Elastic wave propagation in a fluid‐filled borehole and synthetic acoustic logs

Abstract

The propagation and dispersion characteristics of guided waves in a fluid‐filled borehole are studied using dispersion curves and modeling full‐wave acoustic logs by synthetic microseismograms. The dispersion characteristics of the pseudo‐Rayleigh (reflected) and Stoneley waves in a borehole with and without a tool in the center are compared. Effects of different tool properties are calculated. The effect of a rigid tool is to make the effective borehole radius smaller. As an approximation, dispersion characteristics of the guided waves in a borehole with a tool can be calculated as a purely fluid‐filled borehole with a smaller effective radius. Theoretical waveforms (microseismograms) of elastic waves propagating in a borehole are calculated using a discrete wavenumber integration. With an appropriate choice of parameters, our results look similar to the acoustic waveforms recorded in a limestone and a shale formation. Several factors affect the shape of an acoustic log microseismogram. The effective radius of the borehole determines the relative amplitudes of the modes generated. Poisson’s ratio of the formation is the primary factor determining the relative amplitude of the leaky mode following the compressional arrival. Attenuation affects the duration and decay rate of the guided waves.