew Yau
Affiliation:
University of Calgary
Eduard Petrovsky
Affiliation:
Academy of Sciences of the Czech Republic, Prague
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Summary

Observational constraints on geomagnetic field changes from interannual to millenial periods are reviewed, and the current resolution of field models (covering archeological to satellite eras) is discussed. With the perspective of data assimilation, emphasis is put on uncertainties entaching Gauss coefficients, and on the statistical properties of ground-based records. These latter potentially call for leaving behind the notion of geomagnetic jerks. The accuracy at which we recover interannual changes also requires considering with caution the apparent periodiObservational constraints on geomagnetic field changes from interannual to millenial periods are reviewed, and the current resolution of field models (covering archeological to satellite eras) is discussed. With the perspective of data assimilation, emphasis is put on uncertainties entaching Gauss coefficients, and on the statistical properties of ground-based records. These latter potentially call for leaving behind the notion of geomagnetic jerks. The accuracy at which we recover interannual changes also requires considering with caution the apparent periodicity seen in the secular acceleration from satellite data. I then address the interpretation of recorded magnetic fluctuations in terms of core dynamics, highlighting the need for models that allow (or pre-suppose) a magnetic energy orders of magnitudes larger than the kinetic energy at large length-scales, a target for future numerical simulations of the geodynamo. I finally recall the first attempts at implementing geomagnetic data assimilation algorithms.city seen in the secular acceleration from satellite data. I then address the interpretation of recorded magnetic fluctuations in terms of core dynamics, highlighting the need for models that allow (or pre-suppose) a magnetic energy orders of magnitudes larger than the kinetic energy at large length-scales, a target for future numerical simulations of the geodynamo. I finally recall the first attempts at implementing geomagnetic data assimilation algorithms.

Keywords

geomagnetic secular variationgeodynamo simulationsinverse problemdata assimilationEarth’s core dynamics
Type
Chapter
Information
Geomagnetism, Aeronomy and Space Weather
A Journey from the Earth's Core to the Sun
 , pp. 115 - 132
Publisher: Cambridge University Press
Print publication year: 2019

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References

Arneitz, P., Leonhardt, R., Schnepp, E., Heilig, B., Mayrhofer, F., Kovacs, P., Hejda, P., Valach, F., Vadasz, G., Hammerl, C. et al. The histmag database: combining historical, archaeomagnetic and volcanic data. Geophys. J. Int., 210(3):1347–59, 2017.CrossRefGoogle Scholar
Aubert, J.. Earth’s core internal dynamics 1840–2010 imaged by inverse geodynamo modelling. Geophys. J. Int., 197(3):1321–34, 2014.Google Scholar
Aubert, J.. Geomagnetic forecasts driven by thermal wind dynamics in the Earth’s core. Geophys. J. Int., 203(3): 1738–51, 2015.Google Scholar
Aubert, J., Amit, H., Hulot, G. and Olson, P.. Thermochemical flows couple the Earth’s inner core growth to mantle heterogeneity. Nature, 454(7205):758, 2008.Google Scholar
Aubert, J., Finlay, C. C. and Fournier, A.. Bottom-up control of geomagnetic secular variation by the Earth’s inner core. Nature, 502(7470):219, 2013.Google Scholar
Aubert, J., Gastine, T. and Fournier, A.. Spherical convective dynamos in the rapidly rotating asymptotic regime. J. Fluid Mech., 813:558–93, 2017.Google Scholar
