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We study the reflection and transmission (R/T) characteristics of inhomogeneous plane waves at the interface between two dissimilar fluid-saturated thermoporoelastic media at arbitrary incidence angles. The R/T behaviors are formulated based on the classic Lord–Shulman (LS) and Green–Lindsay (GL) heat-transfer models as well as a generalized LS model, respectively. The latter results from different values of the Maxwell-Vernotte-Cattaneo relaxation times. These thermoporoelastic models can predict three inhomogeneous longitudinal (P1, P2, and T) waves and one shear (S) wave. We first compare the LS and GL models for the phase velocities and attenuation coefficients of plane waves, where the homogeneous wave has a higher velocity but weaker thermal attenuation than the inhomogeneous wave. Considering the oil–water contact, we investigate R/T coefficients associated with phase angles and energy ratios, which are formulated in terms of incidence and inhomogeneity angles, with the latter having a significant effect on the interference energy. The proposed thermoporoelastic R/T model predicts different energy partitions between the P and S modes, especially at the critical angle and near grazing incidence. We observe the anomalous behavior for an incident P wave with the inhomogeneity angle near the grazing incidence. The energy partition at the critical angle is mainly controlled by relaxation times and boundary conditions. Beyond the critical angle, the energy flux predicted by the Biot poroelastic and LS models vanishes vertically, becoming the opposite for the GL and generalized LS models. The resulting energy flux shows a good agreement with the R/T coefficients, and they are well proven by the conservation of energy, where the results are valuable for the exploration of thermal reservoirs. [ABSTRACT FROM AUTHOR]

In principle, wave propagation in porous media can simultaneously trigger macroscopic fluid flow and thermal flow, which can be described by Biot's poroelasticity and Lord–Shulman thermoelasticity, respectively. The physical processes of those effects are significantly different, but phenomenologically, they can lead to identical wave attenuation and dispersion and are hard to be distinguished. By using Biot's virtual concept entropy flow, the Biot-consistent General Linear Solid (the GLS) framework and matrix notation, a rigorous and convenient tool is provided to reveal the similarities and disparities between poroelasticity and thermoelasticity. By using the same framework, a Biot-consistent thermo-poroelastic model is proposed to consider macroscopic effects of fluid and thermal flows simultaneously in an elegant way. These similarities allow us to directly translate many of the available results in poroelasticity to thermoelasticity and vice versa by a simple change of notation. The disparities indicate a fundamental difference in physical mechanisms. Plane-wave analysis shows that the primary P -wave modes of thermoelasticity and poroelasticity are all GSLS-equivalent (Generalized Standard Linear Solid) and can be identical if the model parameters are selected properly. However, the corresponding slow-wave modes have significantly different phase velocity dispersion although the attenuation spectra of which are identical. Such a surprising result can be explained by the GSLS non-equivalence of the slow-wave modes and the fundamentally different mechanisms. As expected, the thermo-poroelastic model predicts four wave modes, which are the fast- and slow- P , temperature (T wave) and S waves. Two attenuation peaks due to, respectively, the thermal- and fluid-flow effects are predicted for the fast- P wave. The slow- P wave mode due to fluid flow is influenced by the thermal effects, but the T wave seems unaffected by the fluid flow. The thermo-poroelastic model is then applied to laboratory observations at 200–106 Hz for the brine-saturated tight sandstone under 35 MPa effective pressure. The unified model provides a convenient framework for studying geothermal exploration, thermal-enhanced oil recovery and other applications involving temperature variations within the porous rock. [ABSTRACT FROM AUTHOR]

The theory of wave propagation in non-isothermal porous rocks has been introduced in geophysics in recent years by combining the single-phase-lag (SPL) Lord-Shulman (LS) model of heat conduction with Biot's poroelasticity theory. However, the theory of SPL thermoporoelasticity is inadequate in describing the lagging behavior of thermal relaxation for wave dissipation due to fluid and heat flow effects. We address this problem by incorporating a dual-phase-lags (DPL) model of heat conduction into thermoporoelasticity, utilizing analytical solutions and numerical simulations. The DPL model involves two lagging times: the (macroscopic) heat-flux lagging time τq from the LS model and an additionally introduced lagging time τT of temperature gradient that characterizes the fluid phase. A plane-wave analysis predicts four propagation waves, namely, fast P, slow P, thermal (T), and shear (S). We calculate wavefield snapshots by using a finite-difference solver for the DPL thermoelastic equations and provide further insight into the physics of two lagging times for porous rocks. The simulations show that the DPL model induces higher thermal attenuation and larger velocity dispersion compared to the SPL model, especially at high frequencies. The influence of fluids is crucial for wave propagation within thermoporoelastic media. [ABSTRACT FROM AUTHOR]

Elastic full waveform inversion (EFWI) is essential for obtaining high-resolution multi-parameter models. However, the conventional EFWI may suffer from severe cycle skipping without the low-frequency components in elastic seismic data. To solve this problem, we propose a multistage phase correction-based elastic full waveform inversion method in the frequency-wavenumber domain, which we call PC-EFWI for short. Specifically, the seismic data are first split using 2-D sliding windows; for each window, the seismic data are then transformed into the frequency-wavenumber domain for PC-EFWI misfit. In addition, we introduced a phase correction factor in the PC-EFWI misfit. In this way, it is possible to reduce phase differences between measured and synthetic data to mitigate cycle skipping by adjusting the phase correction factor in different scales. Numerical examples with the 2-D Marmousi model demonstrate that the frequency-wavenumber domain PC-EFWI with multistage strategy is an excellent way to reduce the risk of EFWI cycle skipping and build satisfactory start models for the conventional EFWI. [ABSTRACT FROM AUTHOR]

Cracks widely exist in rocks and are important in various geophysical applications. However, although electrical methods are conventionally employed for the detection and characterization of cracks, the fundamental question whether cracks improve the conductive ability of porous rocks (a quantification of their electrical conductivity if their porosity and saturant are the same) remains largely unaddressed. We address this knowledge gap through theoretical models with confirmed validity. We show that the conductive ability of a rock containing non‐interacting penny‐shaped cracks with random orientation will be improved only in the case when the aspect ratio of the cracks is below a certain value, which is referred to as the critical crack aspect ratio. We also show that the critical crack aspect ratio is uniquely determined by the porosity and electrical conductivity (or cementation exponent) of the porous rock where the cracks reside. We further demonstrate that the critical crack aspect ratio is some representation of the pore structure, and using two times the critical crack aspect ratio as the pore geometry can give rise to a reasonable agreement between modelled and measured P‐ and S‐wave velocities. The critical crack aspect ratio offers a consistent microstructure for the joint elastic–electrical modelling for the improved characterization of cracks through integrated seismic and electrical surveys. [ABSTRACT FROM AUTHOR]

SUMMARY: The pressure sensitivity of stiffness in fractured rocks is closely related to fracture-surface geometries. The resulting stress-dependence of stiffness can be represented by the third-order elastic constants (3oECs). Fracture surfaces are generally rough at various scales, and can significantly affect the 3oECs of pre-stressed fractures as well as the wave-induced fluid flow (WIFF) induced by the Biot slow P -wave between fractures and the background medium. The WIFF usually depends on the fracture width relative to the slow P -wavelength and the fracture-surface roughness. We generate various fracture-surface geometries at different scales of random roughnesses parametrized by the surface standard deviation (SSD) of fracture-surface heights. With theoretical analyses and numerical simulations, we investigate the effect of fracture-surface geometries on the stress- and frequency-dependent stiffness through the 3oECs for pre-stressed rocks with aligned fractures. For the elastic wave in the low-frequency regime of Biot theory with the fracture scale much less than the wavelength, the induced WIFF significantly enhances the effect of fracture-surface geometries on the 3oECs and P - and S -wave moduli. The stiffness of fractured rocks increases with increasing SSDs, yielding a high sensitivity to pre-stresses. Toward the high-frequency limit, however, the fluid diffusion between fractures and the porous background decreases, which reduces the influence of fracture-surface roughnesses with the 3oECs much less than that in the low-frequency regime. The resulting P -wave modulus of aligned fluid-saturated fractures approximates to the background value. [ABSTRACT FROM AUTHOR]

