Transition operator approach to full waveform inversion of anisotropic elastic media

0508959 - GFÚ 2021 RIV CN eng J - Journal Article
Jakobsen, M. - Pšenčík, Ivan - Iversen, E. - Ursin, B.
Transition operator approach to full waveform inversion of anisotropic elastic media.
Communications in Computational Physics. Roč. 28, č. 1 (2020), s. 297-327. ISSN 1815-2406. E-ISSN 1991-7120
Institutional support: RVO:67985530
Keywords : waveform inversion * time-lapse seismic * seismic inverse scattering * terget-oriented inversion * Gaussian beam based Greens function
OECD category: Volcanology
Impact factor: 3.246, year: 2020
Method of publishing: Open access
http://www.global-sci.com/intro/article_detail/cicp/16838.html

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 Frechet 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 crosstalk 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.
Permanent Link: http://hdl.handle.net/11104/0299772