Baerenzung, J., Holschneider, M. and Lesur, V.. The flow at the Earth’s core-mantle boundary under weak prior constraints. J. Geophys. Res., 121(3): 1343–64, 2016.Google Scholar
Baerenzung, J., Holschneider, M., Wicht, J., Sanchez, S. and Lesur, V.. Modeling and predicting the short term evolution of the geomagnetic field. arXiv preprint arXiv:1710.06188, 2017.Google Scholar
Bardsley, O. and Davidson, P. A.. Inertial–Alfvén waves as columnar helices in planetary cores. J. Fluid Mech., 805, 2016.Google Scholar
Barrois, O., Gillet, N. and Aubert, J.. Contributions to the geomagnetic secular variation from a reanalysis of core surface dynamics. Geophys. J. Int., 211(1):50–68, 2017.CrossRefGoogle Scholar
Barrois, O., Hammer, M., Finlay, C., Martin, Y., & Gillet, N., 2018. Assimilation of ground and satellite magnetic measurements: inference of core surface magnetic and velocity field changes, Geophys. J. Int., 215(1), 695–712.CrossRefGoogle Scholar
Beggan, C. and Whaler, K.. Forecasting secular variation using core flows. Earth Planets Space, 62(10):11, 2010.Google Scholar
Bloxham, J.. Simple models of fluid flow at the core surface derived from geomagnetic field models. Geophys. J. Int., 99(1):173–82, 1989.Google Scholar
Bloxham, J. and Jackson, A.. Time-dependent mapping of the magnetic field at the core-mantle boundary. J. Geophys. Res., 97(B13):19537–63, 1992.Google Scholar
Bouligand, C., Gillet, N., Jault, D., Schaeffer, N., Fournier, A. and Aubert, J.. Frequency spectrum of the geomagnetic field harmonic coefficients from dynamo simulations. Geophys. J. Int., 2016.CrossRefGoogle Scholar
Braginsky, S. I.. Torsional magnetohydrodynamic vibrations in the Earth’s core and variations in day length. Geomag. Aeron., 10:1–8, 1970.Google Scholar
Braginsky, S. I.. MAC-oscillations of the hidden ocean of the core. J. Geomag. Geoelec., 45(11–12):1517–38, 1993.CrossRefGoogle Scholar
Braginsky, S. I.. Dynamics of the stably stratified ocean at the top of the core. Phys. Earth Planet. Int., 111(1): 21–34, 1999.Google Scholar
Brodholt, J. and Badro, J.. Composition of the low seismic velocity E’ layer at the top of Earth’s core. Geophys. Res. Lett., 2017.Google Scholar
Brown, M. C., Donadini, F., Korte, M., Nilsson, A., Korhonen, K., Lodge, A., Lengyel, S. N. and Constable, C. G.. GEOMAGIA50. v3: 1. general structure and modifications to the archeological and volcanic database. Earth Planets Space, 67(1):83, 2015.Google Scholar
Buffett, B.. Geomagnetic fluctuations reveal stable stratification at the top of the Earth’s core. Nature, 507(7493): 484, 2014.Google Scholar
Buffett, B. and Matsui, H.. A power spectrum for the geomagnetic dipole moment. Earth Planet. Sci. Lett., 411: 20–26, 2015.Google Scholar
Buffett, B., Mathews, P. and Herring, T.. Modeling of nutation and precession: Effects of electromagnetic coupling. J. Geophys. Res.: Solid Earth, 107(B4), 2002.Google Scholar
Buffett, B., Knezek, N. and Holme, R.. Evidence for MAC waves at the top of Earth’s core and implications for variations in length of day. Geophys. J. Int., 204(3): 1789–1800, 2016.CrossRefGoogle Scholar
Calkins, M. A., Julien, K. and Marti, P.. Three-dimensional quasi-geostrophic convection in the rotating cylindrical annulus with steeply sloping endwalls. J. Fluid Mech., 732:214–44, 2013.Google Scholar
Canet, E., Fournier, A. and Jault, D.. Forward and adjoint quasi-geostrophic models of the geomagnetic secular variation. J. Geophys. Res., 114(B11), 2009.Google Scholar
Canet, E., Finlay, C. and Fournier, A.. Hydromagnetic quasi-geostrophic modes in rapidly rotating planetary cores. Phys. Earth Planet. Inter., 229:1–15, 2014.CrossRefGoogle Scholar
