Journal articles on the topic 'Anisotropy'
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1
Hagiwara, Teruhiko. "Apparent dip and apparent anisotropy from multifrequency triaxial induction measurements." GEOPHYSICS 76, no. 1 (January 2011): F1—F13. http://dx.doi.org/10.1190/1.3511349.
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The triaxial (or multicomponent) induction log is used to measure not only the resistivity anisotropy of an anisotropic formation but also the relative dip of the tool with respect to the formation. The anisotropic resistivity and the relative dip of layered formations are also inverted from the triaxial induction-log measurements at a depth by assuming a homogeneous anisotropic formation or at multiple depths by assuming a multilayered formation model. When the triaxial induction log is run at multiple frequencies, multifrequency focusing can be applied to the log measurements. Then, the apparent dip is algebraically defined from the frequency-focused triaxial induction measurements at a depth. The apparent dip yields the true dip in an anisotropic formation. The algebraically calculated apparent dip may be used to determine the effective dip in layered formations. The apparent dip yields the true dip in thinly bedded formations. The apparentdip also yields the true dip in thick anisotropic formations. However, the apparent dip yields a smaller dip than the true dip when the anisotropy is small (the anisotropy effect). It yields a much smaller dip in thick isotropic formations. Like the apparent dip, the apparent anisotropy is algebraically defined from the frequency-focused triaxial induction measurements at a depth. The apparent anisotropy yields the true anisotropy in an anisotropic formation. The algebraically calculated apparent anisotropy may be applied to layered formations. The apparent anisotropic resistivity (horizontal and vertical) can likewise be determined algebraically from the frequency-focused triaxial data. In contrast to the apparent dip, which yields the true dip in thinly bedded formations but not in thicker formations, the apparent anisotropy yields the true anisotropy in thick anisotropic formations but not in thinner anisotropic formations. The apparent anisotropy is affected by the shoulder-bed anisotropy when the formation is not thick (the shoulder-bed effect).
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Thomsen, Leon. "Weak elastic anisotropy." GEOPHYSICS 51, no. 10 (October 1986): 1954–66. http://dx.doi.org/10.1190/1.1442051.
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Most bulk elastic media are weakly anisotropic. The equations governing weak anisotropy are much simpler than those governing strong anisotropy, and they are much easier to grasp intuitively. These equations indicate that a certain anisotropic parameter (denoted δ) controls most anisotropic phenomena of importance in exploration geophysics, some of which are nonnegligible even when the anisotropy is weak. The critical parameter δ is an awkward combination of elastic parameters, a combination which is totally independent of horizontal velocity and which may be either positive or negative in natural contexts.
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Wu, Feng Min, and Yuh Zhang Fang. "Anisotropic Growth of Metal Chains on Anisotropic Substrate." Solid State Phenomena 121-123 (March 2007): 1129–32. http://dx.doi.org/10.4028/www.scientific.net/ssp.121-123.1129.
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Based on the exchange mechanism of metal islands growth on anisotropic metal surfaces, the growth processes of anisotropic Cu islands on the anisotropic Pd (110) surface are investigated by Monte Carlo simulations with realistic growth model and physical parameters. The anisotropic diffusion and anisotropic sticking of Cu adatoms are included in the simulation model after being considered the anisotropy of Pd (110) surface and compared to the experiments. It is found that the larger diffusion rate along the [110] channels of Pd (110) surface gives rise to a slower growth rate of Cu island in this direction, unless special effect of the anisotropic sticking is invoked. The simulation results show that the shape anisotropy of Cu islands is mainly due to the sticking anisotropy rather than the diffusion anisotropy.
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Zhu, H., and L. M. Zhang. "Characterizing geotechnical anisotropic spatial variations using random field theory." Canadian Geotechnical Journal 50, no. 7 (July 2013): 723–34. http://dx.doi.org/10.1139/cgj-2012-0345.
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In this study, anisotropic heterogeneous geotechnical fields are characterized using random field theory, in which five basic patterns of material anisotropy are simulated including isotropy, transverse anisotropy, rotated anisotropy, general anisotropy, and general rotated anisotropy. Theoretical formulations of scale of fluctuation as a function of directional angle are developed for the five basic patterns of anisotropy through modifications of the coordinate system. These formulations of scale of fluctuation are identical for different correlation structures. Correlation functions for the exponential and Gaussian correlation structures are also derived. The matrix decomposition method is then applied to generate anisotropic random fields. The generated random field correlated data are verified with two realizations of transverse anisotropy and general rotated anisotropy random fields. Test values of the sample mean, sample deviation, and scales of fluctuation in six directions match well with the prescribed values. This study provides a technique to characterize inherent geotechnical variability and anisotropy, which is required to realistically simulate complex geological properties in engineering reliability analysis and design.
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Luo, Tianya, Xiangyun Hu, Longwei Chen, and Guilin Xu. "Investigating the Magnetotelluric Responses in Electrical Anisotropic Media." Remote Sensing 14, no. 10 (May 11, 2022): 2328. http://dx.doi.org/10.3390/rs14102328.
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When interpreting magnetotelluric (MT) data, because of the inherent anisotropy of the earth, considering electrical anisotropy is crucial. Accordingly, using the edge-based finite element method, we calculated the responses of MT data for electrical isotropic and anisotropic models, and subsequently used the anisotropy index and polar plot to depict MT responses. High values of the anisotropy index were mainly yielded at the boundary domains of anomalous bodies for isotropy cases because the conductive differences among isotropic anomalous bodies or among anomalous bodies and background earth can be regarded as macro-anisotropy. However, they only appeared across anomalous bodies in the anisotropy cases. The anisotropy index can directly differentiate isotropy from anisotropy but exhibits difficulty in reflecting the azimuth of the principal conductivities. For the isotropy cases, polar plots are approximately circular and become curves with a big ratio of the major axis to minor axis, such as an 8-shaped curve for the anisotropic earth. Furthermore, the polar plot can reveal the directions of principal conductivities. However, distorted by anomalous bodies, polar plots with a large ratio of the major axis to minor axis occur in isotropic domains around the anomalous bodies, which may lead to the misinterpretation of these domains as anisotropic earth. Therefore, combining the anisotropy index with a polar plot facilitates the identification of the electrical anisotropy.
