Frequency-dependent Anisotropy Research Articles

Quantitative prediction of the fracture scale based on frequency-dependent S-wave splitting

The development of natural fractures has a significant impact on underground reservoirs and leads to seismic anisotropy. Furthermore, the scale of natural fractures directly affects oil and gas preservation, hydraulic fracture construction, and the production development of shale reservoirs. The S-wave anisotropy is a frequency-dependent parameter and the change in S-wave anisotropy with frequency is a function of the fracture scale. We develop an innovative method for predicting the fracture scale quantitatively using frequency-dependent S-wave anisotropy. The quantitative relationship between different fracture scales and the frequency-dependent response of the S-wave splitting (SWS) anisotropy can be obtained using a dynamic rock-physics model. The frequency-dependent S-wave anisotropy is calculated via SWS analysis in the frequency domain, after which this quantitative relationship and the calculated frequency-dependent response are used to establish an objective function for the inversion of the fracture scale at different depths using the least-squares algorithm. We synthesize data under ideal conditions, test our method, apply our method to field data, and find that the quantitative prediction method of the fracture scale yielded reasonable prediction results. The S-wave anisotropy is calculated based on the SWS analysis from the horizontal components of the upgoing wavefields of the field vertical seismic profile. We compare the fracture scale calculated from logging data using our method, and the results obtained indicate that this method can successfully predict the fracture scale quantitatively.

Research on the forward-modeling method of viscoelastic Chapman extension in partially saturated rocks

The propagation of seismic waves in fractured rocks is greatly influenced by the fracture system and fluid content. Seismic anisotropy varies with frequency and fluid saturation. Previous theories on frequency-dependent anisotropy (FDA) are mostly limited to the assumption of single-phase fluid, whereas almost all reservoirs are usually partially or fully saturated with one or more fluids. The inelasticity, heterogeneity, and anisotropy exhibited by real earth media seriously challenge the traditional theory of uniform fully elastic media. Therefore, based on the Chapman elastic theory, we consider the viscoelastic model, the relative mobility of saturated fluids, and the coupled effects of commonly independently considered squirt flow and patch effects on the frequency-dependent anisotropic seismic wave propagation in viscoelastic media. By calculating the frequency-dependent anisotropic elastic coefficients of two-phase immiscible fluid-saturated fractured rocks, a new viscoelastic Chapman extension model for FDA in partially saturated rocks, which includes the unified seismic wave propagation effects of squirt flow and patch effects, is constructed. The effect of relative permeability is significant, and compared to the case of complete saturation, the effective fluid mobility in partially saturated rocks may be lower, which may lead to nonmonotonic changes in elastic modulus and water saturation. Numerical experiments are conducted on our viscoelastic Chapman extension model to discuss the coupling effects of squirt flow and patch effects on the FDA of viscoelastic media in cracked rocks with partially saturated reservoirs, under the conditions of no fractures and the existence of fractures. The simulation results of the P-wave modulus, P-wave velocity, and anisotropy parameters confirm the validity of our method and model. We link the anisotropy of viscoelastic media with fluid flow parameters in fractures, which is conducive to improving the understanding of frequency-dependent seismic anisotropy in partially saturated rocks with fractures and the combination of seismology and reservoir engineering.

Seismic dispersion, attenuation and frequency-dependent anisotropy in a fluid-saturated porous periodically layered medium

SUMMARY The White model is generally used to quantify seismic dispersion and attenuation caused by interlayer wave-induced fluid flow. However, this model derives P-wave dispersion and attenuation only in the direction perpendicular to the layer. Thus, in this study, we derive the exact analytical solutions for full effective stiffness coefficients of a fluid-saturated layered porous medium so as to calculate the angle-dependent seismic dispersion and attenuation and frequency-dependent anisotropy. The analytical solution for fluid pressure is derived using Biot's equations of quasi-static poroelasticity. Then, the mean stress or strain is obtained through its relationship with fluid pressure, and the stress–strain value is used to derive the effective stiffness coefficients. This is followed by the calculation of the angle-dependent seismic dispersion and attenuation and frequency-dependent anisotropy. Our results show that the layered medium with alternating gas- and brine-saturated layers having the same matrix is isotropic at all frequencies. However, the layered medium with periodically distributed highly porous, thin layers shows significant frequency-dependent anisotropy. In the case of P wave, the largest magnitudes of dispersion and attenuation are observed in the direction perpendicular to the layer, while those for SV wave occur at the incident angle of around 45°. When our model is compared with the previous models, the low- and high-frequency limits of our model are found to be identical to the poroelastic Backus averaging. In addition, the widely used single relaxation function approximation is found to be a good approximation of our exact solutions. Our proposed model is easy to use and can be applied in the seismic exploration of the layered earth.