Cardin, P. and Olson, P.. Experiments on core dynamics. In Treatise on Geophysics, 2nd edn. Elsevier BV, Amsterdam, pages 317–39, 2015.Google Scholar
Chao, B. F., Chung, W., Shih, Z. and Hsieh, Y.. Earth’s rotation variations: A wavelet analysis. Terra Nova, 26 (4):260–64, 2014.Google Scholar
Christensen, U. R. and Wicht, J.. Models of magnetic field generation in partly stable planetary cores: Applications to Mercury and Saturn. Icarus, 196(1):16–34, 2008.Google Scholar
Christensen, U. R., Aubert, J. and Hulot, G.. Conditions for Earth-like geodynamo models. Earth Planet. Sci. Lett., 296(3):487–96, 2010.CrossRefGoogle Scholar
Chulliat, A. and Maus, S.. Geomagnetic secular acceleration, jerks, and a localized standing wave at the core surface from 2000 to 2010. J. Geophys. Res., 119(3):1531–43, 2014.Google Scholar
Chulliat, A., Alken, P. and Maus, S.. Fast equatorial waves propagating at the top of the Earth’s core. Geophys. Res. Lett., 42(9):3321–9, 2015.Google Scholar
Constable, C. G. and Johnson, C.. A paleomagnetic power spectrum. Phys. Earth Planet. Inter., 153:61–73, 2005.Google Scholar
Constable, C. G. and Korte, M.. Centennial to millennialscale geomagnetic field variations. In Treatise on Geophysics, 2nd edn., Elsevier BV, Amsterdam, pages 309–41. 2015.Google Scholar
De Santis, A., Barraclough, D. and Tozzi, R.. Spatial and temporal spectra of the geomagnetic field and their scaling properties. Phys. Earth Planet. Inter., 135:125–34, 2003.Google Scholar
Dormy, E., Oruba, L. and Petitdemange, L.. Three branches of dynamo action. Fluid Dyn. Res., 2017.Google Scholar
Finlay, C., Lesur, V., Thèbault, E., Vervelidou, F., Morschhauser, A. and Shore, R.. Challenges handling magnetospheric and ionospheric signals in internal geomagnetic field modelling. Space Sci. Rev., 206(1–4):157–89, 2017.CrossRefGoogle Scholar
Finlay, C. C.. Course 8 waves in the presence of magnetic fields, rotation and convection. Les Houches, 88:403–50, 2008.CrossRefGoogle Scholar
Finlay, C. C. and Jackson, A.. Equatorially dominated magnetic field change at the surface of Earth’s core. Science, 300(5628):2084–6, 2003.CrossRefGoogle ScholarPubMed
Finlay, C. C., Olsen, N., Kotsiaros, S., Gillet, N. and Tøffner-Clausen, L.. Recent geomagnetic secular variation from Swarm. Earth Planets Space, 68(1):1–18, 2016.Google Scholar
Fournier, A., Hulot, G., Jault, D., Kuang, W., Tangborn, A., Gillet, N., Canet, E., Aubert, J. and Lhuillier, F.. An introduction to data assimilation and predictability in geomagnetism. Space Sci. Rev., 155(1–4):247–91, 2010.Google Scholar
Fournier, A., Aubert, J. and Thèbault, E.. Inference on core surface flow from observations and 3-D dynamo modelling. Geophys. J. Int., 186(1):118–36, 2011.CrossRefGoogle Scholar
Fournier, A., Nerger, L. and Aubert, J.. An ensemble Kalman filter for the time-dependent analysis of the geomagnetic field. Geophys. Geochem. Geosyst., 14(10): 4035–43, 2013.Google Scholar
Fournier, A., Aubert, J. and Thèbault, E.. A candidate secular variation model for IGRF-12 based on swarm data and inverse geodynamo modelling. Earth Planets Space, 67(1):1–17, 2015.Google Scholar
Garcia, F., Oruba, L. and Dormy, E.. Equatorial symmetry breaking and the loss of dipolarity in rapidly rotating dynamos. Geophys. Astrophys. Fluid Dyn., 1–14, 2017.Google Scholar
Genevey, A., Gallet, Y., Jesset, S., Thèbault, E., Bouillon, J., Lefèvre, A. and Le Goff, M.. New archeointensity data from french early medieval pottery production (6th–10th century ad). Tracing 1500 years of geomagnetic field intensity variations in Western Europe. Phys. Earth Planet. Inter., 257:205–19, 2016.CrossRefGoogle Scholar
