MULTIPLE-SCATTERING OF SH-WAVES IN 2-D ELASTIC MEDIA WITH DISTRIBUTEDCRACKS

We compute synthetic seismograms of SH waves that are multiply scatter ed by randomly distributed cracks. All the cracks are assumed to have the same length and strike direction; the crack surfaces are assumed t o be stress-free, or to undergo viscous friction. We analyse the deter ministic wave equation, and rigorously treat multiple crack interactio ns. We first calculate the wavefield in the wavenumber domain, and the n we obtain the time-domain solution by its Fourier transform. A plane wave whose time dependence is described by the Ricker wavelet is assu med to be incident upon the region of crack distribution. The scattere d waves are efficiently excited when the half-wavelength of the incide nt wave is close to or shorter than the crack length. High-wavenumber components are shown to be more abundant in the scattered waves when t he crack distribution is denser. The time delay of the arrival of the primary wave, due to crack scattering, is shown to be prominent when t he wavelength of the incident wave is much longer than the crack lengt h. When the crack surfaces are subject to viscous friction, both the a mplitudes of the scattered waves and the time delay of the primary-wav e arrivals are smaller than those for the case of stress-free crack su rfaces. When the crack distribution is statistically homogeneous, the calculated attenuation coefficient Q(-1) and phase velocity upsilon of the primary wave are generally consistent with those obtained by a st ochastic analysis based on Foldy's approximation. A short analysis on the effect of inhomogeneous crack distribution shows that the wavenumb er at which Q(-1) is at its peak value is smaller than that expected f rom the stochastic analysis for homogeneous crack distribution.