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Vladimirov, Ivaylo N., and Stefanie Reese. "Prediction of Springback in Unconstrained Bending by a Model for Evolving Elastic and Plastic Anisotropy." Key Engineering Materials 554-557 (June 2013): 2330–37. http://dx.doi.org/10.4028/www.scientific.net/kem.554-557.2330.
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Sheet metals exhibit anisotropic plastic behavior due to the large plastic deformations that occur during the rolling of the sheet and which induce texture and are responsible for the initial anisotropy. There exist various possibilities to introduce plastic anisotropy into the finite element modelling of sheet metal forming. The initial yield anisotropy can be incorporated either through an anisotropic yield surface or directly by means of a crystallographic texture model. Here, one basically differentiates between empirical and phenomenological anisotropic yield function equations, where the anisotropy coefficients can be obtained from mechanical tests, and texture-based models the coefficients of which are directly determined based on experimentally obtained orientation distributions. Another type of anisotropy that can be usually found in anisotropic materials is the elastic anisotropy. In metal plasticity one often considers the effect of elastic anisotropy significantly smaller than the effect of plastic anisotropy. Consequently, elastic isotropic expressions are often used for elastic stored energy functions with anisotropic yield criteria. However, the influence of elastic anisotropy in the elastoplastic behavior can be very important especially during elastic recovery processes during unloading after forming and springback. This research focuses, therefore, on the study of the influence of elastic anisotropy on the amount of springback in bending processes such as e.g. unconstrained bending. We discuss a finite strain material model for evolving elastic and plastic anisotropy combining nonlinear isotropic and kinematic hardening. The evolution of elastic anisotropy is described by representing the Helmholtz free energy as a function of a family of evolving structure tensors. In addition, plastic anisotropy is modelled via the dependence of the yield surface on the same family of structure tensors. Exploiting the dissipation inequality leads to the interesting result that all tensor-valued internal variables are symmetric. Thus, the integration of the evolution equations can be efficiently performed by means of an algorithm that automatically retains the symmetry of the internal variables in every time step. The material model has been implemented as a user material subroutine UMAT into the commercial finite element software ABAQUS/Standard and has been applied to the simulation of springback of unconstrained bending.
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Secco, R. A., and P. S. Balog. "On the possibility of anisotropic heat flow in the inner core." Canadian Journal of Earth Sciences 38, no. 6 (June 1, 2001): 975–82. http://dx.doi.org/10.1139/e00-116.
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We consider the possibility of anisotropic heat flow in the inner core by examining the potential for anisotropic thermal conductivity of hexagonal close-packed (hcp-)Fe. Because hcp-Fe exists only at pressures above 13 GPa at room temperature, we investigate thermal conductivity anisotropy in analog material Gd by measuring the electrical conductivity and applying the WiedemannFranz Law to determine thermal conductivity (k). The electrical conductivity anisotropy of Gd was measured at pressures up to 1.4 GPa and temperatures up to 873 K in the hcp phase range. At elevated pressure, the variation with temperature of anisotropic thermal conductivity of Gd single crystal resembles the anisotropic behavior at high temperature and 1 atm observed in earlier work. The temperature range of anisotropy of thermal conductivity of Gd, where kc > ka, is extended by pressure, but the anisotropy disappears before the high temperature hcp[Formula: see text]bcc (body-centered cubic) transformation. Our results on hcp-Gd lead us to raise the question of the possibility of hcp-Fe exhibiting anisotropy of thermal conductivity. Together with the known seismic anisotropy of the inner core, and the inferred textural alignment of hcp crystals causing it, we suggest some implications that an anisotropy of thermal conductivity of hcp-Fe, and a concomitant anisotropy of inner core heat flow, could have on thermally driven core processes.
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Zhang, Chao, Xiangzhuang Kong, Xian Wang, Yanxia Du, and Guangming Xiao. "A Predicting Model for the Effective Thermal Conductivity of Anisotropic Open-Cell Foam." Energies 15, no. 16 (August 22, 2022): 6091. http://dx.doi.org/10.3390/en15166091.
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The structural anisotropy of open-cell foam leads to the anisotropy of effective thermal conductivity (ETC). To quantitatively analyze the effect of structural anisotropy on the anisotropy of ETC, a new predicting model for the ETC of anisotropic open-cell foam was proposed based on an anisotropy tetrakaidecahedron cell (ATC). Feret diameters in three orthogonal directions obtained by morphological analysis of real foam structures were used to characterize the anisotropy of ATC. To validate our proposed anisotropic model, the ETCs of real foam structures in three orthogonal directions predicted by it were compared with the numerical results, for which the structures of numerical models are reconstructed by X-ray computed tomography (X-CT). Using the present anisotropic model, the influences of the thermal conductivity ratio (TCR) and porosity of the foams on the anisotropic ratios of ETCs are also investigated. Results show that there is good consistency between the ETCs obtained by the anisotropic model and the numerical method. The maximum relative errors between them are 2.84% and 13.57% when TCRs are 10 and 100, respectively. The present anisotropic model can not only predict the ETCs in different orthogonal directions but also quantitatively predict the anisotropy of ETC. The anisotropies of the ETCs decrease with porosity because the proportion of the foam skeleton decreases. However, the anisotropies of ETCs increase with TCR, and there exist asymptotic values in anisotropic ratios of ETCs as TCR approaches infinity and they are equal to the relative Feret diameters in different orthogonal directions.
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Edwin, Privita Edwina Rayappan George, Sumeet Kumar, Srestha Roy, Basudev Roy, and Saumendra Kumar Bajpai. "Anisotropic 3D confinement of MCF-7 cells induces directed cell-migration and viscoelastic anisotropy of cell-membrane." Physical Biology 20, no. 1 (November 9, 2022): 016003. http://dx.doi.org/10.1088/1478-3975/ac9bc1.
