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Following the derivation of multiple reducts,an ensemble based classification framework can be constructed,which has been demonstrated to be useful in improving the performance of subsequent learning tasks.The approach called super-reduct is exactly suggested with such thinking.Generally,multiple super-reducts are obtained by randomly adding more extra attributes into the fundamental reduct.Therefore,how to search fundamental reduct is the key to performing super-reduct.In view of this,considering both efficiency and effectiveness,not only attribute group but also ensemble selector is introduced into the mechanism of super-reduct:the device of attribute group is used to speed up the process of searching fundamental reduct,the device of ensemble selector is used to find more robust attributes in the procedure of searching reduct.Comprehensive experiments on 20 UCI data sets show that compared with 4 popular strategies,our approach can not only significantly reduce the computational cost but also provide superior stabilities and accuracies for classification tasks.

The rheological models of Lomnitz and Jeffreys have been widely used in earthquake seismology (to simulate a nearly constant Q medium) and to describe the creep and relaxation behavior of rocks as a function of time. Other similar models, such as those of Becker, Scott Blair and Kolsky, show similar properties, particularly the Scott Blair model describes a perfectly constant Q as a function of frequency. We first give a historical overview of the main scientists and the development and versions of the various models and priorities of discovery. Then, we clarify the relationship between the different versions of these models in terms of mathematical expressions of the complex modulus and calculate the phase velocity and quality factor Q as a function of frequency, illustrating the various special cases. In addition, we give useful hints for the numerical calculation of these moduli, which include special cases of the hypergeometric function. [ABSTRACT FROM AUTHOR]

The diffusive viscous (DV) model is a useful tool for interpreting low-frequency seismic attenuation and the influence of fluid saturation on frequency-dependent reflections. Among present methods for the numerical solution of the corresponding DV wave equation, the finite-difference frequency-domain (FDFD) method with complex-valued adaptive coefficients (CVAC) has the advantage of efficiently suppressing both numerical dispersion and numerical attenuation. In this research, the FDFD method with CVAC is first generalized to a 3D DV equation. In addition, the current calculation of CVAC involves the numerical integration of propagation angles, conjugate gradient (CG) iterative optimization, and the sequential selection of initial values, which is difficult and inefficient for implementation. An improved method is developed for calculating CVAC, in which a complex-valued least-squares problem is constructed by substituting the 3D complex-valued plane-wave solutions into the FDFD scheme. The QR-decomposition method is used to efficiently solve the least-squares problem. Numerical dispersion and attenuation analyses reveal that the FDFD method with CVAC requires ∼2.5 spatial points in a wavelength within a dispersion deviation of 1% and an attenuation deviation of 10% for the 3D DV equation. An analytic solution for 3D DV wave equation in homogeneous media is proposed to verify the effectiveness of the proposed method. Numerical examples also demonstrate that the FDFD method with CVAC can obtain accurate wavefield modelling results for 3D DV models with a limited number of spatial points in a wavelength, and the FDFD method with QR-based CVAC requires less computational time than the FDFD method with CG-based CVAC. [ABSTRACT FROM AUTHOR]

Temperature and pressure variations during the geologic diagenesis process can lead to complex pore structures in tight rocks. The effective-medium theory, based on the stress–strain relationship in combination with pore structure parameters, can be used to describe the elastic-wave responses of rocks. In this work, the differential effective medium (DEM) and self-consistent approximation (SCA) models are combined to invert the pore-crack spectrum. The Voigt–Reuss–Hill average is used to estimate the elastic moduli of the minerals. Then, based on SCA, the pore structures are incorporated into the rock matrix to create a new host phase. Subsequently, the DEM theory is used to add cracks with different volume fractions and aspect ratios to the host phase. To predict the structure of pores and cracks (crack density and aspect ratio), an objective function is defined as the sum of variances between experimentally measured and predicted wave velocities. The results show that the modeling predictions of P- and S-wave velocities at different temperatures and pressure ratios agree well with the experimental measurements. Variations in pore structure are determined at a zero effective pressure and different temperatures. We analyze the characteristics of how cracks change with variations in temperature and confining pressure, providing a theoretical basis for characterizing the structure of tight rocks. [ABSTRACT FROM AUTHOR]

