Short note: Normal incidence synthetics in viscoelastic media

P.F. Daley

ABSTRACT

One of the major tasks when introducing viscoelasticity (anelasticity) into synthetic seismogram computations requires selecting a method for accomplishing this and at the same time not introducing non-physical (causality) artefacts into the synthetics. This must be done within a mathematical framework, which can pass at least moderate scrutiny, without invoking questions as to, among other things, its accuracy, applicability and theoretical correctness. If the SEG reprint series (1981), which contains a number of reprints on viscoelastic theory applied to seismic problems, is consulted several (often contentious) points of view may be encountered. 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 . (More realistically, the minimum value of Q should be such that Q > 10 1 .)

Although the problem considered here is fairly simplistic, an earlier version of this algorithm is part of a software package, which as of the date of writing, is still in use in an industry processing package.

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