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Abstract Tumor-associated collagen signature-3 (TACS-3) is a prognostic indicator for breast cancer survival. It is characterized by highly organized, parallel bundles of collagen fibers oriented perpendicular to the tumor boundary, serving as directional, confining channels for cancer cell invasion. Here we design a TACS-3-mimetic anisotropic, confined collagen I matrix and examine the relation between anisotropy of matrix, directed cellular migration, and anisotropy of cell membrane-the first direct contact between TACS-3 and cell-using Michigan Cancer Foundation-7 (MCF-7) cells as cancer-model. Using unidirectional freezing, we generated ∼50 μm-wide channels filled with collagen I. Optical tweezer (OT) microrheology shows that anisotropic confinement increases collagen viscoelasticity by two orders of magnitude, and the elastic modulus is significantly greater along the direction of anisotropic confinement compared to that along the orthogonal direction, thus establishing matrix anisotropy. Furthermore, MCF-7 cells embedded in anisotropic collagen I, exhibit directionality in cellular morphology and migration. Finally, using customized OT to trap polystyrene probes bound to cell-membrane (and not to ECM) of either free cells or cells under anisotropic confinement, we quantified the effect of matrix anisotropy on membrane viscoelasticity, both in-plane and out-of-plane, vis-à-vis the membrane. Both bulk and viscous modulus of cell-membrane of MCF-7 cells exhibit significant anisotropy under anisotropic confinement. Moreover, the cell membrane of MCF-7 cells under anisotropic confinement is significantly softer (both in-plane and out-of-plane moduli) despite their local environment being five times stiffer than free cells. In order to test if the coupling between anisotropy of extracellular matrix and anisotropy of cell-membrane is regulated by cell-cytoskeleton, actin cytoskeleton was depolymerized for both free and confined cells. Results show that cell membrane viscoelasticity of confined MCF-7 cells is unaffected by actin de-polymerization, in contrast to free cells. Together, these findings suggest that anisotropy of ECM induces directed migration and correlates with anisotropy of cell-membrane viscoelasticity of the MCF-7 cells in an actin-independent manner.
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ACHARYYA, MUKTISH. "AXIAL AND OFF-AXIAL DYNAMIC TRANSITIONS IN UNIAXIALLY ANISOTROPIC HEISENBERG FERROMAGNET: A COMPARISON." International Journal of Modern Physics C 14, no. 01 (January 2003): 49–59. http://dx.doi.org/10.1142/s0129183103004206.
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Uniaxially anisotropic Heisenberg ferromagnet, in the presence of a magnetic field varying sinusoidally in time, is studied by Monte Carlo simulation. The axial (field applied only along the direction of anisotropy) and off-axial (field applied only along the direction which is perpendicular to the direction of anisotropy) dynamic transitions are studied. By studying the distribution of the dynamic order parameter component, it is observed that the axial transition is discontinuous for low anisotropy and becomes continuous in high anisotropy. The off-axial transition is found to be continuous for all values of anisotropy. In the infinite anisotropy limit, both types of transitions are compared with that observed in an Ising ferromagnet for the same value of the field and frequency. The infinitely anisotropic axial transition and dynamic transition in the Ising ferromagnet occur at different temperatures, whereas the infinitely anisotropic off-axial transition and the equilibrium ferro-para transition in the Ising model occur at the same temperature.
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Hagiwara, Teruhiko. "Determination of dip and anisotropy from transient triaxial induction measurements." GEOPHYSICS 77, no. 4 (July 1, 2012): D105—D112. http://dx.doi.org/10.1190/geo2011-0503.1.
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The dip and anisotropy of an anisotropic formation were algebraically determined from the transient triaxial induction data without inversion. The time-dependent apparent dip and the apparent anisotropy, algebraically defined from the triaxial transient induction measurements, were applied in a two-layer formation. The apparent dip yielded the true dip in an anisotropic formation, as well as in layered formations, though it yielded the zero dip in an isotropic formation. At early time the apparent anisotropy yielded the true anisotropy of the layer on which the induction tool was located, and at later time the macroscopic anisotropy for a larger volume of investigation. The distance to the layer interface was identified by the transition time when the apparent dip and the apparent anisotropy change the values.
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Martins, Jorge L. "Elastic impedance in weakly anisotropic media." GEOPHYSICS 71, no. 3 (May 2006): D73—D83. http://dx.doi.org/10.1190/1.2195448.
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The original formulation for the P-wave elastic impedance (EI) equation ignores seismic anisotropy. Incorporation of anisotropy effects into the EI formula requires a suitable approximation for reflection coefficients. In order to derive an anisotropic EI equation, this paper uses an approximation for PP-wave reflection [Formula: see text] coefficients which holds for weak-contrast interfaces separating weakly anisotropic media of arbitrary symmetry. Inserting the chosen [Formula: see text] coefficient approximation into the original formalism provides an anisotropic EI formula, which is written as a product of two terms: a modified version for the isotropic EI equation and a correction because of weak anisotropy. The latter term shows dependence of the anisotropic EI formula on the so-called weak anisotropy (WA) parameters, on a reference isotropic medium, and on the azimuthal and incident phase angles. Numerical tests show the performance of the EI formula in calculating anisotropic [Formula: see text] coefficients and in constructing azimuthal far-offset EI logs. Since EI allows applying poststack algorithms without modification, an inversion methodology can be designed for investigating anisotropy in sedimentary formations.
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OTÁLORA, FERMÍN, and JUANMA GARCÍA-RUIZ. "THE ANISOTROPY OF ON-LATTICE SIMULATIONS OF AGGREGATE GROWTH." Fractals 01, no. 04 (December 1993): 867–74. http://dx.doi.org/10.1142/s0218348x93000897.
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The origin of anisotropy in on-lattice simulations of cluster growth is investigated by quantifying the anisotropic behavior of the two processes involved in the simulation: transport and aggregation of nutrient particles. Three different anisotropic effects are described: anisotropic surface kinetics, anisotropic concentration profiles and anisotropic screening. The relevance of these sources of anisotropy in natural systems is discussed.
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Gurevich, Boris, Marina Pervukhina, and Dina Makarynska. "An analytic model for the stress-induced anisotropy of dry rocks." GEOPHYSICS 76, no. 3 (May 2011): WA125—WA133. http://dx.doi.org/10.1190/1.3567950.
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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.
