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Based on Pride theory, we studied the propagation of seismoelectric waves in a fluid-filled poroelastic hollow cylinder. We presented the expressions of seismoelectric waves in the poroelastic hollow cylinder, acoustic and electromagnetic field in inner and outer of the hollow cylinder, and we used the boundary condition to determine acoustic and electromagnetic field. Also this problem is accomplished by using the quasi-static method. The numerical simulation is operated on acoustic field and electromagnetic field in inner fluid of hollow poroelastic cylinder, and the transient waveform is obtained. It shows that there is no difference on the graph between the electric field obtained from Pride equations and that obtained from quasi-static method. The influence of hollow cylinder thickness, molarity and permeability on wave amplitude are discussed. The results show that for the acoustic field the amplitude of longitudinal mode and Stoneley wave will increase with hollow cylinder thickness increasing, and for the converted axial electric field the amplitude of Stoneley wave increases with hollow cylinder thickness increasing, while the amplitude of longitudinal mode will decrease. The amplitude of electric field in inner fluid will decrease with the molarity of fluid increasing. The amplitude of the fluid acoustic and electric field will decrease with the permeability increasing. The influence of impermeable outer surface on the amplitude of longitudinal wave is obviously much larger than that of Stoneley wave in the electric field.

The aim of the study is to increase the reliability of estimation of the acoustic parameters of a layered permeable formation using new software, based on two-velocity continuum equations for 2D numerical simulation of acoustic waves propagating in a borehole. The key method is the method of finite differences as applied to solving equations of the continuum filtration theory. The dissipative characteristics of Stoneley waves have been identified for the case of their propagation in a layered formation. These aspects should be taken into account when using Stoneley waves to estimate the permeability of geologic media.

In this paper, formulae for the velocity of Scholte waves propagating along the interface between a fluid half-space and an isotropic elastic half-space are derived using the complex function method. From these formulae it is shown that if a Scholte wave exists, then it is unique, and for any given parameters of the solid and the fluid, a Scholte wave is always possible.

This paper summarizes part of an ongoing feasibility study that investigates the possible use of the full elastic Born approximation in multipole borehole acoustics. As a first step we exclude the fluid-filled borehole with the motivation that one or two wavelengths away from the fluid-filled borehole, radiating borehole mode amplitudes (e.g., Stoneley wave, formation dipole wave, etc.) are small compared to body wave amplitudes ( P -, SV - and SH -waves). Consequently, for scatterers one or two wavelengths away from the fluid-filled borehole, it suffices to only consider their interaction with body waves. In this paper we apply the contrast-source stress-velocity forward scattering (integral equation) formulation for solid configurations in its first order (Born-) approximation ( De Hoop, 1995 ) assuming a multipole force source excitation in a zero-offset configuration. To scrutinize the validity of the Born approximation, we consider the simplest type of scatterer, i.e., one characterized by a (Heaviside) step function change in one or more of the contrast (perturbation) parameters and we derive analytic zero-offset formulas for the scattered wave particle velocity and displacement in both the space–frequency and space–time domain, respectively. We assume the scatterer to be located in the far-field. More complicated layered configurations can easily be derived by superposition of the given solution types. Explicit results are given for the dipole and quadrupole excitation, where the former is allowed to have an arbitrary orientation relative to the scatterer and where the latter one is located in a plane perpendicular to the scatterer. In the time domain it is shown, how the scattered wave field decomposes in a specular and diffuse wave field (two terms borrowed from ‘Optics’), where the former contribution vanishes in the absence of an imaging condition and where the latter is always present. For the dipole case, we subject our results to a sensitivity analysis with respect to the three independent perturbation parameters (i.e., density and two compliance parameters) and we compare these results to a full waveform benchmark code that has implemented the reflectivity method ( Kennett, 1983 ), for a ‘horizontally’ stratified elastic medium. This allowed us to pinpoint the root cause of the observed (small) differences. As it turns out these deviations could be traced back to the inaccurateness of the first order Born scattering coefficients. An additional confirmation of this fact is provided through a comparison between the zero-offset scattering coefficients and the corresponding Zoeppritz reflection coefficients. Most notably, it was found that the PP first order scattering coefficient needs a higher than quadratic correction in two of the three independent perturbation parameters, i.e., the two compliance parameters, δ Λ and δ M. With respect to the density perturbation parameter ( δρ ) the PP scattering coefficient correction is quadratic with respect to this perturbation parameter, as is to be expected for a first order approximation. Moreover, also the SS first order scattering coefficient only needs a quadratic correction with respect to its associated perturbation parameters, i.e., δρ and δ M. Finally, we give a brief outline on how to numerically implement the Born approximation (employing arbitrary offsets) in a configuration where a source–receiver pair is moving continuously relative to the ‘contrast’ (Geology), as is the case in borehole acoustic applications.

