Full waveform inversion using triangular waveform adapted meshes

TL;DR

This paper presents a novel time-domain full waveform inversion method using variably sized triangular meshes and higher-order finite elements to improve seismic velocity model building, demonstrated with 2D and 3D simulations.

Contribution

It introduces an adaptive mesh approach with higher-order mass lumping for FWI, reducing degrees-of-freedom and enhancing computational efficiency.

Findings

Effective mesh adaptation to wavefield properties

Reduced degrees-of-freedom with higher-order basis functions

Successful 2D and 3D wave simulation results

Abstract

In this article, continuous Galerkin finite elements are applied to perform full waveform inversion (FWI) for seismic velocity model building. A time-domain FWI approach is detailed that uses meshes composed of variably sized triangular elements to discretize the domain. To resolve both the forward and adjoint-state equations, and to calculate a mesh-independent gradient associated with the FWI process, a fully-explicit, variable higher-order (up to degree $k=5$ in $2$D and $k=3$ in 3D) mass lumping method is used. By adapting the triangular elements to the expected peak source frequency and properties of the wavefield (e.g., local P-wavespeed) and by leveraging higher-order basis functions, the number of degrees-of-freedom necessary to discretize the domain can be reduced. Results from wave simulations and FWIs in both $2$D and 3D highlight our developments and demonstrate the benefits and challenges with using triangular meshes adapted to the material proprieties. Software developments are implemented an open source code built on top of Firedrake, a high-level Python package for the automated solution of partial differential equations using the finite element method.