Square-root variable metric based elastic full-waveform inversion—Part 2: uncertainty estimation

The authors are grateful to editor Jean Virieux and reviewer Andreas Fichtner and an anonymous reviewer for improving the initial manuscript. The authors are grateful to Carl Tape for inspiring discussions and valuable inputs to improve the manuscript. This work was supported by the King Abdullah University of Science & Technology (KAUST) Office of Sponsored Research (OSR) under award No. UAPN#2605-CRG4. Computational resources were provided by the Information Technology Division and Extreme Computing Research Center (ECRC) at KAUST.

[1]  M. Sambridge,et al.  Seismic tomography with the reversible jump algorithm , 2009 .

[2]  Qinya Liu,et al.  Tomography, Adjoint Methods, Time-Reversal, and Banana-Doughnut Kernels , 2004 .

[3]  G. McMechan,et al.  Estimation of resolution and covariance for large matrix inversions , 1995 .

[4]  G. Evensen Sequential data assimilation with a nonlinear quasi‐geostrophic model using Monte Carlo methods to forecast error statistics , 1994 .

[5]  M. Morf,et al.  Square-root algorithms for least-squares estimation , 1975 .

[6]  Gary Martin,et al.  Marmousi2 An elastic upgrade for Marmousi , 2006 .

[7]  Jeroen Tromp,et al.  SeisFlows - Flexible waveform inversion software , 2018, Comput. Geosci..

[8]  Stephen J. Wright,et al.  Numerical Optimization (Springer Series in Operations Research and Financial Engineering) , 2000 .

[9]  Ezio Faccioli,et al.  Spectral-domain decomposition methods for the solution of acoustic and elastic wave equations , 1996 .

[10]  Andreas Fichtner,et al.  Hessian kernels of seismic data functionals based upon adjoint techniques , 2011 .

[11]  M. Sambridge,et al.  Seismic Tomography and the Assessment of Uncertainty , 2014 .

[12]  Mark Noble,et al.  Robust elastic nonlinear waveform inversion: Application to real data , 1990 .

[13]  A. Tarantola A strategy for nonlinear elastic inversion of seismic reflection data , 1986 .

[14]  R. E. Kalman,et al.  A New Approach to Linear Filtering and Prediction Problems , 2002 .

[15]  Jon F. Claerbout,et al.  Multidimensional recursive filter preconditioning in geophysical estimation problems , 2003 .

[16]  Géza Seriani,et al.  Spectral element method for acoustic wave simulation in heterogeneous media , 1994 .

[17]  Ludovic Métivier,et al.  Full Waveform Inversion and the Truncated Newton Method , 2013, SIAM J. Sci. Comput..

[18]  Ru-Shan Wu,et al.  Scattering characteristics of elastic waves by an elastic heterogeneity , 1985 .

[19]  B. Kennett,et al.  Subspace methods for large inverse problems with multiple parameter classes , 1988 .

[20]  Jeroen Tromp,et al.  Seismic waveform inversion best practices: regional, global, and exploration test cases , 2016 .

[21]  Jean Virieux,et al.  An overview of full-waveform inversion in exploration geophysics , 2009 .

[22]  A. Tarantola Inversion of seismic reflection data in the acoustic approximation , 1984 .

[23]  L. Métivier,et al.  Ensemble-based uncertainty estimation in Full Waveform Inversion , 2017, Geophysical Journal International.

[24]  A. Fichtner,et al.  Probabilistic full waveform inversion based on tectonic regionalization - development and application to the Australian upper mantle , 2013 .

[25]  D. Hull,et al.  Square-root variable-metric methods for minimization , 1976 .

[26]  Meijian An,et al.  A simple method for determining the spatial resolution of a general inverse problem , 2012 .

[27]  C. Tape,et al.  Square-root variable metric based elastic full-waveform inversion – Part 1: theory and validation , 2019, Geophysical Journal International.

[28]  O. Ghattas,et al.  A Bayesian approach to estimate uncertainty for full-waveform inversion using a priori information from depth migration , 2016 .

[29]  Azzam Haidar,et al.  Seismic wave modeling for seismic imaging , 2009 .

[30]  Andreas Fichtner,et al.  Resolution analysis in full waveform inversion , 2011 .

[31]  M. Sambridge,et al.  Automatic differentiation in geophysical inverse problems , 2005 .

[32]  Albert Tarantola,et al.  Inverse problem theory - and methods for model parameter estimation , 2004 .

[33]  J. Scales,et al.  Bayesian seismic waveform inversion: Parameter estimation and uncertainty analysis , 1998 .

[34]  Nathan Halko,et al.  Finding Structure with Randomness: Probabilistic Algorithms for Constructing Approximate Matrix Decompositions , 2009, SIAM Rev..

[35]  W. Williamson Square Root Variable Metric Method for Function Minimization , 1975 .

[36]  Per-Gunnar Martinsson,et al.  Randomized algorithms for the low-rank approximation of matrices , 2007, Proceedings of the National Academy of Sciences.

[37]  C. Bunks,et al.  Multiscale seismic waveform inversion , 1995 .

[38]  T. Leeuwen,et al.  Resolution analysis by random probing , 2015 .

[39]  Mrinal K. Sen,et al.  2D Full-Waveform Inversion and Uncertainty Estimation using the Reversible Jump Hamiltonian Monte Carlo , 2017 .

[40]  A. Tarantola,et al.  Generalized Nonlinear Inverse Problems Solved Using the Least Squares Criterion (Paper 1R1855) , 1982 .

[41]  Albert Tarantola,et al.  Monte Carlo sampling of solutions to inverse problems , 1995 .

[42]  Andrey Vlasenko,et al.  The efficiency of geophysical adjoint codes generated by automatic differentiation tools , 2016, Comput. Phys. Commun..

[43]  Verification of gradient and Hessian computation for full wavefield inversion using automatic differentiation. , 2010 .

[44]  A. Fichtner,et al.  Resolution tests revisited: The power of random numbers , 2013 .

[45]  A. Tarantola,et al.  Waveform inversion of marine reflection seismograms for P impedance and Poisson's ratio , 1996 .

[46]  Roger Fletcher,et al.  A Rapidly Convergent Descent Method for Minimization , 1963, Comput. J..

[47]  Klaus Mosegaard,et al.  MONTE CARLO METHODS IN GEOPHYSICAL INVERSE PROBLEMS , 2002 .

[48]  R. Pratt Seismic waveform inversion in the frequency domain; Part 1, Theory and verification in a physical scale model , 1999 .

[49]  D. Komatitsch,et al.  Introduction to the spectral element method for three-dimensional seismic wave propagation , 1999 .

[50]  J. Virieux,et al.  Bessel smoothing filter for spectral-element mesh , 2017 .

[51]  D. Nichols,et al.  Model‐uncertainty quantification in seismic tomography: method and applications , 2013 .

[52]  D. Komatitsch,et al.  The spectral element method: An efficient tool to simulate the seismic response of 2D and 3D geological structures , 1998, Bulletin of the Seismological Society of America.

[53]  Guy Chavent,et al.  About the stability of the inverse problem in 1-D wave equations—application to the interpretation of seismic profiles , 1979 .

[54]  Mike Warner,et al.  Adaptive waveform inversion: Theory , 2014 .

[55]  James Martin,et al.  A Computational Framework for Infinite-Dimensional Bayesian Inverse Problems Part I: The Linearized Case, with Application to Global Seismic Inversion , 2013, SIAM J. Sci. Comput..

[56]  Carolo Friederico Gauss Theoria Motus Corporum Coelestium in Sectionibus Conicis Solem Ambientium , 2014 .