The time-fractional Cattaneo (TFC) equation is a practical tool for simulating anomalous dynamics in physical diffusive processes. The existing numerical solutions to the TFC equation generally deal with the Dirichlet boundary conditions. In this paper, we incorporate the absorbing boundary condition as a complex-frequency-shifted (CFS) perfectly matched layer (PML) into the TFC equation. Then, we develop an adaptive-coefficient (AC) finite-difference frequency-domain (FDFD) method for solving the TFC with CFS PML. The corresponding analytical solution for homogeneous TFC equation with a point source is proposed for validation. The effectiveness of the developed AC FDFD method is verified by the numerical examples of four typical TFC models, including the different orders of time-fractional derivatives for both the homogeneous model and the layered model. The numerical examples show that the developed AC FDFD method is more accurate than the traditional second-order FDFD method for solving the TFC equation with the CFS PML absorbing boundary condition, while requiring similar computational costs. [ABSTRACT FROM AUTHOR]

We perform seismic and ultrasonic measurements in carbonate and shaley sandstone samples as a function of differential pressure. The velocities show a strong frequency and pressure dependence. The dispersion disappears with increasing pressure and the squirt flow in turn inhibits the pressure dependence. To model these effects, we combine the Gurevich's squirt-flow model with the Mori–Tanaka scheme and the David Zimmerman model, and extend it with third-order elastic constants, to obtain a frequency-dependent acoustoelasticity model. Comparisons between measurements from this study and literature and modelling results show that the P -wave velocity increases non-linearly first and then nearly linearly, dominated by crack closure and acoustoelasticity, respectively. The pressure dependence of wave velocities is reduced by liquid substitution and further by the squirt-flow mechanism. The effects of fluid properties and crack closure on P -wave velocity decrease with differential pressure. The results will feed a new model and help better understanding the wave propagation in pre-stressed rocks at different scales. [ABSTRACT FROM AUTHOR]

Mesoscopic P-wave attenuation in layered, partially saturated thermo-poroelastic media is analyzed by combining the theories of Biot poroelasticity and Lord–Shulman thermoelasticity (BLS). The attenuation is quantified by estimating the quality factor Q. The mesoscopic attenuation effect, commonly referred to as wave-induced fluid flow (WIFF), is the process that converts fast compressional and shear waves into slow diffusive Biot waves at mesoscopic heterogeneities larger than the pore scale, but much smaller than the dominant wavelengths. This effect was first modeled in White's isothermal theory by quantifying the seismic response of a periodic sequence of planar porous layers that are alternately saturated with gas or water. This work presents a numerical extension of White's theory for the non-isothermal case in this type of sequence. For this purpose, an initial-boundary-value problem (IBVP) for the BLS wave propagation equations is solved using the finite element method, where the particle velocity field is recorded at uniformly distributed receivers. The quality factor is estimated using spectral-ratio and frequency-shift methods. The Q-estimates show that thermal effects influence the attenuation of the P-wave and the velocity dispersion compared to the isothermal case. [ABSTRACT FROM AUTHOR]

Knowledge of how temperature affects the oil–sand acoustic response is useful to exploit these reservoir rocks with seismic methods. We propose three models: double-porosity coherent potential approximation (CPA), lower-bound Hashin–Shtrikmann (HS-), and contact cement (CC), based on different spatial distributions of heavy oil and temperature and frequency-dependent empirical equations. The shear modulus and S-wave velocity are affected by temperature in all the cases. Moreover, the properties of oil sands with heavy oil as a continuous matrix and higher viscosity are more sensitive to temperature. The models can provide theoretical support for the establishment of rock physical models in heavy oil reservoirs so as to quantitatively characterize the seismic response changes caused by thermal mining. [ABSTRACT FROM AUTHOR]