A two-mode method of measuring permeability and electroacoustic constant in the course of borehole logging is considered. The first mode is the Stoneley wave with its electroacoustic ratio; the second mode is the radial wave in the formation around the borehole with the electric field it generates. The radial wave enables one to measure the electroacoustic constant and the Stoneley wave, the electroacoustic ratio, linearly dependent on permeability. Using these measurements jointly enables one to find permeability of the porous medium. All formation evaluation can be reduced to an additional measurement of electric conductivity.

В статье рассмотрены методы расчета кривых горного, порового давления и давления разрыва пласта. Определена область применимости формулы К.Н. Доронкина для расчета порового давления. Показаны сложности применения геофизических программ. Для их полноценного использования при геомеханических расчетах необходимо располагать средствами интегрирования кривых и их экстраполяции до поверхности Земли. Указано на необходимость точного задания начала отсчета глубины. Рассмотрены возможности применения в расчетах волны Стоунли., The paper considers the methods used to estimate the overburden load, pore and fracturing pressures. Range of applicability of the Doronkin equation for pore pressure prediction has been defined. The paper also reveals the implications associated with application of well logging software. To make the utmost use thereof in geomechanical analysis reliable tools for curve integration and extrapolation to the Earth’s surface are required. The importance of precise datum setting for depth domain is also highlighted. Applicability of Stoneley wave in pressure estimates is considered., Нефтяная провинция, Выпуск 2 (10) 2017

The present work aims to study the propagation of Stoneley wave at the common interface of two distinct homogeneous viscoelastic semi-infinite media. The closed-form expression of the velocity equation has been obtained. The real part of the velocity equation corresponds to the phase velocity of Stoneley wave, whereas the imaginary part corresponds to the damped velocity associated with the Stoneley wave. The Lame ratio associated with Lame’s first constant for the upper/lower viscoelastic semi-infinite medium and the frictional parameter associated with the shear strain for the upper/lower viscoelastic semi-infinite medium have significant effects on the phase velocity and the damped velocity of Stoneley wave associated with a longitudinal/transversal wave in the upper/lower viscoelastic semi-infinite medium. Numerical computation and graphical illustration were carried out to highlight the important peculiarities of the problem. Moreover, as a special case, it was observed that the velocity equa...

There is increasing support for the existence of a relationship between Stoneley wave characteristics and permeability in sandstone formations. We evaluated monopole full waveform sonic data sets acquired in a mudded drill hole at the Mirrabooka Aquifer Storage and Recharge trial site in Perth, Western Australia. To increase the spectral range of the full wave form sonic data the hole was logged three times with transmitter centre frequencies at 1, 3 and 15 KHz. Data were recorded in four receivers spaced at 1ft intervals with the first receiver at 3ft from the transmitter. Stoneley waves were clearly identified in the low frequency range of 1?5 KHz, which is characteristic of Stoneley wave propagation in a slow formation. A semblance slowness technique was used to determine the slowness of Stoneley wave. Slowness values ranged from 950 µs/m (VST = 1050 m/s) for sandstone to 1650 µs/m (VST = 600 m/s) for shaley sediments. Observations of the dependence of phase velocity on frequency were made by using multi filter and phase shift transform techniques. The relationship between Stoneley wave dispersion and fast flow, high permeability pathways, as identified in flow and time lapse induction logging data, was clearly observed in an interval from 330 to 333m below ground level. This high permeability sandstone layer can be identified in dispersion curves by assessing frequency and phase velocity shifts. Our outcomes are significant, as they present the possibility of identifying narrow high permeability layers in wells where full waveform sonic logs have been completed.