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Kolomiets, I. S. "Studying anisotropic properties of longitudinal inhomogeneous nondepolarizing media with elliptical phase anisotropy." Semiconductor Physics Quantum Electronics and Optoelectronics 16, no. 4 (December 16, 2013): 366–73. http://dx.doi.org/10.15407/spqeo16.04.366.
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KIM, C. S., and MIN-HO LEE. "RANDOM WALK ON ANISOTROPICALLY GENERATED PERCOLATION CLUSTER AND ANISOTROPIC RANDOM WALK ON PERCOLATION CLUSTER." Modern Physics Letters B 03, no. 10 (July 10, 1989): 765–70. http://dx.doi.org/10.1142/s0217984989001205.
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We studied two subjects related to anisotropy: random walk on percolation cluster having anisotropy (RWAC) and direction dependent (anisotropic) random walk on percolation cluster (AWIC). We find that the anisotropy of the cluster has only time-delaying effect on asymptotic convergence of the spectral dimensionality ds and fractal dimensionality of walk dw, however, the anisotropy of the walk results in lower spectral dimensionality and higher fractal dimensionality, as anisotropy grows larger.
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Pedruelo-González, Luis M., and Juan L. Fernández-Martínez. "Generalization of Snell's Law for the propagation of acoustic waves in elliptically anisotropic media." AIMS Mathematics 9, no. 6 (2024): 14997–5007. http://dx.doi.org/10.3934/math.2024726.
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<abstract> <p>In seismic data processing, both in inversion (Inverse Processing) and modeling (Direct Processing), it is essential to consider anisotropy to unravel the geological structure of the subsoil. Besides, in most cases, the macroscopic model of anisotropy in 2D seismic surveys is elliptical and weak, with ratios of anisotropy close to one. Therefore, it is crucial to have at disposal the analytical formulas for acoustic wave propagation in elliptical anisotropic media. We presented the generalization of the Snell's Law for the case of acoustic wave propagation in elliptically anisotropic media. The generalization of the Snell's Law for acoustic anisotropic media had different applications in digital processing, raytracing, and acoustic inversion to properly consider elliptical anisotropy.</p> </abstract>
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VanderBeek, Brandon P., and Manuele Faccenda. "Imaging upper mantle anisotropy with teleseismic P-wave delays: insights from tomographic reconstructions of subduction simulations." Geophysical Journal International 225, no. 3 (March 1, 2021): 2097–119. http://dx.doi.org/10.1093/gji/ggab081.
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SUMMARY Despite the well-established anisotropic nature of Earth’s upper mantle, the influence of elastic anisotropy on teleseismic P-wave imaging remains largely ignored. Unmodelled anisotropic heterogeneity can lead to substantial isotropic velocity artefacts that may be misinterpreted as compositional heterogeneities. Recent studies have demonstrated the possibility of inverting P-wave delay times for the strength and orientation of seismic anisotropy. However, the ability of P-wave delay times to constrain complex anisotropic patterns, such as those expected in subduction settings, remains unclear as synthetic testing has been restricted to the recovery of simplified block-like structures using ideal self-consistent data (i.e. data produced using the assumptions built into the tomography algorithm). Here, we present a modified parametrization for imaging arbitrarily oriented hexagonal anisotropy and test the method by reconstructing geodynamic simulations of subduction. Our inversion approach allows for isotropic starting models and includes approximate analytic finite-frequency sensitivity kernels for the simplified anisotropic parameters. Synthetic seismic data are created by propagating teleseismic waves through an elastically anisotropic subduction zone model created via petrologic-thermomechanical modelling. Delay times across a synthetic seismic array are measured using conventional cross-correlation techniques. We find that our imaging algorithm is capable of resolving large-scale features in subduction zone anisotropic structure (e.g. toroidal flow pattern and dipping fabrics associated with the descending slab). Allowing for arbitrarily oriented anisotropy also results in a more accurate reconstruction of isotropic slab structure. In comparison, models created assuming isotropy or only azimuthal anisotropy contain significant isotropic and anisotropic imaging artefacts that may lead to spurious interpretations. We conclude that teleseismic P-wave traveltimes are a useful observable for probing the 3-D distribution of upper mantle anisotropy and that anisotropic inversions should be explored to better understand the nature of isotropic velocity anomalies particularly in subduction settings.
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Han, Han. "Influence of Material Anisotropy and Friction on Ring Deformation." Journal of Tribology 124, no. 3 (May 31, 2002): 637–44. http://dx.doi.org/10.1115/1.1473144.
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The influence of material anisotropy and friction on ring deformation has been examined in relation to the distribution of normal pressure and frictional shear stress, deformed ring shapes, and estimated errors in the coefficient of friction. Based on the flow rule associated with von Mises’ and Hill’s yield criteria, the analyses have been carried out with the finite element method (FEM) for three cases, namely, (1) an anisotropic ring oriented 90 deg to the axis of rotational symmetrical anisotropy under uniform coefficient of friction; (2) an isotropic ring under frictional anisotropy condition; and (3) an anisotropic ring oriented 0 deg to the axis of rotational symmetrical anisotropy under uniform coefficient of friction. In the first two cases, the results show that the influence of anisotropy on ring deformation is quite similar to that obtained by changing the frictional condition. Therefore, in the third case, if the anisotropic behavior is mistakenly attributed to friction, the possible estimated error for the coefficient of friction can be as high as 80 percent for a pronounced anisotropic material. Deformed ring shapes have been verified in experiments using the extruded annealed aluminum alloy AA6082 (Al-Si1Mg0.9Mn0.1).
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Mohanty, Sailesh Ranjan, Sayantan Ghosh, Pinku Routaray, H. C. Das, and Bharat Kumar. "The impact of anisotropy on neutron star properties: insights from 𝖨–𝖿–𝖢 universal relations." Journal of Cosmology and Astroparticle Physics 2024, no. 03 (March 1, 2024): 054. http://dx.doi.org/10.1088/1475-7516/2024/03/054.