Classical third‐order thermoelastic constants are generally derived from the theory of small‐amplitude acoustic waves in isotropic materials during heat treatments. Investigating higher‐order thermoelastic constants for higher temperatures is challenging owing to the involvement of the number of unknown parameters. These Taylor‐type thermoelastic constants from the classical thermoelasticity theory are formulated based on the Taylor series of the Helmholtz free energy density for preheated crystals. However, these Taylor‐type thermoelastic models are limited even at low temperatures in characterizing the temperature‐dependent velocities of elastic waves in solid rocks as a polycrystal compound of different mineral lithologies. Thus, we propose using the Padé rational function to the total thermal strain energy function. The resulting Padé thermoelastic model gives a reasonable theoretical prediction for acoustic velocities of solid rocks at a higher temperature. We formulate the relationship between the third‐order Padé thermoelastic constants and the corresponding higher‐order Taylor thermoelastic constants with the same accuracy. Two additional Padé coefficients α1 ${\mathit{\alpha }}_{1}$ and α2 ${\mathit{\alpha }}_{2}$ can be calculated using the second‐, third‐, and fourth‐order Taylor thermoelastic constants associated with the Brugger's constants, which are consistent with those obtained by fitting the experimental data of polycrystalline material. The third‐order Padé thermoelastic model (with four constants) is validated by the fourth‐order Taylor thermoelastic prediction (with six constants) with ultrasonic measurements for polycrystals (olivine samples) and solid rocks (sandstone, granite, and shale). The results demonstrate that the third‐order Padé thermoelastic model can characterize thermally induced velocity changes more accurately than the conventional third‐order Taylor thermoelastic prediction (with four constants), especially for solid rocks at high temperatures. The Padé approximation could be considered a more accurate and universal model in describing thermally induced velocity changes for polycrystals and solid rocks. Plain Language Summary: Using the Taylor series for thermoelastic constants at higher temperatures is challenging owing to the involvement of the number of unknown parameters. Thus, we propose the third‐order Padé approximation to replace the Taylor series. Applications to laboratory measurements show that, with much less complexity, the Padé approximation presents a tendency of higher accuracy than the third‐order Taylor series and has similar precision with the higher‐order Taylor series at higher temperatures (up to 1500 K for polycrystals and 1000°C for solid rocks). Then we use such a model to predict the temperature‐dependent velocities of elastic waves. Finally, we analyze the physics of two additional Padé coefficients by associating them with the thermal expansion mismatch due to rock heterogeneities in lithology and with the thermally induced deformation of microcracks. Key Points: We apply the Padé rational function to the total thermal strain energy functionWe correlate the Padé and higher‐order Taylor thermoelastic constants through the equivalency of approximation accuraciesThe physics of the Padé coefficients is relevant to the thermal expansion mismatch and thermally induced deformation of microcracks [ABSTRACT FROM AUTHOR]

Thermoelastic attenuation of P waves is due to energy conversion to the heat mode, which is diffusive at low frequencies and wave-like at high frequencies, behaving similarly to the Biot slow mode. The conversion is strong in highly heterogeneous media. We consider a layered medium with a random distribution of thermal properties, specifically the Grüneisen ratio, and obtain the phase velocity and quality factor. The relaxation peak of the random medium is wider than those of a periodic sequence of layers and the Zener mechanical model. Indeed, a Cole–Cole fractional model is needed to obtain a good match. These approximations are required to compute wave fields in heterogeneous media. Moreover, the solutions are helpful for studying the physics of thermoelasticity and testing numerical algorithms for wave propagation. [ABSTRACT FROM AUTHOR]

Temperature- and pressure-dependent elastic properties (static and dynamic shear and bulk moduli) of porous rocks are investigated in terms of the characteristics of pore microstructures (i.e., crack density, crack porosity, and crack aspect-ratio distribution). Based on the Mori–Tanaka (MT) and David–Zimmerman (DZ) models, we correlated elastic properties with these microstructural characteristics and indicated that these microstructural properties can be estimated from dynamic and static moduli that are measured by considering the joint effect of thermal stress and confining pressure. Experiments with a tight sandstone under the saturated condition show that the cumulative crack density and porosity obtained from static moduli are higher than those from dynamic moduli. We demonstrated that the MT and DZ models can be used to describe the temperature- and pressure-dependent microstructures using static and dynamic properties. The dynamic bulk compressibility and shear compliance decrease with increasing confining pressures and decreasing temperatures, whereas the corresponding static values experience complex variations due to the joint effect of thermal stress and confining pressure. For the domination of thermal stress exerted by an increase in temperature, the widening of earlier formed micro-cracks during heating reduces the static moduli. However, during the domination by confining pressure, pre-existing micro-cracks will be closed with increasing temperatures, which increases the static moduli. These static elastic properties (Young's modulus, bulk modulus, and Poisson's ratio) share a similar exponential trend with the ratio of thermal stresses to confining pressures, which can be used to correlate dynamic and static moduli. Highlights: We illustrate temperature- and pressure-dependent pore microstructures jointly using static and dynamic moduli based on the Mori-Tanaka and David-Zimmerman models. Experiments with a saturated tight sandstone show that the cumulative crack density and porosity obtained from static moduli are higher than those from dynamic moduli. Static moduli share a similar exponential trend with the ratio of thermal stresses to confining pressures based on which we propose an approach to estimate static moduli from dynamic moduli. [ABSTRACT FROM AUTHOR]

Understanding the stress-dependent elastic moduli of fractured rocks is essential for monitoring geopressure and tectonic stress. The elastic nonlinearity with finite strains can be described by the theory of acoustoelasticity through the third-order elastic constants (3oECs) that are strictly valid for an isotropic homogeneous medium. The extension to fractured rocks becomes particularly interesting because of the sensitivity of fractures to prestress, but remains largely unaddressed. We address this issue through theoretical modeling with confirmed validity by considering a group of homogeneously distributed fractures (ellipses) embedded into a homogeneous background medium subject to a uniform confining pressure. We incorporate both the David-Zimmerman (DZ) and Mori-Tanaka (MT) models into the theory of acoustoelasticity. The DZ model accounts for the closure influence of cracks with different aspect ratios, whereas the MT model is used to estimate the combining effect of the background acoustoelasticity and the elastic nonlinearity due to the closure of cracks. We validate the acoustoelastic DZ-MT model of fractured rocks by experiment data with Fontainebleau and Vosges sandstones. We show that the effective elastic moduli of fractured rocks mainly depend on the background acoustoelasticity and nonlinear elastic deformations induced by closing cracks. The inclusions inside fractures have too low 3oECs that the associated acoustoelastic effect could be neglected for both interconnected and isolated cracks. The effective elastic moduli of rocks change significantly during the closing period of cracks with increasing pressure under low pressure. The influence of cracks can be reduced only when cracks are closed completely, where, unlike the theoretical prediction by the DZ model, the effective elastic moduli of rocks still increase along with increasing pressure because of the acoustoelastic effect of the background. [ABSTRACT FROM AUTHOR]

Geothermal energy is increasingly important for the global environment and for the sustainable development of our society. Electrical surveys are widely employed for the exploration of geothermal energy, because the electrical geophysical properties provide useful information about the fluids at depth. However, although quantitative interpretation of electrical survey data relies on the knowledge about the effects of temperature on the electrical properties of fluid-bearing rocks, it remains poorly understood about how temperature affects the electrical conductivity of clay-free porous rocks. We bridge this knowledge gap by measuring the electrical conductivity and porosity of five brine saturated clean Berea sandstones with temperature ranging between 25 and 140 °C, and analysing all the factors that impact the rock conductivity. We showed that the effects of surface conductivity on the temperature-dependent electrical conductivity can be negligible, whereas the temperature induced variation in the porosity and pore structure quantitatively characterized in terms of cementation exponent can be more significant. We also found that temperature affects the electrical conductivity of brine saturated Berea sandstones by impacting the brine conductivity, and the pore structure and porosity of the samples, with their importance in a descending order. The results have provided new insights into how temperature affects the electrical conductivity of clay-free porous rocks, and will help to improve the quantitative interpretation of electrical survey data for the exploration of geothermal energy. [ABSTRACT FROM AUTHOR]

