Multi-physics adjoint modeling of Earth structure: combining gravimetric, seismic, and geodynamic inversions

Aghasi, A., Kilmer, M., Miller, E.L.: Parametric level set methods for inverse problems. SIAM J. Imag. Sci. 4(2), 618–650 (2011). https://doi.org/10.1137/100800208 Akçelik, V., Biros, G., Ghattas, O.: Parallel multiscale Gauss–Newton–Krylov methods for inverse wave propagation. In: Proceedings of Conference on Supercomputing, ACM/IEEE (2002). https://doi.org/10.1109/SC.2002.10002 Aki, K., Richards, P.G.: Quantitative Seismology, 1st edn. Freeman, San Francisco (1980) Alnæs, M., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The FEniCS Project version 1.5. Arch. Numer. Softw. 3(100), 9–23 (2015) Askan, A., Akcelik, V., Bielak, J., Ghattas, O.: Full waveform inversion for seismic velocity and anelastic losses in heterogeneous structures. Bull. Seismol. Soc. Am. 97(6), 1990–2008 (2007). https://doi.org/10.1785/0120070079 Askan, A., Akcelik, V., Bielak, J., Ghattas, O.: Parameter sensitivity analysis of a nonlinear least-squares optimization-based anelastic full waveform inversion method. CR Mécanique 338(7–8), 364–376 (2010). https://doi.org/10.1016/j.crme.2010.07.002 Aster, R.C., Borchers, B., Thurber, C.H.: Parameter Estimation and Inverse Problems. International Geophysics Series, vol. 90. Elsevier Academic Press, San Diego (2005) Balay, S., Abhyankar, S., Adams, M., Brown, J., Brune, P., Buschelman, K., Dalcin, L., Dener, A., Eijkhout, V., Gropp, W., Karpeyev, D., Kaushik, D., Knepley, M., May, D., McInnes, L.C., Mills, R., Munson, T., Rupp, K., Sanan, P., Smith, B., Zampini, S., Zhang, H.: PETSc Users Manual. Revision 3.11. Technical report, Argonne National Laboratory, Chicago, IL (2019) Berkel, P., Michel, V.: On mathematical aspects of a combined inversion of gravity and normal mode variations by a spline method. Math. Geosci. 42(7), 795–816 (2010). https://doi.org/10.1007/s11004-010-9297-2 Blakely, R.J.: Potential Theory in Gravity and Magnetic Applications. Cambridge University Press, New York (1995) Brown, J.R., Slawinski, M.A.: On Foundations of Seismology: Bringing Idealizations Down to Earth. World Scientific, Singapore (2017) Bunge, H.-P., Richards, M.A., Baumgardner, J.R.: Mantle-circulation models with sequential data assimilation: inferring present-day mantle structure from plate-motion histories. Philos. Trans. R. Soc. London Ser. A 360, 2545–2567 (2002). https://doi.org/10.1098/rsta.2002.1080 Bunge, H.-P., Hagelberg, C.R., Travis, B.J.: Mantle circulation models with variational data assimilation: inferring past mantle flow and structure from plate motion histories and seismic tomography. Geophys. J. Int. 152(2), 280–301 (2003). https://doi.org/10.1046/j.1365-246X.2003.01823.x Bunks, C., Saleck, F.M., Zaleski, S., Chavent, G.: Multiscale seismic waveform inversion. Geophysics 60(5), 1457–1473 (1995). https://doi.org/10.1190/1.1443880 Burger, M.: A level set method for inverse problems. Inverse Probl. 17(5), 1327 (2001). https://doi.org/10.1088/0266-5611/17/5/307 Chao, B.F.: On inversion for mass distribution from global (time-variable) gravity field. J. Geodyn. 39, 223–230 (2005). https://doi.org/10.1016/j.jog.2004.11.001 Claerbout, J.F.: Earth Soundings Analysis: Processing Versus Inversion. Blackwell, Cambridge (1992) Colli, L., Ghelichkhan, S., Bunge, H.