Effects of intrinsic anisotropy on seismic dispersion, attenuation and frequency-dependent anisotropy

层间波致流体流动是饱和流体孔隙层状介质中地震波频散、衰减与频变各向异性的重要机制，目前已提出较多模型对其进行定量表征。然而，现有模型忽略了层状介质中各层本身可具有的各向异性特征（即本征各向异性）。针对此，本文基于Biot孔弹性理论推导了由横向各向同性饱和流体孔隙地层组成的层状介质中地震波频散、衰减与频变各向异性的近似理论模型。同时，为验证理论模型，开展了数值模拟与理论模型进行对比，两者吻合良好。利用理论模型，分析了四种情况（流体性质不同、骨架性质不同、及两者之间的两种不同组合）下本征各向异性的影响。结果表明，对于气层与水层交互形成的层状介质，含水层的本征各向异性对地震波的频散、衰减与频变各向异性影响最大，而对于含高孔薄层的层状介质，背景基质本征各向异性与流体分布起主要影响。本文所构建模型简洁易用，在页岩或致密砂岩等具有明显层理特征的储层中应用前景广阔。

Near-surface seismic anisotropy in Antarctic glacial snow and ice revealed by high-frequency ambient noise

AbstractAmbient seismic recordings taken at broad locations across Ross Ice Shelf and a dense array near West Antarctic Ice Sheet (WAIS) Divide, Antarctica, show pervasive temporally variable resonance peaks associated with trapped seismic waves in near-surface firn layers. These resonance peaks feature splitting on the horizontal components, here interpreted as frequency-dependent anisotropy in the firn and underlying ice due to several overlapping mechanisms driven by ice flow. Frequency peak splitting magnitudes and fast/slow axes were systematically estimated at single stations using a novel algorithm and compared with good agreement with active source anisotropy measurements at WAIS Divide determined via active sources recorded on a 1 km circular array. The approach was further applied to the broad Ross Ice Shelf (RIS) array, where anisotropy axes were directly compared with visible surface features and ice shelf flow lines. The near-surface firn, depicted by anisotropy above 30 Hz, was shown to exhibit a novel plastic stretching mechanism of anisotropy, whereby the fast direction in snow aligns with accelerating ice shelf flow.

Water Dynamics and Structure of Highly Concentrated LiCl Solutions Investigated Using Ultrafast Infrared Spectroscopy.

In highly concentrated salt solutions, the water hydrogen bond (H-bond) network is completely disrupted by the presence of ions. Water is forced to restructure as dictated by the water-ion and ion-ion interactions. Using ultrafast polarization-selective pump-probe (PSPP) spectroscopy measurements of the OD stretch of dilute HOD, we demonstrate that the limited water-water H-bonding present in concentrated lithium chloride solutions (up to four waters per ion pair) is, on average, stronger than that occurring in bulk water. Furthermore, information on the orientational dynamics and the angular restriction of water H-bonded to both water oxygens and chloride anions was obtained through analysis of the frequency-dependent anisotropy decays. It was found that, when the salt concentration increased, the water showed increasing restriction and slowing at frequencies correlated with strong H-bonding. The angular restriction of the water molecules and strengthening of water-water H-bonds are due to the formation of a water-ion network not present in bulk water and dilute salt solutions. The structural evolution of the ionic medium was also observed through spectral diffusion of the OD stretch using 2D IR spectroscopy. Compared to bulk water, there is significant slowing of the biexponential spectral diffusion dynamics. The slowest component of the spectral diffusion (13 ps) is virtually identical to the time for complete reorientation of HOD measured with the PSPP experiments. This result suggests that the slowest component of the spectral diffusion reflects rearrangement of water molecules in the water-ion network.

