Anisotropy In Sedimentary Rocks Research Articles

Thomsen-type parameters and attenuation coefficients for constant-Q transverse isotropy

Transversely isotropic (TI) media with the frequency-independent quality-factor elements (also called “constant- Q” transverse isotropy) are often used to describe attenuation anisotropy in sedimentary rocks. The attenuation coefficients in constant- Q TI models can be conveniently defined in terms of the Thomsen-type attenuation-anisotropy parameters. Recent research indicates that not all those parameters for such constant- Q media are frequency-independent. Here, we present concise analytic formulas for the Thomsen-type attenuation parameters for Kjartansson’s constant- Q TI model and show that one of them ([Formula: see text]) varies with frequency. The analytic expression for [Formula: see text] helps evaluate the frequency dependence of the normalized attenuation coefficients of P- and SV-waves by introducing the newly defined “dispersion factors.” These factors are frequency-independent and expressed in terms of the Thomsen and Thomsen-type parameters defined at a specified reference frequency. Viscoacoustic constant- Q transverse isotropy is also discussed as a special case, for which the elliptical condition and simplified expressions for the parameters [Formula: see text] and [Formula: see text] are derived. Our results show that, in the presence of significant absorption, the attenuation coefficients of the constant- Q model vary with frequency for oblique propagation with respect to the symmetry axis. This variation needs to be taken into account when applying the spectral-ratio method and other attenuation-analysis techniques.

Development of Anisotropy in Sandstone Subjected to Repeated Frost Action

In cold regions, the anisotropy of sedimentary rocks is modified by repeated frost action, potentially increasing the risks of rock engineering. Hence, a deep understanding of the development of rock anisotropy due to frost action is essential. In this work, two sets of sandstone samples were cored and used in experiments, which contained bedding planes either perpendicular or parallel to the height direction. The P-wave velocity, uniaxial compressive strength, tensile strength, and shear strength of samples were tested after different numbers of freeze–thaw cycles. Several anisotropic indexes were defined by the above parameters and their variations with freeze–thaw cycles were analysed. The results demonstrate that (1) the P-wave velocity, uniaxial compressive strength, tensile strength, and shear strength of both sets of sandstone samples decayed with increasing freeze–thaw cycles; however, (2) the initial values and decay rates of these parameters differed significantly between the two sets. (3) Sandstone bears strong inherent anisotropy and (4) it is enhanced by repeated frost action. Based on direct observations of bedding structures by magnetic resonance imaging, we suggest that the enhancement of anisotropy in sandstone results from a combination of its inherent anisotropy and anisotropic frost damage accumulation. Both originate from sandstone’s structure of interbedded coarse- and fine-grained layers.

Determining anisotropic elastic parameters of transversely isotropic rocks through single torsional shear test and theoretical analysis

Deformation properties of sedimentary rock is quite important for evaluating the industrial production of shale gas and the effective design of tunnel constructions, deep rock foundations for nuclear power plant and deep geological disposal. Anisotropic sedimentary rocks, such as shale, can exhibit significantly different material properties in different directions. Knowledge of the anisotropic features of such rocks is, therefore, essential. When a hollow cylinder of an anisotropic material such as a sedimentary rock is torsionally-sheared, the axisymmetry is violated and the stress varies in the rotational direction. Utilizing such stress distributions, we propose a method to determine the parameters of the transversely isotropic elasticity of such a material, including the dominant orientation, via a single torsional shear test using a single hollow cylindrical specimen. A newly designed instrumented cap is also employed. Unlike existing methods, the specimen can be sampled in any arbitrary direction. An overview of the method is presented and its validity is checked both theoretically and numerically. The strain and stress distributions in a hollow cylindrical specimen of a transversely isotropic material is first investigated theoretically, and the stress and strain fields (to which random measurement errors are added) are back-analyzed using the proposed method. The results demonstrate that five elastic parameters, as well as the orientation of the transverse isotropy plane, can be determined uniquely via the proposed method.

Influence of anisotropic permeability on convection in porous media: Implications for geological CO2 sequestration

Solute convection in porous media at high Rayleigh-Darcy numbers has important fundamental features and may also bear implications for geological CO2 sequestration processes. With the aid of direct numerical simulations, we examine the role of anisotropic permeability on the distribution of solutal concentration in fluid saturated porous medium. Our computational analyses span over few decades of Rayleigh-Darcy number and confirm the linear scaling of Nusselt number that was previously found in the literature. In addition, we find that anisotropic permeability γ < 1, i.e., with vertical permeability smaller than horizontal permeability, effectively increases the Nusselt number compared with isotropic conditions. We link this seemingly counterintuitive effect with the occurring modifications to the flow topology in the anisotropic conditions. Finally, we use our data computed for the two-sided configuration (i.e., Dirichlet conditions on upper and lower boundaries) to examine the time evolution of solutal dynamics in the one-sided configuration, and we demonstrate that the finite-time (short-term) amount of CO2 that can be dissolved in anisotropic sedimentary rocks is much larger than in isotropic rocks.