Geometric heterogeneities in tight reservoir rocks saturated with a fluid mixture may exhibit different scale distribution characteristics. Conventional models of rock physics based on poroelasticity, which usually consider single‐scale pore structure and fluid patches, are inadequate for describing elastic wave responses. A major challenge is to establish the relationship between the wave response at different spatial scales and frequencies. To address this problem, three sets of observational data over a wide frequency range were obtained from a tight oil reservoir in the Ordos Basin, China. Ultrasonic measurements were made on eight sandstone samples at partial oil‐water saturation at 0.55 MHz. Data from six borehole measurements and seismic profiles were acquired and analyzed at about 10 kHz and 30 Hz, respectively. Analysis of the cast thin sections shows that dissolution pores and microcracks generally develop, with fractal dimensions of the pores ranging from 2.45 to 2.67 for the samples with porosities between 5.1% and 10.2%. Compressional wave velocity and attenuation were estimated from the observed data. The results show that the velocity dispersion from seismic to ultrasonic frequencies is 10.02%, mostly occurring between sonic and ultrasonic frequencies. The attenuation is stronger at higher oil saturation. The relationships between velocity, attenuation, and wavelength were established and can be used for further forward modeling and seismic interpretation studies. A partial saturation model has been derived based on effective differential medium theory and a double double‐porosity model, assuming that the medium contains fractal cracks and fluid patches. The effects of scale and saturation on wave responses are prevalent. Modeling results consistent with observed data show that the radii of cracks and fluid patches range from 0.1 μm to 2.8 mm, affecting ultrasonic, acoustic, and seismic attenuation. The multiscale data and proposed model quantify the relationship between fracture and fluid distributions and attenuation and could be useful for upscaling to the reservoir scale. The study helps improve the understanding of seismic wave propagation in partially saturated rocks, which has potential applications in seismic exploration, hydrocarbon production in reservoirs, and CO2 sequestration in aquifers. Plain Language Summary: The physical properties of the rock and fluid can be inferred from the measured elastic wave responses and energy dissipation characteristics. However, the effects of heterogeneities of different sizes and at different frequencies can hinder studies to quantify wave responses in a partially saturated porous medium, which are usually based on laboratory measurements. A major problem is the difference between observed frequencies and scales: megahertz in the laboratory, 10 of kilohertz in the borehole scale, and hertz in the seismic exploration scale. In this work, the frequency‐ and saturation‐dependent compressional velocity and attenuation are investigated using three geophysical data sets from the same tight reservoirs. A strong velocity dispersion over the measured frequency range is observed. The stronger attenuation at partial saturation may be caused by the multiscale heterogeneities of the pore structure and fluid patch distribution. A fractal poroelasticity model is developed by gradually inserting inclusions of different sizes with compliant pores and liquid patches into a homogeneous host skeleton. The wave responses are significantly affected by scale distribution and saturation. The proposed model, verified by the measured data, can be useful in interpreting the anelasticity of tight heterogeneous reservoirs in a broadband range. Key Points: We investigate how fluid saturation affects wave attenuation and dispersion over a wide frequency range in tight sandstone layersA partial saturation model describes the fractal properties of the layersThe size of the cracks and fluid patches are determined by applying the fractal model to the multiscale data [ABSTRACT FROM AUTHOR]

