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The problem of calculating the reflection and transmission coefficients of elastic P-wave incident from a porous half-space onto a fluid-filled crack is solved. The influence of capillary effects arising at the interface between a crack and a porous matrix on these coefficients is analyzed. In the first-order (single-) scattering approximation, the wave number of the effective P-wave propagating in a porous-fractured medium is calculated. It is shown that the hydrodynamic effects associated with fluid filtration at cracks’ boundaries in the field of an acoustic wave lead to significant frequency dispersion of the effective P-wave velocity.

In the present article, the dependencies of the acoustic signal total energy and the energies of the wave packets of different types of the waves on the elastic parameters and permeability of rocks have been studied. We have considered traditional logging tools containing acoustical monopole source. Calculations were performed in a frequency range of dozens of kilohertz, typical for acoustic well logging. It was shown that in a typical high-velocity formation (vs > vf, where vs and vf are the velocities of the shear wave in the rock and of the compressional wave in the borehole fluid, respectively), the pseudo-Rayleigh waves, whose elastic properties depend mainly on the shear modulus of the rock, contributed significant energy to the total signal energy in the borehole. The energies of different wave packets depend on the permeability in different ways. The greatest sensitivity to permeability change has been shown by the acoustic signal total energy and the energy of the low-velocity part of the pseudo-Rayleigh wave packet. The theoretical analysis was illustrated by real sonic log data.

We have calculated the waveforms of sonic reflection logging for a fluid-filled borehole located in a transversely isotropic rock. Calculations have been performed for an acoustic impulse source with the characteristic frequency of tens of kilohertz that is considerably less than the frequencies of acoustic borehole imaging tools. It is assumed that the borehole axis coincides with the axis of symmetry of the transversely isotropic rock. It was shown that the reflected wave was excited most efficiently at resonant frequencies. These frequencies are close to the frequencies of oscillations of a fluid column located in an absolutely rigid hollow cylinder. We have shown that the acoustic reverberation is controlled by the acoustic impedance of the rock Z = Vp h ρ s for fixed parameters of the borehole fluid, where Vp h is the velocity of horizontally propagating P-wave; ρ s is the rock density. The methods of waveform processing to determine the parameters characterizing the reflected wave have been discussed.