In a large body of rock-physics research, seismic wave velocity dispersion and attenuation in fluid-saturated porous rock are studied by constructing analytical or numerical models for time- or frequency-dependent dynamic (effective, or viscoelastic) moduli. A key and broadly used model of such kind is the Zener's, or the standard linear solid (SLS). This model is qualitatively successful in explaining many field and laboratory observations and serves as the key element of many generalizations such as the Burgers model for plastic deformations or the generalized SLS explaining band-limited or near-constant seismic attenuation. However, as a physical model of fluid-saturated porous rock, the SLS has several major limitations: disregard of inertial effects, absence of secondary wave modes and lack of key physical parameters such as porosity and Skempton coefficients. Grainy and porous rock is an unconsolidated material in which the effective density is frequency-dependent, and its effects on wave velocities may exceed those of the dynamic modulus. To overcome these limitations of the empirical SLS, we propose a rigorous rheologic model based on classical continuum mechanics and called the extended SLS, or eSLS. This rheology explains the available attenuation and dispersion observations equally well, but it is also close to Biot's model, honours all poroelastic relations, includes inertial effects, and reveals several new physical properties of the material. Detailed comparison of the eSLS and Biot's models gives a physical-mechanism-based classification of wave-induced fluid flow (WIFF) phenomena. In this classification, the so-called 'global-scale' flows occur in Biot's type structures within the material, whereas the 'local-scale' WIFF occurs in eSLS-type structures. Combining Biot's and eSLS models gives a broad class of rheologies for linear anelastic phenomena within rock with a single type of porosity. The model can be readily generalized to multiple porosities and different types of internal variables, such as describing squirt flows, wetting or thermoelastic effects. Modelling is conducted with relatively little effort, using a single matrix equation similar to a mechanical form of the standard SLS. By combining the eSLS and Biot's models, observations of dynamic-modulus dispersion and attenuation can be inverted for macroscopic mechanical properties of porous materials. [ABSTRACT FROM AUTHOR]

Fractured hydrate-bearing reservoirs are extensively discovered worldwide and show notable anisotropic geophysical properties. Hydrate distribution in fractures significantly affects the anisotropic properties, and hence plays an important role in the accurate assessment of hydrate resources. However, the knowledge about how the hydrate distribution impacts the anisotropic geophysical properties of fractured reservoirs, which is the premise for the identification and quantification of hydrate in fractured reservoirs, is still poorly understood. To obtain such knowledge, we forward study the effects of various hydrate distribution (including floating, bridging and evolving hydrate distribution) in aligned fractures on the anisotropic elastic, electrical and joint elastic–electrical properties of a digital core using validated numerical methods. We show that for all the hydrate distribution, the anisotropic velocities increase, while the conductivities decrease with increasing hydrate saturation, with the effects of the floating and bridging distribution being the least and greatest, respectively. We also show that the anisotropic velocities and conductivities for the floating and bridging distribution vary approximately linearly with hydrate saturation, leading to linear correlations between the elastic and electrical properties. Further investigation illustrates that the difference in the slopes of the linear joint correlations between the two distribution is significantly greater than that of the individual properties as a function of hydrate saturation. The results have revealed the distinct effects of hydrate distribution on the anisotropic elastic and electrical properties of fractured reservoirs, and have confirmed the superiority of the joint elastic–electrical properties for the distinguishment of hydrate distribution in fractures over individual physical properties. [ABSTRACT FROM AUTHOR]

Poro-acoustoelastic theory has made a great progress in both theoretical and experimental aspects, but with no publications on the joint research from theoretical analyses, experimental measurements, and numerical validations. Several key issues challenge the joint research with comparisons of experimental and numerical results, such as digital imaging of heterogeneous poroelastic properties, estimation of acoustoelastic constants, numerical dispersion at high frequencies and strong heterogeneities, elastic nonlinearity due to compliant pores, and contamination by boundary reflections. Conventional poro-acoustoelastic theory, valid for the linear elastic deformation of rock grains and stiff pores, is modified by incorporating a dual-porosity model to account for elastic nonlinearity due to compliant pores subject to high-magnitude loading stresses. A modified finite-element method is employed to simulate the subtle effect of microstructures on wave propagation in prestressed digital cores. We measure the heterogeneity of samples by extracting the autocorrelation length of digital cores for a rough estimation of scattering intensity. We conductexperimental measurements with a fluid-saturated sandstone sample under a constant confining pressure of 65 MPa and increasing pore pressures from 5 to 60 MPa. Numerical simulations for ultrasound propagation in the prestressed fluid-saturated digital core of the sample are followed based on the proposed poro-acoustoelastic model with compliant pores. The results demonstrate a general agreement between experimental and numerical waveforms for different stresses, validating the performance of the presented modeling scheme. The excellent agreement between experimental and numerical coda quality factors demonstrates the applicability for the numerical investigation of the stress-associated scattering attenuation in prestressed porous rocks. [ABSTRACT FROM AUTHOR]

P and SV wave scattering by thermally constrained saturated cracks couples elastic deformation with temperature. We estimate the scattering attenuation and velocity dispersion by aligned fluid‐saturated cracks with finite thickness, which are sparsely and randomly embedded in an isothermal and isotropic elastic medium. By incorporating thermoelastic effects into the representation theorem with the non‐interaction Foldy approximation, we formulate the dispersion and attenuation of P and SV waves induced by displacement discontinuities across aligned cracks constrained by a thermoelastic boundary condition. The frequency‐dependent response as a function of temperature is calculated for various P and SV wave incidence angles. The resulting scattering attenuation and dispersion are compared with those of the conventional aligned‐crack model. The examples show that the dissipation increases with increasing temperature, but the scattering is inhibited at a given temperature. The P wave shows a strong sensitivity to temperature along the direction normal to the cracks, whereas the SV wave has an opposite behavior. This theory has the potential to assess the distribution of temperature from seismic attributes. Key Points: We study the thermoelastic dispersion and attenuation of P and SV wave scattering by aligned‐crack in an isothermal elastic mediumThe dissipation increases with increasing temperature, but the scattering is inhibited at a given temperatureThe P wave shows a strong sensitivity to temperature along the crack normal, whereas the SV wave behaves in opposite manner [ABSTRACT FROM AUTHOR]

Due to the lack of petroleum resources, stratigraphic reservoirs have become an important source of future discoveries. We describe a methodology for predicting reservoir sands from complex reservoir seismic data. Data analysis involves a bio-integrated framework called multi-modal machine learning fusion (MMMLF) based on neural networks. First, acoustic-related seismic attributes from post-stack seismic data were used to characterize the reservoirs. They enhanced the understanding of the structure and spatial distribution of petrophysical properties of lithostratigraphic reservoirs. The attributes were then classified as varied modal inputs into a central fusion engine for prediction. We applied the method to a dataset from Northeast China. Using seismic attributes and rock physics relationships as input data, MMMLF was performed to predict the spatial distribution of lithology in the Upper Guantao substrata. Despite the large scattering in the acoustic-related data properties, the proposed MMMLF methodology predicted the distribution of lithological properties through the gamma ray logs. Moreover, complex stratigraphic traps such as braided fluvial sandstones in the fluvio–deltaic deposits were delineated. These findings can have significant implications for future exploration and production in Northeast China and similar petroleum provinces around the world. [ABSTRACT FROM AUTHOR]

Two adjacent groundwater wells on the North China Platform are used to study how earthquakes impacted aquifers. We use the response of water level to solid Earth tides to document changes after earthquakes and how aquifer and fracture properties recovered to pre‐earthquake properties. We consider two models for the phase and amplitude of water level response to the lunar diurnal (O1) and semidiurnal (M2) tides: a leaky aquifer model, and a model in which fracture orientation determines the response. In the leaky aquifer model, changes arise from changes in permeability and storage; in the fracture model, changes are due to changes in apparent orientation of transmissive fractures. Responses in one well are best explained by the leaky aquifer model, and can explain the large amplitude coseismic water level and permeability changes and the non‐recoverable changes after the largest earthquake. Responses in the other well are consistent with the fracture model and show little coseismic change in water level but changes in apparent fracture orientation. Larger ground motions lead to larger coseismic water level changes and longer recovery times. We propose that the well in the more permeable and shallow aquifer has less variable pore‐pressures around the well. Larger coseismic strains from water level changes may enable longer‐lasting changes in aquifer properties. We conclude that relatively high permeability aquifers are less susceptible to impacts from seismic waves, and thus have small changes in water levels and hydrogeological properties. Plain Language Summary: After large earthquakes, the properties of aquifers can change, leading to changes in water levels in wells. We study changes in water levels that we attribute to changes in the properties of fractures or the permeabilities of aquifers that connect to the wells. We do so by monitoring how deformation caused by tides leads to changes in water levels in two wells. The deeper well in a less permeable formation has larger changes. The larger the ground motion from earthquakes and the larger the amplitude of the coseismic water level changes, the more likely and larger the changes in permeabilities. The larger the changes, the slower the recovery to pre‐earthquake properties. The shallower well in a more permeable formation has smaller changes and no long‐term changes in water level and hydrogeological properties, which we attribute to more uniform pore‐pressures around the well. Key Points: high permeability aquifers are less susceptible to disruption by seismic waveshydraulic property changes depend on the amplitude and frequency of ground motionlarger water level changes accompany larger changes in fracture orientation and irreversible changes in aquifer properties [ABSTRACT FROM AUTHOR]

