Elastic full waveform inversion based on mode decomposition: the approach and mechanism

Abstract

Elastic full waveform inversion (EFWI) aims to reduce the misfit between recorded and modelled multicomponent seismic data for deducing a detailed model of elastic parameters in the subsurface. Because the explicit computation and inversion of the Hessian matrix is extremely resource intensive, a gradient-based (rather than Hessian-based) minimization is generally applied for large-scale applications. However, the multiparameter trade-off effects cause cross-talks in the computed gradients and thus severely affect the convergence and the quality of the inverted model. Recently, preconditioning the gradients based on elastic wave mode decomposition has been suggested for mitigating the parameter trade-offs in the EFWI process. In this paper, we propose a mode decomposition (MD)-based EFWI approach in which the preconditioned gradients are obtained through the cross-correlation of the forward and decomposed adjoint wavefields in the time domain. Based on the decomposed Frechét derivatives, we explain the mechanism of this approach through analyses of Hessian and resolution matrices and comparison with the Gauss–Newton gradients. Numerical examples of a simple fluid-saturated model and the Marmousi-II model demonstrate that the MD-based preconditioned conjugate-gradient approach can mitigate the trade-off between the P- and S-wave velocities and achieve fast convergence without any Hessian-involved calculations.