This paper is concerned with the propagation of Stoneley waves in two bonded isotropic elastic half-spaces with the same bulk wave velocities. Our main purpose is to find formulas for the wave velocity and the wave slowness. By applying the complex function method, the exact formulas for the wave velocity and the wave slowness have been derived. The derivation of these formulas also shows that there always exists a unique Stoneley wave for the case under consideration.

A mudcake formed on the borehole wall between a fluid-filled porous formation and the borehole fluid can affect Stoneley wave propagation used to estimate the formation permeability. The mudcake effect on the permeability dependence of radial oscillations of borehole fluid is investigated in a system with a source generating radial acoustic waves in the borehole and hydrophones (pressure sensors) that record the respective attenuating oscillations of the borehole fluid. The permeability of the porous formation is estimated from theoretical permeability dependence of the attenuation exponent, knowing the time dependence of the exponential attenuation of borehole fluid oscillations.

The effect of a fluid on the surface waves moving in a waveguide along its boundary with the fluid is considered. The effect of the shear and volume viscosities of the fluid on the damping coefficient of such a surface wave is estimated. It is shown that the effect of fluids may be neglected at a measurement accuracy of about 10−3 if their shear viscosities are lower than 0.1 Pa s. At a higher viscosity, corrections that take into account the contribution of viscous losses to the measured damping coefficient of a surface wave should be introduced. A technique for calibrating a density sensor for low-viscosity fluids is described, and the densities of NaCl and saccharose solutions in distilled water are measured. The experimental results agree qualitatively with the theoretical estimates. It is noted that this method of measuring the longitudinal impedance of a fluid can use the same apparatus design in both the principle (pulsed) and the frequency range (1–10 MHz) for measuring the density, both viscosities, the velocity, and the sound absorption coefficient of a fluid. This design almost coincides with the apparatus used in the means of nondestructive quality control of materials and articles.

Rock deformation and unstable failure of slope is controlled by weak structural plane whose identification and evaluation is greatly influenced by deformation failure prediction of slope and design treatment. Based on the propagation characteristics of acoustic wave in shaft lining strata, attenuation of stoneley wave and inherent attenuation of strata are analyzed and permeability relationship among shaft lining strata is researched. The relationship between reflected stoneley-wave intensity and the width and filling ability of strata crack is studied. By application example of landslide investigation, attribute parameters and characteristics of acoustic wave are discussed. Strata division, the practicability and accuracy of recognition for fracture and holes evaluation and mechanic characteristics of rock mass also are studied.

The analysis of lithological composition was carried out. Reservoir elastic moduli were estimated with the lithological composition taken into account. The technique for permeability prediction according to the Stoneley wave parameters and a calculation example are presented. The comparison of permeability calculation with the proposed technique and other technologies is demonstrated. The application of the developed technique for permeability calculation provides theoretically proven outcomes.

In this paper, a method is proposed to invert permeability from seismoelectric logs in fluid-saturated porous formations. From the analysis of both the amplitude and the phase of simulated seismoelectric logs, we find that the Stoneley wave amplitude of the ratio of the converted electric field to the pressure (REP) is sensitive to porosity rather than permeability while the tangent of the REP's phase is sensitive to permeability. The REP's phase reflects the phase discrepancy between the electric field and the pressure at the same location in the borehole. We theoretically derive the frequency-dependent expression of the REP of the low-frequency Stoneley wave and find that the tangent of the REP's argument is approximately in inverse proportion to permeability. We obtain an inversion formula and present the permeability inversion method by using the tangent of the REP's phase. To test this method, the permeabilities of different sandstones are inverted from the synthetic full-waveform data of seismoelectric logs. A modified inversion process is proposed based on the analysis of inversion errors, by which the relative errors are controlled below 25% and they are smaller than those of the permeability inversion from the Stoneley wave of acoustic logs.

