Anelastic (poroviscoelastic ) medium - the SH - wave problem

P. F. Daley

When considering the problem of extending seismic wave propagation in an elastic medium to a poroviscoelastic medium, replacing real quantities by complex equivalents has been the accepted way to proceed. Given the number of works dealing with, what could be called the inadequacy of this method of this approach, another line of reasoning might be in order. Starting with Biot's equations for a poroviscoelastic medium, employing a simplification route, results in the (modified) potential related to the vector equation of motion. Biot's theoretical development of wave propagation in a medium comprised of a fluid within a porous solid may be overly complicated for the pursuit of an alternate methodology for addressing this problem in its most basic form. As a consequence, the telegraph equation might be a more modest, yet informative analogue to consider, as it is a well studied problem from mathematical and physical perspectives. In what follows a potential wave equation is considered with attenuation introduced in a manner similar to that inherent in the telegraph equation. Additionally, the difficult situation (Krebes and Daley, 2007) will again be revisited, as it might be rationalized that a 1 - 2% modification of a real quantity such as velocity produces imperceptible effects in, say a reflection coefficient, while the same amount of perturbation introduced to make velocity a complex quantity results in significant dissimilarities between nearly similar initial input data. This is difficult to comprehend and seemingly at least as problematic to explain.