Acoustic wave propagation in a cylindrical borehole with fractures

Abstract

We study the problem of acoustic wave propagation in a cylindrical borehole possessing a finite number of transverse discontinuities. We model the field behavior through Green's function techniques. We formulate an integral equation whose solution will enable us to solve for the acoustic field everywhere within our structure. We investigate asymptotic forms to speed the numerical convergence of our solution. To solve the integral equation we employ both the method of moments and the low frequency approximation. We study the reflection coefficient in the time and frequency domains. Finally after presenting solutions for the one and two fracture case, we generalize our analysis for many fractures.