Theoretical modelling of seismic dispersion, attenuation and frequency-dependent anisotropy in a fluid-saturated porous rock with intersecting fractures

SUMMARYDetection of intersecting open fractures is an important task in many earth science domains. To quantify the seismic responses in the fluid-saturated porous rock with intersecting open fractures, we develop a theoretical model based on Biot's equations of dynamic poroelasticity. The seismic dispersion, attenuation and frequency-dependent anisotropy due to joint effects of fracture–background wave-induced fluid flow (FB-WIFF), and fracture–fracture wave-induced fluid flow (FF-WIFF), as well as elastic scattering are investigated. The numerical results on a fluid-saturated porous and fractured sandstone show that the characteristic frequency of FF-WIFF is controlled by fracture connectivity and fluid viscosity. Variations of fracture connectivity and fluid viscosity may result in the coupling of FF-WIFF with FB-WIFF or elastic scattering. When the fracture connectivity tends to zero, the FF-WIFF vanishes and FB-WIFF becomes most significant. Besides fracture connectivity and fluid viscosity, the fracture geometry and fluid bulk modulus also affect the magnitudes of these three mechanisms and their interplay. Due to effects of these three mechanisms, the P-wave anisotropy varies greatly with frequencies. Furthermore, the fracture intersection angle also influences the P-wave anisotropy significantly. Our model agrees well with previous models in the frequency limits and for the special case with parallel fractures. Since our model incorporates the effects of FF-WIFF, it has a great potential to be applied in the detection for effective fracture networks for fluid flow.

On the optical anisotropy in 2D metal-halide perovskites.

Two-dimensional metal-halide perovskites (MHPs) are versatile solution-processed organic/inorganic quantum wells where the structural anisotropy creates profound anisotropy in their electronic and excitonic properties and associated optical constants. We here employ a wholistic framework, based on semiempirical modeling (k·p/effective mass theory calculations) informed by hybrid density functional theory (DFT) and multimodal spectroscopic ellipsometry on (C6H5(CH2)2NH3)2PbI4 films and crystals, that allows us to link the observed optical properties and anisotropy precisely to the underlying physical parameters that shape the electronic structure of a layered MHP. We find substantial frequency-dependent anisotropy in the optical constants and close correspondence between experiment and theory, demonstrating a high degree of in-plane alignment of the two-dimensional planes in both spin-coated thin films and cleaved single crystals made in this study. Hybrid DFT results elucidate the degree to which organic and inorganic frontier orbitals contribute to optical transitions polarized along a particular axis. The combined experimental and theoretical approach enables us to estimate the fundamental electronic bandgap of 2.65-2.68 eV in this prototypical 2D perovskite and to determine the spin-orbit coupling (ΔSO = 1.20 eV) and effective crystal field (δ = -1.36 eV) which break the degeneracy of the frontier conduction band states and determine the exciton fine structure. The methods and results described here afford a better understanding of the connection between structure and induced optical anisotropy in quantum-confined MHPs, an important structure-property relationship for optoelectronic applications and devices.

Effects of porosity, orientation and connectivity of microcracks on dispersion and attenuation of fluid-saturated rocks using an upscaling numerical modelling of the squirt flow mechanism

Squirt flow is a wave-induced fluid flow mechanism to account for the velocity dispersion and attenuation of fluid-saturated porous media. Theoretical models of squirt flow cannot deal with complex microcrack-pore networks and thus cannot give accurate dispersion and attenuation curves with respect to frequency. We adopt a numerical oscillatory compressibility test method, based on the quasi-static poroelastic equation of Biot, to model the squirt flow and calculate corresponding P-wave modulus dispersion and attenuation. We also designed nine porous medium models containing different crack-pore configurations and investigated the effects of microcrack porosity, orientation and connectivity on the elastic responses. Modelling results show that not only microcrack porosity but also their orientation has control on the magnitude of the P-wave modulus dispersion and attenuation. Preferentially aligned microcracks may cause frequency-dependent anisotropy in the P-wave modulus and attenuation. Microcrack connectivity has a negligible influence on the dispersion and attenuation magnitude but a large influence on the characteristic frequency of the squirt flow, which is not predicted by theoretical models based on simple representative element volume of crack-pore structure. Therefore, detailed geometry of crack-pore network, of which microcrack porosity, orientation, aspect ratio and connectivity are vital factors, dictates the unique variations in the elastic modulus and associated attenuation with frequency caused by the squirt flow. Pore structure obtained by CT scanning representative of that of the whole rock is needed to obtain more accurate poroelastic responses of the rock with the numerical oscillatory compressibility test method. In this regard, we provide a powerful tool for evaluating dispersion and attenuation of fluid-saturated rock media with complex crack-pore structure, which have potential applications in seismic exploration of hydrocarbon in the subsurface.