The main aim of this paper is to prove, for the general case, the uniqueness of Stoneley waves propagating along the bonded interface of two pre-stressed incompressible elastic half-spaces. In order to do that the authors have used the complex function method. By this approach, it is shown that the secular equation of Stoneley waves in pre-stressed incompressible elastic half-spaces has at most one solution in the complex plane. This says that if a Stoneley wave exists, then it is unique.

New inversion algorithms have been developed for estimating the formation shear and borehole-fluid slownesses, using either the borehole Stoneley or dipole flexural dispersion in well-bonded cased boreholes surrounded by a fast or slow isotropic and purely elastic formation. Two inversion algorithms have been developed for each type of formation. The first algorithm inverts either the measured borehole Stoneley or flexural dispersion at select frequencies for the formation shear slowness when all other model parameters are known. The second algorithm inverts either the borehole Stoneley or flexural dispersion for both the formation shear and borehole-fluid compressional slownesses. Optimal bandwidths for the inversion of the Stoneley and dipole flexural dispersions for the formation shear slowness range from about 5 to 8 kHz. The well-bonded cased borehole dispersion sensitivity to formation shear slowness becomes larger at these higher frequencies than in an open-hole. Moreover, the Stoneley dispersion sensitivity to the borehole-fluid compressional slowness is so large that it becomes necessary to input an extremely accurate estimate of fluid compressional slowness in the inversion algorithm. Inverted formation shear slowness from the Stoneley data in a fast formation exhibits an uncertainty of about 3%, whereas the input borehole-fluid slowness has an uncertainty of 0.5%. Given a certain amount of uncertainty in the borehole-fluid slowness, one can then estimate possible variances in the inverted formation shear slowness. In contrast, inversion of the flexural dispersion for formation shear slowness is less sensitive to the input borehole-fluid compressional slowness in the preferred frequency band of 5 to 8 kHz. Inverted formation shear slownesses in slow formations that use either the Stoneley or flexural dispersion are also far less sensitive to uncertainties in the borehole-fluid compressional slowness.

Formulas for the velocity of Stoneley waves propagating along the loosely bonded interface of two isotropic elastic half-spaces are derived using the complex function method. The derivation also shows that if a Stoneley wave exists, then it is unique. By using the obtained formulas, we can easily reproduce the numerical results previously obtained by Murty [G. S. Murty, Phys. Earth Planet. Interiors 11 (1975), 65–79.] by directly solving the secular equation.

Measurement of compressional, shear, and Stoneley wave velocities, carried out by dipole sonic imager (DSI) logs, provides invaluable data in geophysical interpretation, geomechanical studies and hydrocarbon reservoir characterization. The presented study proposes an improved methodology for making a quantitative formulation between conventional well logs and sonic wave velocities. First, sonic wave velocities were predicted from conventional well logs using artificial neural network, fuzzy logic, and neuro-fuzzy algorithms. Subsequently, a committee machine with intelligent systems was constructed by virtue of hybrid genetic algorithm-pattern search technique while outputs of artificial neural network, fuzzy logic and neuro-fuzzy models were used as inputs of the committee machine. It is capable of improving the accuracy of final prediction through integrating the outputs of aforementioned intelligent systems. The hybrid genetic algorithm-pattern search tool, embodied in the structure of committee machine, assigns a weight factor to each individual intelligent system, indicating its involvement in overall prediction of DSI parameters. This methodology was implemented in Asmari formation, which is the major carbonate reservoir rock of Iranian oil field. A group of 1,640 data points was used to construct the intelligent model, and a group of 800 data points was employed to assess the reliability of the proposed model. The results showed that the committee machine with intelligent systems performed more effectively compared with individual intelligent systems performing alone.

Acoustic wave propagation in fluid-saturated porous cylindrical shell is investigated in this paper by using the Biot’s theory. The Expressions for acoustic pressure and radical displacement in and out fluid, the expressions for components of solid and filtration displacement and pore fluid pressure and stress tensor are given. The numerical simulation is operated on acoustic field in fluid of poroelastic cylindrical shell, and the full-waveform is obtained by Fourier transform, and acoustic pressure field in frequency-wavenumber domain is analyzed, as well as the influence of inner and outer radii on wave amplitude is discussed. It shows that if the thickness of shell remains constant, the amplitude of longitudinal mode increases and that of Stoneley wave decreases when inner and outer radii increasing. In the fast formation the influence of inner and outer radii on the amplitude of longitudinal mode is notable. In the slow formation the amplitude of Stoneley wave will decrease with inner and outer radii increasing.

