Search

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]

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]

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]

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]

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]

SUMMARY: Geophysical exploration technologies are developed not only to detect and quantify the geofluid in a reservoir but also with the expectation to identify the reservoir's permeability that determines its exploitability. However, the knowledge about whether there is a geophysically invertible pore parameter that determines the permeability of a rock, the key to the geophysical identification of permeability, remains poorly understood. We address this knowledge gap by establishing, through dedicated laboratory measurements and theoretical modelling, the correlations between permeability and the porosity and aspect ratios of the dual-pore structure in artificial sandstones with approximately the same porosity but with different permeability. Permeability is found to increase with increasing compliant porosity but show no apparent relations with the dual-pore aspect ratios, indicating compliant porosity is the key parameter determining the permeability of rocks with the same porosity. The results reveal the key factor that influences permeability in sandstones with the same porosity, and provide a potential way to simply identify the permeability to indicate the exploitability of a geofluid reservoir. [ABSTRACT FROM AUTHOR]

Seismic exploration of deep oil/gas reservoirs involves the propagation of seismic waves in high-pressure media. Traditional elastic wave equations are not suitable for describing such media. The theory of acoustoelasticity establishes the dynamic equation of wave propagating in prestressed media through constitutive relation using third-order elastic constants. Many studies have been carried out on numerical simulations for acoustoelastic waves, but are mainly limited to 2D cases. A standard staggered-grid (SSG) finite-difference (FD) approach and the perfectly matched layer (PML) absorbing boundary are combined to solve 3D first-order velocity-stress equations of acoustoelasticity to simulate wave propagating in 3D prestressed solid medium. Our numerical results are partially validated by plane-wave analytical solution through the comparison of calculated and theoretical P-/S-wave velocities as a function of confining prestress. We perform numerical simulations of acoustoelastic waves under confining, uniaxial and pure-shear prestressed conditions. The results show the stress-induced velocity anisotropy in acoustoelastic media, which is closely related to the direction of prestresses. Comparisons to seismic simulations based on the theory of elasticity illustrate the limitation of conventional elastic simulations for prestressed media. Numerical simulations prove the significant effect of prestressed conditions on seismic responses. [ABSTRACT FROM AUTHOR]

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]

OBJECTIVE To investigate the characteristics of left ventricular layer-specific strain in patients with chronic kidney disease (CKD). METHODS Eighty-five patients of chronic kidney disease in the Department of Nephrology of our hospital from March 2020 to August 2021 were selected and divided into three groups according to the estimated GFR: Group A (CKD stage 1–2), Group B (CKD stage 3–4), and Group C (CKD stage 5), 40 hypertensive patients without renal insufficiency were gathered as hypertension (HT) group and 40 gender and age-matched healthy volunteers were selected as the control group. Then, (i) Routine echocardiographic parameters: left ventricular diameter, left atrium diameter, wall thickness, LVEF. (ii) Myocardial strain: global longitudinal strain (GLS), longitudinal strain in endocardium (SL-endo), longitudinal strain in average (SL-ave), longitudinal strain in epicardium (SL-epi), global circumferential strain (GCS), global circumferential strain in endocardium (SC-endo), global circumferential strain in average (SC-ave), global circumferential strain in epicardium (SC-epi), and global radial strain (GRS) were analyzed. RESULTS (i) Compared with the control group, the structure of the left heart and LVEF in groups A and B had no significant changes, left ventricular remodeling appeared, and diastolic function declined in HT group and group C, LVEF decreased in group C (all P  < 0.05). (ii) Only SL-endo decreased in the HT group. All of SL-endo, SL-ave, and SL-epi were reduced in the CKD group and were lowest in group C. Radial strain decreased only in group C (all P < 0.05). (iii) The global and layer-specific longitudinal strain were correlated with estimated glomerular filtration rate (eGFR) (r  = 0.541–0.559, all P < 0.05), LVEF was correlated with longitudinal and circumferential strain (r  = 0.406–0.424, all P < 0.05). Multiple linear regression analysis showed that longitudinal strain in different layers were independently correlated with different stages of CKD and the occurrence of secondary hypertension or not (β = −0.251 to −0.443, all P < 0.05). Circumferential strain in all layers were independently correlated with the appearance of secondary hypertension or not (β = −0.255 to −0.31, all P < 0.05). CONCLUSIONS The degree and range of the impairment of left ventricular strain in CKD patients are related to the stage of eGFR and secondary hypertension, which may affect the global systolic pump function by involving the circumferential strain. [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]