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Abstract Anisotropy in pressure within a star emerges from exotic internal processes. In this study, we incorporate pressure anisotropy using the Quasi-Local model. Macroscopic properties, including mass (M), radius (R), compactness (C), dimensionless tidal deformability (Λ), the moment of inertia (I), and oscillation frequency (f), are explored for the anisotropic neutron star. Magnitudes of these properties are notably influenced by anisotropy degree. Universal I–f–C relations for anisotropic stars are explored in this study. The analysis encompasses various EOS types, spanning from relativistic to non-relativistic regimes. Results show the relation becomes robust for positive anisotropy, weakening with negative anisotropy. The distribution of f-mode across M–R parameter space as obtained with the help of C–f relation was analyzed for different anisotropic cases. Using tidal deformability data from GW170817 and GW190814 events, a theoretical limit for canonical f-mode frequency is established for isotropic and anisotropic neutron stars. For isotropic case, canonical f-mode frequency for GW170817 event is f 1.4 = 2.606+0.457 -0.484kHz; for GW190814 event, it is f 1.4 = 2.097+0.124 -0.149kHz. These relationships can serve as reliable tools for constraining nuclear matter EOS when relevant observables are measured.
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Zhang, Xiangxiang, J. G. Wang, Xiaolin Wang, and Feng Gao. "Numerical Simulations on the Front Motion of Water Permeation into Anisotropic Porous Media." Geofluids 2019 (March 4, 2019): 1–13. http://dx.doi.org/10.1155/2019/7692490.
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Water permeation into a porous medium is a common but important phenomenon in many engineering fields such as hydraulic fracturing. The water permeation front moves with time and may significantly impact the field variable evolution near the water front. Many algorithms have been developed to calculate this water front motion, but few numerical algorithms have been available to calculate the water front motion in anisotropic fluid-solid couplings with high computational efficiency. In this study, a numerical model is proposed to investigate the front motion of water permeation into an anisotropic porous medium. This model fully couples the mechanical deformation, fluid flow, and water front motion. The water front motion is calculated based on a directional Darcy’s flow in the anisotropic porous medium, and a revised formula with a correction coefficient is developed for the estimation of permeation depth. After verification with three sets of experimental data, this model is used to numerically investigate the impacts of permeability, viscosity, permeability anisotropy, and mechanical anisotropy on water front motion. Numerical results show that the proposed model can well describe the anisotropic water permeation process with reasonable accuracy. The permeation depth increases with permeability, mobility, and mechanical anisotropy but decreases with viscosity and permeability anisotropy. The correction coefficient mainly depends on porosity evolution, flow pattern, mobility, permeability anisotropy, and mechanical anisotropy.
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Wijesinghe, Dilmini, and Bradley J. Roth. "Indentation of Anisotropic Tissue Using a Three-Dimensional Mechanical Bidomain Model." Fibers 10, no. 8 (August 19, 2022): 69. http://dx.doi.org/10.3390/fib10080069.
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Computation-based mathematical models of tissue indentation are capable of predicting the distribution of forces and mechanical properties of soft tissues. This paper presents a three-dimensional mathematical model of anisotropic tissue indentation developed using the mechanical bidomain model. The mechanical bidomain model hypothesizes that the relative displacement between intra- and extracellular spaces triggers a force on the mechanosensitive proteins in the membrane: integrins. Some soft tissues, such as cardiac muscle, are anisotropic, a property which arises from the fibrous structure of the tissue. The degree of anisotropy in intra- and extracellular spaces can be different. Tissue indentation for different anisotropy ratios that indicate isotropy, equal anisotropy and unequal anisotropy, were tested using the model. Results of the tissue indentation analysis compared the spatial distribution of the magnitude of bidomain displacement for different anisotropy conditions between monodomain and bidomain models. The proposed mathematical model predicted unexpected spatial patterns of cardiac mechanotransduction for unequal anisotropy ratios of mechanical modulus.
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Boitz, Nepomuk, Anton Reshetnikov, and Serge A. Shapiro. "Visualizing effects of anisotropy on seismic moments and their potency-tensor isotropic equivalent." GEOPHYSICS 83, no. 3 (May 1, 2018): C85—C97. http://dx.doi.org/10.1190/geo2017-0442.1.
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Radiation patterns of earthquakes contain important information on tectonic strain responsible for seismic events. However, elastic anisotropy may significantly impact these patterns. We systematically investigate and visualize the effect of anisotropy on the radiation patterns of microseismic events. For visualization, we use a vertical-transverse-isotropic (VTI) medium. We distinguish between two different effects: the anisotropy in the source and the anisotropy on the propagation path. Source anisotropy mathematically comes from the matrix multiplication of the anisotropic stiffness tensor with the source strain expressed by the potency tensor. We analyze this effect using the corresponding radiation pattern and the moment tensor decomposition. Propagation anisotropy mathematically comes from the deviation between the polarization and the propagation direction of a quasi P-wave in an anisotropic medium. We investigate both effects separately by either assuming the source to be anisotropic and the propagation to be isotropic or vice versa. We find that both effects have a significant impact on the radiation pattern of a pure-slip source. Finally, we develop an alternative visualization of source mechanisms by plotting beach balls proportional to their potency tensors. For this, we multiply the potency tensor with an isotropic elasticity tensor having the equivalent shear modulus [Formula: see text] and [Formula: see text]. In this way, we visualize the tectonic deformation in the source, independently of the rock anisotropy.
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Thomsen, Leon. "Reflection seismology over azimuthally anisotropic media." GEOPHYSICS 53, no. 3 (March 1988): 304–13. http://dx.doi.org/10.1190/1.1442464.
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Recent surveys have shown that azimuthal anisotropy (due most plausibly to aligned fractures) has an important effect on seismic shear waves. Previous work had discussed these effects on VSP data; the same effects are seen in surface recording of reflections at small to moderate angles of incidence. The anisotropic effects on different polarization components of vertically traveling shear waves permit the recognition and estimation of very small degrees of azimuthal anisotropy (of order ⩾1 percent), as in an interferometer. Anisotropic effects on traveltime yield estimates of anisotropy which are averages over large depth intervals. Often, raw field data must be corrected for these effects before the reflectors may be imaged; two variations of a rotational algorithm to determine the “principal time series” are derived. Anisotropic effects on moveout lead to abnormal moveout unless the survey line is parallel to the fractures. Anisotropic effects on reflection amplitude permit the recognition and estimation of anisotropy (hence fracture intensity) differences at the reflecting horizon, i.e., with high vertical resolution.
