zbMATH — the first resource for mathematics

A time-domain preconditioned truncated Newton approach to visco-acoustic multiparameter full waveform inversion. (English) Zbl 1394.65045

65K10 Numerical optimization and variational techniques
35R30 Inverse problems for PDEs
86A15 Seismology (including tsunami modeling), earthquakes
Full Text: DOI
[1] T. Alkhalifah and R. Plessix, A recipe for practical full-waveform inversion in anisotropic media: An analytical parameter resolution study, Geophysics, 79 (2014), pp. R91–R101, .
[2] J. E. Anderson, L. Tan, and D. Wang, Time-reversal checkpointing methods for RTM and FWI, Geophysics, 77 (2012), pp. S93–S103.
[3] A. Askan, V. Akcelik, J. Bielak, and O. Ghattas, Full waveform inversion for seismic velocity and anelastic losses in heterogeneous structures, Bull. Seismol. Soc. Am., 97 (2007), pp. 1990–2008.
[4] O. Barkved, P. Heavey, J. H. Kommedal, J.-P. van Gestel, R. S.ynnøve, H. Pettersen, C. Kent, and U. Albertin, Business impact of full waveform inversion at Valhall, in SEG Technical Program Expanded Abstracts, 2010, pp. 925–929.
[5] C. Boehm, M. Hanzich, J. de la Puente, and A. Fichtner, Wavefield compression for adjoint methods in full-waveform inversion, Geophysics, 81 (2016), pp. R385–R397.
[6] C. Boehm and M. Ulbrich, A semismooth Newton-CG method for constrained parameter identification in seismic tomography, SIAM J. Sci. Comput., 37 (2015), pp. S334–S364, . · Zbl 1325.86001
[7] Y. Capdeville, L. Guillot, and J.-J. Marigo, 2-D non-periodic homogenization to upscale elastic media for P-SV waves, Geophys. J. Int., 182 (2010), pp. 903–922.
[8] J. Carcione, D. Kosloff, and R. Kosloff, Wave propagation simulation in a linear viscoacoustic medium, Geophys. J. Int., 93 (1988), pp. 393–401. · Zbl 0635.73037
[9] J. Carcione, D. Kosloff, and R. Kosloff, Wave-propagation simulation in an elastic anisotropic (transversely isotropic) solid, Quart. J. Mech. Appl. Math., 41 (1988), pp. 319–345. · Zbl 0656.73020
[10] E. Causse, R. Mittet, and B. Ursin, Preconditioning of full-waveform inversion in viscoacoustic media, Geophysics, 64 (1999), pp. 130–145.
[11] C. Cerjan, D. Kosloff, R. Kosloff, and M. Reshef, A nonreflecting boundary condition for discrete acoustic and elastic wave equations, Geophysics, 50 (1985), pp. 2117–2131.
[12] G. Chavent, Nonlinear Least Squares for Inverse Problems, Springer, Dordrecht, Heidelberg, London, New York, 2009. · Zbl 1191.65062
[13] P. Chen, T. Jordan, and L. Zhao, Full three-dimensional tomography: A comparison between the scattering-integral and adjoint-wavefield methods, Geophys. J. Int., 170 (2007), pp. 175–181.
[14] Y. Choi and C. Shin, Frequency-domain elastic full waveform inversion using the new pseudo-Hessian matrix: Experience of elastic Marmousi \(2\) synthetic data, Bull. Seismol. Soc. Am., 98 (2008), pp. 2402–2415.
[15] S. M. Day and J. B. Minster, Numerical simulation of attenuated wavefields using a Padé approximant method, Geophys. J. Int., 78 (1984), pp. 105–118. · Zbl 0587.73150
[16] E. Duveneck and P. M. Bakker, Stable P-wave modeling for reverse-time migration in tilted TI media, Geophysics, 76 (2011), pp. S65–S75.
[17] S. C. Eisenstat and H. F. Walker, Choosing the forcing terms in an inexact Newton method, SIAM J. Sci. Comput., 17 (1996), pp. 16–32, . · Zbl 0845.65021
[18] H. Emmerich and M. Korn, Incorporation of attenuation into time-domain computation of seismic wavefield, Geophysics, 52 (1987), pp. 1252–1264.