Gillet, N., Jault, D., Canet, E. and Fournier, A.. Fast torsional waves and strong magnetic field within the Earth’s core. Nature, 465(7294):74, 2010.Google Scholar
Gillet, N., Schaeffer, N. and Jault, D.. Rationale and geophysical evidence for quasi-geostrophic rapid dynamics within the Earth’s outer core. Phys. Earth Planet. Inter., 187:380–90, 2011.Google Scholar
Gillet, N., Jault, D., Finlay, C. C. and Olsen, N.. Stochastic modelling of the Earth’s magnetic field: inversion for covariances over the observatory era. Geophys. Geochem. Geosyst., 14:766–86, 2013.CrossRefGoogle Scholar
Gillet, N., Barrois, O. and Finlay, C. C.. Stochastic forecasting of the geomagnetic field from the COV-OBS.x1 geomagnetic field model, and candidate models for IGRF-12. Earth Planets Space, 67(1):71, 2015a.Google Scholar
Gillet, N., Jault, D. and Finlay, C.. Planetary gyre, time-dependent eddies, torsional waves, and equatorial jets at the Earth’s core surface. J. Geophys. Res., 120(6):3991–4013, 2015b.CrossRefGoogle Scholar
Gillet, N., Jault, D. and Canet, E.. Excitation of traveling torsional normal modes in an Earth’s core model. Geophys. J. Int., 2017.Google Scholar
Gubbins, D., Willis, A. P. and Sreenivasan, B.. Correlation of Earth’s magnetic field with lower mantle thermal and seismic structure. Phys. Earth Planet. Inter., 162(3):256–60, 2007.CrossRefGoogle Scholar
Helffrich, G. and Kaneshima, S.. Outer-core compositional stratification from observed core wave speed profiles. Nature, 468(7325):807, 2010.Google Scholar
Hellio, G. and Gillet, N.. Geomagnetic field changes over the past three millennia, and their uncertainties. Geophys. J. Int., submitted, 2018.Google Scholar
Hide, R.. Free hydromagnetic oscillations of the Earth’s core and the theory of the geomagnetic secular variation. Philos. Trans. R. Soc. London A, 259(1107):615–47, 1966.Google Scholar
Holme, R.. Electromagnetic core-mantle coupling II: Probing deep mantle conductance. In The Core-Mantle Boundary Region, American Geophysical Union, Washington, DC, pages 139–51, 1998.Google Scholar
Holschneider, M., Lesur, V., Mauerberger, S. and Baerenzung, J.. Correlation-based modeling and separation of geomagnetic field components. J. Geophys. Res., 121(5):3142–60, 2016.Google Scholar
Hori, K., Teed, R. and Jones, C.. The dynamics of magnetic Rossby waves in spherical dynamo simulations: A signature of strong-field dynamos? Phys. Earth Planet. Inter., 2017.CrossRefGoogle Scholar
Jackson, A. and Finlay, C.. Geomagnetic secular variation and its applications to the core. In Treatise on Geophysics, 2nd edn., Elsevier BV, Amsterdam, pages 137–84, 2015.Google Scholar
Jackson, A., Jonkers, A. R. T. and Walker, M. R.. Four centuries of geomagnetic secular variation from historical records. Philos. Trans. R. Soc. London A, 358:957–90, 2000.Google Scholar
Jault, D.. Axial invariance of rapidly varying diffusionless motions in the Earth’s core interior. Phys. Earth Planet. Inter., 166(1):67–76, 2008.Google Scholar
Jault, D.. Illuminating the electrical conductivity of the lowermost mantle from below. Geophys. J. Inter., 202:482–96, 2015.CrossRefGoogle Scholar
Jault, D. and Finlay, C.. Waves in the core and mechanical core-mantle interactions. In Treatise on Geophysics, 2nd edn., Elsevier BV, Amsterdam, pages 225–45, 2015.Google Scholar
Jones, C.. Thermal and compositional convection in the outer core. In Treatise on Geophysics, 2nd edn., Elsevier BV, Amsterdam, pages 115–59, 2015.Google Scholar
