Synthetic microseismograms; logging in porous formations

Abstract
Biot's theory of wave propagation in a fluid-filled porous elastic solid takes account of energy dissipation due to relative motion between viscous pore fluid and solid matrix. This theory has been applied to a numerical study of sound pulses propagating along a cylindrical borehole and along a plane interface. It is found that properties such as permeability affect the attenuation of the signal only at high frequencies. For the plane interface, the effect on the P-arrival is small; on the S-arrival it is moderate; and on the Stoneley-wave it is large, but only if source and detector are close to the interface and the flow of fluid across the interface is relatively unrestricted. With a wide-band signal, the low-frequency pseudo-Rayleigh wave can partially mask the S-arrival. Similar conclusions hold for the logging tool centered in the borehole, and arrivals other than the first P may be difficult to pick, especially for narrow-band signals. The amplitude of the wave train arriving with approximately the tube-wave velocity is particularly sensitive to the fluid-transfer conditions at the borehole wall. The results suggest that acoustic permeability logging tools require high-frequency signals: their performance could depend critically on the acoustic characteristics of mud cake in situ. Narrow-band signals are not suitable for the identification of phases other than the first P-arrival; attenuation measurements probably must be based on the energies observed in gated sections of the pressure response. For signals in the seismic range, inelastic effects predicted by Biot's theory are too small for the detection of formation properties, especially when thin impermeable beds are also present.