Multipole acoustic waveforms in nonaxisymmetric boreholes and formations

Using a 2.5-dimensional velocity-stress finite-difference (vs-fd) technique, waveforms are calculated for multipole excitation of azimuthally nonsymmetric boreholes and formations. Axial uniformity of the borehole cross section and formation is assumed. The vs-fd waveforms agree with previous transform methods for circular boreholes, and the modes found for elliptical boreholes agree with those derived by a boundary integral technique. Borehole ellipticity substantially reduces monopole compressional headwave amplitudes in fast formations. Low-frequency dipole waveforms in elliptical boreholes show marked sensitivity to source dipole orientation in fast formations, but small sensitivity in slow formations. Waveforms from dipole receivers perpendicular to the source dipole may be comparable in amplitude to those recorded by parallel dipole receivers. Dipole waveforms from an exaggerated ‘‘keyhole’’-shaped borehole are quite similar to those from an elliptical borehole of similar aspect ratio in a slow formation. Finally, the behavior of early compressional headwaves arising from a nearby faster bed parallel to the borehole axis is qualitatively similar to that for a point source above a simple planar interface.