Theoretical and numerical modeling of Rayleigh wave scattering by an elastic inclusion

TL;DR

This paper develops and compares theoretical and numerical models for Rayleigh wave backscattering by elastic inclusions, highlighting their agreement and limitations based on inclusion size and anisotropy.

Contribution

It introduces a combined theoretical and finite element modeling approach for Rayleigh wave scattering by elastic inclusions of arbitrary shape and symmetry.

Findings

Good agreement between models when wavelength exceeds inclusion size

Agreement decreases with increasing anisotropy

Theoretical model is useful for quantitative surface/subsurface characterization

Abstract

This work presents theoretical and numerical models for the backscattering of two-dimensional Rayleigh waves by an elastic inclusion, with the host material being isotropic and the inclusion having arbitrary shape and crystallographic symmetry. The theoretical model is developed based on the reciprocity theorem using the far-field Green's function and the Born approximation, assuming a small acoustic impedance difference between the host and inclusion materials. The numerical finite element (FE) model is established to deliver relatively accurate simulation of the scattering problem and to evaluate the approximations of the theoretical model. Quantitative agreement is observed between the theoretical model and the FE results for arbitrarily-shaped surface/subsurface inclusions with isotropic/anisotropic properties. The agreement is excellent when the wavelength of the Rayleigh wave is larger than, or comparable to, the size of the inclusion, but it deteriorates as the wavelength gets smaller. Also, the agreement decreases with the anisotropy index for inclusions of anisotropic symmetry. The results lay the foundation for using Rayleigh waves for quantitative characterization of surface/subsurface inclusions, while also demonstrating its limitations.