Analysis of S waves singularity points in porous rock with two orthogonal sets of mesoscale fractures

SUMMARY The shear waves phase velocity surfaces in orthorhombic (ORT) and lower symmetry anisotropic models touch each other in one or more points resulting in so called singularity points or acoustic axes. These singularity points result in dramatic changes of velocities, amplitudes and polarizations creating problems in seismic data processing and analysis. Considering the frequency-dependent anisotropy due to mesoscale fractures in Chapman's model, we describe the singularity points in porous rock with two orthogonal sets of mesoscale fractures. First, we give the equations for frequency-dependent phase velocities of P, S1 and S2 waves in this anelastic ORT media. Then, we derive the expressions for frequency-dependent singularity points within the symmetry planes and discuss the conditions to detect the existence of singularity point. Finally, the influences of frequency, porosity, fracture density, fracture scale and saturating fluid style on the positions of singularity points within the symmetry plane are investigated.

Frequency-dependent anisotropy due to non-orthogonal sets of mesoscale fractures in porous media

SUMMARY The monoclinic medium with a horizontal symmetry plane is gradually being studied for seismic anisotropy characterization. The principle goal of this paper is to investigate the effect of fracture parameters (azimuth angle, density, aspect ratio, scale) on the exact and approximate monoclinic anisotropy parameters. We derive the monoclinic porous media based on the Chapman model which accounts for the wave-induced fluid flow and give the expressions of the Thomsen-style anisotropy parameters (nine orthorhombic anisotropy parameters: VP0, VS0, ϵ1, ϵ2, γ1, γ2, δ1, δ2, δ3, three exact monoclinic parameters: ζ1, ζ2, ζ3 and three approximate monoclinic parameters: $\widetilde{\zeta _{1}}, \widetilde{\zeta _{2}}, \widetilde{\zeta _{3}}$). The dependence of Thomsen-style anisotropy parameters associated with azimuth angle between two fracture sets is analysed. The orthorhombic anisotropy parameters and monoclinic anisotropy parameters have the same period (π) on the azimuth angle between two fracture sets. The exact and approximate monoclinic anisotropy parameters responsible for the rotation of the P-wave NMO ellipse have a similar trend versus the azimuth angle, while those responsible for the rotation of the S1- and S2-wave NMO ellipses have significant discriminations. The influence of fracture density, aspect ratio, and scale on the monoclinic parameters are also analysed. The monoclinic anisotropy parameters responsible for the rotation of the P-wave NMO ellipse decrease with fracture density and aspect ratio increasing from 0 to 0.1, while those responsible for the rotation of S1- and S2-wave NMO ellipses increase with the fracture parameters. The fracture density has a bigger influence on the monoclinic anisotropy parameters than the fracture aspect ratio. When saturated with different fluids (water and CO2), the monoclinic parameters have a similar behaviour versus the azimuth angle between two fracture sets.

Frequency-dependent anisotropy in partially saturated porous rock with multiple sets of mesoscale fractures

SUMMARY Accurate modelling of the frequency-dependence of seismic wave velocity related to fracture system and fluid content is crucial to the quantitative interpretation of seismic data in fractured reservoirs. Both mesoscale fractures and patchy saturation effects can cause significant velocity dispersion and attenuation in the seismic frequency band due to wave-induced fluid flow (WIFF) mechanism. Considering the coupled impact of ‘mesoscale fractures’ and ‘patchy saturation’, we derive expressions for the frequency-dependent anisotropy in partially saturated porous rock containing two fracture sets with different orientations, sizes and connectivities. Especially, we simplify the rock-physics model as an orthorhombic (ORT) media by assuming the mesoscale fractures to be orthogonal and give the explicit expressions for frequency-dependent elastic constants. Finally, we give the expressions for the frequency-dependent phase velocity in patchy saturated and fractured ORT media and investigate the effect of patchy saturation on P-wave velocity at different polar and azimuth angles. In this paper, we investigate the effects of fluid saturation and fluid pressure on frequency-dependent velocities and Thomsen anisotropy parameters. Also, the effect of the relative permeability is very noticeable. The relaxation frequency can be lower in partially saturated fractured rocks compared with the fully saturated case, which makes the rock have a larger stiffness. The non-monotonic relationships between frequency-dependent anisotropy and fluid saturation add complexity to seismic forward modelling and inversion in reservoirs with complex fracture patterns.