Wave propagation in anelastic rocks is a relevant scientific topic in basic research with applications in exploration geophysics. The classical Biot theory laid the foundation for wave propagation in porous media composed of a solid frame and a saturating fluid, whose constitutive relations are linear. However, reservoir rocks may have a high-viscosity fluid, which exhibits a non-Newtonian (nN) behaviour. We develop a poroelasticity theory, where the fluid stress-strain relation is described with a Kelvin–Voigt mechanical model, thus incorporating viscoelasticity. First, we obtain the differential equations from first principles by defining the strain and kinetic energies and the dissipation function. We perform a plane-wave analysis to obtain the wave velocity and attenuation. The validity of the theory is demonstrated with three examples, namely, considering a porous solid saturated with a nN pore fluid, a nN fluid containing solid inclusions and a pure nN fluid. The analysis shows that the fluid may cause a negative velocity dispersion of the fast P (S)-wave velocities, that is velocity decreases with frequency. In acoustics, velocity increases with frequency (anomalous dispersion in optics). Furthermore, the fluid viscoelasticity has not a relevant effect on the wave responses observed in conventional field and laboratory tests. A comparison with previous theories supports the validity of the theory, which is useful to analyse wave propagation in a porous medium saturated with a fluid of high viscosity. [ABSTRACT FROM AUTHOR]

We study the anelastic properties (attenuation and velocity dispersion) of surface waves at an interface between a finite water layer and a porous medium described by Biot theory including the frequency-dependent effects due to mesoscopic flow. A closed-form dispersion equation is derived, based on potential functions and open and sealed boundary conditions (BC) at the interface. The analysis indicates the existence of high-order surface modes for both BCs and a slow true surface mode only for sealed BC. The formulation reduces to two particular cases in the absence of water and with infinite-thickness water layer, with the presence of pseudo-versions of Rayleigh and Stoneley waves. The mesoscopic flow affects the propagation of all the pseudo-surface waves, causing significant velocity dispersion and attenuation, whereas the effect of the BC is mainly evident at high frequencies, due to the presence of the slow Biot wave. The mesoscopic-flow peak moves to low frequencies as the thickness of the water layer increases. In all cases, the true surface wave resembles the slow P2 wave, and is hardly affected by the flow. [ABSTRACT FROM AUTHOR]

Seismic wave propagation is affected by wave‐induced local fluid flow between stiff pores and multiscale fractures. To investigate this phenomenon, forced vibration (1–100 Hz) and ultrasonic (106 Hz) measurements are performed on two tight sandstones with complex pore geometry in dry and water‐saturated scenarios. Porosity, permeability, and ultrasonic velocities were also measured at different differential pressures. The results indicate that the nonlinear behavior of these properties is strongly influenced by the presence of cracks, and the correlations between the permeability/ultrasonic velocities and porosity are different. A wave propagation model is then developed in which penny‐shaped cracks are inclusions introduced stepwise into a porous medium to describe the wave anelasticity in a wide frequency band at different pressures. As a result, the model provides good agreement with the measured P‐wave velocity dispersion, and the pore aspect ratio spectrum and crack radii are determined. We then compare the estimated crack radii and pore size distributions from nuclear magnetic resonance spectroscopy. Published data of a tight sandstone and a low porosity sandstone in the frequency range (2–200, 106) and (1–3,000) Hz at different differential pressures are also analyzed to validate the model. The aspect ratios, volume fractions, and radii of pores/cracks are used to describe the measured permeability. The present work can provide new insights into the geophysical properties of reservoir rocks with complex pore geometry. Plain Language Summary: Multiscale cracks exert an important influence on the dispersion and attenuation of broadband acoustic waves. To better understand the underlying mechanism, we measured frequency‐dependent elastic moduli and pressure‐dependent porosity, permeability, and ultrasonic wave velocities of two tight sandstones. These data show that velocity dispersion is observable in water‐saturated rock and that permeability and ultrasonic velocities are differentially correlated with porosity. A proposed wave propagation model, in which penny‐shaped cracks are inclusions introduced stepwise into a porous medium, successfully describes the experimental data and other published data on tight sandstone and low‐porosity sandstone, and aspect ratios, volume fractions, and radii of pores/cracks are determined. Key Points: We propose a model to investigate the effect of multiscale cracks on seismic waves in tight sandstonesThe pore aspect ratio and crack‐radius spectra are estimated at different differential pressuresThe permeability is obtained according to the pore geometry [ABSTRACT FROM AUTHOR]