The Lord–Shulman thermoelasticity theory combined with Biot equations of poroelasticity, describes wave dissipation due to fluid and heat flow. This theory avoids an unphysical behaviour of the thermoelastic waves present in the classical theory based on a parabolic heat equation, that is infinite velocity. A plane-wave analysis predicts four propagation modes: the classical P and S waves and two slow waves, namely, the Biot and thermal modes. We obtain the frequency-domain Green's function in homogeneous media as the displacements-temperature solution of the thermo-poroelasticity equations. The numerical examples validate the presence of the wave modes predicted by the plane-wave analysis. The S wave is not affected by heat diffusion, whereas the P wave shows an anelastic behaviour, and the slow modes present a diffusive behaviour depending on the viscosity, frequency and thermoelasticity properties. In heterogeneous media, the P wave undergoes mesoscopic attenuation through energy conversion to the slow modes. The Green's function is useful to study the physics in thermoelastic media and test numerical algorithms. [ABSTRACT FROM AUTHOR]

A modified LSM is proposed by introducing an independent micro-rotational inertia, which may help characterize the scale-dependent effect and avoid the Poisson's ratio limitation of regular triangle lattices in two dimensions. For this method, some factors may affect data pickup and modeling accuracy, but the 'optimal' inputs, like stiffness ratio, numerical damping, and micro-rotational inertia, could be obtained from parameter identification by the Dakota toolkit (Adams et al., Tech Rep SAND2010–2183, 2009), when a suitable excitation source function and lattice spacing are set up. By comparing with the modified couple stress theory, we analyze the dispersion relationship of elastic waves for the estimation of the characteristic material length. It shows that this modified LSM may provide an alternative and promising way to investigate the size-dependent wave propagation in elastic media numerically. [ABSTRACT FROM AUTHOR]

Thermoelasticity extends the classical elastic theory by coupling the fields of particle displacement and temperature. The classical theory of thermoelasticity, based on a parabolic-type heat-conduction equation, is characteristic of an unphysical behaviour of thermoelastic waves with discontinuities and infinite velocities as a function of frequency. A better physical system of equations incorporates a relaxation term into the heat equation; the equations predict three propagation modes, namely, a fast P wave (E wave), a slow thermal P wave (T wave), and a shear wave (S wave). We formulate a second-order tensor Green's function based on the Fourier transform of the thermodynamic equations. It is the displacement–temperature solution to a point (elastic or heat) source. The snapshots, obtained with the derived second-order tensor Green's function, show that the elastic and thermal P modes are dispersive and lossy, which is confirmed by a plane-wave analysis. These modes have similar characteristics of the fast and slow P waves of poroelasticity. Particularly, the thermal mode is diffusive at low thermal conductivities and becomes wave-like for high thermal conductivities. [ABSTRACT FROM AUTHOR]

Temperature-induced variations of elastic moduli in solid media are generally characterized by a strong nonlinear dependence on temperature associated with complex deformations under thermal treatments. Conventional thermoelasticity with third-order elastic constants for the one-order temperature dependence has been extensively studied for crystals, but encountering problems of divergent and limited velocity variations for rocks as a polycrystal mixture, especially at high temperatures. The extension of the theory beyond high-order elastic constants to solid media is addressed in this article to describe the nonlinear temperature dependence of both elastic constants and wave velocities. The total strain is divided into the background component associated with temperature variations and the infinitesimal component induced by propagating waves. A third-order temperature dependence of velocity variations is formulated by taking into account fourth-order elastic constants. Applications to solid rocks (sandstone, granite, and olivine) demonstrate an accurate description of temperature-induced variations, especially for high temperatures. Unlike crystals, the synthetic averaging elastic constants for a solid rock (as a polycrystal mixture) change less than 10% with temperatures. The thermal sensitivity of P-wave velocities is much more than that of S-wave velocities over the vast majority of temperatures examined. [ABSTRACT FROM AUTHOR]

Experiments with ten groups of limestone specimens (four samples per group) under ten specific temperatures, 25 °C, 100 °C, 200 °C, 300 °C, 400 °C, 500 °C, 600 °C, 700 °C, 800 °C, and 900 °C, show that the high-temperature effect on the elastic modulus of rocks conforms to thermoelastic responses with a quadratic temperature function. The thermal damage factor can be reduced, by ignoring the effect of Poisson's ratios and densities, to simply a ratio of the P -wave velocities before and after high-temperature treatments. Based on the collected experimental data, we correlate the P -wave velocities change rate with both the peak compressive strength and effective solid matrix. It demonstrates that the high-temperature effect on the thermal damage factor can be directly expressed as the rate of change in the peak compressive strength and effective solid matrix. All these properties (thermal damage factor calculated by the P -wave velocity, peak compressive strength, and effective solid matrix) share a similar exponential trend with increasing temperature. The rates of change in the elastic modulus, P -wave velocity, peak compressive strength, and effective solid matrix also exhibit a similar powerful trend with increasing temperature. This study provides insight into the detailed characteristics of thermal damage related to the mechanical property of limestones exposed to high temperature. [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]

A new methodology is presented to quantify reservoir heterogeneities based on a Monte Carlo parameter estimation technique from sonic logs. The acoustic reservoir heterogeneities are then quantified as an indicator to differentiate depositional environments and reservoir facies for geological interpretation in this study. Fractal statistics provides us with a framework to model reservoir heterogeneities with different Hurst numbers, correlation lengths and fluctuation standard deviations from sonic logs. These fractal parameters are derived from the von Karman autocorrelation model and estimated by an improved methodology using a Monte Carlo parameter estimation technique. Unlike the regular estimation method, the Monte Carlo parameter estimation technique is more stable. The resulting Hurst numbers, correlation lengths and root mean square (RMS) heights from 20 sonic logs are mapped in a reservoir with sandstone–mudstone sequences over complex continental deposits in north-eastern China. The spatial distribution of estimated reservoir heterogeneity parameters are then correlated with depositional facies interpretation derived from seismic attributes and petrophysical properties based on prior geological knowledge. Numerical experiments show that the Monte Carlo parameter estimation technique is successful in recovering acoustic heterogeneity parameters from sonic logs. Results from qualitative correlational analysis of sonic logs from the complex continent deposits in north-eastern China show that these parameters can be key discriminants for depositional facies and environments and may be utilised as a constraint in reservoir characterisation. Maps of Hurst numbers and correlation lengths strongly correspond with reservoir facies distributions, whereas maps of RMS heights correlate significantly with fluvial depositional patterns. The results were generally uniform even when different depth ranges within the formation of interest were used as input for parameter estimation. Numerical values of reservoir heterogeneity parameters may not fully recover the geology of a given reservoir but their distribution in space is an important indication of the morphological features of depositional environments. A new methodology for quantifying reservoir heterogeneities based on a Monte Carlo parameter estimation technique using fractal parameters derived from the von Karman autocorrelation function is proposed. The reservoir heterogeneity parameters computed from sonic logs in an oilfield show that these parameters can be discriminants for depositional environments. [ABSTRACT FROM AUTHOR]

Seismic acquisition geometries have a significant influence on the quality of seismic data in the oil and gas exploration process. Therefore, prior analyses are beneficial to the design of acquisition geometries before implementation of seismic acquisition. The focal beam analysis method can provide quantitative insights into the combined influence of acquisition geometries and subsurface structures. This approach involves a large calculation burden concerning 3D wavefield extrapolation in the case of complex media, thus inhibiting the practical application of focal beam analysis in complex media when using regular CPUs. Therefore, using a graphics processing unit (GPU) to accelerate focal beam analysis becomes imperative. We have developed a fast parallel algorithm to speed up the focal beam analysis for 3D acquisition geometries in complex media on GPUs. Three-dimensional numerical examples show that the GPU-based focal beam analysis runs about 17 times faster than a serial CPU-based one. We also demonstrate the validity and scalability of the proposed approach with numerical examples. The boost in performance afforded by the GPU architecture allows us to analyse 3D acquisition geometries in complex media with less time and at lower cost of hardware. [ABSTRACT FROM AUTHOR]