-P., Oeser, J.: 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 Res. 53, 252–272 (2018). https://doi.org/10.1016/j.gr.2017.04.027 Condie, K.C.: Mantle Plumes and Their Record in Earth History. Cambridge University Press, Cambridge (2001) Conrad, C.P., Molnar, P.: The growth of Rayleigh–Taylor-type instabilities in the lithosphere for various rheological and density structures. Geophys. J. Int. 129(1), 95–112 (1997). https://doi.org/10.1111/j.1365-246X.1997.tb00939.x Conrad, C.P., Steinberger, B., Torsvik, T.H.: Stability of active mantle upwelling revealed by net characteristics of plate tectonics. Nature 498(7455), 479–482 (2013). https://doi.org/10.1038/nature12203 Crestel, B., Stadler, G., Ghattas, O.: A comparative study of structural similarity and regularization for joint inverse problems governed by PDEs. Inverse Probl. 35, 024003 (2018). https://doi.org/10.1088/1361-6420/aaf129 Dahlen, F.A., Tromp, J.: Theoretical Global Seismology. Princeton University Press, Princeton (1998) de Hoop, M.V., Smith, H., Uhlmann, G., van der Hilst, R.D.: Seismic imaging with the generalized Radon transform: a curvelet transform perspective. Inverse Probl. 25(2), 025005 (2009). https://doi.org/10.1088/0266-5611/25/2/025005 Domenzain, D., Bradford, J., Mead, J.: Joint inversion of GPR and ER data. In: SEG Technical Program Expanded Abstracts, Society of Exploration Geophysicists, Denver, CO, pp. 4763–4767 (2018). https://doi.org/10.1190/segam2018-2997794.1 Dorman, L.M., Lewis, B.T.R.: Experimental isostasy: 1. Theory of the determination of the Earth’s isostatic response to a concentrated load. J. Geophys. Res. 75(17), 3357–3365 (1970) Dorn, O., Lesselier, D.: Level set methods for structural inversion and image reconstruction. In: Scherzer, O. (ed.) Handbook of Mathematical Methods in Imaging. Springer, New York (2015) Elkins-Tanton, L.T.: Continental magmatism caused by lithospheric delamination. Geol. Soc. Am. Spec. Pap. 388, 449–461 (2005) Elkins-Tanton, L .T.: Continental magmatism, volatile recycling, and a heterogeneous mantle caused by lithospheric gravitational instabilities. J. Geophys. Res. 112(B3), B03,405 (2007). https://doi.org/10.1029/2005JB004072 Fichtner, A., Simutė, S.: Hamiltonian Monte Carlo inversion of seismic sources in complex media. J. Geophys. Res. 123(4), 2984–2999 (2018). https://doi.org/10.1002/2017JB015249 Fichtner, A., Trampert, J.: Hessian kernels of seismic data functionals based upon adjoint techniques. Geophys. J. Int. 185(2), 775–798 (2011). https://doi.org/10.1111/j.1365-246X.2011.04966.x Fichtner, A., Bunge, H.-P., Igel, H.: The adjoint method in seismology—II Applications: traveltimes and sensitivity functionals. Phys. Earth Planet. Inter. 157(1–2), 105–123 (2006a). https://doi.org/10.1016/j.pepi.2006.03.018 Fichtner, A., Bunge, H.-P., Igel, H.: The adjoint method in seismology—I. Theory. Phys. Earth Planet. Inter. 157(1–2), 86–104 (2006b). https://doi.org/10.1016/j.pepi.2006.03.016 Fischer, D., Michel, V.: Sparse regularization of inverse gravimetry–case study: spatial and temporal mass variations in South America. Inv. Probl. 