Full Wave Logging in an Irregular Borehole

We present a boundary integral equation formulation for the problem of wave propagation in a borehole of irregular cross-section. The method consists in representing 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 field in the borehole fluid and in the elastic rock are then expressed using the discrete wavenumber method. The application of the boundary conditions at discretized locations along the borehole wall leads to a linear system of equations. The inversion of this system 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. The results show that when the change is smooth, the 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 diameter is different at the source and at the receiver levels, the microseismograms obtained are somewhat of an average between the ones that would be recorded in boreholes of constant radius equal to the radius at the source and at the receiver. The presence of small-scale fluctuations in borehole diameter reduces the amplitude of the Stoneley wave and decreases its velocity and the pseudo-Rayleigh wave velocity. 1 Now at Etudes et Productions Schlumberger, 26 Rue de la Cavee, 92142 Clamart, France 34 Bouchon and Schmitt