[19] I. Epanomeritakis, V. Akçelik, O. Ghattas, and J. Bielak, A Newton-CG method for large-scale three-dimensional elastic full waveform seismic inversion, Inverse Problems, 24 (2008), pp. 1–26. · Zbl 1142.65052
[20] A. Fichtner, B. L. N. Kennett, H. Igel, and H. P. Bunge, Full waveform tomography for radially anisotropic structure: New insights into present and past states of the Australasian upper mantle, Earth Planet. Sci. Lett., 290 (2010), pp. 270–280.
[21] A. Fichtner and J. Trampert, Hessian kernels of seismic data functionals based upon adjoint techniques, Geophys. J. Int., 185 (2011), pp. 775–798, .
[22] G. H. F. Gardner, L. W. Gardner, and A. R. Gregory, Formation velocity and density—the diagnostic basics for stratigraphic traps, Geophysics, 39 (1974), pp. 770–780.
[23] S. Greenhalgh, B. Zhou, and A. Green, Solutions, algorithms and inter-relations for local minimization search geophysical inversion, J. Geophys. Eng., 3 (2006), pp. 101–113.
[24] A. Griewank, Achieving logarithmic growth of temporal and spatial complexity in reverse automatic differentiation, Optim. Methods Softw., 1 (1992), pp. 35–54.
[25] A. Griewank and A. Walther, Algorithm 799: Revolve: An implementation of checkpointing for the reverse or adjoint mode of computational differentiation, ACM Trans. Math. Software, 26 (2000), pp. 19–45. · Zbl 1137.65330
[26] B. Hak and W. A. Mulder, Seismic attenuation imaging with causality, Geophys. J. Int., 184 (2011), pp. 439–451, .
[27] M. Hinze, R. Pinnau, M. Ulbrich, and S. Ulbrich, Optimization with PDE Constraints, Math. Model Theory Appl. 23, Springer, Dordrecht, 2009. · Zbl 1167.49001
[28] K. A. Innanen, Seismic AVO and the inverse Hessian in precritical reflection full waveform inversion, Geophys. J. Int., 199 (2014), pp. 717–734, .
[29] A. Kalogeropoulos, J. van der Kruk, J. Hugenschmidt, S. Busch, and K. Merz, Chlorides and moisture assessment in concrete by GPR full waveform inversion, Near Surf. Geophys., 9 (2011), pp. 277–285.
[30] R. Kamei and R. G. Pratt, Inversion strategies for visco-acoustic waveform inversion, Geophys. J. Int., 194 (2013), pp. 859–894.
[31] A. Klotzsche, J. van der Kruk, G. A. Meles, and H. Vereecken, Crosshole GPR full-waveform inversion of waveguides acting as preferential flow paths within aquifer systems, Geophysics, 77 (2012), pp. H57–H62.
[32] N. Korta, A. Fichtner, and V. Sallares, Block-diagonal approximate Hessian for preconditioning in full waveform inversion, in Expanded Abstracts of the 75th EAGE Conference & Exhibition incorporating SPE EUROPEC 2013, London, 2013.
[33] P. Lailly, The seismic inverse problem as a sequence of before stack migrations, in Conference on Inverse Scattering, Theory and Application, R. Bednar and Weglein, eds., SIAM, Philadelphia, 1983, pp. 206–220.
[34] A. R. Levander, Fourth-order finite-difference P-SV seismograms, Geophysics, 53 (1988), pp. 1425–1436.
[35] D. C. Liu and J. Nocedal, On the limited memory BFGS method for large scale optimization, Math. Programming, 45 (1989), pp. 503–528. · Zbl 0696.90048
[36] H.-P. Liu, D. L. Anderson, and H. Kanamori, Velocity dispersion due to anelasticity; implications for seismology and mantle composition, Geophys. J. Int., 47 (1976), pp. 41–58.
[37] J. Martin, L. C. Wilcox, C. Burstedde, and O. Ghattas, A stochastic Newton MCMC method for large-scale statistical inverse problems with application to seismic inversion, SIAM J. Sci. Comput., 34 (2012), pp. A1460–A1487, . · Zbl 1250.65011
[38] L. Métivier, F. Bretaudeau, R. Brossier, S. Operto, and J. Virieux, Full waveform inversion and the truncated Newton method: Quantitative imaging of complex subsurface structures, Geophys. Prospect., 62 (2014), pp. 1353–1375, .