28, 065012 (2012). https://doi.org/10.1088/0266-5611/28/6/065012 Forte, A.M., Mitrovica, J.X.: Deep-mantle high-viscosity flow and thermochemical structure inferred from seismic and geodynamic data. Nature 410(6832), 1049–1056 (2001). https://doi.org/10.1038/35074000 Freeden, W.: Chapter 1: Geomathematics: its role, its aim, and its potential. In: Freeden, W., Nashed, M.Z.Z., Sonar, T. (eds.) Handbook of Geomathematics, pp. 3–78. Springer, Berlin (2015). https://doi.org/10.1007/978-3-642-01546-5_1 Freeden, W., Nashed, M.Z.: Inverse gravimetry: background material and multiscale mollifier approaches. Int. J. Geomath. 9(2), 199–264 (2018). https://doi.org/10.1007/s13137-018-0103-5 Gauthier, O., Virieux, J., Tarantola, A.: Two-dimensional nonlinear inversion of seismic waveforms: numerical results. Geophysis 51(7), 1387–1403 (1986) Geng, Y., Innanen, K., Pan, W.: Subspace method for multi-parameter FWI. Commun. Math. Phys. 28, 228–248 (2020). https://doi.org/10.4208/cicp.OA-2018-0087 Gerya, T.: Introduction to Numerical Geodynamic Modelling. Cambridge University Press, Cambridge (2019) Ghelichkhan, S., Bunge, H.-P.: The compressible adjoint equations in geodynamics: derivation and numerical assessment. Int. J. Geomath. 7(1), 1–30 (2016). https://doi.org/10.1007/s13137-016-0080-5 Glatzmaier, G.A.: Introduction to Modeling Convection in Planets and Stars: Magnetic Field, Density Stratification, Rotation. Princeton University Press, Princeton (2014) Gouveia, W.P., Scales, J.A.: Bayesian seismic waveform inversion: Parameter estimation and uncertainty analysis. J. Geophys. Res. 103(B2), 2759–2779 (1998). https://doi.org/10.1029/97JB02933 Harig, C., Zhong, S., Simons, F .J.: Constraints on upper-mantle viscosity inferred from the flow-induced pressure gradient across a continental keel. Geochem. Geophys. Geosyst. 11(6), Q06,004 (2010). https://doi.org/10.1029/2010GC003038 Hofmann-Wellenhof, B., Moritz, H.: Physical Geodesy, 2nd edn. Springer, New York (2006) Horbach, A., Bunge, H.-P., Oeser, J.: 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. Int. J. Geomath. 5(2), 163–194 (2014). https://doi.org/10.1007/s13137-014-0061-5 Kellogg, O.D.: Foundations of Potential Theory. Springer, New York (1967) Kennett, B.L.N., Bunge, H.-P.: Geophysical Continua. Cambridge University Press, Cambridge (2008) Laurain, A.: A level set-based structural optimization code using FEniCS. Struct. Multidiscip. Optim. 58(3), 1311–1334 (2018). https://doi.org/10.1007/s00158-018-1950-2 Lewis, K .W., Simons, F .J.: Local spectral variability and the origin of the Martian crustal magnetic field. Geophys. Res. Lett. 39, L18,201 (2012). https://doi.org/10.1029/2012GL052708 Lithgow-Bertelloni, C., Richards, M.A.: The dynamics of Cenozoic and Mesozoic plate motions. Rev. Geophys. 36, 27–78 (1998) Liu, Q., Tromp, J.: Finite-frequency sensitivity kernels based upon adjoint methods. Bull. Seismol. Soc. Am. 96(6), 2383–2397 (2006). https://doi.org/10.1785/0120060041 Liu, Q., Tromp, J.: Finite-frequency sensitivity kernels for global seismic wave equation based upon adjoint methods. Geophys. J. Int. 174, 265–286 (2009). https://doi.org/10.1111/j.1365-246X.2008.03798.x Logg, A., Andre-Mardal, K., Wells, G.N.: Automated solution of differential equations by the finite element method: The FEniCS book. Lecture Notes in Computational Science and Engineering, vol. 84. Springer, Berlin (2012) Ma, Y., Hale, D.: Quasi-Newton full-waveform inversion with a projected Hessian matrix. Geophysics 