@Article{CiCP-28-1,
author = {Morten, Jakobsen 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 = {<p style="text-align: justify;">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&#39;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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2018-0197},
url = {https://global-sci.com/article/79683/transition-operator-approach-to-seismic-full-waveform-inversion-in-arbitrary-anisotropic-elastic-media}
}