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

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.

Keywords:

• Time-domain full waveform inversion
• time dispersive and dissipative (TDD) system
• poroelastic equations
• adjoint problems

2010 Mathematics Subject Classification:

• 35M10

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The work of MYO is partially sponsored by US National Science Foundation [grant numbers DMS-1413039 and DMS-1821857]. The work of J. Xie is partially supported by China NSFC [grant numbers 12171274 and 11871139].