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Conventional sonic logging tools are destined mainly for the determination of elastic waves’ velocities. In this paper, we have considered a different type of sonic logging tool that is destined for the registration of parameters of reflected waves in a borehole. We have calculated the mechanical impedance loading an acoustic source located on the axis of a fluid‐filled borehole. The problem was solved for a borehole drilled in a poroelastic formation. The solution was obtained in the framework of the Biot theory of poroelasticity. We have considered two limiting cases with permeable and impermeable (mudcake at the boundary between the borehole and porous rock) borehole wall. We have obtained the frequency dependences of the mechanical impedance. It was shown that the acoustic system ‘logging tool – fluid‐filled borehole – porous rock’ presents several resonance frequencies. These resonances’ frequencies are close to the resonance frequencies of a liquid layer between two rigid cylinders with radii equal to the source and borehole radii. The mechanical impedance calculated at the resonance frequency depends on the porosity and permeability that allows one to use impedance measurements in the frequency range near the resonance to determine the filtration properties of highly permeable rocks (of order higher than 10 mD). We have calculated the mechanical impedance in the low‐frequency range. The results obtained have shown that the use of low‐frequency impedance measurements provides a good way to evaluate the permeability of porous media.

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.

Many natural composite materials contain systems of partially oriented thin low-resistivity inclusions (for example, water-saturated microcracks in a double porosity sedimentary formation). We have calculated the components of the electrical conductivity tensor of such materials as a function of crack density. The results were obtained for thin ellipsoidal inclusions with conductivity (electrical or thermal) much larger than the matrix conductivity. To calculate the effective conductivity, we have used the effective field method (EFM). We have obtained the explicit expressions for the effective parameters of inhomogeneous materials. The application of the EFM allows one to describe the influence of the peculiarities in the spatial distribution of inclusions on the effective properties of the medium. General explicit expressions, obtained in this work, are illustrated by calculation examples for inclusions, homogeneously distributed in the sector [-Beta, Beta], where Beta is the disorientation angle, and some continuous angle distribution functions. The calculations have shown that the spatial distribution of the crack-like inclusions strongly affects the conductive properties of the effective medium and the symmetry of their tensor.

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.

In the present work, the waveforms of reflected wave sonic log for open and cased boreholes are calculated. Calculations are performed for a borehole containing an acoustic multipole source (monopole, dipole, or quadrupole). A reflected wave is more efficiently excited at resonant frequencies. These frequencies for all source types are close to the frequencies of oscillations of a fluid column located in an absolutely rigid hollow cylinder. It is shown that the acoustic reverberation is controlled by the acoustic impedance of the rock Z = Vp ρs for fixed parameters of the borehole fluid, where Vp is the compressional wave velocity in the rock, and ρs is the rock density. This result is correct for all types of acoustic sources (monopole, dipole, or quadrupole). Methods of the waveform processing for determining parameters characterizing the reflected wave are discussed.

In the present work the effective elastic moduli of a rock containing one or more systems of parallel inclusions of 3D-ellipsoidal shape were calculated. The calculations were performed for the conditions of constant strain and stress at infinity. The results were obtained for non-interacting inclusions (low concentration). The presence of movable fluid in the rock is described by the universal Gassmann relations for an anisotropic medium. The comparison of the results obtained with the experimental data has shown that it is possible to apply the proposed calculation technique for the determination of elastic moduli and acoustic waves' velocities in rocks, for example, for double-porosity carbonate formations.

The influence of the elastic and hydrodynamic properties of a rock on the time attenuation coef� ficient of an acoustic wave, which is reflected from the borehole wall, is considered using the methods of the mechanics of saturated porous media. The calculations were performed for a system consisting of an acoustic logging tool of a finite with a finite diameter, a fluidfilled borehole, and a porous permeable rock. The per� formed simulation showed that in rocks with a low hydrodynamic permeability, the acousticreverberation time is determined by the acoustic impedance of the borehole wall (product of the rock density and the lon� gitudinalwave velocity in it). In the case of rocks wi th a permeability of about several hundred millidarcy, the time signal's attenuation coefficient substantially depends on the rock's permeability.

Self-consistent effective field method is applied to the calculation of effective properties of a medium that consists of a viscoelastic host material (matrix) and a random set of elliptical fluid-filled cracks. Viscoelastic behavior of the matrix phase is described by a linear Boltzman model with a weak singular kernel. The conventional principle of correspondence between elastic and viscoelastic problems allows deriving explicit expressions for the effective viscoelastic parameters of an isotropic medium containing a set of parallel cracks or cracks with homogeneous distribution over the orientations. For long elastic waves, the complex wave numbers of propagating waves in the medium with cracks are obtained. The wave velocities and quality factors of some real cracked rock materials are calculated.