Anelastic media: wave propagation near vertical incidence
P. F. Daley
Some of what is presented here was addressed in an earlier work (Daley, 2003). However, as a result of recent papers in the geophysical literature it was determined that this topic should be revisited and specific problems, detailed in the next section, investigated in a numerical manner. When introducing anelasticity into synthetic seismogram computations, selecting a method for accomplishing this while at the same time not introducing non-physical ( causality) artefacts into the synthetics is a requisite. This must be done within a mathematical framework without initiating questions as to, among other things, its accuracy, applicability and theoretical correctness. The SEG reprint series (1981), which contains a number of papers on anelastic theory applied to seismic problems. After a significant amount of numerical testing and consultation with other texts and papers related to this matter and with several academic and industry researchers, the theory presented by Futterman ( 1962) was deemed to be the most useful and accurate when used together with the high frequency geometrical optics solution method of computing synthetic traces. An assumption used in his discussion of seismic wave propagation in a viscoelastic medium is that Q>30. (After numerical experimentation, a minimum value of Q be such that Q>30 might be more realistic)
Although the problem considered here is fairly simplistic, an earlier version of some of the computer code used here is part of a software package, which as of 2008 was still in use in an industry processing package.