Abraham I. Beltzer, Joanne Wegner, Bernard R. Tittman, James B. Haddow; Pulse propagation in random media by a causal approach. Bulletin of the Seismological Society of America ; 79 (1): 113–126. doi:
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A causal approach is applied to investigate pulse propagation in random media, which exhibit scattering and viscoelastic losses. Since the approach allows for evaluation of the effective wave number for the entire frequency interval, the transients may be investigated by the classical Fourier method. The scattering mechanism is described by a model introduced by Wu, and the viscoelastic losses by a slightly modified Azimi's law. Extensive numerical results for a transient response of this Wu-Azimi model are presented. It is shown how the pulse reinforcing and delaying effects of multiple scattering are interrelated through a causality constraint.