Skip to main content Accessibility help
×
Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-23T09:09:21.207Z Has data issue: false hasContentIssue false

15 - Solving Larger Seismic Inverse Problems with Smarter Methods

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

Published online by Cambridge University Press:  20 June 2023

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: The continuously increasing quantity and quality of seismic waveform data carry the potential to provide images of the Earth’s internal structure with unprecedented detail. Harnessing this rapidly growing wealth of information, however, constitutes a formidable challenge. While the emergence of faster supercomputers helps to accelerate existing algorithms, the daunting scaling properties of seismic inverse problems still demand the development of more efficient solutions. The diversity of seismic inverse problems – in terms of scientific scope, spatial scale, nature of the data, and available resources – precludes the existence of a silver bullet. Instead, efficiency derives from problem adaptation. Within this context, this chapter describes a collection of methods that are smart in the sense of exploiting specific properties of seismic inverse problems, thereby increasing computational efficiency and usable data volumes, sometimes by orders of magnitude. These methods improve different aspects of a seismic inverse problem, for instance, by harnessing data redundancies, adapting numerical simulation meshes to prior knowledge of wavefield geometry, or permitting long-distance moves through model space for Monte Carlo sampling.

Type
Chapter
Information
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

Afanasiev, M., Boehm, C., van Driel, M. et al. (2019). Modular and flexible spectral-element waveform modelling in two and three dimensions. Geophysical Journal International, 216, 1675–92.Google Scholar
Afanasiev, M. V., Pratt, R. G., Kamei, R., and McDowell, G. (2014). Waveform-based simulated annealing of crosshole transmission data: A semi-global method for estimating seismic anisotropy. Geophysical Journal International, 199, 1586–607.Google Scholar
Ajo-Franklin, J. B. (2009). Optimal experiment design for time-lapse traveltime tomography. Geophysics, 74, Q27Q40.Google Scholar
Backus, G. E., and Gilbert, F. (1968). The resolving power of gross Earth data. Geophysical Journal of the Royal Astronomical Society, 16, 169205.Google Scholar
Backus, G. E., and Gilbert, F. (1970). Uniqueness in the inversion of inaccurate gross Earth data. Philosophical Transactions of the Royal Society A, 266(1173), 123–92.Google Scholar
Bamberger, A., Chavent, G., and Lailly, P. (1977). Une application de la théorie du contrôle à un problème inverse sismique. Annales Geophysicae, 33, 183200.Google Scholar
Bamberger, A., Chavent, G., Hemons, C., and Lailly, P. (1982). Inversion of normal incidence seismograms. Geophysics, 47, 757–70.Google Scholar
Bayes, T. (1764). An essay toward solving a problem in the doctrine of chances. Philosophical Transactions of the Royal Society of London, 53, 370-418.Google Scholar
Bernauer, M., Fichtner, A., and Igel, H. (2014). Optimal observables for multi-parameter seismic tomography. Geophysical Journal International, 198, 1241–54.Google Scholar
Betancourt, M. (2017). A conceptual introduction to Hamiltonian Monte Carlo. arXiv:1701.02434 [stat.ME].Google Scholar
Blom, N., Boehm, C., and Fichtner, A. (2017). Synthetic inversion for density using seismic and gravity data. Geophysical Journal International, 209, 1204–20.Google Scholar
Bodin, T., Sambridge, M., Rawlinson, N., and Arroucau, P. (2012). Transdimensional tomography with unknown data noise. Geophysical Journal International, 189, 1536–56.Google Scholar
Bozdag, E., Peter, D., Lefebvre, M. et al. (2016). Global adjoint tomography: First-generation model. Geophysical Journal International, 207, 1739–66.Google Scholar
Bui-Thanh, T., Ghattas, O., Martin, J., and Stadler, G. (2013). A computational framework for infinite-dimensional Bayesian inverse problems. Part I: The linearized case, with application to global seismic inversion. SIAM Journal on Scientific Computing, 35, A2494A2523.Google Scholar
Calvetti, D., and Somersalo, E. (2017). Inverse problems: From regularization to Bayesian inference. Computational Statistics, 10(3). http://doi.org/10.1002/wics.1427.Google Scholar
Capdeville, Y., Guillot, L., and Marigo, J. J. (2010). 2-D non-periodic homogenization to upscale elastic media for P–SV waves. Geophysical Journal International, 182, 903–22.Google Scholar