Quantification of the Impact of Seismic Anisotropy in Microseismic Location

Seismic anisotropy in sedimentary rocks, due to either layered bedding or fracturing, may bias microseismic locations if unaccounted in velocity models. To quantitatively assess such biases, we have applied a nonlinear location method to synthetic travel time data in seven models from isotropy to different levels of VTI (Vertical Transverse Isotropy) and HTI (Horizontal Transverse Isotropy) cases. Synthetic waveforms are recorded at two vertical receiver arrays in a three-layer velocity model using a pseudo-spectral method. Both P and S wave arrivals are used to locate three events assuming an effective isotropic velocity model. The average location error is 59 m for isotropic case, about the size of the grid interval in the velocity model, and is 156 m (158 m), 237 m (244 m), and 258 m (265 m) for 5%, 10% and 15% VTI (HTI) cases, respectively. These results suggest that even 5% seismic anisotropy, if not properly accounted, can cause significant biases in microseismic event locations.

A micromechanical model of inherently anisotropic rocks

A micromechanical elastoplastic model is proposed in this study for anisotropic sedimentary rocks. With a two-step homogenization procedure, a macroscopic criterion is established for geomaterials made up of a porous matrix reinforced by rigid inclusions. The effects of porosity, inclusions and the inherent anisotropy are explicitly taken into account. Based on [18], a scalar anisotropy parameter is introduced to describe the anisotropic characteristics of the material. With a non-associated plastic flow rule and a strain hardening law, the proposed model is applied to describe the macroscopic mechanical behavior of Tournemire shale with different initial confining pressures and different loading orientations. Comparing numerical results with experimental data, the efficiency of the proposed micromechanical model is assessed and verified.

Induced anisotropic damage and plasticity in initially anisotropic sedimentary rocks

This work is devoted to the description of plastic deformation and induced damage in sedimentary rocks with structural anisotropy. Due to oriented growth of microcracks, the damage leads to an induced anisotropy in materials. The emphasis is put on the coupling between the inherent and induced anisotropies. A fabric tensor is first defined in order to characterize the inherent orientation-dependent properties of materials. A discrete thermodynamic approach is then extended. Macroscopic plastic deformation and material damage are considered as the result of frictional sliding along weakness planes randomly distributed in spatial orientations. Local plastic flow rule and damage evolution law are formulated for each family of weakness planes. The mechanical properties in each orientation depend on the inherent anisotropic structure. The coupling between the inherent and induced anisotropies is properly described using the fabric tensor and discrete approach. A series of numerical simulations are performed in order to verify the predictive performance of the proposed model. Comparisons between numerical results and test data show the present model is able to describe the main mechanical behaviors of anisotropic geomaterials, by taking into account the coupling between the inherent and induced anisotropies.

Diffusive flux and pore anisotropy in sedimentary rocks

Diffusion of dissolved contaminants into or from bedrock matrices can have a substantial impact on both the extent and longevity of dissolved contaminant plumes. For layered rocks, bedding orientation can have a significant impact on diffusion. A series of laboratory experiments was performed on minimally disturbed bedrock cores to measure the diffusive flux both parallel and normal to mineral bedding of four different anisotropic sedimentary rocks. Measured effective diffusion coefficients ranged from 4.9×10(-8) to 6.5×10(-7)cm(2)/s. Effective diffusion coefficients differed by as great as 10-folds when comparing diffusion normal versus parallel to bedding. Differences in the effective diffusion coefficients corresponded to differences in the "apparent" porosity in the orientation of diffusion (determined by determining the fraction of pore cross-sectional area measured using scanning electron microscopy), with the difference in apparent porosity between normal and parallel bedding orientations differing by greater than 2-folds for two of the rocks studied. Existing empirical models failed to provide accurate predictions of the effective diffusion coefficient in either bedding orientation for all four rock types studied, indicating that substantial uncertainty exists when attempting to predict diffusive flux through sedimentary rocks containing mineral bedding. A modified model based on the apparent porosity of the rocks provided a reasonable prediction of the experimental diffusion data.