Superdeep fault-karst carbonate reservoirs discovered over 7 km deep are controlled by strike-slip fault zones and karst collapses in Tarim Basin, Northwest China. The resulting fracture-cave system provides favorable migration channels and reservoir spaces for hydrocarbon, while the characterization of the internal fault structures remains enigmatic. Based on seismic imaging data, we conducted an integrated study on fault damage zones by seismic curvature attributes, velocity anisotropies, and seismic attenuations. The results show that three typical fault-zone patterns can be identified in the study area, including paratactic multiple fault cores, interactive fault cores and one primary-several subsidiary fault cores. These typical patterns can be clearly characterized via curvature attributes. The elastic characteristics of fault damage zones are significantly affected by seismic frequencies, which are manifested from velocity anisotropies and seismic attenuations. The maximum seismic attenuation occurs along with the orientation of fault cores. There is a strong anisotropic characteristic of P-wave phase velocity with incident angle of three fault-zone models. It appears that seismic attributes associated with geological steering are an effective tool for the subsurface characterization of fault damage zones. [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]

Elastic and electrical properties can be jointly interpreted for better characterizations of rocks with cracks that are common in geological rocks. However, the cross-property relationship between the elastic and electrical properties of cracked rocks, which forms the key to the successful joint elastic–electrical interpretation, remains poorly understood. We investigate the pressure effects on the joint elastic–electrical properties in brine-saturated artificial sandstones with aligned non-interacting penny-shaped cracks that are far from percolation. We measured and compared the anisotropic electrical conductivity and ultrasonic velocity in the artificial sandstones with and without aligned cracks under applied effective stress from 5 to 50 MPa. We showed that the existence of aligned cracks significantly enhanced the elastic and electrical anisotropies of the rocks, and the difference in the elastic and electrical anisotropies between the cracked and intact samples reduced as the effective stress increased. We also showed that the pressure-dependent electrical conductivity and ultrasonic velocity exhibited strong linear correlations in both the intact and cracked samples cored in different directions, and a difference existed in the slopes between the samples with and without aligned cracks. The distinct contributions of the pressure-induced deformation of cracks to the anisotropic elastic and electrical properties, as well as their different sensitivity to the cracks, were found to plausibly explain the observed experimental results. Theoretical modelling for quantitative interpretation of the experimental data is presented in a companion paper. [ABSTRACT FROM AUTHOR]

The reservoir rocks from Chang-7 member of Yanchang Formation of Ordos Basin are characterised with heterogeneous fabric structures at the pore scale, and low porosity/permeability is exhibited at the macro scale. Precise prediction of reservoir brittleness is of great significance to oil production. Ultrasonic experiments are performed on tight sandstones collected from the target formation. A rock-physics model (RPM) is presented based on the Voigt–Reuss–Hill average (VRH), self-consistent approximation (SCA) and differential effective medium (DEM) theory. The brittleness characteristics relying on mineral composition, porosity and microcrack properties are explored by using the RPM. The Young's modulus increases and Poisson ratio decreases with increasing quartz content. Based on experimental, log and seismic data, brittle mineral analysis of rock physical model is performed at multiple scales. The model accuracy is verified by experimental data and well log data. The brittleness distribution is predicted on the basis of log and seismic data, which can be instructive for the reservoir rock fracturing in actual engineering operations. [ABSTRACT FROM AUTHOR]