[39] L. Métivier and R. Brossier, The SEISCOPE optimization toolbox: A large-scale nonlinear optimization library based on reverse communication, Geophysics, 81 (2016), pp. F11–F25.
[40] L. Métivier, R. Brossier, S. Operto, and J. Virieux, Acoustic multi-parameter FWI for the reconstruction of P-wave velocity, density and attenuation: Preconditioned truncated Newton approach, in SEG Technical Program Expanded Abstracts, 2015, pp. 1198–1203.
[41] L. Métivier, R. Brossier, and J. Virieux, Combining asymptotic linearized inversion and full waveform inversion, Geophys. J. Int., 201 (2015), pp. 1682–1703, .
[42] L. Métivier, R. Brossier, J. Virieux, and S. Operto, Full waveform inversion and the truncated Newton method, SIAM J. Sci. Comput., 35 (2013), pp. B401–B437, . · Zbl 1266.86002
[43] J. Minet, S. Lambot, E. C. Slob, and M. Vanclooster, Soil surface water content estimation by full-waveform GPR signal inversion in the presence of thin layers, IEEE Trans. Geosci. Remote Sens., 48 (2010), pp. 1138–1150.
[44] P. Moczo and J. Kristek, On the rheological models used for time-domain methods of seismic wave propagation, Geophys. Res. Lett., 32 (2005), L01306.
[45] J. L. Morales and J. Nocedal, Automatic preconditioning by limited memory quasi-Newton updating, SIAM J. Optim., 10 (2000), pp. 1079–1096, . · Zbl 1020.65019
[46] W. A. Mulder and B. Hak, An ambiguity in attenuation scattering imaging, Geophys. J. Int., 178 (2009), pp. 1614–1624.
[47] S. G. Nash, A survey of truncated Newton methods, J. Comput. Appl. Math., 124 (2000), pp. 45–59. · Zbl 0969.65054
[48] J. Nocedal, Updating quasi-Newton matrices with limited storage, Math. Comp., 35 (1980), pp. 773–782. · Zbl 0464.65037
[49] J. Nocedal and S. J. Wright, Numerical Optimization, 2nd ed., Springer, New York, 2006. · Zbl 1104.65059
[50] S. Operto, R. Brossier, Y. Gholami, L. Métivier, V. Prieux, A. Ribodetti, and J. Virieux, A guided tour of multiparameter full waveform inversion for multicomponent data: From theory to practice, The Leading Edge, 32 (2013), pp. 1040–1054.
[51] S. Operto, A. Miniussi, R. Brossier, L. Combe, L. Métivier, V. Monteiller, A. Ribodetti, and J. Virieux, Efficient 3-D frequency-domain mono-parameter full-waveform inversion of ocean-bottom cable data: Application to Valhall in the visco-acoustic vertical transverse isotropic approximation, Geophys. J. Int., 202 (2015), pp. 1362–1391.
[52] S. Operto, J. Virieux, J. X. Dessa, and G. Pascal, Crustal seismic imaging from multifold ocean bottom seismometer data by frequency domain full waveform tomography: Application to the eastern Nankai trough, J. Geophys. Res., 111 (2006), .
[53] R. E. Plessix, A review of the adjoint-state method for computing the gradient of a functional with geophysical applications, Geophys. J. Int., 167 (2006), pp. 495–503.
[54] R. E. Plessix and C. Perkins, Full waveform inversion of a deep water ocean bottom seismometer dataset, First Break, 28 (2010), pp. 71–78.
[55] R. G. Pratt, C. Shin, and G. J. Hicks, Gauss-Newton and full Newton methods in frequency-space seismic waveform inversion, Geophys. J. Int., 133 (1998), pp. 341–362.
[56] V. Prieux, R. Brossier, Y. Gholami, S. Operto, J. Virieux, O. Barkved, and J. Kommedal, On the footprint of anisotropy on isotropic full waveform inversion: The Valhall case study, Geophys. J. Int., 187 (2011), pp. 1495–1515, .
[57] V. Prieux, R. Brossier, S. Operto, and J. Virieux, Multiparameter full waveform inversion of multicomponent OBC data from Valhall. Part 1: Imaging compressional wavespeed, density and attenuation, Geophys. J. Int., 194 (2013), pp. 1640–1664, .