The dependence of the Stoneley attenuation length on the concentration and composition of salt in pore fluid observed in experiments may be associated with osmosis. The salinity dependence is relevant to methods in which the permeability of porous formations is estimated from its relationship with the Stoneley attenuation length.

The Stroh formalism is employed to study Rayleigh and Stoneley waves in exponentially graded elastic materials of general anisotropy under the influence of gravity. The 6×6 fundamental matrix N is no longer real. Nevertheless the coefficients of the sextic equation for the Stroh eigenvalue p are real. The orthogonality and closure relations are derived. Also derived are three Barnett-Lothe tensors. They are not necessarily real. Secular equations for Rayleigh and Stoneley wave speeds are presented. Explicit secular equations are obtained when the materials are orthotropic. In the literature, the secular equations for Stoneley waves in orthotropic materials are obtained without using the Stroh formalism. As a result, it requires computation of a 4×4 determinant. The secular equation presented here requires computation of a 2×2 determinant, and hence is fully explicit. A Rayleigh or Stoneley wave exists in the exponentially graded material under the influence of gravity if the wave can propagate in the homogeneous material without the influence of gravity. As the wave number k→∞, the Rayleigh or Stoneley wave speed approaches the speed for the homogeneous material.

A new algorithm is suggested for joint calculation of three key parameters of reservoir rocks: permeability, electroacoustic constant, and velocity of second bulk compressional wave (slow wave). The algorithm is advantageous in the use of Stoneley waves which are most stable in acoustoelectric log waveform data.

SUMMARY This paper describes a new algorithm based on the spectral method for the computation of Stoneley wave dispersion and attenuation propagating in cylindrical structures composed of fluid, elastic and poroelastic layers. The spectral method is a numerical method which requires discretizationofthestructurealongtheradialaxisusingChebyshevpoints.Toapproximatethe differential operators of the underlying differential equations, we use spectral differentiation matrices. After discretizing equations of motion along the radial direction, we can solve the problem as a generalized algebraic eigenvalue problem. For a given frequency, calculated eigenvaluescorrespondtothewavenumbersofdifferentmodes.Theadvantageofthisapproach is that it can very efficiently analyse structures with complicated radial layering composed of different fluid, solid and poroelastic layers. This work summarizes the fundamental equations, followed by an outline of how they are implemented in the numerical spectral schema. The interface boundary conditions are then explained for fluid/porous, elastic/porous and porous interfaces. Finally, we discuss three examples from borehole acoustics. The first model is a fluid-filledboreholesurroundedbyaporoelasticformation.Thesecondconsidersanadditional elastic layer sandwiched between the borehole and the formation, and finally a model with radially increasing permeability is considered.

Using the integral Fourier-transform technique, we obtain a solution in integral form to the problem of excitation of elastic waves in a homogeneous isotropic solid half-space and the bordering homogeneous gas by the time-dependent forces which are arbitrarily distributed in a solid over the plane parallel to the interface of the media. Different configurations of the force sources are analyzed from the viewpoint of excitation of different types of seismoacoustic waves. Expressions for the time-averaged radiated powers of the Stoneley wave at the gas–solid interface and the Rayleigh wave at the solid–vacuum interface as well as analytical expressions for the Rayleigh wave displacements, which are valid for large distances from the source, are obtained for the harmonic dependence of forces on time. Excitation of a Rayleigh wave by the point sources oriented vertically, i.e., along the normal to the surface of elastic half-space, and horizontally, i.e., parallel to this surface, is analyzed in detail. Analytical expressions for the Rayleigh-wave radiated power are obtained. The dependences of these powers on the source orientation and depth are derived. It is shown that the Rayleigh-wave radiated power decreases with distance between the point of the force application and the boundary and turns to zero for a source depth of about 17.5% of the wavelength of the transverse wave in the case of a horizontally oriented subsurface source and a medium with identical Lame parameters λ and μ. This power increases and reaches a relative maximum when the source depth becomes equal to about 42.4% of the wavelength of the transverse wave and then exponentially falls off as the source depth increases. This maximum is about 5.5% of the surface-source radiated power.

