Seismic‐wave attenuation operators for arbitrary Q

Abstract

Under the minimum‐phase condition attenuation operators are derived from arbitrary intrinsic or scattering Q as a function of frequency, and a simple method is described to calculate these operators with the aid of Fourier transformation. In the case of scattering attenuation, the medium may contain both 1‐D, 2‐D or 3‐D heterogeneities. For illustration, the method is applied to a 1‐D model of statistically layered media with 12 per cent standard deviation of relative velocity fluctuation. The theoretical scattering Q, deduced from single‐scattering theory, is determined for a numerical autocorrelation function and an exponential autocorrelation function, as well as for a modified exponential autocorrelation function, which is introduced here. The corresponding attenuation operators are calculated. The theoretical Q and simulated seismograms, calculated with the attenuation operators, agree very well with the exact results of synthetic‐seismogram calculations. Copyright © 1991, Wiley Blackwell. All rights reserved