Recovery of a material parameter of a soft elastic layer
Résumé
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 () in the estimator different (from its
counterpart ) in the predictor. It is shown that the rigidity contrast is
recovered with an accuracy that depends on the difference between and .