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
Chen, P., Jordan, T. H., and Zhao, L. (2007a). Full 3D waveform tomography: A comparison between the scattering-integral and adjoint-wavefield methods. Geophysical Journal International, 170, 175–81.CrossRefGoogle Scholar
Chen, P., Zhao, L., and Jordan, T. H. (2007b). Full 3D tomography for the crustal structure of the Los Angeles region. Bulletin of the Seismological Society of America, 97, 1094–120.Google Scholar
Chib, S., and Greenberg, E. (1995). Understanding the Metropolis-Hastings algorithm. American Statistician, 49, 327–35.Google Scholar
Choi, Y., and Alkhalifah, T. (2011). Source-independent time-domain waveform inversion using convolved wavefields: Application to the encoded multisource waveform inversion. Geophysics, 76, R125R134.Google Scholar
Clouzet, P., Masson, Y., and Romanowicz, B. (2018). Box tomography: First application to the imaging of upper mantle shear velocity and radial anisotropy structure beneath the north American continent. Geophysical Journal International, 213, 1849–75.Google Scholar
Curtis, A. (1999). Optimal experiment design: Cross-borehole tomographic examples. Geophysical Journal International, 136, 637–50.Google Scholar
de la Puente, J., Dumbser, M., Käser, M., and Igel, H. (2007). An arbitrary high-order discontinuous Galerkin method for elastic waves on unstructured methods. IV. Anisotropy. Geophysical Journal International, 169, 1210–28.Google Scholar
Djikpesse, H. A., Khodja, M. R., Prange, M. D., Duchenne, S., and Menkiti, H. (2012). Bayesian survey design to optimize resolution in waveform inversion. Geophysics, 77, R81R93.Google Scholar
Duane, S., Kennedy, A. D., Pendleton, B. J., and Roweth, D. (1987). Hybrid Monte Carlo. Physics Letters B, 195, 216–22.Google Scholar
Dziewonski, A. M., and Anderson, D. L. (1981). Preliminary reference Earth model. Physics of the Earth and Planetary Interiors, 25, 297356.Google Scholar
Fichtner, A., Bunge, H.-P., and Igel, H. (2006). The adjoint method in seismology – I. Theory. Physics of the Earth and Planetary Interiors, 157, 105–23.Google Scholar
Fichtner, A., Kennett, B. L. N., Igel, H., and Bunge, H.-P. (2009). Full seismic waveform tomography for upper-mantle structure in the Australasian region using adjoint methods. Geophysical Journal International, 179, 1703–25.Google Scholar
Fichtner, A. (2010). Full seismic waveform modeling and inversion. Heidelberg: Springer.Google Scholar
Fichtner, A., and Trampert, J. (2011). Resolution analysis in full waveform inversion. Geophysical Journal International, 187, 1604–24.Google Scholar
Fichtner, A. (2021). Lecture Notes on Inverse Theory. Cambridge: Cambridge Open Engage, http://doi.org/10.33774/coe-2021-qpq2j.Google Scholar
Fichtner, A., van Herwaarden, D.-P., Afanasiev, M. et al. (2018). The Collaborative Seismic Earth Model: Generation I. Geophysical Research Letters, 45, 4007–16.CrossRefGoogle Scholar
Fichtner, A., and van Leeuwen, T. (2015). Resolution analysis by random probing. Journal of Geophysical Research: Solid Earth, 120, 5549–73.Google Scholar
Gebraad, L., Boehm, C., and Fichtner, A. (2020). Bayesian elastic full‐waveform inversion using Hamiltonian Monte Carlo. Journal of Geophysical Research: Solid Earth, 125, e2019JB018428.Google Scholar
Green, P. J. (1995). Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika, 82, 711–32.Google Scholar
Hardt, M., and Scherbaum, F. (1994). The design of optimum networks for aftershock recordings. Geophysical Journal International, 117, 716–26.Google Scholar
Huang, Y., and Schuster, G. T. (2018). Full‐waveform inversion with multisource frequency selection of marine streamer data. Geophysical Prospecting, 66, 1243–57.Google Scholar
Hunziker, J., Laloy, E., and Linde, N. (2019). Bayesian full-waveform tomography with application to crosshole ground penetrating radar data. Geophysical Journal International, 218, 913–31.Google Scholar
Igel, H. (2016). Computational Seismology: A Practical Introduction. Cambridge: Cambridge University Press.Google Scholar
Kijko, A. (1977). An algorithm for the optimum distribution of a regional seismic network – I. Pure and Applied Geophysics, 115, 9991009.Google Scholar
Komatitsch, D., and Vilotte, J.-P. (1998). The spectral element method: An effective tool to simulate the seismic response of 2D and 3D geological structures. Bulletin of the Seismological Society of America, 88, 368–92.Google Scholar
