Applying finite element analysis to the memory variable formulation of wave propagation in anelastic media

Finite-element methods are applied to solution of seismic wave motion in linear viscoelastic media using the memory variable formalism. The displacements are represented as a superposition of a set of basis functions. It is shown that if memory variables are represented using the spatial derivatives of those basis functions, rather than the basis functions themselves, the equations to be solved are simpler and require less computer memory. Using this formulation, results for SH waves in one and two dimensions are calculated using a simple explicit finite-element-in-space/finite-difference-in-time scheme. These results agree with those found with a "method of lines" solution. Results in a homogeneous medium also agree with the frequency domain solutions of Kjartansson's constant-Q method.