Acoustic modes of propagation in the borehole and their relationship to rock properties

Abstract

Acoustic waveform measurements in boreholes have important applications in fracture hydrology and radioactive waste disposal, but ambiguities in existing interpretation techniques remain a problem. We have addressed the problem by using residue theory to predict the relative excitation of various modes contained in experimental waveforms. A plane‐geometry model involving a layer of fluid between two elastic half‐spaces is shown to provide velocity dispersion curves for propagating modes that are very similar to those for the fluid‐filled borehole. We use the plane‐geometry model to illustrate the effects of the confined borehole fluid on surface and body waves traveling along the borehole in the elastic solid. We also computed excitation functions for some of the lowest‐order symmetric modes, calculated the time‐domain response of the trapped modes following the shear head waves, and compared them to waveforms recorded in boreholes through several homogeneous formations. The insight into the mode composition of the experimental waveforms obtained in these formations is used to construct amplitude logs that should be especially sensitive to variations in the presence of fluid‐filled fractures in the borehole wall. Initial tests show the technique is most successful when the waveform is dominated by the fundamental tube wave, and yet frequencies remain relatively high. The model analysis indicates these conditions can only be obtained when the borehole diameter is not much larger than that of the logging tool.