Abstract

A new boundary integral equation formulation for wave propagation in a borehole of irregular cross-section represents the wave field diffracted at the borehole-rock interface by the radiation from a distribution of surface sources applied along the borehole wall. The wave fields in the borehole fluid and in the elastic rock are then expressed using the discrete wavenumber method. Application of boundary conditions at discretized locations along the borehole wall leads to a linear system of equations, whose inversion yields the required source distribution.We have used the method to investigate the effect of changes in borehole diameter on the pressure wave field inside the borehole. When the change is smooth, records obtained ahead of the discontinuity location are not affected by its presence. In the case of a steep variation, however, a significant amount of the Stoneley-wave energy is reflected. When the borehole diameters are different at the source and receiver levels, the microseismograms obtained are somewhat of an average of those that would have been recorded in constant-radius source and receiver boreholes, respectively. Small-scale fluctuations in borehole diameter decrease the velocity of the Stoneley wave and of the pseudo-Rayleigh wave.

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