Semiclassical inverse spectral problem for elastic Rayleigh waves in isotropic media

TL;DR

This paper addresses the inverse spectral problem for elastic Rayleigh surface waves in isotropic media, establishing uniqueness and reconstruction methods for S-wave speed profiles from spectral data under specific conditions.

Contribution

It extends previous work on Love waves to Rayleigh waves, providing a new reconstruction scheme for S-wave speed with multiple wells assuming constant Poisson ratio.

Findings

Proves uniqueness of the inverse spectral problem for Rayleigh waves.

Develops a reconstruction scheme for S-wave speed profiles.

Extends inverse spectral analysis from Love to Rayleigh surface waves.

Abstract

We analyze the inverse spectral problem on the half line associated with elastic surface waves. Here, we extend the treatment of Love waves [arXiv: 1908.10529] to Rayleigh waves. Under certain conditions, and assuming that the Poisson ratio is constant, we establish uniqueness and present a reconstruction scheme for the S-wave speed with multiple wells from the semiclassical spectrum of these waves.