Modeling the effects of fracture infill on frequency-dependent anisotropy and AVO response of a fractured porous layer

In a fractured porous hydrocarbon reservoir, wave velocities and reflections depend on frequency and incident angle. A proper description of the frequency dependence of amplitude variations with offset (AVO) signatures should allow effects of fracture infills and attenuation and dispersion of fractured media. The novelty of this study lies in the introduction of an improved approach for the investigation of incident-angle and frequency variations-associated reflection responses. The improved AVO modeling method, using a frequency-domain propagator matrix method, is feasible to accurately consider velocity dispersion predicted from frequency-dependent elasticities from a rock physics modeling. And hence, the method is suitable for use in the case of an anisotropic medium with aligned fractures. Additionally, the proposed modeling approach allows the combined contributions of layer thickness, interbedded structure, impedance contrast and interferences to frequency-dependent reflection coefficients and, hence, yielding seismograms of a layered model with a dispersive and attenuative reservoir. Our numerical results show bulk modulus of fracture fluid significantly affects anisotropic attenuation, hence causing frequency-dependent reflection abnormalities. These implications indicate the study of amplitude versus angle and frequency (AVAF) variations provides insights for better interpretation of reflection anomalies and hydrocarbon identification in a layered reservoir with vertical transverse isotropy (VTI) dispersive media.

Frequency-dependent anisotropy in porous rocks with aligned cracks containing compressible fluid–a model based on poroelastic spring condition and exact solution of scattering by a circular crack at oblique incidence

SUMMARYThorough understanding of seismic signatures in cracked rocks is essential to estimate rock physical properties. Wave-induced fluid flow (or diffusion), scattering and Biot's global flow are three major mechanisms in controlling frequency-dependent attenuation and dispersion. To shed light on how those mechanisms and their interference affect the anisotropic features in cracked porous rocks, we develop an analytic model to estimate the angle-dependent attenuation and dispersion in such media. The most noteworthy feature of the model is that it is developed upon the exact solution of the problem of elastic wave scattered by a crack at oblique incidence. In particular, the poroelastic spring condition is applied to describe the influences of crack thickness and crack-filling fluid elasticity on wave scattering. Regardless of its complexity, we have showed that the model agrees with many benchmark theories under corresponding conditions, demonstrating its reasonability. It is found that the key factors that dominate anisotropic attenuation and dispersion are different in separating frequency regimes. At diffusion-dominated frequencies, the frequency-dependent anisotropic properties are mainly determined by the normal stress on the crack faces. In contrast, in Rayleigh scattering regime, they are greatly determined by the applied shear stress. At higher frequencies (Mie scattering regime), affected by the wave reflections between the crack edges, the frequency-dependent anisotropy becomes complex. The angle-dependent velocity can largely deviate from elliptic-shaped profile. As a result, the material properties cannot be described within the framework of the transversely isotropic medium model. Moreover, it is found that the attenuation is sensitive to the fluid compressibility and crack thickness, showing evidences that it is possible to invert fluid saturation and permeability from seismic attenuation. We also conclude that using a simple linear superposition of the attenuations due to wave-induced fluid flow and elastic scattering from their corresponding equivalent medium models will leads to an overestimation of the total attenuation. Our results demonstrate it is necessary to account for the mechanism interference to allow for an adequate estimation of the intrinsic attenuation of cracked porous rocks.

TD-DFT Studies on sp- and sp2-Hybridized Single Vacancy-Defected [60]Fullerene: Electronic Excitation and Nonlinear Optical Properties of C59 [9-4] and C59 [8-5] Isomers.