[58] V. Prieux, R. Brossier, S. Operto, and J. Virieux, Multiparameter full waveform inversion of multicomponent OBC data from Valhall. Part 2: Imaging compressional and shear-wave velocities, Geophys. J. Int., 194 (2013), pp. 1665–1681, .
[59] J. O. A. Robertsson, A numerical free-surface condition for elastic/viscoelastic finite-difference modeling in the presence of topography, Geophysics, 61 (1996), pp. 1921–1934.
[60] F. Santosa and W. W. Symes, Computation of the Hessian for least-squares solutions of inverse problems of reflection seismology, Inverse Problems, 4 (1988), pp. 211–233. · Zbl 0642.65052
[61] C. Shin, S. Jang, and D. J. Min, Improved amplitude preservation for prestack depth migration by inverse scattering theory, Geophys. Prospect., 49 (2001), pp. 592–606.
[62] L. Sirgue, O. I. Barkved, J. Dellinger, J. Etgen, U. Albertin, and J. H. Kommedal, Full waveform inversion: The next leap forward in imaging at Valhall, First Break, 28 (2010), pp. 65–70.
[63] W. Sun and L.-Y. Fu, Two effective approaches to reduce data storage in reverse time migration, Comput. and Geosci., 56 (2013), pp. 69–75.
[64] W. W. Symes, Reverse time migration with optimal checkpointing, Geophysics, 72 (2007), pp. SM213–SM221, .
[65] C. Tape, Q. Liu, A. Maggi, and J. Tromp, Seismic tomography of the southern California crust based on spectral-element and adjoint methods, Geophys. J. Int., 180 (2010), pp. 433–462.
[66] A. Tarantola, Inversion of seismic reflection data in the acoustic approximation, Geophysics, 49 (1984), pp. 1259–1266.
[67] L. A. Thomsen, Weak elastic anisotropy, Geophysics, 51 (1986), pp. 1954–1966.
[68] D. Vigh, K. Jiao, D. Watts, and D. Sun, Elastic full-waveform inversion application using multicomponent measurements of seismic data collection, Geophysics, 79 (2014), pp. R63–R77.
[69] J. Virieux and S. Operto, An overview of full waveform inversion in exploration geophysics, Geophysics, 74 (2009), pp. WCC1–WCC26.
[70] Y. Wang, L. Dong, Y. Liu, and J. Yang, 2D frequency-domain elastic full-waveform inversion using the block-diagonal pseudo-Hessian approximation, Geophysics, 81 (2016), pp. R247–R259.
[71] M. Warner, A. Ratcliffe, T. Nangoo, J. Morgan, A. Umpleby, N. Shah, V. Vinje, I. Stekl, L. Guasch, C. Win, G. Conroy, and A. Bertrand, Anisotropic \(3\)D full-waveform inversion, Geophysics, 78 (2013), pp. R59–R80.
[72] P. Yang, R. Brossier, L. Métivier, and J. Virieux, A review on the systematic formulation of 3D multiparameter full waveform inversion in viscoelastic medium, Geophys. J. Int., 207 (2016), pp. 129–149, .
[73] P. Yang, R. Brossier, L. Métivier, and J. Virieux, Wavefield reconstruction in attenuating media: A checkpointing-assisted reverse-forward simulation method, Geophysics, 81 (2016), pp. R349–R362, .
[74] P. Yang, R. Brossier, and J. Virieux, Downsampling plus interpolation for wavefield reconstruction by reverse propagation, in 78th EAGE Conference & Exhibition Expanded Abstracts, 2016, SBT5 08.
[75] P. Yang, R. Brossier, and J. Virieux, Wavefield reconstruction from significantly decimated boundaries, Geophysics, 80 (2016), pp. T197–T209, .
[76] W. Zhou, R. Brossier, S. Operto, and J. Virieux, Full waveform inversion of diving & reflected waves for velocity model building with impedance inversion based on scale separation, Geophys. J. Int., 202 (2015), pp. 1535–1554.
[77] H. Zhu, E. Bozdağ, D. Peter, and J. Tromp, Structure of the European upper mantle revealed by adjoint tomography, Nat. Geosci., 5 (2012), pp. 493–498, .
[78] H. Zhu, E. Bozdağ, and J. Tromp, Seismic structure of the European upper mantle based on adjoint tomography, Geophys. J. Int., 201 (2015), pp. 18–52.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.