Jonkers, A. R., Jackson, A. and Murray, A.. Four centuries of geomagnetic data from historical records. Rev. Geophys., 41(2), 2003.CrossRefGoogle Scholar
Kageyama, A., Miyagoshi, T. and Sato, T.. Formation of current coils in geodynamo simulations. Nature, 454(7208):1106, 2008.Google Scholar
Konȏpková, Z., McWilliams, R. S., Gómez-Pèrez, N. and Goncharov, A. F.. Direct measurement of thermal conductivity in solid iron at planetary core conditions. Nature, 534:99–101, 2016.CrossRefGoogle ScholarPubMed
Korte, M. and Constable, C.. Improving geomagnetic field reconstructions for 0–3 ka. Phys. Earth Planet. Inter., 188:247–59, 2011.Google Scholar
Kuang, W. and Tangborn, A.. Dynamic responses of the Earth’s outer core to assimilation of observed geomagnetic secular variation. Prog. Earth Planet. Sci., 2(1):40, 2015.Google Scholar
Kuang, W., Tangborn, A., Wei, Z. and Sabaka, T.. Constraining a numerical geodynamo model with 100 years of surface observations. Geophys. J. Int., 179(3):1458–68, 2009.Google Scholar
Kuang, W., Wei, Z., Holme, R. and Tangborn, A.. Prediction of geomagnetic field with data assimilation: a candidate secular variation model for IGRF-11. Earth Planets Space, 62(10):7, 2010.Google Scholar
Labbé, F., Jault, D. and Gillet, N.. On magnetostrophic inertialess waves in quasi-geostrophic models of planetary cores. Geophys. Astrophys. Fluid Dyn., 109(6):587–610, 2015.Google Scholar
Le Bars, M., Cèbron, D. and Le Gal, P.. Flows driven by libration, precession, and tides. Ann. Rev. Fluid Mech., 47:163–93, 2015.Google Scholar
Lesur, V., Wardinski, I., Hamoudi, M. and Rother, M.. The second generation of the GFZ reference internal magnetic model: GRIMM-2. Earth Planets Space, 62(10):6, 2010.Google Scholar
Lesur, V., Heumez, B., Telali, A., Lalanne, X. and Soloviev, A.. Estimating error statistics for Chambonla-Forêt observatory definitive data. Ann. Geophys., 35:939, 2017a.Google Scholar
Lesur, V., Wardinski, I., Baerenzung, J. and Holschneider, M.. On the frequency spectra of the core magnetic field gauss coefficients. Phys. Earth Planet. Inter., 2017b.Google Scholar
Lhuillier, F., Aubert, J. and Hulot, G.. Earth’s dynamo limit of predictability controlled by magnetic dissipation. Geophys. J. Int., 186(2):492–508, 2011.Google Scholar
Licht, A., Hulot, G., Gallet, Y. and Thèbault, E.. Ensembles of low degree archeomagnetic field models for the past three millennia. Phys. Earth Planet. Inter., 224:38–67, 2013.CrossRefGoogle Scholar
Liu, D., Tangborn, A. and Kuang, W.. Observing system simulation experiments in geomagnetic data assimilation. J. Geophys. Res., 112(B8), 2007.Google Scholar
Livermore, P. W., Ierley, G. and Jackson, A.. The evolution of a magnetic field subject to taylor s constraint using a projection operator. Geophys. J. Int., 187(2):690–704, 2011.Google Scholar
Macmillan, S. and Olsen, N.. Observatory data and the Swarm mission. Earth Planets Space, 65(11):15, 2013.Google Scholar
Maffei, S. and Jackson, A.. Kinematic validation of a quasigeostrophic model for the fast dynamics in the Earth’s outer core. Geophys. J. Int., 2017.Google Scholar
Malkus, W. V.. Hydromagnetic planetary waves. J. Fluid Mech., 28(4):793–802, 1967.Google Scholar
Mandea, M. and Olsen, N.. A new approach to directly determine the secular variation from magnetic satellite observations. Geophys. Res. Lett., 33(15), 2006.Google Scholar
Mandea, M., Holme, R., Pais, A., Pinheiro, K., Jackson, A. and Verbanac, G.. Geomagnetic jerks: Rapid core field variations and core dynamics. Space Sci. Rev., 155(1):147–75, 2010.Google Scholar
Meduri, D. G. and Wicht, J.. A simple stochastic model for dipole moment fluctuations in numerical dynamo simulations. Frontiers Earth Sci., 4:38, 2016.Google Scholar
