An Elastic-Wave Full-Waveform Inversion for the Reconstruction of Material Profiles using a Spectral Element Method

Abstract

This paper presents a full-waveform inversion (FWI) method for the reconstruction of the material profile of elastic media using two-dimensional spectral elements. The FWI method attempts to estimate the spacial variation of elastic material parameters using the surficial response of the domain to impact loads. For the simulation of elastic waves in the half-space, perfectly-matched-layer (PML) absorbing boundaries are used to truncate the semi-infinite extent and to remove artificial reflections from the truncated domain boundaries. The FWI method is implemented based on a PDE-constrained optimization framework, which seeks the optimal values of elastic moduli of the PML-truncated domain while minimizing Lagrangian functional. The Lagrangian consists of a least-squares objective functional and regularization terms, augmented by the weak imposition of PML-endowed elastic wave equations via Lagrange multipliers. To alleviate the ill-posedness of the inverse problem, Tikhonov and total variation regularization schemes are used. The full-waveform inversion approach with spectral elements has been implemented using parallel computing based on a message-passing interface (MPI) to solve a large-scale inverse problem. Numerical examples with various grid scales are presented to show the effect of the spatial-scale variation on the inversion result. The accuracy and efficiency of inversion results, as well as the extension to realworld problems, are discussed. The large-scale full-waveform inversion method can be applied to various engineering problems such as structural health monitoring, geophysical probing, and site characterization.