Green's function for the viscoelastic and isotropic half-space

TL;DR

This paper derives a comprehensive 3D Green's function for viscoelastic, isotropic half-spaces, enabling improved modeling of wave propagation and boundary interactions in geophysical and engineering applications.

Contribution

It provides a closed-form Green's function for viscoelastic isotropic half-spaces, facilitating both standalone analysis and boundary element methods for complex boundary conditions.

Findings

Closed-form 3D Green's function derived

Applicable for boundary integral equation formulations

Supports mesh-reducing boundary element methods

Abstract

A dynamic 3D Green's function for the homogeneous, isotropic and viscoelastic (of the Zener type) half-space is derived in a closed form. The results obtained here can be used as either stand-alone solutions for simple problems or in conjunction with a boundary integral equation formulations to account for complex boundary conditions. In the later case, mesh-reducing boundary element formulations can be constructed as an alternative method for numerical implementation purposes.