An analytic model for the stress-induced anisotropy of dry rocks

One of the main causes of azimuthal anisotropy in sedimentary rocks is anisotropy of tectonic stresses in the earth’s crust. We have developed an analytic model for seismic anisotropy caused by the application of a small anisotropic stress. We first considered an isotropic linearly elastic medium (porous or nonporous) permeated by a distribution of discontinuities with random (isotropic) orientation (such as randomly oriented compliant grain contacts or cracks). The geometry of individual discontinuities is not specified. Instead, their behavior is defined by a ratio B of the normal to tangential excess compliances. When this isotropic rock is subjected to a small compressive stress (isotropic or anisotropic), the number of cracks along a particular plane is reduced in proportion to the normal stress traction acting on that plane. This effect is modeled using the Sayers-Kachanov noninteractive approximation. The model predicts that such anisotropic crack closure yields elliptical anisotropy, regardless of the value of the compliance ratio B. It also predicts the ratio of Thomsen’s anisotropy parameters [Formula: see text] as a function of the compliance ratio B and Poisson’s ratio of the unstressed rock. A comparison of the model predictions with the results of laboratory measurements indicates a reasonable agreement for moderate magnitudes of uniaxial stress (as high as 30 MPa). These results can be used for differentiating stress-induced anisotropy from that caused by aligned fractures. Conversely, if the cause of anisotropy is known, then the anisotropy pattern allows one to estimate P-wave anisotropy from S-wave anisotropy.

TTI reverse time migration using the pseudo-analytic method

Reverse time migration (RTM) was first introduced in the early 1980s (Whitmore, 1983), but was seemingly dormant until recent advances in computer hardware helped propel it onto the stage as a powerful depth-imaging method. RTM is now standard for areas where large velocity contrasts and/or steep dips pose a challenge, for instance below salt in the Gulf of Mexico. In recent years, where called for by the data, the migration tool of choice has gone from isotropic RTM to anisotropic RTM. The most common representations of anisotropy in sedimentary rocks are VTI (transverse isotropy with a vertical axis of symmetry) and TTI (tilted transverse isotropy). While isotropic and VTI RTM have become somewhat routine, TTI RTM remains challenging due to the complexity, stability, computational cost, and the difficulty in estimating the anisotropic parameters for TTI media.

Coupled elastoplastic damage modeling of anisotropic rocks

Abstract A coupled elastoplastic damage model is proposed for the description of strongly anisotropic sedimentary rocks. In order to describe the inherent anisotropy of the material, a scalar anisotropy parameter is introduced using the concept of fabric tensor. Using this parameter, an anisotropic plastic model is formulated taking into account influence of loading orientation. Plastic deformation is then coupled with induced damage by growth of microcracks. The proposed model is applied to typical sedimentary rock; Tournemire shale. The procedure for model’s parameters identification is presented. A series of numerical simulations are performed for triaxial compression tests performed with different confining pressures and various loading orientations. Comparisons between numerical predictions and experimental results show that the proposed model is capable to reproduce the main features of mechanical behavior of strongly anisotropic rocks.

Upscaling of elastic properties of anisotropic sedimentary rocks

SUMMARY In this paper, the term ‘upscaling’ means the theoretical prediction of rock's elastic properties at lower frequency (seismic or cross-well data) using higher frequency logging data on sonic velocities (VP, VS1 and VS2), porosity and density. The mineral composition and water saturation derived from other logs are used. Due to the special treatment of sonic logging data provided by the dipole sonic probe, all the sonic velocities are obtained in the principal coordinate system of the rock's stiffness tensor. The upscaling procedure includes two steps. The first step involves the solution of an inverse problem on reconstruction of the parameters of the rock's microstructure from the logging data. The inversion is based on the effective medium theory. As a result of the inverse problem solution, the effective stiffness tensor is found for depths at which the sonic wave velocities are measured. At the second step, the velocities of waves at given lower frequencies are calculated as propagating in a layered medium. The number of layers in the medium depends on the given frequency and logging step. Each layer of the medium has the stiffness tensor found at the first step. This upscaling procedure has been applied to a wellbore for which the dipole sonic data are available. The rocks penetrated by the well are shales. In general, the resulting medium exhibits orthorhombic symmetry at sonic frequency. This symmetry results from the preferential orientation of clay platelets and grain-related cracks and vertical cracks. The existence of the latter is indicated by the dipole sonic tool. Depending on the microstructure parameters (orientation of clay platelets and cracks, pore/crack connectivity and shale mineralogical composition), the shales, at lower frequency, have either transversely isotropic symmetry (with the vertical axis of symmetry, a.k.a. VTI) or orthorhombic symmetry.

