Numerical simulation of wave propagation in finely layered and attenuated medium
Lawrence H. T. Le, Robert Burridge
Burridge (1991) presents an approximate theory of wave propagation of a plane wave through a stack of finely layered and anelastic structure. The theory goes beyond previous works (Burridge and Chang, 1989a & b) in two aspects: (a) the sample autocorrelation rather than the averaged autocorrelation is used so that the coda of the computed response is preserved; (b) anelastic effect due to intrinsic attenuation is incorporated and by "order of magnitude" argument, the terms governing the scattering and anelastic effects enter separately but in a similar way.
The present work is a numerical justification of the approximate theory. Using the SH case as an example, we computed the impulse response using two methods: the approximate method and an exact method for an anelastic medium at both normal and oblique incidence. Using a simple standard linear solid model with two relaxation parameters, the medium is made anelastic. Impulse responses obtained by both methods agree well for both elastic and anelastic cases. The results of this preliminary investigation can be summarized in several points: (a) accuracy is best for the head of the pulse; (b) the larger the angle of incidence, the better is the comparison; (c) the presence of anelasticity exhibits the time delay and dispersion of the broad pulse; (d) the broad pulse due to scattering effect is comparable to the pulse due to anelasticity only; (e) the perturbation code is 90 times faster than the exact code for the anelastic case.