Solving 3D Anisotropic Elastic Wave Equations on Parallel GPU Devices |
The equations governing elastic wave propagation in 3D transversely isotropic media, when assuming linearized elasticity theory and a stress-stiffness tensor formulation, are fairly straightforward to implement in a numerical scheme. Our goal is to develop finite-difference (FD) operators of 2 - and 8 -order temporal and spatial accuracy, respectively, that are well-suited for GPU hardware by virtue of being a compact stencil with a regular memory access pattern.
The linear theory of elasticity [e.g., Landau and Lifshitz (1986)] establishes a relationship between a vector seismic wavefield displaced infinitesimally from rest and the dimensionless linear strain tensor. In indicial notation we write
The linear strain tensor, , is related to the Cauchy stress tensor, , through a constitutive relationship that describes the elastic material properties through a fourth-order stiffness tensor :
Solving 3D Anisotropic Elastic Wave Equations on Parallel GPU Devices |