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Grech, M. Graziella Kirtland, Don C. Lawton, and Samuel H. Gray. "A multioffset vertical seismic profiling experiment for anisotropy analysis and depth imaging." GEOPHYSICS 67, no. 2 (March 2002): 348–54. http://dx.doi.org/10.1190/1.1468595.
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A multioffset vertical seismic profile (VSP) was carried out in the Rocky Mountain foothills of southern Alberta, Canada. The purpose of this experiment was to investigate whether the dipping shale strata exhibit P‐wave velocity anisotropy and, if so, to calculate the Thomsen anisotropy parameters for use in anisotropic depth migration. Traveltime inversion of first‐arrival data from the multioffset VSP revealed that the dipping Mesozoic clastics in the area exhibit seismic velocity anisotropy of about 10%. The anisotropy parameters derived from this experiment were then used in anisotropic prestack depth migration of data from a surface seismic line close to the VSP well. Comparison of the anisotropic migration with the corresponding isotropic prestack depth migration showed that the target was imaged incorrectly in the isotropic case; a lateral shift of 180 m in the updip direction of the overlying beds was observed. The image obtained with an anisotropic velocity model was also better focused than that obtained assuming isotropic velocities.
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Guo, Songfeng, Shengwen Qi, Bowen Zheng, Lei Xue, Xueliang Wang, Ning Liang, Yu Zou, et al. "The Confinement-Affected Strength Variety of Anisotropic Rock Mass." Materials 15, no. 23 (November 27, 2022): 8444. http://dx.doi.org/10.3390/ma15238444.
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It has been recognized that the anisotropic structures dominate the deformation and strength properties of laminated rock masses. The resultant strength anisotropy is strongly affected by confining pressures beyond anisotropic structures. Nevertheless, the effects of confinement are inconsistent among existing experiments and not fully understood. This study focuses on the effects of confining pressure on strength anisotropy through theoretical derivation together with experimental results analysis. The variations in the possibility of anisotropic structural plane dominant failure and strength anisotropy degree under different confining pressures are discussed. The different types of anisotropic structural planes, i.e., the fresh contact discontinuity or soft, thick layer, are found as the key factor resulting in different confinement effects. The strength anisotropy weakens gradually and vanishes eventually as confining stress increases for the anisotropic rock mass with the structural plane of fresh contact discontinuity. On the other hand, the strength does not vanish at very high confining stress and the anisotropic strength difference even rises as confining stress increases for the anisotropic rock mass with the anisotropic structural plane of the soft layer. This study improves the understanding of anisotropic rock mass mechanical behavior, especially at high confining stress, and may promote the development of excavation and supporting techniques for underground projects.
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JAIN, PANKAJ, MONINDER S. MODGIL, and JOHN P. RALSTON. "SEARCH FOR GLOBAL METRIC ANISOTROPY IN TYPE 1a SUPERNOVA DATA." Modern Physics Letters A 22, no. 16 (May 30, 2007): 1153–65. http://dx.doi.org/10.1142/s0217732307023389.
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We examine the Type 1a supernova data in order to determine if it shows any signal of large scale anisotropy. The anisotropy is modelled by an extended Gödel metric, which incorporates expansion along with rotation. The model is smoothly connected to the usual FRW type, while expressing anisotropic metric effects depending on certain parameters. We find no significant signal of anisotropy in the data. We obtain bounds on an anisotropic redshift versus magnitude relationship, and accompanying parameters of the Gödel–Obukhov metric.
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Pranowo, Waskito, and Sonny Winardhi. "Application of Velocity Variation with Angle (VVA) Method on an Anisotropic Model with Thomsen Delta Anisotropy Parameters." Jurnal Geofisika 16, no. 2 (September 19, 2018): 6. http://dx.doi.org/10.36435/jgf.v16i2.371.
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Anisotropic properties will influence seismic propagation, for example it will affect wave velocity. One of well-known anisotropi equation for Transversaly Isotropic media is weak anisotropy with Thomsen's notation. Supriyono [2011] tried to estimate all of these variables by using velocity variation with angle (VVA) attribute. This research uses synthetic data, which is CMP Gather to know limitations of VVA attribute, to identify the error values, and to determine the best indicator of anisotropic eect. This research also uses another analysis method, which is grid search inversion to estimate VP0. From this research, Both VVA and grid search invesion still produce signcant error. The effects which will appear because of anisotropic property's presence are hockey-stick and over NMO-stretching.
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Wei, Qiqi, Hailong Wang, Xupeng Zhao, and Jianhua Zhao. "Electron mobility anisotropy in (Al,Ga)Sb/InAs two-dimensional electron gases epitaxied on GaAs (001) substrates." Journal of Semiconductors 43, no. 7 (July 1, 2022): 072101. http://dx.doi.org/10.1088/1674-4926/43/7/072101.
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Abstract The electron mobility anisotropy in (Al,Ga)Sb/InAs two-dimensional electron gases with different surface morphology has been investigated. Large electron mobility anisotropy is found for the sample with anisotropic morphology, which is mainly induced by the threading dislocations in the InAs layer. For the samples with isotropic morphology, the electron mobility is also anisotropic and could be attributed to the piezoelectric scattering. At low temperature (below transition temperature), the piezoelectric scattering is enhanced with the increase of temperature, leading to the increase of electron mobility anisotropy. At high temperature (above transition temperature), the phonon scattering becomes dominant. Because the phonon scattering is isotropic, the electron mobility anisotropy in all the samples would be reduced. Our results provide useful information for the comprehensive understanding of electron mobility anisotropy in the (Al,Ga)Sb/InAs system.
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Khudaiberdiev, D. A., M. L. Savchenko, D. A. Kozlov, N. N. Mikhailov, and Z. D. Kvon. "Scattering anisotropy in HgTe (013) quantum well." Applied Physics Letters 121, no. 8 (August 22, 2022): 083101. http://dx.doi.org/10.1063/5.0101932.
