The problem of acoustic wave propagation in a cylindrical borehole possessing a finite number of transverse discontinuities is studied. The field behavior is modeled through Green’s function techniques and an integral equation is formulated to solve for the acoustic field everywhere within the structure. Asymptotic forms are investigated to speed the numerical convergence of our solution. To solve the integral equation both the method of moments and a low-frequency approximation are employed. The reflection coefficient in the time and frequency domains is studied. After presenting solutions for the one and two fracture case, the analysis is generalized for many fractures.
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Spring et al. (1992) studied this question.
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