Thermally coupled constitutive relations are generally used to determine material constants and elastic moduli (Young's modulus and shear modulus) of solid media. Conventional studies on this issue are mainly based on the linear temperature dependence of elastic moduli, whereas analytical difficulties are often encountered in theoretical studies on nonlinear temperature dependence, particularly at high temperatures. This study investigates the thermally coupled constitutive relations for elastic moduli and material constants using the assumption of axisymmetric fields, with applications to geologic materials (marble, limestone and granite). The Taylor power series of the Helmholtz free energy function within dimensionless temperatures could be used to develop the thermally coupled constitutive relations. The thermoelastic equivalent constitutive equations were formulated under the generalized Hooke's law. The material constants of solid rocks were determined by fitting experimental data using axisymmetric stress and strain fields at different temperatures, based on their thermomechanical properties. For these geologic materials, the resultant equivalent elastic moduli and deformations were in good agreement with those from the experimental measurements. Thermal stresses, internal moisture evaporation and internal rock compositions significantly affected the experimental results. This study provides a profound understanding of the thermally coupled constitutive relations that are associated with the thermomechanical properties of solid rocks exposed to high temperatures. [ABSTRACT FROM AUTHOR]

Natural fractures are usually multiscale in size, orientations and distribution, resulting in complex anisotropic characteristics. Analytical methods for quantifying the associated effective elastic properties are based on some assumptions, such as dilute fracture concentration and regular-shaped fractures, which do not occur in actual reservoirs. Here, we conduct anisotropic finite-element modeling of effective elastic properties of complex fractured rocks using the least-square fitting method. The algorithm is developed for a 3D case and validated by classical effective medium theories for models with different fracture densities. The results of the 3D numerical method agree well with the theoretical predictions at low fracture density. The model also considers the interactions among fractures to calculate equivalent stiffness tensors at high fracture density. Three 2D fracture models are simulated to demonstrate the basic behavior of stress interactions and their effect on the overall elasticity under different fracture densities. We applied the developed model to 3D natural fractures built from a real outcrop, and we found that the fracturing pattern significantly affects the effective anisotropy properties. The resultant P-wave phase velocities as functions of the incidence angle and frequency are anisotropic. This study provides a great potential to calculate equivalent stiffness tensors and anisotropic properties of 3D multiscale natural fractures. [ABSTRACT FROM AUTHOR]

Natural rocks are polymineral composites with complex microstructures. Such strong heterogeneities significantly affect the estimation of effective moduli by some theoretical models. First, we have compared the effective moduli of isotropic rocks predicted by the Kuster–Toksöz (KT) model and the Mori–Tanaka (MT) model. The widely used KT model only has finite precision in many cases because of its assumption that is restricted to the first-order scattering approximation. However, the MT model based on the Eshelby tensor in mesomechanics has the advantage of predicting effective moduli of rocks, especially when the volume fraction of embedded inclusions is sufficiently large. In addition, the MT model can be used to predict the effective modulus of anisotropic rocks, but the KT model cannot. For a certain kind of shale or tight sandstones, which are viewed as isotropic composites, both the models work well. For the medium containing spherical pores, both the models produce the same results, whereas for ellipsoidal pores the MT model is more accurate than the KT model, validated by the finite element simulations. In what follows, the applicable ranges of simplified formulas for pores with needle, coin and disk shapes, widely used in engineering, are quantitatively given based on the comparison with the results according to the reduced ellipsoidal formulas of the MT and KT models. These findings provide a comprehensive understanding of the two models in calculating the effective modulus of rocks, which are beneficial to such areas as petroleum exploration and exploitation, civil engineering, and geophysics. [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]