We simulate variations in the P- and S-wave velocities due to CO2 injection in basalt, caused by water replacement and mineralization in the form of carbonate cements. Carbonization can be monitored with seismic data on the basis of changes in velocity. We consider basalts composed of (Fe, Ca and Mg) minerals mainly, and the pore space is assumed to be initially saturated with water. The mineralization is based on a model that estimates the volume of precipitated cement and resulting porosity loss, and the velocities as a function of injection time are calculated with a patchy cement model. In the example, there are two stages: 1 week of CO2 injection and 29 weeks of frame cementation. After 1 week, water has been replaced by CO2, where density and P-wave velocity decrease, and cementation implies an increase in bulk density, P-wave velocity, whereas porosity and surface area are reduced. To our knowledge there are no models relating the effects of carbon mineralization on seismic properties. The present model can be applied to other rocks, where CO2 injection induces mineralization and storage. [ABSTRACT FROM AUTHOR]

SUMMARY: We consider surface-wave propagations at an interface separating a fluid layer and a double-porosity medium embedded with cracks. The theory is based on a generalization of the Biot-Rayleigh model from spherical cavities to penny-shaped cracks randomly embedded into a host medium, where mesoscopic local fluid flow (LFF) plays an important role. We derive closed-form dispersion equations of surface waves, based on potentials and suitable boundary conditions (BCs), to obtain the phase velocity and attenuation by using numerical iterations. Two special cases are considered by letting the thickness of the fluid (water) layer to be zero and infinity. We obtain pseudo-Rayleigh and pseudo-Stoneley waves for zero and infinite thickness and high-order surface modes for finite nonzero thickness. Numerical examples confirm that the LFF affects the propagation at low frequencies, causing strong attenuation, whereas the impact of BCs is mainly observed at high frequencies, due to the propagation of slow wave modes. The crack density mainly affects the level of attenuation, whereas the aspect ratio the location of the relaxation peak. The fundamental mode undergoes a significant velocity dispersion, whose location moves to low frequencies as the thickness increases. In all cases, there also exist two slower surface modes that resemble the two slow body waves, only present for sealed BCs. [ABSTRACT FROM AUTHOR]

Deep carbonate reservoirs are subject to in-situ conditions of high temperature and high pressure. We consider six water-saturated dolomite specimens from these reservoirs and perform ultrasonic experiments to obtain the P- and S-wave waveforms and velocities under different pressure and temperature conditions. The P-wave attenuation is estimated using the spectral-ratio method. The results show that with the increase of temperature, the velocities slightly decrease and attenuation increases. At effective pressures <40 MPa, the P-wave velocities increase sharply with pressure and then approximately linearly at higher pressures, while attenuation decreases gradually with pressure. The crack porosity as a function of pressure is obtained from the experimental data. The P-wave velocities decrease with this porosity while attenuation shows an opposite behavior. Then, a multiscale poroelasticity model considering micro-, meso- and macro-scale fluid-flow mechanisms is proposed to analyze the effects of the fluid properties, temperature and crack content on the wave responses. The model results agree well with the experimental data at different pressures, which provides a theoretical basis for the analysis of broadband wave velocity dispersion and attenuation phenomena of carbonate reservoirs and underground porous media in general. [ABSTRACT FROM AUTHOR]

As an important geophysical data processing technique, seismic inversion estimates subsurface rock properties with seismic observations. However, anisotropic inversion, intended for a vertical transverse isotropy (VTI) media that primarily describes shale gas/oil resources, suffers from high nonlinearity. Simulated annealing is a widely used global optimization algorithm for solving nonlinear seismic inverse problems, but it involves multiple optimization parameters (e.g., initial temperature, search limit, and perturbation range). The importance of such parameters has been proven whilst the relevant analysis is limited in seismic inversion studies. This work hereby proposes a sequential anisotropic inversion method for VTI media, wherein we combine Bayesian linear and simulated annealing nonlinear inversion schemes. The simulated annealing is featured by adaptive optimization parameters aided by the linear result. Rather than the conventional method, the adaptive setting can be implemented trace by trace for complex reservoirs, which endows the method with enhanced stability and extended applicability. Synthetic tests and practical application demonstrate the validity of the method, wherein the obtained stiffness parameters facilitate the characterization of potential shale reservoirs with an improved accuracy. [ABSTRACT FROM AUTHOR]