Effect of plastic deformation in laboratory conditions on magnetic anisotropy of sedimentary rocks

In order to correlate the degree of plastic deformation and low-field magnetic anisotropy, a series of laboratory pressure experiments were carried out on a batch of grey marls. Samples were gradually deformed using triaxial high-pressure device. The confining pressure of 300 MPa was used, yielding maximum relative deformation up to 20% depending upon the uniaxial differential stress. In the range of initial deformation, irregular changes of the anisotropy parameters were typically observed. This effect is related to variable pre-deformation orientation of the anisotropy ellipsoid in the samples. At higher deformation, samples are characterized by increasing degree of magnetic anisotropy and by increasing foliation. Reorientation of paramagnetic phyllosilicate grains due to plastic deformation seems to be the most probable mechanism of the magnetic anisotropy changes.

Lattice preferred orientation and seismic anisotropy in sedimentary rocks

SUMMARY Although it is well known that sedimentary rocks can be seismically anisotropic, there have been few detailed investigations of the underlying cause of such anisotropy. Here, we investigate anisotropy due to the preferred orientation of minerals, or lattice preferred orientation (LPO), in a suite of sedimentary rocks. Seismic properties are predicted by averaging single-crystal elastic constants of minerals according to their crystal orientation and modal volume fraction in the rock aggregate. Both Electron Backscattered Diffraction (EBSD) and X-ray Texture Goniometry (XTG) are tested as quantitative techniques for measuring the LPO of sedimentary rocks. Although EBSD has promise for future LPO measurements in polymineralic sedimentary rocks, problems currently remain in measuring low-symmetry phases (e.g. feldspars) and very small clay or mica particles. However, the LPO of very fine-grained phyllosilicates can be measured using XTG and the LPO of low-symmetry minerals can be measured using manual EBSD pattern analysis. Here, we use such a hybrid approach to estimate LPO in a suite of sedimentary samples. The seismic properties calculated from LPO data show anisotropy values for P-waves ranging from 1.5 per cent in sandstones, to over 3.5 per cent in a siltstone, to 12 per cent in a shale. The effect of thin multilayering on long-wavelength propagation in a siltstone is predicted by applying Backus-type averaging. The layering does not enhance the anisotropy because of the small differences in density and in elasticity between the two layer types. The LPO of phyllosilicates and to a lesser extent dolomite and siderite seem to contribute significantly to the seismic anisotropy of phyllosilicate-rich rocks (siltstones and shales). The weak LPO of quartz in sandstones causes a few per cent anisotropy. Cumulatively, our results suggest that field observations of seismic anisotropy have the potential to be used as an indicator of rock lithology.

Seismic anisotropy in sedimentary rocks, part 1: A single‐plug laboratory method

A single‐plug method for measuring seismic velocities and transverse isotropy in rocks has been rigorously validated and laboratory tested. The method requires only one sample to measure the velocities needed to derive the five independent elastic constants for transversely isotropic materials. In this method, piezoelectric transducers are fitted to the top, bottom, and sides of the cylindrical sample. Laboratory velocity and anisotropy can be measured as functions of pressure, temperature, fluid saturation, and fluid displacement. Because this method uses a horizontal core plug that has much higher permeability than a vertical core plug, it is especially suitable for low‐permeability shale measurements. It reduces the sample preparation and velocity measurement time by more than two‐thirds.

Seismic anisotropy in sedimentary rocks, part 2: Laboratory data

Part one of this paper presents a method for measuring seismic velocities and transverse isotropy in rocks using a single core plug. This method saves at least two‐thirds of the time for preparing core samples and measuring velocities in transversely isotropic (TI) rocks. Using this method, we have measured velocity and anisotropy of many shale and reservoir rocks from oil and gas fields around the world. We present some of the data in this paper, which include seismic velocity and anisotropy in 17 brine‐saturated shale samples, 1 gas‐ and brine‐saturated coal sample, 8 brine‐saturated sands, 12 gas‐saturated sands, 32 gas‐saturated carbonate samples, and 25 brine‐saturated carbonate samples. The results show that clays and fine layering in sedimentary rocks are the main causes of seismic anisotropy. Very little intrinsic anisotropy exists in unfractured reservoir rocks such as sands, sandstones, and carbonates under reservoir conditions. In contrast, all shales were found seismically anisotropic: anisotropy ranges from 6% to 33% for P‐waves and from 2% to 55% for S‐waves. The magnitude of shale anisotropy seems to decrease exponentially with increasing porosity. At present, the magnitude of shale anisotropy cannot be predicted accurately from other data without laboratory measurements. This paper also presents some best practices for laboratory measurements of shale velocity and anisotropy.