Käufl, P., Fichtner, A., and Igel, H. (2013). Probabilistic full waveform inversion based on tectonic regionalisation: Development and application to the Australian upper mantle. Geophysical Journal International, 193, 437–51.Google Scholar
Kotsi, P., Malcolm, A., and Ely, G. (2020). Time-lapse full-waveform inversion using Hamiltonian Monte Carlo: A proof of concept. SEG Technical Program Expanded Abstracts, 845–49.CrossRefGoogle Scholar
Krampe, V., Edme, P., and Maurer, H. (2021). Optimized experimental design for seismic full waveform inversion: A computationally efficient method including a flexible implementation of acquisition costs. Geophysical Prospecting, 69, 152–66.Google Scholar
Krebs, J. R., Anderson, J. E., Hinkley, D. et al. (2009). Fast full-wavefield seismic inversion using encoded sources. Geophysics, 74, WCC177–WCC188.Google Scholar
Krebs, J. R., Cha, Y. H., Lee, S. et al. ExxonMobil Upstream Research Co (2018). Orthogonal Source and Receiver Encoding. U.S. Patent 10,012,745.Google Scholar
Kullback, S., and Leibler, R. A. (1951). On information and sufficiency. Annals of Mathematical Statistics, 22, 7986.Google Scholar
Kuo, C., and Romanowicz, B. (2002). On the resolution of density anomalies in the Earth’s mantle using spectral fitting of normal mode data. Geophysical Journal International, 150, 162–79.CrossRefGoogle Scholar
Leng, K., Nissen-Meyer, T., and van Driel, M. (2016). Efficient global wave propagation adapted to 3-D structural complexity: A pseudospectral/spectral-element approach. Geophysical Journal International, 207, 1700–21.Google Scholar
Liu, Q., and Gu, Y. (2012). Seismic imaging: From classical to adjoint tomography. Tectonophysics, 566–567, 3166.Google Scholar
Liu, Q., and Peter, D. (2019). Square-root variable metric based elastic full-waveform inversion. Part 2: Uncertainty estimation. Geophysical Journal International, 218(2), 1100–20.Google Scholar
Liu, Q., and Wang, D. (2016). Stein variational gradient descent: A general purpose Bayesian inference algorithm. Advances in Neural Information Processing Systems, 2378–86. arXiv:1608.04471.Google Scholar
Liu, Q., Peter, D., and Tape, C. (2019). Square-root variable metric based elastic full-waveform inversion. Part 1: Theory and validation. Geophysical Journal International, 218(2), 1121–35.Google Scholar
Masson, Y., and Romanowicz, B. (2017). Fast computation of synthetic seismograms within a medium containing remote localized perturbations: A numerical solution to the scattering problem. Geophysical Journal International, 218, 674–92.Google Scholar
Maurer, H., Nuber, A., Martiartu, N. K. et al. (2017). Optimized experimental design in the context of seismic full waveform inversion and seismic waveform imaging. In Nielsen, L., ed., Advances in Geophysics, vol. 58. Cambridge, MA: Academic Press, pp. 145.Google Scholar
Malinverno, A. (2002). Parsimonious Bayesian Markov chain Monte Carlo inversion in a nonlinear geophysical problem. Geophysical Journal International, 151, 675–88.CrossRefGoogle Scholar
Moczo, P., Kristek, J., Vavrycuk, V., Archuleta, R., and Halada, L. (2002). 3D heterogeneous staggered-grid finite-difference modeling of seismic motion with volume harmonic and arithmetic averaging of elastic moduli. Bulletin of the Seismological Society of America, 92, 3042–66.Google Scholar
Mosegaard, K. (2012). Limits to nonlinear inversion. In Jónasson, K., ed., Applied Parallel and Scientific Computing, Berlin: Springer, pp. 1121.Google Scholar
Neal, R. M. (2011). MCMC using Hamiltonian dynamics. In Brooks, S., Gelman, A., Jones, G., and Meng, X.-L., eds., Handbook of Markov chain Monte Carlo. New York: Chapman and Hall, pp. 113–62.Google Scholar
Plessix, R.-E. (2006). A review of the adjoint-state method for computing the gradient of a functional with geophysical applications. Geophysical Journal International, 167, 495503.Google Scholar
Rabinowitz, N., and Steinberg, D. M. (1990). Optimal configuration of a seismographic network: A statistical approach. Bulletin of the Seismological Society of America, 80, 187–96.Google Scholar
Resovsky, J., and Trampert, J. (2002). Reliable mantle density error bars: An application of the Neighbourhood Algorithm to normal-mode and surface wave data. Geophysical Journal International, 150, 665–72.Google Scholar
Romero, L. A., Ghiglia, D. C., Ober, C. C., and Morton, S. A. (2000). Phase encoding of shot records in prestack migration. Geophysics, 65, 426–36.Google Scholar
Ronchi, C., Iacono, R., and Paolucci, P. S. (1996). The ‘cubed sphere’: A new method for the solution of partial differential equations in spherical geometry. Journal of Computational Physics, 124, 93114.Google Scholar
