PML‐Based Family of Stretched Coordinate Systems for Wave Propagation in Poroelastic Transversely Isotropic Half‐Space

Abstract

Investigating wave propagation in transversely isotropic saturated poroelastic material and introducing a family of stretched coordinate transformations to be used for defining a perfectly matched layer (PML) are the main aims of this paper. To this end, the formulation of Biot is adopted as the governing framework of the porous media. The coupled equations of motion and transport equation are uncoupled by means of the recently proposed two scalar potential functions in cylindrical coordinate system. Two separated families of continuous stretched coordinate transformations are introduced for each of radial and axial coordinates, which allows the whole half‐space to be replaced by a finite cylinder surrounded by an outer cylinder/cube with both finite height and radius. It is shown that the displacements and pore fluid pressure, determined from the analysis of the replaced cylindrical domain, is exactly collapsed on the analytical solution in the inner cylinder, while they are, based on the stretched coordinate transformation, attenuated very fast in the outer cylinder to prevent the reflection from the most exterior boundaries. The results of this study may be used in any wave propagation analysis containing either isotropic or transversely isotropic half‐ or full‐space.