There is a mathematical analogy between the poroelastic and thermoelastic behavior of the compressional P wave, whose dissipation is due to the coupling between the elastic deformation and the phenomenon of pressure and heat diffusion, represented by Darcy's law and heat conduction, respectively. This attenuation effect is more pronounced in heterogeneous media, where conversion of the fast P wave to the slow (Biot) and thermal diffusive modes occurs at material interfaces. Specifically, the problem is to obtain the P-wave properties of a porous medium due to temperature gradients between the solid and fluid phases. Then, we consider a simplified one-dimensional porous medium and obtain the quality factor, Q, and phase velocity as a a function of frequency, based on an isostress condition and using Gassmann equation and the Kramers Kronig relations.The model allows for the incorporation of a relaxation time to simulate a proper wave-like behavior at high frequencies, avoiding in this way infinite velocities. Moreover, we perform a complete analysis varying the different parameters, namely, the heat conduction, the specific heat, the thermal expansion, the types of solid and fluid and the pore size. [ABSTRACT FROM AUTHOR]

We investigate the effect of temperature on the elastic properties of rocks by combining the thermal-damage factor (TDF) with the Gassmann equation. The resulting model is tested in carbonate samples by analyzing the ultrasonic wave velocity. A comparison between the estimated and measured TDF shows that the model quantitatively describes the behavior of carbonates at relatively low temperatures, while the high-temperature one is underestimated. The dry- and wet-rock TDF difference increases significantly with increasing temperature, and the TDF is highly affected by the rock permeability and microcrack aspect ratio. [ABSTRACT FROM AUTHOR]

The acoustic-electrical (AE) response of subsurface hydrocarbon reservoirs is highly affected by rock heterogeneity. In particular, the characterization of the microstructure of tight (low-permeability) rocks can be aided by a joint interpretation of AE data. To this purpose, we evaluate cores from a tight-oil reservoir to obtain the rock mineralogy and pore structure by X-ray diffraction and casting thin sections. Then, ultrasonic and resistivity experiments are performed under different confining pressures to analyze the effects of pores, microcracks and mineralogy on the AE properties. We have developed acoustic and electrical models based on effective-medium theories, and the Cole–Cole and triple-porosity equations, to simulate the response to total and soft (crack) porosities and clay content. The results show that these properties play a significant role. Then, a 3D rock-physical template is built and calibrated by using the core samples and well-log data. The template is applied to tight-oil reservoirs to estimate the rock properties, which are validated with log data. The good match between the predictions and these data indicates that the model can effectively explain the effects of the heterogeneous microstructure on the AE data. Article Highlights: Tight rock microstructure is analyzed with X-ray diffraction, thin sections and ultrasonic and electrical resistivity tests Rock acoustic-electrical properties are obtained by the effective-medium and triple-porosity theories Practical application is given based on an acoustic-electrical rock physics template [ABSTRACT FROM AUTHOR]