By removing one carbon atom from [60]Fullerene (C60), two different isomers (C59 [9-4] and C59 [8-5]) are generated for the C59 cluster. Inspired by their structural and electronic properties, we, theoretically, studied the static and frequency-dependent electronic (hyper)polarizabilities of sp- and sp2-hybridized isomers in vacuum by TD-DFT calculations. The simulated absorption spectra showed that all absorption bands of C59 [9-4] and C59 [8-5] are attributed to π → π* and n → π* transitions. Regarding their nonlinear optical properties, it is found that the frequency-dependent polarizability anisotropy αanisotropy(λ = 1064.80 nm) of C59 [8-5] is 4 times larger than the static regime, revealing a notable polarization anisotropy, due to the delocalized π electrons around the vacancy defect. By decreasing the incident wavelengths from λ = 1908 nm to λ =589.08 nm, the dispersion of optical nonlinearity of C59 [8-5] has achieved the maximum at βxxx (λ = 1064.8 nm) = 38.150 au and (γxxxx (λ = 589.08 nm) = -9.896 × 107 au), indicating that the resonance effect of the hyperpolarizability amplified with the decrease of incident wavelengths. Hyperpolarizability density analyses in X and Z directions displayed that the conspicuous negative ρxxx(3)(r⃗) and -zρzzz(3)(r⃗) are more expanded on the C59 [8-5] cage when the main contributions stem from the π electrons instead to the sp-hybridized carbon.

Frequency-dependent AVAZ for fractured reservoirs

Frequency-dependent anisotropy can be used for detection and evaluation of fractured reservoirs. In this study, three numerical models of fractured reservoirs are designed to study the frequency dependence of amplitude variation with azimuth (AVAZ). Here, two factors, which can make the AVAZ responses frequency dependent, are taken into consideration, the fluid flow and the tuning effect. Model I is used for the analysis of frequency-dependent AVAZ induced only by the fluid flow. Model II is used to study frequency-dependent AVAZ induced only by the tuning effect. For Model III, these two factors are in the presence at the same time. In this study, the fluid flow is simulated by Chapman’s multi-scale rock physics model, and the azimuthal seismic gathers are generated by propagating matrix method. Spectral decomposition is implemented based on the smoothed pseudo Wigner-Ville distribution, so that the frequency dependence for the AVAZ gathers can be discussed. It is demonstrated that both the fluid flow and the tuning effect can cause significant frequency-dependent AVAZ, and the frequency-dependent AVAZ is helpful for fluid identification and anisotropic thin bed detection. Besides, for both factors, the incident angle can influence the frequency-dependent AVAZ responses, accordingly azimuthal seismic gathers with large incident angles are necessary for field data application.

Monitoring the Physiological State in the Dark Fermentation of Maize/Grass Silage Using Flow Cytometry and Electrooptic Polarizability Measurements

Dark fermentation (DF), a key biohydrogen-producing process, is generally operated as a black-box, by monitoring different operative macroscopic process parameters without evaluating or tracking the physiology of the biotic phase. The biotic phase in DF is constituted by a large variety of microorganisms, mainly fermentative bacteria. The present study uses two (electro)optical techniques, flow cytometry (FC) and frequency-dependent polarizability anisotropy (FDPA) measurements, to gain insights into the physiology of open mixed consortia throughout the DF process. The mixed consortia for DF were obtained from a methanogenic sludge, selecting spore-forming bacteria by means of an acid treatment. Then, DF systems with and without pH control were studied, using as substrate a mixture of maize and grass silage (9:1 w/w). Over the course of fermentation, the butyric pathway was dominant in both systems, and relevant titers of acetate, formate, and ethanol were detected; while hydrogen yields amounted to 20.80 ± 0.05 and 17.08 ± 0.05 NmL/gVS under pH-regulated and non-regulated conditions, respectively. The cytometric pattern analysis of the culture together with microscopic observations made it possible, over the course of fermentation, to identify and track the predominant morphologies in play (i.e., free spore, rod-shaped, and endospore, which are typical of Clostridium spp.). Furthermore, the use of the fluorescent dye DiBAC4(3) in FC and FDPA measurements provided similar information regarding the physiological state (PS) of the mixed consortia during the different phases of the culture.Graphical

Frequency-dependent P-wave anisotropy due to scattering in rocks with aligned fractures

