Fast solutions for three-dimensional elastic-Wave imaging of piecewise-homogeneous bodies.

摘要

The focus of this study is a 3D inverse scattering problem underlying non-invasive reconstruction of defects in a semi-infinite layered solid or in a finite piecewise-homogeneous body from surface elastic waveforms. A modern solution technique called the linear sampling method is employed. This technique, which is computationally faster than most traditional methods, represents an optimization-free approach to the full-waveform tomography wherein the support of a buried obstacle is exposed using measurements of the scattered field (due to prescribed excitation) over an observation surface. The algorithm suggests sampling a volume of interest by solving the so-called full-waveform integral equation. A solution of the latter equation, whose kernel is constructed from the experimental data and whose right-hand side varies with sampling coordinates, is used to determine whether the sampling point belongs to the obstacle. Owing to an ill-posed nature of the featured integral equation, a stable approximate solution is sought using Tikhonov regularization.; As in other imaging techniques, a necessary prerequisite for the foregoing reconstruction methodology is the knowledge of material characteristics of the supporting medium. To resolve the subsurface stratigraphy beforehand in the case of a layered half-space as a reference domain, an analytical and computational platform for the spectral analysis of horizontally-polarized Love surface waves is developed. It is shown that the use of Love waves as a sounding tool rules out the effect of the Poisson's and P-wave damping ratios in each layer, thus substantially reducing the number of parameters involved in seismic data interpretation. Performance of both inverse methods is illustrated through numerical examples.