Modelling of inherent anisotropy in sedimentary rocks

This paper presents a constitutive relation for modelling the inelastic response of sedimentary rocks. The inherent anisotropy of this class of materials is described by employing a second-order microstructure tensor, whose eigenvectors define the principal material triad. Higher-order dyadic products of this tensor are incorporated in the distribution function, which specifies the directional dependence of strength parameters. The mathematical formulation is applied to model the mechanical characteristics of Tournemire shale. Several triaxial tests are simulated, at various initial confining pressures, for samples tested at different orientation relative to the loading direction. The results are compared with the available experimental data.

Accuracy and limitations of the near-offset P-wave NMO velocity estimation in transversely isotropic media

The accuracy and limitations of the near-offset P-wave NMO velocity estimation in transversely isotropic media have been studied using numerical and physical modelling studies. An expression for the near-offset P-wave NMO velocity for a single horizontal reflector in a vertically transversely isotropic layer has been previously obtained: vnmo=αo1+2δwhere αo and δ respectively represent the vertical P-wave velocity and the P-wave critical anisotropy at oblique angles. The above equation is presented as being valid for any degree of anisotropy. The accuracy of this expression is subject to practical testing in this paper.Single layered horizontal models were used to carry out the numerical modelling studies. A computer program that calculates P-wave NMO velocities in transversely isotropic media was used. This program uses the exact ray and phase velocity equations in generating velocity functions to be used in ray tracing and is known to give accurate results. Using the elastic parameters for measured anisotropy in sedimentary rocks, the near-offset NMO velocities are computed using our computer program and the above expression. The results obtained at varying degrees of P-wave anisotropy are compared. The degree of anisotropy varied from very weak to strong and contrasting velocity functions were used in numerical modelling simulations.Phenolite materials with contrasting velocity functions were used to simulate transversely isotropic media with vertical axes of symmetry in physical modelling tests. Experimental reflection data were collected and velocity analysis was conducted for near-offset traces, and the NMO velocity determined by the maximum stack response. The elastic parameters, αo, and δ, of the Phenolite materials were recovered by an iterative inversion of first arrival travel times. These parameters were used to estimate the nearoffset P-wave NMO velocity in Phenolite using the NMO expression and also with our computer program. The NMO velocities obtained from these two methods were compared to that obtained from velocity analysis of the experimental seismic data. These comparisons enabled the validity of the above expression in yielding an accurate P-wave NMO velocity to be tested, in the limit of small offsets.Numerical and physical modelling results obtained from this study indicate that the accuracy of the near-offset P-wave NMO equation depends on the nature and degree of anisotropy encountered in a given area, and is not valid for all degrees of P-wave anisotropy. Since this equation is commonly used in estimating the near-offset P-wave NMO velocity when processing seismic data acquired over anisotropic sedimentary basins, processing geophysicists should proceed with caution when using this equation.

P-wave propagation in weakly anisotropic media

SUMMARY The variation of P-wave speed with direction in a weakly anisotropic homogeneous elastic medium of arbitrary symmetry is expanded as a series of spherical harmonics. The results given may be used to assess the information content of measurements of the P-wave speed acquired over a restricted angular range, and to design experiments with the objective of imaging a limited number of anisotropy parameters. Simplifications which occur for various symmetries typical of sedimentary rocks with and without fractures are discussed. Application is made to the determination of the azimuthal anisotropy of sedimentary rocks. For propagation direction n with polar angle χ and azimuthal angle χ defined with respect to some convenient choice of reference axes Ox1x2x3, the variation of P-wave speed νp(χ, η) with η for fixed χ is described by 12 parameters in the absence of symmetry. If the material contains a plane of mirror symmetry, and the axes are chosen with OX3 perpendicular to the symmetry plane, the variation of νp(χ, η) with η for fixed χ depends on six anisotropy parameters. For orthotropic symmetry the number of required parameters is reduced to three. For small polar angles χ, νp(χ, η) then varies with azimuth as cos 2η, with amplitude determined by a single anisotropy parameter (c13–c23–2c44+ 2c55).

Anisotropy in sedimentary rocks modelled as random media : Kerner, C GeophysicsV57, N4, April 1992, P564–576

Anisotropy in sedimentary rocks modelled as random media : Kerner, C GeophysicsV57, N4, April 1992, P564–576