The wave-induced interlayer flow between mesoscopic-scale heterogeneities (i.e., larger than pore scale but smaller than the predominant wavelengths) is the most important cause of attenuation at frequencies below 1 kHz. According to the White's layered model ( White et al., 1975 ), the wave-induced flow at an interface is symmetrical in periodically layered porous media due to its symmetrical structure. However, in one-dimensional (1-D) randomly layered porous rocks, layers of various thicknesses lead to different types of the interlayer flow. The coexistence of various wave-induced interlayer flow patterns at different interfaces results in interactions. The numerical creep test and a volume average of White's analytical solution were used to analyse the interactions in the two kinds of models (i.e., representative elementary volumes and randomly layered models). One of the parameters used to build a randomly layered model is the standard deviation of the thickness of the water-saturated layer, which could control the interaction strength of the interlayer flow. The detailed characteristics of the interlayer flow interaction were demonstrated by analysing the relative fluid velocity, while the statistical characteristics of the interlayer flow interaction were demonstrated by analysing the average solid velocity. We investigated the effect of the interaction on the amplitude versus the deviation at the interface between a non-dispersive medium and a patchy-saturated dispersive medium in three types of reservoirs. These results are beneficial for describing the distribution of oil/gas patches based on the statistical seismic properties in a layered formation with random disorder. [ABSTRACT FROM AUTHOR]

Abstract: The characteristics of internal lithospheric discontinuities carry crucial information regarding the origin and evolution of the lithosphere. However, the formation and mechanisms of the midlithosphere discontinuity (MLD) are still enigmatic and controversial. We investigate the midlithospheric discontinuities beneath the Archean Western Australian Craton, which represents one of the oldest continents on the globe, using a novel receiver‐based reflectivity approach combined with other geophysical information comprising tomographic P and S wave velocity, radial anisotropy, electrical resistivity, and heat flow data. The MLD is rather shallow with a depth of 68–82 km. Multiple prominent discontinuities are observed in the lithospheric mantle using constructed high‐frequency (0.5–4 Hz) P wave reflectivities. These multiple discontinuities coincide well with the broad‐scale reduction of relative P and SV wave velocities at the top of the graded transition zone from the lithosphere to the asthenosphere. Strong radial anisotropy in the upper lithosphere mantle tends to be weak across the MLD, which might reflect quasi‐laminar lithospheric heterogeneity behavior with a horizontal correlation length that is greater than its vertical correlation length. Broad‐scale electrical resistivity variations show little coherence with the MLD. Given these various geophysical observations, the upper lithosphere exhibits rigid and elastic properties above the MLD, while the lower lithosphere tends to be ductile and rheological or viscous. A model comprising quasi‐laminar lithospheric heterogeneity could effectively represent the MLD characteristics beneath the Archean continent. [ABSTRACT FROM AUTHOR]

Earth medium is not completely elastic, with its viscosity resulting in attenuation and dispersion of seismic waves. Most viscoelastic numerical simulations are based on the finite-difference and finite-element methods. Targeted at viscoelastic numerical modeling for multilayered media, the constant- Q acoustic wave equation is transformed into the corresponding wave integral representation with its Green's function accounting for viscoelastic coefficients. An efficient alternative for full-waveform solution to the integral equation is proposed in this article by extending conventional frequency-domain boundary element methods to viscoelastic media. The viscoelastic boundary element method enjoys a distinct characteristic of the explicit use of boundary continuity conditions of displacement and traction, leading to a semi-analytical solution with sufficient accuracy for simulating the viscoelastic effect across irregular interfaces. Numerical experiments to study the viscoelastic absorption of different Q values demonstrate the accuracy and applicability of the method. [ABSTRACT FROM AUTHOR]

Correlations between the calculated Coulomb stress changes and observed seismicity rate changes after the Wenchuan earthquake are investigated in this article. Three improvements are made in the calculation of static stress change, including employing a dislocation method with triangular elements rather than traditional rectangular elements, setting up a more realistic source-slip model and a more complete receiver fault model, and resolving stress changes on assumed receiver faults with spatially variable focal mechanisms based on well-determined focal mechanisms at different calculation points. The recorded aftershocks are mapped for comparison with the spatial distribution of stress changes. The results indicate that the Wenchuan earthquake encourages not only three major fault systems (the East Kunlun, south of Xianshuihe and west of Qinling Southern Frontal) but also several other regions including Tazang, north of Min Jiang, north of Pingwu-Qingchuan and west of Chongqing. In particular, the eastern segment of Longriba is shown to be quite dangerous with dramatic stress increase. The influence of depth and frictional coefficient is analyzed. The depth of calculation beyond the depth range of the source model will make a significant difference to the stress-change map and thus cannot be neglected. Many aftershocks occurring in the stress shadow zone near the main rupture can be attributed to dynamic stress triggering and the fractal structure of the main fault. The observed seismicity rate changes are compared with the static stress changes. The results show that high background seismicity rates will amplify the effect of stress change. The observed seismicity rate changes support the forecast rate of 10-year seismicity after the Wenchuan earthquake based on the rate- and state-dependent friction model. Coulomb stresses increase on the focal mechanisms away from the main rupture, which demonstrates the influence of the Wenchuan earthquake over a wide range. Especially, the focal mechanism for Lushan earthquake undergoes a stress increase by more than 2.0 bars, which suggests that the Lushan earthquake has been effectively promoted by the Wenchuan earthquake. [ABSTRACT FROM AUTHOR]

Ultrasonic coda waves are widely used to study high-frequency scattering. However, ultrasonic coda waves are strongly affected by interference from by boundary-reflected waves. To understand the effect of boundary-reflected waves, we performed ultrasonic experiments using aluminum and shale samples, and the rotating staggered-mesh finite-difference method to simulate the wavefield. We analyzed the wavefield characteristics at the different receiving points and the interference characteristics of the boundary-reflected waves with the ultrasonic coda wave, and the effect of sample geometry on the ultrasonic coda waves. The increase in the aspect ratio of the samples delays the interference effect of the laterally reflected waves and reduces the effect on the ultrasonic coda waves. The main waves interfering with the ultrasonic coda waves are laterally reflected PP-, PS-, PPP-, and PPS-waves. The scattering and attenuation of the high-frequency energy in actual rocks can weaken the interference of laterally reflected waves with the ultrasonic coda waves. [ABSTRACT FROM AUTHOR]

Zuojiazhuang and Baodi are two adjacent wells (~50 km apart) in northern China. The large 2008 M 7.9 Wenchuan and 2011 M 9.1 Tohoku earthquakes induced different co-seismic water-level responses in these far-field (>1000 km) wells. The co-seismic water-level changes in the Zuojiazhuang well exhibited large amplitudes (~2 m), whereas those in the Baodi well were small and unclear (~0.05 m). The mechanism of the different co-seismic hydraulic responses in the two wells needs to be revealed. In this study, we used the barometric responses in different frequency domains and the phase shifts and amplitude ratios of the tidal responses (M wave), together with the well logs, to explain this inconformity. Our calculations show that the co-seismic phase shifts of the M wave decreased or remained unchanged in the Baodi well, which was quite different from the Zuojiazhuang well and from the commonly accepted phenomena. According to the well logs, the lithology of the Baodi well is characterized by the presence of a significant amount of shale. The low porosity/permeability of shale in the Baodi well could be the cause for the unchanged and decreased phase shifts and tiny co-seismic water-level responses. In addition, shale is one of the causes of positive phase shifts and indicates a vertical water-level flow, which may be due to a semi-confined aquifer or the complex and anisotropic fracturing of shale. [ABSTRACT FROM AUTHOR]

