Approximate absorption corrections for complete SH seismograms

Summary An approximate absorption correction is proposed that can be applied retroactively to the response of a perfectly elastic medium, not decomposed into elementary waves, for example in the finite-difference method. As the duration of excitation decreases, the approximate correction approaches the exact, and becomes quite exact for impulsive excitation. The correction makes use of the perfectly elastic response and dissipation operator, but their relation is not simply convolutory. The method is restricted to a spatially constant Q with an arbitrary power-law frequency dependence. The advantage of the approximate solutions, as compared to the exact, in which the absorption is included in the equation of motion, is in a considerable saving of computer time if several absorption models (or several Q values) are repeatedly applied to the same structure. The simplest computations are for Q linearly dependent of the frequency, where the absorption correction reduces to an exponential time windowing.