Sambridge, M. S., Bodin, T., Gallagher, K., and Tkalcic, H. (2013). Transdimensional inference in the geosciences. Philosophical Transactions of the Royal Society A, 371, 20110547.Google Scholar
Sambridge, M. S., Gallagher, K., Jackson, A., and Rickwood, P. (2006). Trans-dimensional inverse problems, model comparison, and the evidence. Geophysical Journal International, 167, 528–42.Google Scholar
Schiemenz, A., and Igel, H. (2013). Accelerated 3-D full-waveform inversion using simultaneously encoded sources in the time domain: Application to Valhall ocean-bottom cable data. Geophysical Journal International, 195, 1970–88.CrossRefGoogle Scholar
Sieminski, A., Trampert, J., and Tromp, J. (2009). Principal component analysis of anisotropic finite-frequency kernels. Geophysical Journal International, 179, 1186-98.Google Scholar
Sirgue, L., and Pratt, R. G. (2004). Efficient waveform inversion and imaging: A strategy for selecting temporal frequencies. Geophysics, 69, 231–48.Google Scholar
Sirgue, L., Barkved, O. I., Dellinger, J. et al, (2010). Full-waveform inversion: The next leap forward in imaging at Valhall. First Break, 28, 6570.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. (1988). Theoretical background for the inversion of seismic waveforms, including elasticity and attenuation. Pure and Applied Geophysics, 128, 365–99.Google Scholar
Tarantola, A. (2005). Inverse Problem Theory and Methods for Model Parameter Estimation, 2nd ed. Philadelphia, PA: Society for Industrial and Applied Mathematics.Google Scholar
Thrastarson, S., van Driel, M., Krischer, L. et al. (2020). Accelerating numerical wave propagation by wavefield adapted meshes. Part II: full-waveform inversion. Geophysical Journal International, 221, 1591–604.Google Scholar
Thrastarson, S., van Herwaarden, D.-P. and Fichtner, A. (2021). Inversionson: Fully Automated Seismic Waveform Inversions. EarthArXiv, http://doi.org/10.31223/X5F31V.Google Scholar
Thrastarson, S., van Herwaarden, D.-P., Krischer, L. et al. (2022). Data-adaptive global full-waveform inversion. Geophysical Journal International, 230, 1374–93, https://doi.org/10.1093/gji/ggac122.Google Scholar
Tromp, J., Tape, C., and Liu, Q. (2005). Seismic tomography, adjoint methods, time reversal and banana-doughnut kernels. Geophysical Journal International, 160, 195216.CrossRefGoogle Scholar
Tromp, J., and Bachmann, E. (2019). Source encoding for adjoint tomography. Geophysical Journal International, 218, 2019–44.Google Scholar
van Driel, M., Boehm, C., Krischer, L., and Afanasiev, M. (2020). Accelerating numerical wave propagation using wavefield adapted meshes. Part I: forward and adjoint modelling. Geophysical Journal International, 221, 1580–90.Google Scholar
van Herwaarden, D.-P., Boehm, C., Afanasiev, M. et al. (2020). Accelerated full-waveform inversion using dynamic mini-batches. Geophysical Journal International, 221, 1427–38.Google Scholar
van Herwaarden, D.-P., Afanasiev, M., Thrastarson, S., and Fichtner, A. (2021). Evolutionary full-waveform inversion. Geophysical Journal International, 224, 306–11.Google Scholar
van Leeuwen, T., and Herrmann, F. J. (2013). Fast waveform inversion without source‐encoding. Geophysical Prospecting, 61, 1019.Google Scholar
Virieux, J. (1986). P-SV wave propagation in heterogeneous media: Velocity-stress finite difference method. Geophysics, 51, 889901.Google Scholar
Virieux, J., and Operto, S. (2009). An overview of full waveform inversion in exploration geophysics. Geophysics, 74, WCC127–WCC152.Google Scholar
Visser, G., Guo, P., and Saygin, E. (2019). Bayesian transdimensional seismic full-waveform inversion with a dipping layer parameterization. Geophysical Journal International, 84(6), R845R858.Google Scholar
Woodhouse, J. H., and Dziewonski, A. M. (1984). Mapping the upper mantle: Three-dimensional modeling of Earth structure by inversion of seismic waveforms. Journal of Geophysical Research: Solid Earth, 89, 5953–86.Google Scholar
Wolpert, D. H., and Macready, W. G. (1997). No Free Lunch theorems for optimization. IEEE Transactions on Evolutionary Computation, 1, 6788.CrossRefGoogle 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, 1659–81.Google Scholar
Zhang, X., and Curtis, A. (2020). Variational full-waveform inversion. Geophysical Journal International, 222, 406–11.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] 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
×