Coherent elastic wave propagation through nonuniform spatial distributions of cracks

Models for multiple scattering of elastic waves usually concern uniform distributions of scatterers. The aim of this work is to predict the propagation of SH coherent waves through nonuniform distribution of parallel closed cracks. The spatial variation of the distribution properties is taken into account via replacing heterogeneous media by stacks of effective homogeneous layers. Propagation in each layer is then governed by the effective acoustic impedance and the effective wave number, derived in the framework of Waterman and Truell approach. On this basis, the reflection and transmission coefficients of the nonuniform distributions are calculated by using the transfer matrix method. We focus especially on distributions of crack size and concentration. Impact of the distribution profiles is also investigated. The semianalytical predictions are compared with numerical results obtained by using a finite-difference code.