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We report on a detailed experimental study of the electron transport anisotropy in HgTe (013) quantum well of 22 nm width in the directions [Formula: see text] and [Formula: see text] as the electron density function n. The anisotropy is absent at the minimal electron density near a charge neutrality point. The anisotropy increases with the increase in n and reaches about 10% when the Fermi level is within the first subband H1. There is a sharp increase in the anisotropy (up to 60%) when the Fermi level reaches the second subband E2. We conclude that the first effect is due to the small intra-subband anisotropic interface roughness scattering, and the second one is due to the strongly anisotropic inter-subband roughness scattering, but the microscopical reason for such a strong change in the anisotropy remains unknown.
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Liu, Yajun, Pritam Yogeshwar, Xiangyun Hu, Ronghua Peng, Bülent Tezkan, Wiebke Mörbe, and Jianhui Li. "Effects of electrical anisotropy on long-offset transient electromagnetic data." Geophysical Journal International 222, no. 2 (May 2, 2020): 1074–89. http://dx.doi.org/10.1093/gji/ggaa213.
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SUMMARY Electrical anisotropy of formations has been long recognized by field and laboratory evidence. However, most interpretations of long-offset transient electromagnetic (LOTEM) data are based on the assumption of an electrical isotropic earth. Neglecting electrical anisotropy of formations may cause severe misleading interpretations in regions with strong electrical anisotropy. During a large scale LOTEM survey in a former mining area in Eastern Germany, data was acquired over black shale formations. These black shales are expected to produce a pronounced bulk anisotropy. Here, we investigate the effects of electrical anisotropy on LOTEM responses through numerical simulation using a finite-volume time-domain (FVTD) algorithm. On the basis of isotropic models obtained from LOTEM field data, various anisotropic models are developed and analysed. Numerical results demonstrate that the presence of electrical anisotropy has a significant influence on LOTEM responses. Based on the numerical modelling results, an isolated deep conductive anomaly presented in the 2-D isotropic LOTEM electric field data inversion result is identified as a possible artifact introduced by using an isotropic inversion scheme. Trial-and-error forward modelling of the LOTEM electric field data using an anisotropic conductivity model can explain the data and results in a reasonable quantitative data fit. The derived anisotropic 2-D model is consistent with the prior geological information.
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Watson, Julian Matthew, Abouzar Vakili, and Mateusz Jakubowski. "Rock Strength Anisotropy in High Stress Conditions: A Case Study for Application to Shaft Stability Assessments." Studia Geotechnica et Mechanica 37, no. 1 (March 1, 2015): 115–25. http://dx.doi.org/10.1515/sgem-2015-0013.
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Abstract Although rock strength anisotropy is a well-known phenomenon in rock mechanics, its impact on geotechnical design is often ignored or underestimated. This paper explores the concept of anisotropy in a high stress environment using an improved unified constitutive model (IUCM), which can account for more complex failure mechanisms. The IUCM is used to better understand the typical responses of anisotropic rocks to underground mining. This study applies the IUCM to a proposed rock shaft located in high stress/anisotropic conditions. Results suggest that the effect of rock strength anisotropy must be taken into consideration when assessing the rock mass response to mining in high stress and anisotropic rock conditions.
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Ren, Qi, and Kyle T. Spikes. "Modeling the effects of microscale fabric complexity on the anisotropy of the Eagle Ford Shale." Interpretation 4, no. 2 (May 1, 2016): SE17—SE29. http://dx.doi.org/10.1190/int-2015-0120.1.
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Microscale fabric influences the elastic properties of rock formations. The complexity of the microscale fabric of shale results from composition, platy clay minerals, kerogen, and their preferred orientation patterns. This microscale fabric is also the likely cause of the elastic anisotropy of the rock. In this paper, we have developed a comprehensive three-step rock-physics approach to model the anisotropic elastic properties of the Upper Eagle Ford Shale. We started with anisotropic differential effective medium modeling, followed by an orientation correction, and then a pressure adjustment. This method accounts for the microscale fabric of the rock in terms of the complex composition, shape, and alignment of clay minerals, pore space, and kerogen. In addition, we accounted for different pressure-dependent behaviors of P- and S-waves. Our modeling provides anisotropic stiffnesses and pseudologs of anisotropy parameters. The modeling results match the log measurements relatively well. The clay content, kerogen content, and porosity decreased the rock stiffness. The anisotropy increases with kerogen content, but the influence of clay content was more complex. Comparing the anisotropy parameter pseudologs with clay content shows that clay content increases anisotropy at small concentrations; however, the anisotropy stays constant, or even slightly decreases, as the clay content continues to increase. This result suggests that the preferred orientation of clay clusters is preserved at low clay concentration but vanishes at high clay concentration. This method could also be applied to other shales with carefully chosen parameters to model anisotropic elastic properties.
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Kyriakides, S., and M. K. Yeh. "Plastic Anisotropy in Drawn Metal Tubes." Journal of Engineering for Industry 110, no. 3 (August 1, 1988): 303–7. http://dx.doi.org/10.1115/1.3187886.
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A relatively simple experimental procedure for establishing the anisotropic yield characteristics of commercially available drawn metal tubes is described. Hill’s [4] extension of the Von Mises yield criterion to anisotropic yielding is used to describe the anisotropy present. Results from commercially available stainless steel are presented where the anisotropy is characterized by differences between the yield stresses in the circumferential and axial directions.
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Zalizniak, Roman. "MODELING AND IMPROVEMENT OF ANISOTROPIC STRENGTHENING OF ORTHOTROPIC CRYSTALLINE MATERIALS." Vibrations in engineering and technology, no. 1 (108) (May 1, 2023): 99–103. http://dx.doi.org/10.37128/2306-8744-2023-1-11.