New way for quantitative evaluation of any value of formation permeability based on numerical experiments with Pride's model of electrokinetic phenomena is presented. This approach is based on simultaneous measurement of pressure field and axial component of electric field excited by an acoustic source in fluid-filled borehole with help a set of receivers in borehole. Frequency dependence of ratio of the complex-valued amplitudes of the electric Stoneley wave to the pressure Stoneley wave obtained as a result of plane-wave decomposition of pressure field and mentioned component of electric field carries important information about permeability. In case of open and sealed pores on borehole wall were obtained enough simple analytical expressions for this ratio.

Conventionally discussed dynamic mechanisms of elastic strain energy redistribution in near-contact surface regions include P and S elastic wave pulses radiating from the contact surface. At the same time, the elastic strain energy can be transferred by localized vortex-like elastic waves (Rayleigh, Love, Stoneley wave, and so on). In the paper, we numerically studied the main features of the formation and propagation of localized vortex-like waves in the surface layers under the contact zone. The study was done using the numerical method of movable cellular automata. We showed that the initial phase of dynamic contact interaction with a nonzero tangential component of contact velocity is accompanied by the formation of a so-called elastic vortex. The elastic vortex is a fully dynamic object, which is characterized by shear stress concentration and propagates at the shear wave speed. We first revealed the ability of the elastic vortex to propagate toward the bulk of the material and transfer elastic strain energy deep into the surface layer in a localized manner. We analyzed the dependence of the direction of vortex propagation on the tangential contact velocity, contact pressure and Young’s modulus of the material. The results of the study are important for better understanding the dynamic mechanisms contributing to inelastic strain accumulation or gradual degradation of surface layers.

Compressional, shear and Stoneley wave velocities (V"p, V"s and V"s"t, respectively) are important reservoir characteristics that have many applications in petrophysical, geophysical and geomechanical studies. In this study V"p, V"s and V"s"t were predicted from well log data using genetic algorithms, fuzzy logic and neuro-fuzzy techniques in an Iranian carbonate reservoir (Sarvak Formation). A total of 3030 data points from the Sarvak carbonate reservoir which have V"p, V"s, V"s"t and conventional well log data were used. These data were divided into two groups; one group included 2047 data points used for constructing intelligent models, and the other included 983 data points used for models testing. The measured mean squared errors (MSEs) of predicted V"p in the test data, using genetic algorithms, fuzzy logic and neuro-fuzzy techniques, were 0.0296, 0.0148 and 0.029, respectively, for V"s these errors were 0.0153, 0.0084 and 0.0184, respectively, and for V"s"t they were 0.00035, 0.00020 and 0.00062, respectively. Despite different concepts in these intelligent techniques, the results (especially those from fuzzy logic) seem to be reliable.

Just as uni-directional Rayleigh waves at the traction-free surface of a transversely isotropic elastic half-space and Stoneley waves at the interface between two such media may have arbitrary waveform and may be represented in terms of a single function harmonic in a half-plane, it is shown that surface-guided waves travelling simultaneously in all directions parallel to the surface may be represented, at each instant, in terms of a single function satisfying Laplace’s equation in a three-dimensional half-space. That harmonic function is determined so that its normal derivative at the surface equals the normal displacement of the surface (or interface). It is shown, moreover, that the time evolution of that normal displacement may be any solution to the membrane equation with wave speed being equal to that of classical, uni-directional, time-harmonic Rayleigh or Stoneley waves. A similar representation is also shown to exist for Schölte waves at a fluid–solid interface, in the non-evanescent case. Thus, every surface- or interface-guided disturbance in media having rotational symmetry about the surface normal is governed by the membrane equation with appropriate wave speed, provided that the combination of materials allows uni-directional, time-harmonic waves that are non-evanescent. Conversely, each solution to the membrane equation may be used to construct a representation of either a Rayleigh wave, a Stoneley wave or a (non-evanescent) Schölte wave. In each case, the disturbance at all depths may be represented at each instant in terms of a single function harmonic in a half-space.

