Frederick L. Paillet
U.S. Geological Survey
Denver, Colorado
ABSTRACT
This paper relates the complicated theory of acoustic propagation in boreholes to the practical needs of the log analyst by means of a simplified model for the prediction of borehole waveforms. The major limitations imposed on the use of the model to predict acoustic waveforms stem from the assumption of a simple acoustic-energy source description. Model calculations are used to demonstrate the physical mechanisms responsible for the general character of experimentally observed waveforms. The results show that the presence of a rigid logging tool in the borehole allows for fluid resonances that significantly affect the compression and ahead arrivals under normal logging conditions. The model also shows that the normal modes represent a hybridization of fluid and wall waves, so that the wall mode cannot appear as a pseudo-Rayleigh wave that might interfere with the recognition of shear arrivals. This fact also is related to the relatively narrow separation between logging tool and borehole wall with respect to typical acoustic wavelengths. The resonance condition demonstrated by these model studies is incorporated into an equivalent plane geometry model designed to provide a more realistic approximation to the borehole situation than the plane interface of classical seismic interpretation. This model can be used as an interpretation tool for more complex situations involving anisotropy or wall permeability.