Pressure prediction has long been one of subject of research focuses in petroleum geology and exploration, but is traditionally limited to moderately overpressured formations due to disequilibrium compaction based on the empirical velocity-pressure model. Overpressures in the Xihu depression are caused by fluid expansion due to the generation of natural gas in source rocks. The resulting abnormally pressured gas reservoirs manifest as a high-pressure structure with the thick mud-coated thin sand (MCS) that remains largely unaddressed in prediction. Such gas-producing overpressures make traditional prediction methods unapplicable because of the significant influence of high gas contents on seismic velocities. We employ a frequency-dependent quality factor Q –pressure petrophysical model because of the sensitivity of acoustic attenuation to overpressures. However, acoustic attenuations from rock physics and sonic logging present an uncertain dependence on pore pressures. This implies that overpressure prediction is a typical physical system that is characterized by both deterministic mechanism and statistical behavior, which resorts to physics-informed deep learning methods. We take the Q –pressure petrophysical model as the activation function of Caianiello convolutional neurons with an attempt to combine deterministic and statistical mechanisms for overpressure prediction. Such convolutional neurons render strong feature extraction and powerful learning ability and are used to construct physics-informed Caianiello convolutional neural networks (CCNNs) for overpressure prediction in the Xihu depression. The comprehensive CCNNs-based seismic inversion scheme for overpressures consists of reservoir petrophysical modeling, deep learning for neural wavelets, well-seismic correlation analysis, deconvolution-based inversion for an initial pressure model, and input-signal reconstruction to improve the initial pressure model. With drill stem tests (DSTs), well logs, and 3D seismic data, we conduct the overpressure prediction associated with cross validation in the Xihu depression, which demonstrates the applicability of the physics-informed CCNNs inversion scheme. Predicting reliability away from the training wells usually depends on the geological complexity of areas under study. Nevertheless, the information representation in the trained CCNNs can be improved gradually by feeding new well data during the development of an oil field. • We conduct a seismic inversion for overpressure prediction using physics-informed Caianiello convolutional neural networks. • Instead of velocity, we employ quality factor Q to correlate seismic attenuation coefficients, impedances, and frequencies. • The natural gas in Pinghu Formation is migrated locally to adjacent thin sand bodies, resulting in strong overpressure. • The overpressure prediction demonstrates the applicability of joint seismic inversions by the physics-informed CCNNs. [ABSTRACT FROM AUTHOR]

The dependence of elastic moduli of shales on the mineralogy and microstructure of shales is important for the prediction of sweet spots and shale gas production. Based on 3D digital images of the microstructure of Longmaxi black shale samples using X-ray CT, we built detailed 3D digital images of cores with porosity properties and mineral contents. Next, we used finite-element (FE) methods to derive the elastic properties of the samples. The FE method can accurately model the shale mineralogy. Particular attention is paid to the derived elastic properties and their dependence on porosity and kerogen. The elastic moduli generally decrease with increasing porosity and kerogen, and there is a critical porosity (0.75) and kerogen content (ca. ≤3%) over which the elastic moduli decrease rapidly and slowly, respectively. The derived elastic moduli of gas- and oil-saturated digital cores differ little probably because of the low porosity (4.5%) of the Longmaxi black shale. Clearly, the numerical experiments demonstrated the feasibility of combining microstructure images of shale samples with elastic moduli calculations to predict shale properties. [ABSTRACT FROM AUTHOR]

Three large earthquakes (the 2007 M w 8.4 Sumatra, the 2008 M w 7.9 Wenchuan, and the 2011 M w 9.0 Tohoku) induce coseismic water-level increment at far fields (epicentral distances > 1000 km) in the Fuxin well located in the Fuxin City, northeastern China (the well with the observation of both water levels and volume strains). A comprehensive analysis for the mechanism of far-field coseismic water-level changes is performed by analyzing the in-situ permeability, Skempton's coefficient B , and with the broadband seismograms from a nearby station. We observe an undrained compaction with a decreasing permeability induced by the shaking of teleseismic waves in the far field. Shaking by teleseismic waves can induce compaction or dilatation in the aquifer of Fuxin well; is able to enhance permeability and thus build a new pore-pressure equilibrium system between the Fuxin well and the nearby Sihe reservoir (150 m away from the Fuxin well). The resulting interstitial fluid flow across the region increases coseismic water levels in the aquifer of Fuxin well. [ABSTRACT FROM AUTHOR]

Spatial sampling has a crucial influence on the horizontal resolution of seismic imaging, but how to quantify the influence is still controversial especially in complex media. Most of the studies on horizontal resolution focus on the measurement of wavelet widths for seismic migration, but neglect to evaluate the effect of side-lobe perturbations on spatial resolution. The side-lobe effect, as a migration noise, is important for seismic imaging in complex media. In this article, with focal beam analysis, we define two parameters to represent the horizontal resolution of an acquisition geometry: the width of the main lobe (WML) along the inline and crossline directions and the ratio of the main-lobe amplitude to the total amplitude (RMT) in a focal beam. We provide examples of typical acquisition geometries to show how spatial sampling affects the horizontal resolution, measured in terms of WML and RMT values. WML defines the horizontal resolution to image the target, whereas RMT describes the clarity of the imaging. Migration noise reduces with increasing RMT, indirectly improving both the vertical and horizontal resolutions of seismic imaging. Case studies of seismic migration with 3D seismic data from an oil field of China, demonstrate how the acquisition geometries with different WML and RMT values influence the performance of seismic imaging. Prior WML and RMT analyses to predict the quality of acquired datasets can optimize acquisition geometries before the implementation of seismic acquisition. [ABSTRACT FROM AUTHOR]

Abstract: For wave propagation simulation in piecewise heterogeneous media, Gaussian-elimination-based full-waveform solutions to the generalized Lippmann–Schwinger integral equation (GLSIE) are highly accurate, but involved with extremely time-consuming computations because of the very large size of the resulting boundary–volume integral equation matrix to be inverted. Several flexible approximations to the GLSIE are scaled in an iterative way to adapt numerical solutions to the smoothness of heterogeneous media in terms of incident wavelengths, with a great saving of computing time and memory. Among various typical iterative schemes to the GLSIE matrix, the generalized minimal residual method (GMRES) is an efficient approach to reduce the computational intensity to some degree. The most efficient approximation can be obtained using a Born series, as an alternative iterative solution, to both the boundary-scattering and volume-scattering waves, leading to the Born-series approximation (BSA) scheme and the improved Born-series approximation (IBSA) scheme. These iteration schemes are validated by dimensionless frequency responses to a heterogeneous semicircular alluvial valley, and then applied to a heterogeneous multilayered model by calculating synthetic seismograms to evaluate approximation accuracies. Numerical experiments, compared with the full-waveform numerical solution, indicate that the convergence rates of these methods decrease gradually with increasing velocity perturbations. The comparison also shows that the BSA scheme has a faster convergence than the GMRES method for velocity perturbations less than 10 percent, but converges slowly and even hardly achieves convergence for velocity perturbations greater than 15 percent. The IBSA scheme gives a superior performance over the other methods, with the least iterations to achieve the necessary convergence. [Copyright &y& Elsevier]

Differential effective medium (DEM) model has been widely employed for the interpretation of electrical survey data. However, the contact of grains that is inevitably happening in reservoir rocks is not taken into account by the DEM model, making the model prediction underestimate the measured formation factor of clean granular rocks. We have developed a modified DEM model by introducing a geometric factor to account for the contact of grains that complicates the pore network and thus deviates the transportation of electrical current. The geometric factor is derived by fitting the measured formation factor from a large published data set of 111 clean sandstone samples, and is found to decrease exponentially with rock porosity. Comparison with laboratory data sets of various artificial and real clean sandstones shows that the modified DEM model improves the modelling results and fits satisfactorily the measured formation factor with varying porosity. The results illustrate the practical applicability of the developed closed-form model for the improved simulation of electrical properties of clean granular rocks, and suggest grain contact as a potential link for the joint elastic-electrical characterization of granular rocks through integrated seismic and electromagnetic surveys. [ABSTRACT FROM AUTHOR]