The properties of harmonic surface waves in an elastic cylinder filled with a liquid are studied. The case of elastic material for which the shear wave velocity is higher than the sound velocity in a liquid is considered. The wave motion is described based on the complete system of equations of the dynamic theory of elasticity and the equation of motion of an ideal compressible liquid. The asymptotic analysis of the dispersion equation in the region of large wave numbers and qualitative analysis of the dispersion spectrum showed that in such a waveguiding system there exist two surface waves, the Stoneley and the Rayleigh waves. The lowest normal wave forms the Stoneley wave on the internal surface of the cylinder. In this waveguide phase, velocities of all normal waves, except for the lowest one, have the velocity of sound in the liquid as their limit. Therefore, the Rayleigh wave on the external surface of the cylinder is formed by all normal waves in the range of frequencies and wave numbers in which phase velocities of normal waves of the composite waveguide and the lowest normal wave of the elastic hollow cylinder coincide.

SUMMARY The Frenkel-Biot theory is used to study a propagation of Stoneley elastic wave at the boundary of two fluid-saturated porous media. The velocity and attenuation of the Stoneley surface wave are determined. I show that the dispersion equation coincides with the equation for the Stoneley wave at the interface of two elastic half-spaces in the low-frequency range. Numerical examples of calculations are presented for two important cases: two different fluids lying in the same viscoelastic skeleton (gas–water interface) and two poroelastic half-spaces with different porosity and permeability containing the same fluid. To take into account the absorption in the solid matrix, I use well-known Stoll’s model. Our calculation results have shown that the Stoneley wave absorption is determined by the energy dissipation in the solid matrix for consolidated rocks. As the frequency is increased, hydrodynamic effects connected with the presence of a movable fluid in the pores begin to play a significant role.

This paper addresses the canonical two dimensional problem of diffraction of the plane wave by a semi-infinite interfacial crack sandwiched between two isotropic solids. We restrict ourselves to a ubiquitous case of solids whose contact boundary does not support the Stoneley wave. Its solution can be used in applications to model diffraction from curved cracks with curvature that is small compared to a wavelength. A correction to this article has been appended at the end of the pdf file.

SUMMARY We design a numerical algorithm for wave simulation in a borehole due to multipole sources. The stress–strain relation of the formation is based on the Kelvin–Voigt mechanical model to describe the attenuation. The modelling, which requires two anelastic parameters and twice the spatial derivatives of the lossless case, simulates 3-D waves in an axisymmetric medium by using the Fourier and Chebyshev methods to compute the spatial derivatives along the vertical and horizontal directions, respectively. Instabilities of the Chebyshev differential operator due to the implementation of the fluid–solid boundary conditions are solved with a characteristic approach, where the characteristic variables are evaluated at the source central frequency. The algorithm uses two meshes to model the fluid and the solid. The presence of the logging tool is modelled by imposing rigid boundary conditions at the inner surface of the fluid mesh. Examples illustrating the propagation of waves are presented, namely, by using monopoles, dipoles and a quadrupoles as sources in hard and soft formations. Moreover, the presence of casing and layers is considered. The modelling correctly simulates the features—traveltime and attenuation—of the wave modes observed in sonic logs, namely, the P and S body waves, the Stoneley wave, and the dispersive S waves in the case of multipole sources.

The propagating properties of the mode waves excited by multipole sources in a fluid-filled borehole embedded in radially layered transversely isotropic porous formation are investigated. The results show that the propagating characteristics of the mode waves are determined largely by the virgin formation in the low frequency band, and with the frequency increasing the characteristics of the mode waves are controlled by the invaded zone gradually. In the Biot theory the attenuation is easier to be affected by the formation around the borehole wall than the velocity. The frequency-dependent sensitivity coefficients with respect to the parameters of the radial layers are computed quantitatively. Comparing the horizontal permeability with the vertical permeability, the horizontal mobility plays the predominant role over the entire frequency range. The Stoneley wave is more sensitive to the velocity of the horizontally propagating SH wave than the flexural wave. The results of the work also show that the acoustic logging tool with broadband and distributed receiver array is advantageous to image the acoustic parameters in different radial depths.