Thermoelastic attenuation is similar to wave-induced fluid-flow attenuation (mesoscopic loss) due to conversion of the fast P wave to the slow (Biot) P mode. In the thermoelastic case, the P - and S -wave energies are lost because of thermal diffusion. The thermal mode is diffusive at low frequencies and wave-like at high frequencies, in the same manner as the Biot slow mode. Therefore, at low frequencies, that is, neglecting the inertial terms, a mathematical analogy can be established between the diffusion equations in poroelasticity and thermoelasticity. We study thermoelastic dissipation for spherical and cylindrical cavities (or pores) in 2-D and 3-D, respectively, and a finely layered system, where, in the latter case, only the Grüneisen ratio is allowed to vary. The results show typical quality-factor relaxation curves similar to Zener peaks. There is no dissipation when the radius of the pores tends to zero and the layers have the same properties. Although idealized, these canonical solutions are useful to study the physics of thermoelasticity and test numerical algorithm codes that simulate thermoelastic dissipation. [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]

Electrical surveys are among the most important geophysical applications to understand the subsurface Earth, where anisotropic rock matrix is frequently encountered. Knowledge of the electrical properties of such rocks and their relationships with information of geological features included in the anisotropic rocks is crucial for the interpretation of electrical survey data. For this purpose, we first derive rigorous theoretical models for the electrical anisotropy of transversely isotropic (TI) rocks with spheroidal inclusions. The models assume the anisotropic background behaves isotropically in the direction whey the electrical field is applied parallel to the TI axes, and account for both aligned and randomly distributed inclusions and reduce to classical electrical models in the case of isotropic background. We then study systematically, through the obtained new models, the combined effects of geometry, concentration and alignment of both conductive and insulating spheroidal inclusions on the electrical anisotropy of TI rocks. We show that for aligned inclusions, the impact of inclusion volume fraction and aspect ratio is most significant in the direction when the electrical conductivity is measured along and perpendicular to the inclusions for conductive and insulating inclusions, respectively. For randomly distributed inclusions, both horizontal and vertical conductivity increases with decreasing aspect ratio of conductive inclusions and decreases with reducing aspect ratio of insulating inclusions. Most importantly, it is shown that the effects of randomly distributed conductive and insulating inclusions on the electrical anisotropy are similar although the rocks with insulating inclusions exhibit greater electrical anisotropy. The results provide new insights into the roles of spheroidal inclusions on the electrical anisotropy of TI rocks and pave a way for the successful interpretation of electrical survey data acquired in anisotropic rocks. [ABSTRACT FROM AUTHOR]

Objective To investigate myocardial apoptosis and the expression of apoptosis-related proteins [B-cell lymphoma-2 (Bcl-2) and Bax], cardiac hypertrophy, and function in spontaneously hypertensive rats (SHR) during aging. Methods Male SHR (n = 36) and Wistar-Kyoto rats (WKY, n = 30) were monitored for their cardiac function from 14 to 102 weeks of age using echocardiography. Myocardial apoptosis in the subendocardium and subepicardium was analyzed using TUNEL staining. The apoptosis-related proteins (Bcl-2 and Bax) were assessed by Western blot analysis. Results Left ventricular mass index (LVMI) in SHR increased progressively with age. Left ventricular ejection fraction (LVEF) showed no significant difference from 14 to 66 weeks of age, but decreased significantly in SHR from 84 to 102 weeks of age. The apoptotic index (APOI) of myocardial cells in SHR increased with age, in which subendocardial APOI (APOI-endo) increased at 66 weeks and was significantly higher than the age-matched WKY (9.83 ± 3.97 vs. 4.03 ± 2.06, P < 0.05). Additionally, the subepicardial APOI (APOI-epi) increased significantly at 84 weeks of age (P < 0.05). Bax/Bcl-2 ratio was higher in SHR than WKY at 66 weeks (3.98 ± 0.80 vs. 0.29 ± 0.06, P < 0.05), and enhanced further at 102 weeks of age (10.54 ± 1.60 vs. 0.70 ± 0.13, P < 0.05). Myocardial APOI was positively correlated with LVMI (r = 0.83, P < 0.01), negatively with LVEF in 66–102 weeks (r = −0.81, P < 0.01), and positively with Bax/Bcl-2 ratio (r = 0.79, P < 0.01). Conclusion Myocardial apoptosis increases with aging and is associated with progressive left ventricular remodeling and cardiac dysfunction in SHR. [ABSTRACT FROM AUTHOR]