Volume 28, Issue 1
Transition Operator Approach to Seismic Full-Waveform Inversion in Arbitrary Anisotropic Elastic Media

Morten Jakobsen, Ivan Pšenčík, Einar Iversen & Bjørn Ursin

Commun. Comput. Phys., 28 (2020), pp. 297-327.

Published online: 2020-05

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  • Abstract

We generalize the existing distorted Born iterative T-matrix (DBIT) method to seismic full-waveform inversion (FWI) based on the scalar wave equation, so that it can be used for seismic FWI in arbitrary anisotropic elastic media with variable mass densities and elastic stiffness tensors. The elastodynamic wave equation for an arbitrary anisotropic heterogeneous medium is represented by an integral equation of the Lippmann-Schwinger type, with a 9-dimensional wave state (displacement-strain) vector. We solve this higher-dimensional Lippmann-Schwinger equation using a transition operator formalism used in quantum scattering theory. This allows for domain decomposition and novel variational estimates. The tensorial nonlinear inverse scattering problem is solved iteratively by using an expression for the Fréchet derivatives of the scattered wavefield with respect to elastic stiffness tensor fields in terms of modified Green's functions and wave state vectors that are updated after each iteration. Since the generalized DBIT method is consistent with the Gauss-Newton method, it incorporates approximate Hessian information that is essential for the reduction of multi-parameter cross-talk effects. The DBIT method is implemented efficiently using a variant of the Levenberg-Marquard method, with adaptive selection of the regularization parameter after each iteration. In a series of numerical experiments based on synthetic waveform data for transversely isotropic media with vertical symmetry axes, we obtained a very good match between the true and inverted models when using the traditional Voigt parameterization. This suggests that the effects of cross-talk can be sufficiently reduced by the incorporation of Hessian information and the use of suitable regularization methods. Since the generalized DBIT method for FWI in anisotropic elastic media is naturally target-oriented, it may be particularly suitable for applications to seismic reservoir characterization and monitoring. However, the theory and method presented here is general.

  • Keywords

Waveform inversion, time-lapse seismic, seismic inverse scattering, target-oriented inversion, Green's function.

  • AMS Subject Headings

81U40, 74J25, 74J20, 45Dxx

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

Morten.Jakobsen@uib.no (Morten Jakobsen)

ip@ig.cas.cz (Ivan Pšenčík)

Einar.Iversen@uib.no (Einar Iversen)

Bjorn.Ursin@ntnu.no (Bjørn Ursin)

  • BibTex
  • RIS
  • TXT
@Article{CiCP-28-297, author = {Jakobsen , Morten and Pšenčík , Ivan and Iversen , Einar and Ursin , Bjørn }, title = {Transition Operator Approach to Seismic Full-Waveform Inversion in Arbitrary Anisotropic Elastic Media}, journal = {Communications in Computational Physics}, year = {2020}, volume = {28}, number = {1}, pages = {297--327}, abstract = {

We generalize the existing distorted Born iterative T-matrix (DBIT) method to seismic full-waveform inversion (FWI) based on the scalar wave equation, so that it can be used for seismic FWI in arbitrary anisotropic elastic media with variable mass densities and elastic stiffness tensors. The elastodynamic wave equation for an arbitrary anisotropic heterogeneous medium is represented by an integral equation of the Lippmann-Schwinger type, with a 9-dimensional wave state (displacement-strain) vector. We solve this higher-dimensional Lippmann-Schwinger equation using a transition operator formalism used in quantum scattering theory. This allows for domain decomposition and novel variational estimates. The tensorial nonlinear inverse scattering problem is solved iteratively by using an expression for the Fréchet derivatives of the scattered wavefield with respect to elastic stiffness tensor fields in terms of modified Green's functions and wave state vectors that are updated after each iteration. Since the generalized DBIT method is consistent with the Gauss-Newton method, it incorporates approximate Hessian information that is essential for the reduction of multi-parameter cross-talk effects. The DBIT method is implemented efficiently using a variant of the Levenberg-Marquard method, with adaptive selection of the regularization parameter after each iteration. In a series of numerical experiments based on synthetic waveform data for transversely isotropic media with vertical symmetry axes, we obtained a very good match between the true and inverted models when using the traditional Voigt parameterization. This suggests that the effects of cross-talk can be sufficiently reduced by the incorporation of Hessian information and the use of suitable regularization methods. Since the generalized DBIT method for FWI in anisotropic elastic media is naturally target-oriented, it may be particularly suitable for applications to seismic reservoir characterization and monitoring. However, the theory and method presented here is general.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2018-0197}, url = {http://global-sci.org/intro/article_detail/cicp/16838.html} }
TY - JOUR T1 - Transition Operator Approach to Seismic Full-Waveform Inversion in Arbitrary Anisotropic Elastic Media AU - Jakobsen , Morten AU - Pšenčík , Ivan AU - Iversen , Einar AU - Ursin , Bjørn JO - Communications in Computational Physics VL - 1 SP - 297 EP - 327 PY - 2020 DA - 2020/05 SN - 28 DO - http://doi.org/10.4208/cicp.OA-2018-0197 UR - https://global-sci.org/intro/article_detail/cicp/16838.html KW - Waveform inversion, time-lapse seismic, seismic inverse scattering, target-oriented inversion, Green's function. AB -

We generalize the existing distorted Born iterative T-matrix (DBIT) method to seismic full-waveform inversion (FWI) based on the scalar wave equation, so that it can be used for seismic FWI in arbitrary anisotropic elastic media with variable mass densities and elastic stiffness tensors. The elastodynamic wave equation for an arbitrary anisotropic heterogeneous medium is represented by an integral equation of the Lippmann-Schwinger type, with a 9-dimensional wave state (displacement-strain) vector. We solve this higher-dimensional Lippmann-Schwinger equation using a transition operator formalism used in quantum scattering theory. This allows for domain decomposition and novel variational estimates. The tensorial nonlinear inverse scattering problem is solved iteratively by using an expression for the Fréchet derivatives of the scattered wavefield with respect to elastic stiffness tensor fields in terms of modified Green's functions and wave state vectors that are updated after each iteration. Since the generalized DBIT method is consistent with the Gauss-Newton method, it incorporates approximate Hessian information that is essential for the reduction of multi-parameter cross-talk effects. The DBIT method is implemented efficiently using a variant of the Levenberg-Marquard method, with adaptive selection of the regularization parameter after each iteration. In a series of numerical experiments based on synthetic waveform data for transversely isotropic media with vertical symmetry axes, we obtained a very good match between the true and inverted models when using the traditional Voigt parameterization. This suggests that the effects of cross-talk can be sufficiently reduced by the incorporation of Hessian information and the use of suitable regularization methods. Since the generalized DBIT method for FWI in anisotropic elastic media is naturally target-oriented, it may be particularly suitable for applications to seismic reservoir characterization and monitoring. However, the theory and method presented here is general.

Morten Jakobsen, Ivan Pšenčík, Einar Iversen & Bjørn Ursin. (2020). Transition Operator Approach to Seismic Full-Waveform Inversion in Arbitrary Anisotropic Elastic Media. Communications in Computational Physics. 28 (1). 297-327. doi:10.4208/cicp.OA-2018-0197
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