This article simulates the 3D wave propagation in a fluid-filled borehole, embedded in an elastic medium containing an empty crack, when excited by a sonic tool placed inside the borehole. The crack is assumed to be empty with thickness tending toward zero. The geometry of the cross section of the borehole and the crack are assumed to be constant along the borehole axis, allowing the 3D problem to be solved as a summation of 2D responses for different wavenumbers along the z direction (2.5D formulation). The problem is formulated in the frequency domain using a coupled formulation incorporating the traction boundary element method, capable of modeling thin-body geometries, and the conventional direct boundary element method. In this formulation all singular and hypersingular integrals are computed analytically. This article assesses the influence of the length of the crack, its orientation, and its position in relation to the acoustic well in the wave field recorded inside the borehole.

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