Frequency-dependent P-wave anisotropy due to scattering often occurs in fractured formations, whereas the corresponding theoretical study is lacking. Hence, based on a newly developed P-wave scattering model, we have studied the frequency-dependent P-wave scattering anisotropy in rocks with aligned fractures. To describe P-wave scattering anisotropy, we develop the corresponding anisotropy parameters similar to those for elastic anisotropy. Our results indicate that the P-wave velocity anisotropy parameters [Formula: see text] and [Formula: see text] do not change with frequency monotonically, which is different from that caused by wave-induced fluid flow. Fluid saturation in fractures can greatly decrease the P-wave velocity anisotropy, whose effects depend on the ratio of the fluid bulk modulus to the fracture aspect ratio. The P-wave exhibits elliptical anisotropy for the dry fracture case at low frequencies, but anelliptical anisotropy for the case with fluid-filled fractures. The P-wave attenuation anisotropy parameters [Formula: see text] and [Formula: see text] vanish in the low- and high-frequency limits but reach their maxima at the characteristic frequency when the P-wavelength is close to the fracture length. The influence of fluid on the P-wave attenuation anisotropy is similar to that on the velocity anisotropy. To further analyze frequency-dependent P-wave scattering anisotropy, theoretical predictions are compared with experimental results, which indicate reasonable agreement between them.

Frequency-dependent anisotropy due to two orthogonal sets of mesoscale fractures in porous media

SUMMARY Seismic anisotropy can occur in rocks that have complicated internal structures and thin layering. Wave-induced fluid flow (WIFF) is one of the major causes of elastic wave dispersion and anisotropy. The principle goal of this paper is to combine the effects of WIFF and layer-induced anisotropy in orthorhombic (OTR) models that are often used in the seismic industry nowadays to describe azimuthal and polar anisotropy. We derive the effective frequency-dependent anisotropy parameters based on the Chapman model that accounts for the WIFF mechanism. First, we summarize two major problems to establish the link between the frequency-dependent seismic anisotropy and the multiple sets of fractures with different scales and orientations. Then we specify the multiple mesoscale fractures to be vertical and orthogonal so as to simplify the rock physics model to be an ORT medium. We also give the explicit expressions for the effective stiffness and the Thomsen-style parameters (vP0, vS0, ϵ1, ϵ2, γ1, γ2, δ1, δ2, δ3). Finally, we derive the effective frequency-dependent anisotropy parameters for ORT multiple layers using the Backus averaging under the approximation of weak contrast between layers. We also investigate the influence of frequency, fracture parameters (density and scale), effective porosity and volume fraction on the Thomsen-style parameters.

Dynamics anisotropy in a porous solid with aligned slit fractures

Crustal rocks are commonly permeated by aligned fractures which may control the wave anisotropy and permeability pattern. In the presence of pore fluid the mechanical and hydraulic features of such rocks become more complex. Understanding the dynamic anisotropy in fluid-saturated fractured rocks is important for detecting and characterizing fractured reservoirs and fault zones with applications in geomechanics, hydrogeology, exploration geophysics and reservoir engineering. For waves propagating normal to the fractures, the effects of wave-induced fluid flow (WIFF) due to the presence of permeable fractures on seismic dispersion and attenuation are significant and have been quantified in earlier studies. But previous literatures are restricted to low frequency range within which the fracture size is much smaller than the incident wavelength. In this paper, we extend low-frequency normal incidence results to full-frequency oblique incidence. We first derive exact solutions of the scattering problem of obliquely incident plane waves by a single slit fracture in a poroelastic solid. Based on previous analysis, for ideal fractures with infinitesimal thickness, the fracture fluid can be modelled as an incompressible one. Then, based on the solutions and Foldy's scattering theorem we develop a dynamic-effective-medium model to estimate frequency-dependent anisotropy of wave propagation in a fluid-saturated poroelastic rock with a sparse set of aligned fractures. We find that for the oblique incidence problem apart from WIFF there exist another two important attenuation mechanisms, i.e., the elastic scattering (scattering into fast P and S waves via mode conversion at the fracture faces) and Biot's global flow, in causing velocity dispersion and attenuation. The mixed-boundary problem reveals that the WIFF is controlled by the normal displacement discontinuity that is determined by effective normal stress applied on the fracture faces, while the scattering effects by the tangential displacement discontinuity that is determined by effective shear stress. Because the effective normal and shear stresses depends on incident angles and frequency, the dispersion and attenuation of both P and S waves are anisotropic and frequency-dependent. In contrast, Biot's global flow is an intrinsic energy loss mechanism that can play a role in causing velocity dispersion and attenuation at higher frequency range but it is independent of the presence of fractures or incident angle.