On the time-domain full waveform inversion for time-dissipative and dispersive poroelastic media

TL;DR

This paper develops a time-domain full waveform inversion method for dispersive and dissipative poroelastic media, deriving the adjoint problem and analyzing energy evolution to improve inversion accuracy.

Contribution

It introduces an adjoint problem formulation for FWI in dispersive poroelastic media and performs energy analysis to enhance inversion techniques.

Findings

Derived the adjoint problem for dispersive poroelastic FWI

Implemented a numerical solver for the forward and adjoint problems

Analyzed energy evolution to inform inversion stability

Abstract

This paper concerns the Time-Domain Full Waveform Inversion (FWI) for dispersive and dissipative poroelastic materials. The forward problem is an initial boundary value problem (IBVP) of the poroelastic equations with a memory term; the FWI is formulated as a minimization problem of a least-square misfit function with the (IBVP) as the constraint. In this paper, we derive the adjoint problem of this minimization problem, whose solution can be applied to computed the direction of steepest descent in the iterative process for minimization. The adjoint problem has a similar numerical structure as the forward problem and hence can be solved by the same numerical solver. Because the tracking of the energy evolution plays an important role in the FWI for dissipative and dispersive equations, the energy analysis of the forward system is also carried out in this paper.