Nataf, H.-C. and Schaeffer, N.. Turbulence in the core. In Treatise on Geophysics, 2nd edn., Elsevier BV, Amsterdam, pages 161–81. 2015.Google Scholar
Nilsson, A., Muscheler, R. and Snowball, I.. Millennial scale cyclicity in the geodynamo inferred from a dipole tilt reconstruction. Earth Planet. Sci. Lett., 311(3):299–305, 2011.Google Scholar
Ohta, K., Kuwayama, Y., Hirose, K., Shimizu, K. and Ohishi, Y.. Experimental determination of the electrical resistivity of iron at Earth’s core conditions. Nature, 534(7605):95–8, 2016.Google Scholar
Oke, P. R., Sakov, P. and Corney, S. P.. Impacts of localisation in the enkf and enoi: experiments with a small model. Ocean Dyn., 57(1):32–45, 2007.CrossRefGoogle Scholar
Olsen, N. and Kotsiaros, S.. The geomagnetic field gradient tensor, properties and parametrization in terms of spherical harmonics. Int. J. Geomath., 2012.Google Scholar
Olsen, N., Glassmeier, K.-H. and Jia, X.. Separation of the magnetic field into external and internal parts. Space Sci. Rev., 152(1–4):135–57, 2010.Google Scholar
Olsen, N., Lühr, H., Finlay, C. C., Sabaka, T. J., Michaelis, I., Rauberg, J. and Tøffner-Clausen., L. The CHAOS-4 geomagnetic field model. Geophys. J. Int., 197(2):815–27, 2014.CrossRefGoogle Scholar
Olson, P., Christensen, U. and Driscoll, P.. From superchrons to secular variation: A broadband dynamo frequency spectrum for the geomagnetic dipole. Earth Planet. Sci. Lett., 319–20:75–82, 2012.Google Scholar
Olson, P., Landeau, M. and Reynolds, E.. Dynamo tests for stratification below the core-mantle boundary. Phys. Earth Planet. Inter., 271:1–18, 2017.Google Scholar
Pais, M. and Jault, D.. Quasi-geostrophic flows responsible for the secular variation of the Earth’s magnetic field. Geophys. J. Int., 173(2):421–43, 2008.Google Scholar
Panovska, S., Finlay, C. and Hirt, A.. Observed periodicities and the spectrum of field variations in Holocene magnetic records. Earth Planet. Sci. Lett., 379:88–94, 2013.Google Scholar
Panovska, S., Korte, M., Finlay, C. and Constable, C.. Limitations in paleomagnetic data and modelling techniques and their impact on holocene geomagnetic field models. Geophys. J. Int., 202(1):402–18, 2015.CrossRefGoogle Scholar
Pavón-Carrasco, F. J., Osete, M. L., Torta, J. M. and De Santis, A.. A geomagnetic field model for the holocene based on archaeomagnetic and lava flow data. Earth Planet. Sci. Lett., 388:98–109, 2014.Google Scholar
Pozzo, M., Davies, C., Gubbins, D. and Alfe`, D.. Thermal and electrical conductivity of iron at Earth’s core conditions. Nature, 485(7398):355–58, 2012.Google Scholar
Roberts, P. H. and Wu, C.-C.. On the modified taylor constraint. Geophys. Astrophys. Fluid Dyn., 108(6):696–715, 2014.Google Scholar
Sabaka, T. J., Olsen, N. and Purucker, M. E.. Extending comprehensive models of the earth’s magnetic field with Ørsted and CHAMP data. Geophys. J. Int., 159(2): 521–47, 2004.CrossRefGoogle Scholar
Sabaka, T. J., Hulot, G. and Olsen, N.. Mathematical properties relevant to geomagnetic field modeling. In Handbook of Geomathematics, Springer, pages 503–38, 2010.Google Scholar
Sabaka, T. J., Olsen, N., Tyler, R. H. and Kuvshinov, A.. Cm5, a pre-swarm comprehensive geomagnetic field model derived from over 12 yr of CHAMP, Ørsted, SAC-C and observatory data. Geophys. J. Int., 200(3):1596–1626, 2015.Google Scholar
Sakuraba, A. and Roberts, P. H.. Generation of a strong magnetic field using uniform heat flux at the surface of the core. Nat. Geosci., 2(11):802–5, 2009.Google Scholar
Sanchez, S.. Assimilation of geomagnetic data into dynamo models, an archeomagnetic study. PhD thesis, Institut de Physique du Globe de Paris, 2016.Google Scholar
