Most existing implementations of full-waveform inversion (FWI) are limited to acoustic approximations. In this paper, we present an algorithm for time-domain elastic FWI in laterally heterogeneous VTI (transversely isotropic with a vertical symmetry axis) media. The adjoint-state method is employed to derive the gradients of the objective function with respect to the stiffness coefficients and then to a chosen set of VTI parameters. To test the algorithm, we introduce Gaussian anomalies in the Thomsen parameters of a homogeneous VTI medium and perform 2D FWI of multicomponent transmission data for two different model parameterizations. To analyze the sensitivity of the objective function to the model parameters, the Fréchet kernel of FWI is obtained by linearizing the elastic wave equation using the Born approximation and employing the asymptotic Green’s function. The amplitude of the kernel (“radiation pattern”) yields the angle-dependent energy scattered by a perturbation in a certain model parameter. Then we convert the general expressions into simple approximations for the radiation patterns of P- and SV-waves in VTI media. These analytic developments provide valuable insight into the potential of multicomponent elastic FWI and help explain the numerical results for models with Gaussian anomalies in the VTI parameters.
Bibliographical noteKAUST Repository Item: Exported on 2022-05-31
Acknowledgements: We are grateful to the members of the A(nisotropy) team at CWP, Tariq Alkhalifah (KAUST), and Andreas Ruger (Landmark Graphics) for fruitful discussions. Research reported in this publication was supported by the Consortium Project on Seismic Inverse Methods for Complex Structures at CWP, the CIMMM Project of the Unconventional Natural Gas Institute at CSM, and competitive research funding from King Abdullah University of Science and Technology (KAUST). The reproducible numeric examples in this paper are generated with the Madagascar open-source software package freely available from http://www.ahay.org.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.