77(5), R207–R216 (2012). https://doi.org/10.1190/GEO2011-0519.1 Malevsky, A.V., Yuen, D.A.: Strongly chaotic non-Newtonian mantle convection. Geophys. Astrophys Fluid Dyn. 65(1–4), 149–171 (1992) Malvern, L.E.: Introduction to the Mechanics of a Continuous Medium. Prentice-Hall, Englewood Cliffs (1969) Martin, D., Nokes, R.: Crystal settling in a vigorously convecting magma chamber. Nature 332(6164), 534–536 (1988). https://doi.org/10.1038/332534a0 Martin, D., Nokes, R.: A fluid-dynamical study of crystal settling in convecting magmas. J. Petrol. 30(6), 1471–1500 (1989). https://doi.org/10.1093/petrology/30.6.1471 Martin, J., Wilcox, L.C., Burstedde, C., Ghattas, O.: A stochastic Newton MCMC method for large-scale statistical inverse problems with application to seismic inversion. SIAM J. Sci. Comput. 34(3), A1460–A1487 (2012). https://doi.org/10.1137/110845598 Mead, J.L., Ford, J.F.: Joint inversion of compact operators. J. Inverse Ill-posed Probl. 28(1), 105–118 (2020). https://doi.org/10.1515/jiip-2019-0068 Melosh, H.J., Raefsky, A.: The dynamical origin of subduction zone topography. Geophys. J. Int. 60(3), 333–354 (1980). https://doi.org/10.1111/j.1365-246X.1980.tb04812.x Michel, V.: Regularized wavelet-based multiresolution recovery of the harmonic mass density distribution from data of the Earth’s gravitational field at satellite height. Inverse Probl. 21, 997–1025 (2005). https://doi.org/10.1088/0266-5611/21/3/013 Michel, V.: Chapter 32: Tomography: problems and multiscale solutions. In: Freeden, W., Nashed, M.Z., Sonar, T. (eds.) Handbook of Geomathematics, 2nd edn, pp. 2087–2119. Springer, Berlin (2015). https://doi.org/10.1007/978-3-642-01546-5_32 Michel, V., Fokas, A.S.: A unified approach to various techniques for the non-uniqueness of the inverse gravimetric problem and wavelet-based methods. Inverse Probl. 24, 045019 (2008). https://doi.org/10.1088/0266-5611/24/4/045019 Michel, V., Orzlowski, S.: On the nullspace of a class of Fredholm integral equations of the first kind. J. Inverse Ill-posed Probl. 24(6), 1–24 (2015). https://doi.org/10.1515/jiip-2015-0026 Michel, V., Simons, F.J.: A general approach to regularizing inverse problems with regional data using Slepian wavelets. Inverse Probl. 33(12), 12,501 (2017). https://doi.org/10.1088/1361-6420/aa9909 Mora, P.: Elastic wave-field inversion of reflection and transmission data. Geophysics 53(6), 750–759 (1988) Mora, P.: Inversion = migration + tomography. Geophysics 54(12), 1575–1586 (1989) Morgan, W .J.: Gravity anomalies and convection currents. 1. A sphere and cylinder sinking beneath surface of a viscous fluid. J. Geophys. Res. 70(24), 6175–6185 (1965). https://doi.org/10.1029/JZ070i024p06,175 Morgan, W.J.: Convection plumes in the lower mantle. Nature 230(5288), 42–43 (1971). https://doi.org/10.1038/230,042a0 Nolet, G.: A Breviary for Seismic Tomography. Cambridge University Press, Cambridge (2008) Nolet, G.: Transmission tomography in seismology. In: Freeden, W., Nashed, M.Z., Sonar, T. (eds.) Handbook of Geomathematics, 2nd edn, pp. 1887–1904. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-642-54551-1_58 Oldenburg, D.W.: The inversion and interpretation of gravity anomalies. Geophysics 39(4), 526–536 (1974). https://doi.org/10.1190/1.1440,444 Pan, W., Wang, Y.: On the influence of different misfit functions for attenuation estimation in viscoelastic full-waveform inversion: synthetic study. Geophys. J. Int. 221(2), 1292–1319 (2020). https://doi.org/10.1093/gji/ggaa089 Parker, R.L.: The rapid calculation of potential anomalies. Geophys. J. R. Astron. Soc. 31(4), 447–455 (1973). https://doi.org/10.1111/j.1365-246X.1973.tb06513.x Parmentier, E.M., Turcotte, D.L., Torrance, K.E.: Studies of finite amplitude non-Newtonian thermal convection with application to convection in the Earth’s mantle. J. Geophys. Res. 81(11), 1839–1846 (1976). https://doi.org/10.1029/JB081i011p01839 Peltier, W.R.: Mantle convection and viscoelasticity. Annu. Rev. Fluid Mech. 17(1), 561–608 (1985). https://doi.org/10.1146/annurev.fl.17.010185003021 Peng, D., Merriman, B., Osher, S., Zhao, H., Kang, M.: A PDE-based fast local level set method. J. Comput. Phys. 155(2), 410–438 (1999). https://doi.org/10.1006/jcph.1999.6345 Petra, N., Zhu, H., Stadler, G., Hughes, T.J.R., Ghattas, O.: An inexact Gauss–Newton method for inversion of basal sliding and rheology parameters in a nonlinear Stokes ice sheet model. J. Glaciol. 58(211), 889–903 (2012). https://doi.org/10.3189/2012JoG11J182 Petra, N., Martin, J., Stadler, G., Ghattas, O.: A computational framework for infinite-dimensional Bayesian inverse problems, Part II: stochastic Newton MCMC with application to ice sheet flow inverse problems. SIAM J. Sci. Comput. 36(4), A1525–A1555 (2014). https://doi.org/10.1137/130934,805 Plattner, A.M.: GPRPy: open-source ground-penetrating radar processing and visualization software. Lead. Edge 39(5), 332–337 (2020). https://doi.org/10.1190/tle39050,332.1 Plessix, R.-E.: A review of the adjoint-state method for computing the gradient of a functional with geophysical applications. Geophys. J. Int. 167(2), 495–503 (2006). https://doi.org/10.1111/j.1365-246X.2006.02,978.x Ranalli, G.: Rheology of the Earth, 2nd edn. Chapman and Hall, London (1995) Ratnaswamy, V., Stadler, G., Gurnis, M.: Adjoint-based estimation of plate coupling in a non-linear mantle flow model: theory and examples. Geophys. J. Int. 202(2), 768–786 (2015). https://doi.org/10.1093/gji/ggv166 Reuber, G., Holbach, L., Popov, A., Hanke, M., Kaus, B.: Inferring rheology and geometry of subsurface structures by adjoint-based inversion of principal stress directions. Geophys. J. Int. 223(2), 851–861 (2020). https://doi.org/10.1093/gji/ggaa344 Reuber, G.S., Kaus, B.J.P., Popov, A.A., Baumann, T.S.: Unraveling the physics of the Yellowstone magmatic system using geodynamic simulations. Front. Earth Sci. 6, 117 (2018). https://doi.org/10.3389/feart.2018.00117 Robbins, A.R., Plattner, A.: Offset-electrode profile acquisition strategy for electrical resistivity tomography. J. Appl. Geoph. 151, 66–72 (2018). https://doi.org/10.1016/j.jappgeo.2018.01.027 Scherzer, O., Weickert, J.: Relations between regularization and diffusion filtering. J. Math. Imaging Vis. 12(1), 43–63 (2000). https://doi.org/10.1023/A:1008344608808 Schubert, G., Turcotte, D.L., Olson, P.: Mantle Convection in the Earth and Planets. Cambridge University Press, Cambridge (2001) Schuster, G.T.: Seismic Inversion. Society of Exploration Geophysicists, Tulsa (2017) Sheriff, R.E., Geldart, L.P.: Exploration Seismology. Cambridge University Press, Cambridge (1995) Sleep, N.H.: Stress and flow beneath island arcs. Geophys. J. Int. 42(3), 827–857 (1975). https://doi.org/10.1111/j.1365-246X.1975.tb06454.x Sleep, N.H.: Hotspots and mantle plumes: some phenomenology. J. Geophys. Res. 95(B5), 6715–6736 (1990). https://doi.org/10.1029/JB095iB05p06,715 Stefanov, P., Uhlmann, G., Vasy, A., Zhou, H.: Travel time tomography. Acta Math. Sin. 35(6), 1085–1114 (2019). https://doi.org/10.1007/s10,114-019-8338-0 Stern, R.J.: Subduction zones. Rev. Geophys. (2002). https://doi.org/10.1029/2001RG000108 Symes, W .W.: The seismic reflection inverse problem. Inverse Probl. 25(12), 123008 (2009). https://doi.org/10.1088/0266-5611/25/12/123008 Tarantola, A.: Linearized inversion of seismic reflection data. Geophys. Prospect. 34(2), 998–1015 (1984a). https://doi.org/10.1111/j.1365-2478.1984.tb00751.x Tarantola, A.: Inversion of seismic reflection data in the acoustic approximation. Geophysics 49(8), 1259–1266 (1984b). https://doi.org/10.1190/1.1441754 Tarantola, A.: A strategy for nonlinear elastic inversion of seismic reflection data. Geophysics 51(10), 1893–1903 (1986) Tarantola, A.: Theoretical background for the inversion of seismic waveforms, including elasticity and attenuation. Pure Appl. Geophys. 128(1–2), 365–399 (1988) Tikhonov, A .N., Arsenin, V .Y.: Solutions of Ill-Posed Problems. V. H. Winston & Sons, Washington (1977) Tröltzsch, F.: Optimal Control of Partial Differential Equations: Theory, Methods and Applications. Graduate Studies in Mathematics, vol. 112. American Mathematical Society, Providence (2010) Tromp, J.: Seismic wavefield imaging of Earth’s interior across scales. Nat. Rev. Earth Environ. 1, 40–53 (2020). https://doi.org/10.1038/s43017-019-0003-8 Tromp, J., Tape, C., Liu, Q.: Seismic tomography, adjoint methods, time reversal and banana-doughnut kernels. Geophys. J. Int. 160(1), 195–216 (2005). https://doi.org/10.1111/j.1365-246X.2004.02453.x van den Berg, A.P., van Keken, P., Yuen, D.A.: The effects of a composite non-Newtonian and Newtonian rheology on mantle convection. Geophys. J. Int. 115(1), 62–78 (1993). https://doi.org/10.1111/j.1365-246X.1993.tb05588.x Villa, U., Petra, N., Ghattas, O.: hIPPYlib: An extensible software framework for large-scale inverse problems gioverned by PDEs: Part I: Deterministic inversion and linearized Bayesian inference. arXiv:1909.03948 (2019) Virieux, J., Operto, S.: An overview of full-waveform inversion in exploration geophysics. Geophysics 74(6), WCC1–WCC26 (2009). https://doi.org/10.1190/1.3238367 Wilson, J.T.: Mantle plumes and plate motions. Tectonophysics 19(2), 149–164 (1973). https://doi.org/10.1016/0040-1951(73)90037-1 Woodward, M.J.: Wave-equation tomography. Geophysics 57(1), 15–26 (1992). https://doi.org/10.1190/1.1443179 Xu, P.: Determination of surface gravity anomalies using gradiometric observables. Geophys. J. Int. 110, 321–332 (1992a) Xu, P.: The value of minimum norm estimation of geopotential fields. Geophys. J. Int. 111, 170–178 (1992b) Yilmaz, Ö.: Seismic Data Analysis, vol. 1-2. Society of Exploration Geophysicists, Tulsa (2001) Yuan, Y .O., Simons, F.J.: Multiscale adjoint waveform-difference tomography using wavelets. Geophysics 79(3), WA79–WA95 (2014). https://doi.org/10.1190/GEO2013-0383.1 Zienkiewicz, O.C.: The Finite Element Method, 3rd edn. McGraw-Hill, London (1977)