Sanchez, S., Fournier, A., Aubert, J., Cosme, E. and Gallet, Y.. Modelling the archaeomagnetic field under spatial constraints from dynamo simulations: a resolution analysis. Geophys. J. Int., 207:983–1002, 2016.CrossRefGoogle Scholar
Schaeffer, N. and Jault, D.. Electrical conductivity of the lowermost mantle explains absorption of core torsional waves at the equator. Geophys. Res. Lett., 43(10):4922–8, 2016.Google Scholar
Schaeffer, N., Jault, D., Nataf, H.-C. and Fournier, A.. Turbulent geodynamo simulations: A leap towards Earth’s core. Geophys. J. Int., 211(1):1–29, 2017.Google Scholar
Soderlund, K. M., King, E. M. and Aurnou, J. M.. The influence of magnetic fields in planetary dynamo models. Earth Planet. Sci. Lett., 333:9–20, 2012.CrossRefGoogle Scholar
Soloviev, A., Chulliat, A. and Bogoutdinov, S.. Detection of secular acceleration pulses from magnetic observatory data. Phys. Earth Planet. Inter., 270:128–42, 2017.Google Scholar
Sreenivasan, B. and Jones, C. A.. Helicity generation and subcritical behaviour in rapidly rotating dynamos. J. Fluid Mech., 688:5, 2011.CrossRefGoogle Scholar
Takehiro, S.-I.. Penetration of Alfvèn waves into an upper stably-stratified layer excited by magnetoconvection in rotating spherical shells. Phys. Earth Planet. Inter., 241:37–43, 2015.Google Scholar
Takehiro, S.-I. and Lister, J. R.. Penetration of columnar convection into an outer stably stratified layer in rapidly rotating spherical fluid shells. Earth Planet. Sci. Lett., 187(3):357–66, 2001.Google Scholar
Takehiro, S.-I. and Sasaki, Y.. Penetration of steady fluid motions into an outer stable layer excited by MHD thermal convection in rotating spherical shells. Phys. Earth Planet. Inter., 2017.Google Scholar
Tangborn, A. and Kuang, W.. Geodynamo model and error parameter estimation using geomagnetic data assimilation. Geophys. J. Int., 200(1):664–75, 2015.Google Scholar
Taylor, J.. The magneto-hydrodynamics of a rotating fluid and the Earth’s dynamo problem. Proc. R. Soc. London A, 274(1357):274–83, 1963.Google Scholar
Teed, R. J., Jones, C. A. and Tobias, S. M.. The transition to Earth-like torsional oscillations in magnetoconvection simulations. Earth Planet. Sci. Lett., 419:22–31, 2015.Google Scholar
Thomson, A. W. and Lesur, V.. An improved geomagnetic data selection algorithm for global geomagnetic field modelling. Geophys. J. Int., 169(3):951–63, 2007.Google Scholar
Tøffner-Clausen, L., Lesur, V., Olsen, N. and Finlay, C. C.. In-flight scalar calibration and characterisation of the Swarm magnetometry package. Earth Planets Space, 68(1):129, 2016.Google Scholar
Turner, G., Rasson, J. and Reeves, C.. Observation and measurement techniques. In Treatise on Geophysics, 2nd edn., Elsevier BV, Amsterdam, pages 91–135, 2015.Google Scholar
Velímskỳ, J.. Electrical conductivity in the lower mantle: Constraints from CHAMP satellite data by time-domain em induction modelling. Phys. Earth Planet. Inter., 180(3):111–17, 2010.Google Scholar
Vidal, J. and Schaeffer, N.. Quasi-geostrophic modes in the Earth’s fluid core with an outer stably stratified layer. Geophys. J. Int., 202(3):2182–93, 2015.Google Scholar
Walker, M., Barenghi, C. and Jones, C.. A note on dynamo action at asymptotically small ekman number. Geophys. Astrophys. Fluid Dyn., 88(1–4):261–75, 1998.Google Scholar
Yadav, R. K., Gastine, T., Christensen, U. R., Wolk, S. J. and Poppenhaeger, K.. Approaching a realistic force balance in geodynamo simulations. Proc. Natl. Acad. Sci. USA, 113(43):12065–70, 2016.Google Scholar

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