We obtain the amplitude and energy reflection coefficients of seismic waves in porous media with penny-shaped inclusions, based on the generalized Biot-Rayleigh model that takes into account the attenuation due to mesoscopic local fluid flow (LFF). We consider two cases, including a contact between two porous media having either different fluids (gas–water contact) or crack density and aspect ratio, as well as a water half-space overlying a porous medium, and study the frequency-dependent reflection-transmission (scattering) coefficients for open- and sealed-pore boundary conditions. Our examples show that the LFF mechanism mainly reduces the reflection coefficients (amplitude and energy) at the gas–water contact and at a water–porous medium interface for frequencies less than 10 kHz, due to the fact that the velocity in the lower medium decreases. For the latter case, if the fluid is gas, the LFF effect becomes only important at frequencies between 0.0001 and 10 Hz for the open-pore case. This is due to the fact that the acoustic impedance contrast between water and gas is high. At frequencies less than 0.0001 Hz, the interface is equivalent to a water–elastic medium one, and hence the results are the same as those of the sealed-pore case. Moreover, the crack density and aspect ratio affect the mesoscopic attenuation and relaxation frequency, and therefore the reflection coefficients. [ABSTRACT FROM AUTHOR]

The elastic properties of rocks depend on the mineral constituents, pore structure, saturating fluids, and stress (loading) conditions. To study these properties, we measured ultrasonic P‐ and S‐wave velocities as a function of the differential (confining minus pore) pressure and propose an unrelaxed double‐porosity acoustoelasticity model, which generalizes the single‐porosity one. The new approach includes the effects of crack closure, based on the David‐Zimmerman model, and the squirt‐flow mechanism, based on the Gurevich model. When cracks are open at low differential pressures, their properties dominate the wave velocity variations, followed by the squirt‐flow mechanism. Then, a transition occurs, where cracks partially close, and the squirt‐flow effect vanishes. At high pressures, cracks close and acoustoelasticity effects prevail. This behavior is observed in sedimentary rocks, whereas in granites, which have a low crack content, the acoustoelastic effect is dominant at all pressures. Plain Language Summary: It is well known that physical properties of rocks are important factors affecting the elastic wave velocities. However, how these properties affect the velocity‐pressure relations are not well understood. We conducted laboratory experiments and observed that the variation of wave velocities is related to crack closure, squirt flow and acoustoelasticity effects. To study the combined effects of these mechanisms, we propose an unrelaxed double‐porosity acoustoelasticity model. The theoretical results compared with the experimental data shows that, in sedimentary rocks, the crack properties dominate the pressure‐dependent velocities, followed by the squirt‐flow mechanism at low differential pressures. At high pressures, cracks approach full closure and the acoustoelasticity effect is the most significant. For low porosity granites, the acoustoelasticity effect dominates at all pressures. Key Points: We measure elastic wave velocities in saturated rocks, to analyze the effects of crack closure, squirt flow and acoustoelasticityTo this purpose, we develop an unrelaxed double‐porosity acoustoelasticity modelCrack closure dominates, followed by the squirt‐flow mechanism at low differential pressures, while acoustoelasticity effects are important at high differential pressures. In granites, the last effect prevails [ABSTRACT FROM AUTHOR]

Petrophysical seismic inversion, aided by rock physics, aims at estimating reservoir properties based on reflection events, but it is generally based on the Gassmann equation, which precludes its applicability to complex reservoirs. To overcome this problem, we present a methodology based on the double-porosity Biot–Rayleigh (BR) model, which takes into account the rock heterogeneities. The volume ratio of inclusions in the BR model is treated as a spatially varying parameter, facilitating a better description of the pore microstructure. The method includes the Zoeppritz equations to extract reservoir properties from prestack data. To handle the ill-posedness of the inversion and achieve a stable solution, the algorithm is formulated as a multi-objective optimization based on the Bayes theorem, where the reservoir-property estimation is jointly conditioned to seismic and elastic data with multiple prior terms. The method is validated with field data of a tight gas sandstone reservoir, illustrating its effectiveness compared to the Gassmann-based estimation, reducing uncertainties and improving the accuracy of identifying gas zones. Article Highlights: The petrophysical seismic inversion is based on the double-porosity Biot–Rayleigh model Spatially varying inclusion volumes are used to describe complex pore structures A multi-objective optimization with joint data misfit enables stable results [ABSTRACT FROM AUTHOR]