Recovery of a material parameter of a soft elastic layer

Abstract

We treat the inverse seismological problem of the recovery of the rigidity contrast from the temporal response on the ground (a flat stress-free surface) separating air from a homogeneous, isotropic, solid substratum overlain by a homogeneous, isotropic, solid layer (in contact with the ground) solicited by a shear-horizontal (SH) plane impulsive body wave incident in the substratum (a seismic solicitation whose sources are deep within the substratum). The forward-scattering analysis is first carried out in the frequency domain and subsequently in the time domain. A (complex eigenfrequency) method is elaborated for the computation of the time history and gives rise to the reliable numerical solutions for a large variety of configurations of interest in the geophysical setting under the hypothesis of non-dissipative, dispersionless media. The inverse-scattering analysis is carried out using the complex eigenfrequency method to generate synthetic data (predictor) as well as to constitute the theoretical model by which the data is inverted (estimator). The inverse crime is avoided by making one of the supposedly-known parameters (Γ) in the estimator different (from its counterpart γ) in the predictor. It is shown that the rigidity contrast is recovered with an accuracy that depends on the difference between Γ and γ.

Keywords:

• elastic layers
• inverse scattering

AMS Subject Classifications:

• 65N21, 74H05, 74H45, 74J15, 74J20, 74J25