Abstract

In the computation of conventional theoretical (or "synthetic") seismograms, the effects of the variation of frequency-dependent absorption with depth are presently ignored. Such absorption can produce significant differences in both the relative amplitudes and frequency spectra of primary and multiple reflections having the same arrival time. This paper describes a feasible way, using a digital computer of the IBM 7090 class, for computing theoretical seismograms which properly take into account the variation of absorption with both frequency and depth, it being assumed that the absorption coefficient varies linearly with frequency. It is pointed out that attempts to solve the problem using Fourier analysis in the frequency domain would lead to significant aliasing errors. Consequently, a method borrowed from the field of network theory utilizing deconvolution is devised whereby solutions are obtained directly in the time domain. Both "primary" and "primary-plus-all-multiple" traces are computed, the former including the "peg-leg" multiples described by Anstey and Webster. These calculations demonstrate that absorption can reduce the multiple content of theoretical seismograms.

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