High-precision finite difference (FD) wavefield simulation is one of the key steps for the successful implementation of full-waveform inversion and reverse time migration. Most explicit FD schemes for solving seismic wave equations are not compact, which leads to difficulty and low efficiency in boundary condition treatment. Firstly, we review a family of tridiagonal compact FD (CFD) schemes of various orders and derive the corresponding optimization schemes by minimizing the error between the true and numerical wavenumber. Then, the optimized CFD (OCFD) schemes and a second-order central FD scheme are used to approximate the spatial and temporal derivatives of the 2D acoustic wave equation, respectively. The accuracy curves display that the CFD schemes are superior to the central FD schemes of the same order, and the OCFD schemes outperform the CFD schemes in certain wavenumber ranges. The dispersion analysis and a homogeneous model test indicate that increasing the upper limit of the integral function helps to reduce the spatial error but is not conducive to ensuring temporal accuracy. Furthermore, we examine the accuracy of the OCFD schemes in the wavefield modeling of complex structures using a Marmousi model. The results demonstrate that the OCFD4 schemes are capable of providing a more accurate wavefield than the CFD4 scheme when the upper limit of the integral function is 0.5π and 0.75π. [ABSTRACT FROM AUTHOR]

Ordovician fractured carbonates under study are over 7000 m deep in northwest China. Multistage tectonic activities result in numerous fractures along the strike-slip faults, accompanied with karst collapses due to atmospheric freshwater seepage. The resultant cave-fracture system provides numerous channels favorable for the migration and storage of hydrocarbons. Azimuthal anisotropy analyses with wide-azimuth and high-density 3D seismic data facilitate fracture estimation from migrated CRP gathers in this area. Compared with azimuthal velocity variations, azimuthal amplitude variations are quite sensitive to fractures, but suffer many negative factors. Major difficulties with azimuthal amplitudes to map superdeep fractured reservoirs include non-uniform distribution of azimuths and offsets, extremely low S/N ratio (SNR), anisotropic effect of strike-slip faults, and shielding effect of overlying irregular igneous strata. We propose an integrated scheme with azimuthal P–P amplitude/frequency attributes for prestack prediction of fractures based on the migrated CRP gathers. First, we analyze the distribution of azimuths, offsets, and bins to identify appropriate bins with the best range of offsets and the uniform distribution of azimuths. The selected wide-azimuthal CMP gathers are regrouped in terms of five azimuths, followed by azimuthal prestack migration. The resulting subazimuthal CRP gathers are optimized by denoising, flattening by residual static correction, and wavelet shaping to improve both SNR and resolution. We then conduct a local stacking in 100 m × 100 m bin for the best range of offsets from 1000 to 5600 m, followed by matched filtering to remove the footprint effect of overlying igneous strata. Frequency-related amplitude attributes are extracted for sensitive analyses in azimuths by ellipse fitting, yielding several optimal attributes for fracture prediction. We demonstrate that the coupled amplitude and frequency attributes in terms of energy percentages are the best in this area. Case studies show the applicability of the presented scheme for detecting superdeep fracture sets from extremely low SNR seismic data. • A complete processing workflow is proposed, which provides reliable basic data for prestack fracture prediction. • We analyze the effects of azimuths, offsets, bins, and folds for wide-azimuth and high-density 3D seismic acquisition, which ensure that the offsets and azimuths. • Frequency-related amplitude attributes are extracted in the azimuthal P–P migrated CRP gathers for sensitive analyses in azimuths by ellipse fitting. • Our method has a good applicability to the detection of superdeep fracture sets from extremely low SNR seismic data. [ABSTRACT FROM AUTHOR]

Abstract: Ultrasonic wave propagation in heterogeneous porous cores under laboratory studies is an extremely complex process involved with strong scattering by microscale heterogeneous structures. The resulting coda waves, as an index to measure scattering attenuation, are recorded as continuous waveforms in the tail portion of wavetrains. Because of the contamination of reflections from the side ends and reverberations between the sample surfaces, it is difficult to extract pure coda waves from ultrasonic measurements for the estimation of the P- and S-coda attenuation quality factors. Comparisons of numerical and experimental ultrasonic wave propagation in heterogeneous porous cores can give important insight into understanding the effect of boundary reflections on the P- and S-codas in the laboratory experiment. It challenges numerical modeling techniques by three major issues: the creation of a digital core model to map heterogeneous rock properties in detail, the perfect simulation with a controllable and accurate absorbing boundary, and overcoming the numerical dispersions resulting from high-frequency propagation and strong heterogeneity in material. A rotated staggered-grid finite-difference method of Biot's poroelastic equations is presented with an unsplit convolutional perfectly matched layer (CPML) absorbing boundary to simulate poroelastic wave propagation in isotropic and fluid-saturated porous media. The contamination of boundary reflections on coda waves is controlled by the CPML absorbing coefficients for the comparison between numerical and experimental ultrasonic waveforms. Numerical examples with a digital porous core demonstrate that the boundary reflections contaminate coda waves seriously, causing much larger coda quality factors and thus underestimating scattering attenuation. [Copyright &y& Elsevier]

Piecewise heterogeneous media that the earth presents are composed of large-scale boundary structures and small-scale volume heterogeneities. Wave propagation in such piecewise heterogeneous media can be accurately superposed through the generalized Lippmann-Schwinger integral equation (GLSIE). Two different Born series modeling schemes are formulated for the boundary-volume integral equation with 2-D antiplane motion ( SH waves). Both schemes decompose the resulting boundary-volume integral equation matrix into two parts: the self-interaction operator handled with a fully implicit manner, and the extrapolation operator approximated by a Born series. The first scheme associates the self-interaction operator with each boundary itself and the volume itself, and interprets the extrapolation operator as the cross-interaction between each boundary and other boundaries/volume scatterers in a subregion. The second scheme relates the self-interaction operator to each boundary itself and its cross-interaction with the volume scatterers on both sides, and expresses the extrapolation operator as both the direct and indirect (through the volume scatterers) cross-interactions between different boundaries in a subregion. By eliminating the displacement field from the volume scatterers, the second scheme reduces the dimension of the resulting boundary-volume integral equation matrix, leading to a faster convergence than the first scheme. Both the numerical schemes are validated by dimensionless frequency responses to a heterogeneous alluvial valley with the velocity perturbed randomly in the range of ca 5-20 %. The schemes are applied to wave propagation simulation in a heterogeneous multilayered model by calculating synthetic seismograms. Numerical experiments, compared with the full-waveform numerical solution, indicate that the Born series modeling schemes significantly improve computational efficiency, especially for high frequencies. [ABSTRACT FROM AUTHOR]

Abstract: Prestack reverse time migration (RTM) requires extensive data storage since it computes wavefields in forward time and accesses wavefields in reverse order. We first review several successful schemes that have been proposed to reduce data storage, but require more computational redundancies. We propose two effective strategies to reduce data storage during RTM. The first strategy is based on the Nyquist sampling theorem, which involves no extra computational cost. The fact is that the time sampling intervals required by numerical algorithms or given by field records is generally several times smaller than that satisfied by the Nyquist sampling theorem. Therefore, we can correlate the source wavefields with the receiver wavefields at the Nyquist time step, which helps decrease storage of time history. The second strategy is based on a lossless compression algorithm, which is widely used in computer science and information theory. The compression approach reduces storage significantly at a little computational cost. Numerical examples show that the two proposed strategies are effective and efficient. [Copyright &y& Elsevier]

Considering the anisotropy of the earth media is helpful in reducing the depth error between seismic and drilling and providing reliable imaging data for seismic interpretation and inversion. Transversely isotropic media with a vertical axis of symmetry are the most common type of anisotropic media and have been under constant study. The separation of the P‐ and S‐wavefields, which affects the accuracy of elastic wave imaging and the inversion in transversely isotropic media with a vertical axis of symmetry, is a hot research topic. Among the commonly used wavefield decoupling methods, the S‐wave is typically obtained by subtracting the P‐wave from the total wavefield. However, this kind of wavefield decoupling method often leads to severe P‐wave crosstalk in the separated S‐wavefield; thus, it needs further development. In this paper, the principle that the divergence of the S‐wave is zero is employed to solve the unresolved S‐wave elastic parameters of the S‐wave stiffness matrix by utilizing the modified zero‐order pseudo‐Helmholtz decomposition operator. The obtained S‐wave elastic parameters are employed to construct the qS‐wave stress and facilitate the derivation of the relationship between the qS‐wave particle velocity and the qS‐wave stress. Furthermore, a qS‐wave decoupling first‐order velocity–stress equation, which matches the qP‐wave decoupling first‐order velocity–stress equation, is derived. By jointly using the decoupling equations of qS‐ and qP‐wave, the separation of the P‐ and S‐wavefields in transversely isotropic media with a vertical axis of symmetry is realized. The efficiency of the proposed method is demonstrated via numerical tests conducted to assess the wavefield separation. Moreover, a complex model is employed to perform elastic reverse‐time migration, resulting in the acquisition of accurate imaging results for PP, PS, SP, and SS waves, without the presence of significant artefacts. The correctness of the qS‐wave decoupling equation in transversely isotropic media with a vertical axis of symmetry is confirmed by the comparative tests using decoupling methods in isotropic media. [ABSTRACT FROM AUTHOR]

As one of wavefield separation methods in elastic reverse time migration, the decoupled wave equation succeeds to separate the particle velocity of P‐ and S‐wave without mode crosstalk. However, it fails to decouple the stress of P‐ and S‐wave which encounters with the problem of crosstalk. To overcome the crosstalk, the paper has proposed the quasi‐stress equations to decouple the stress tensor wavefields of P‐ and S‐wave based on the decoupled stress–strain relationship. Because P‐ and S‐wave stress wavefields are second‐order tensors, different from the imaging method of vector decoupled particle velocity wavefields, a double dot product imaging condition is proposed to obtain scalar images. Based on the total source‐stress tensor wavefields and separated receiver‐stress tensor wavefields, we obtain the scalar images of quasi‐PP and quasi‐PS from the stress information by the double dot product imaging condition. Several numerical examples are evaluated to demonstrate the effectiveness of the separation of P‐ and S‐wave stress and advantage of the proposed imaging condition from the second‐order stress tensor wavefields. [ABSTRACT FROM AUTHOR]

Seismic and electromagnetic explorations are two of the most successful geophysical applications for understanding the subsurface earth, and the joint interpretation of seismic and electromagnetic survey data can help to better characterize the rocks because they contain independent and complementary information about the rocks. However, the success of the joint interpretation depends on the understanding of the correlations between the elastic and electrical rock properties and their influencing factors. Confining pressure is an important geological parameter that has been found to give rise to linear elastic–electrical correlations in sandstones. However, it is still poorly known what controls the slopes of the pressure-dependent linear correlations, even though slope is one of the most important parameters determining the linear correlation. We make artificial sandstones with controlled porosity and permeability, respectively, and measure their pressure-dependent elastic (electrical resistivity) and electrical (P -wave velocity) properties simultaneously, as well as porosity. We show that the slopes of the measured electrical resistivity versus P -wave velocity as an implicit function of confining pressure correlate positively with the compliant porosity in all the samples. The results not only reveal the petrophysical parameter that controls the slopes of the pressure-dependent linear elastic–electrical correlations in sandstones, but also provide a basis for the discrimination of the slope-controlling parameter from the simultaneously measured elastic and electrical properties. [ABSTRACT FROM AUTHOR]

Joint seismic and controlled‐source electromagnetic surveys can reduce uncertainty and improve hydrocarbon quantification. However, the successful interpretation of joint seismic and controlled‐source electromagnetic survey data requires a valid rock physics model to link the elastic and electrical rock properties. A cross‐property differential effective medium is recently proposed with pores embedded in the mineral matrix. We have presented a technique to test the applicability of the cross‐property differential effective medium model to the joint elastic‐electrical properties of reservoir sandstones. The method is based on the common employment of measured sample porosity and inverted equivalent pore aspect ratio from cementation exponent for the modelling. Application of the modelling approach to a laboratory joint elastic‐electrical dataset shows that there is a systematic discrepancy in the modelled and measured joint elastic–electrical properties. It is also found that an equivalent pore aspect ratio is existing to reasonably predict the trend of the joint elastic–electrical data; however, the porosity used in the modelling is far from their measured values. Conversely, if the measured sample porosity is employed, the mentioned equivalent pore aspect ratio fails to fit either of the measured elastic and electrical rock properties. The results indicate the incapability of the cross‐property differential effective medium model for the joint elastic–electrical modelling of reservoir rocks and suggest the requirement of a new model to link the elastic and electrical properties. [ABSTRACT FROM AUTHOR]

Viscous effects cause strong energy decay and waveform changes of seismic waves. These distortions can be corrected using Q- compensated reverse time migration ($Q$ -RTM) algorithms, and high-resolution migration images can be obtained. However, all $Q$ -RTM methods require a relatively accurate $Q$ model. The traditional wave-equation $Q$ tomography can invert the $Q$ model by eliminating the difference in peak frequency between the observed and synthetic early arrivals. However, this approach only can be used to invert the $Q$ value only for large-scale applications or on the surface. Moreover, the reflected wave can also be applied in the extended domain, but its computational efficiency is low compared to that of the early arrivals. To overcome these problems, this work proposes a new wave-equation-based $Q$ inversion methodology to evaluate more accurate underground $Q$ values in local domain. The proposed approach is applicable both to the early arrivals and reflected waves. Accordingly, we first transform the seismic data into the local domain using a sliding Gaussian window to alleviate the crosstalk noise in nearby seismic waves. Then, we use an improved cross correlation algorithm between the amplitude spectra of the observed and synthetic data to calculate the peak frequency shift of each seismic event in local domain. Thus, the inversion accuracy of $Q$ can be improved by using different kinds of waves. The numerical inversion examples demonstrate the ability of our proposed method to produce satisfactory inversion results, especially in high-attenuation and deep areas. The $Q$ -RTM images further illustrate the accuracy of our proposed $Q$ tomography method. [ABSTRACT FROM AUTHOR]

Understanding the electrical properties of reservoir rocks has important applications in oil and gas exploration. Small‐scale fractures that are widely existing in reservoir rocks are usually aligned along a certain preferential direction due to reasons such as tectonic movement, making the electrical conductivity of the rocks anisotropic. Since all rocks are experiencing geological pressure, it is theoretically and practically important to study the influence of pressure on the fractures and its control on the anisotropic conductivity of reservoir rocks. We first prepared artificial porous sandstone samples with and without penny‐shaped fractures and experimentally measured the anisotropic conductivity of the samples under differential pressure (the difference between confining pressure and pore fluid pressure). Then, we inverted from the experimental data for the fracture porosity and fracture aspect ratio at each differential pressure. The variation of the fracture parameters caused by the differential pressure and their influence on the anisotropic electrical conductivity of the rocks were further analysed theoretically. The results show that as the differential pressure increases, the measured anisotropic conductivity of the artificial samples with and without fractures all decreases exponentially. We also show that both the inverted fracture porosity and fracture aspect ratio decrease exponentially with the increase of differential pressure, and the fracture porosity and fracture aspect ratio are linearly correlated as an implicit function of differential pressure. The modelling results show that the differential pressure‐induced decrease in the fracture porosity reduces the electrical conductivity in all directions, and the conductivity reduction in the rock parallel to the direction of the fractures is most significant. Comparing with the influence of the fracture porosity resulting from the applied differential pressure, the pressure‐caused variation in the fracture aspect ratio was shown to play a secondary role on affecting the pressure‐dependent anisotropic electrical properties. [ABSTRACT FROM AUTHOR]

Cracks are widely existing in natural rocks, and the effects of cracks on the elastic and electrical properties of rocks make it possible to establish appropriate joint interpretation to detect the crack characteristics more accurately. However, the premise is the knowledge of the joint elastic–electrical properties of cracked rocks. We aim to study theoretically the pressure-dependent joint elastic–electrical properties of porous rocks with aligned penny-shaped cracks. To do so, we developed a model describing the deformation of cracks in a transversely isotropic (TI) background with stress, and combined with existing models for the anisotropic elastic and electrical properties of TI rocks with aligned cracks. The impacts of crack deformation on the anisotropic elastic and electrical properties of cracked rocks, and the effects of crack porosity and crack aspect ratio on the pressure-dependent joint elastic–electrical properties were then studied. We showed that the modelling results compared satisfactorily with experimental data. The modelling results demonstrated that the crack compaction with stress reduced the elastic and electrical anisotropy. We also found that the anisotropic elastic wave velocities and electrical conductivities of cracked rocks exhibited approximately negative linear correlations when linked by the effective stress, and the slopes and intercepts of the linear relationships were shown to be systematically dependent on the porosity and aspect ratio of the aligned cracks. The above knowledge of the pressure-dependent joint elastic–electrical properties of TI rocks with aligned cracks can be employed for quantitative interpretation of the joint elastic and electrical exploration data. [ABSTRACT FROM AUTHOR]