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Sheet material subject to stamping, as a rule, has an anisotropy of mechanical properties due to the brand of the material and the technological modes of its production. The anisotropy of the mechanical properties of the workpiece material can have both a positive and a negative effect on the steady course of technological processes of pressure metal processing. In the processes of plastic deformation, the initial anisotropy of the mechanical properties changes and depends on the processing modes. When analyzing the technological processes of processing anisotropic metals by pressure, the initial anisotropy of the mechanical properties is mainly taken into account. Accounting for the influence of the initial anisotropy is carried out within the framework of an ideal plastic or isotropic body that is being strengthened. However, these assumptions do not allow us to estimate the change in anisotropy of mechanical properties during plastic processing. Most of the existing theories of anisotropic strengthening of an initially isotropic and anisotropic body are based on isotropic expansion and movement of the load surface in the stress space and differ from each other in the approaches to describing the movement of the center of the load surface, which can be specified in the form of finite and differential relations. They are designed for small elastoplastic deformations. The article gives the main ratios that must be used in the analysis of cold stamping processes of orthotropic anisotropically strengthening materials and proposes mathematical models of anisotropic strengthening of orthotropic crystalline materials. The deformation intensity value and components of the strain tensor in the main axes of anisotropy are used as strengthening parameters, and the accumulated amount of damage is also taken into account.
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Gavin, Lisa J., and David Lumley. "Stress-induced seismic azimuthal anisotropy, sand-shale content, and depth trends offshore North West Australia." GEOPHYSICS 82, no. 2 (March 1, 2017): C77—C90. http://dx.doi.org/10.1190/geo2015-0709.1.
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Seismic azimuthal anisotropy is apparent when P-wave velocities vary with source-receiver azimuth and downward-propagating S-waves split into two quasi-S-waves, polarized in orthogonal directions. Not accounting for these effects can degrade seismic image quality and result in erroneous amplitude analysis and geologic interpretations. There are currently no physical models available to describe how azimuthal anisotropy induced by differential horizontal stress varies with sand-shale lithology and depth; we develop a model that does so, in unconsolidated sand-shale sequences offshore North West Australia. Our method naturally introduces two new concepts: “critical anisotropy” and “anisotropic depth limit.” Critical anisotropy is the maximum amount of azimuthal anisotropy expected to be observed at the shallowest sediment burial depth, where the confining pressure and sediment compaction are minimal. The anisotropic depth limit is the maximum depth where the stress-induced azimuthal anisotropy is expected to be observable, where the increasing effects of confining pressure, compaction, and cementation make the sediments insensitive to differential horizontal stress. We test our model on borehole log data acquired in the Stybarrow Field, offshore North West Australia, where significant differential horizontal stress and azimuthal anisotropy are present. We determine our model parameters by performing regressions using dipole shear log velocities, gamma-ray shale volume logs, and depth trend data. We perform a blind test using the model parameters derived from one well to accurately predict the azimuthal anisotropy values at two other wells in an adjacent area. We use our anisotropy predictions to improve the well-tie match of the modeled angle-dependent reflectivity amplitudes to the 3D seismic amplitude variation with offset data observed at the well locations. Future applications of our method may allow the possibility to estimate the sand-shale content over a wide exploration area using anisotropic parameters derived from surface 3D seismic data.
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Carrion, Philip, Jesse Costa, Jose E. Ferrer Pinheiro, and Michael Schoenberg. "Cross‐borehole tomography in anisotropic media." GEOPHYSICS 57, no. 9 (September 1992): 1194–98. http://dx.doi.org/10.1190/1.1443333.
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Anisotropy has significant effect on traveltime cross‐borehole tomography. Even relatively weak anisotropy cannot be ignored if accurate velocity estimates are desired, since isotropic traveltime tomography treats anisotropy as inhomogeneity. Traveltime data in our examples were synthetically generated by a ray‐tracing code for anisotropic media, and the computed quasi‐P‐wave traveltimes were subsequently inverted using the “dual tomography” technique (Carrion, 1991). The results of the tomographic inversion show typical artifacts due to the anisotropy, and that accurate imaging is impossible without taking the anisotropy into account.
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Kan, V., V. F. Sofieva, and F. Dalaudier. "Variable anisotropy of small-scale stratospheric irregularities retrieved from stellar scintillation measurements by GOMOS/Envisat." Atmospheric Measurement Techniques 7, no. 6 (June 25, 2014): 1861–72. http://dx.doi.org/10.5194/amt-7-1861-2014.
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Abstract. In this paper, we consider possibilities for studying the anisotropy of small-scale air density irregularities using satellite observations of bi-chromatic stellar scintillations during tangential occultations. Estimation of the anisotropy coefficient (the ratio of the characteristic horizontal to vertical scales) and other atmospheric parameters is based on the comparison of simulated/theoretical and experimental auto-spectra and coherency spectra of scintillation. Our analyses exploit a 3-D model of the spectrum of atmospheric inhomogeneities, which consists of anisotropic and isotropic components. For the anisotropic component, a spectral model with variable anisotropy is used. Using stellar scintillation measurements by GOMOS (Global Ozone Monitoring by Occultation of Stars) fast photometers, estimates of the anisotropy coefficient are obtained for atmospheric irregularities with vertical scales of 8–55 m at altitudes of 43–30 km. It is shown that the anisotropy increases from about 10 to 50 with increasing vertical scales.
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Kan, V., V. F. Sofieva, and F. Dalaudier. "Variable anisotropy of small-scale stratospheric irregularities retrieved from stellar scintillation measurements by GOMOS/Envisat." Atmospheric Measurement Techniques Discussions 7, no. 2 (February 10, 2014): 1275–304. http://dx.doi.org/10.5194/amtd-7-1275-2014.
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Abstract. In this paper, we consider possibilities for studying the anisotropy of small-scale air density irregularities using satellite observations of bi-chromatic stellar scintillations during tangential occultations. Estimation of the anisotropy coefficient (the ratio of the characteristic horizontal to vertical scales) and other atmospheric parameters is based on the comparison of simulated/theoretical and experimental auto-spectra and coherency spectra of scintillation. Our analyses exploit a 3-D model of the spectrum of atmospheric inhomogeneities, which consists of anisotropic and isotropic components. For the anisotropic component, a spectral model with variable anisotropy is used. Using stellar scintillation measurements by GOMOS (Global Ozone Monitoring by Occultation of Stars) fast photometers, estimates of the anisotropy coefficient are obtained for atmospheric irregularities with vertical scales of 8–55 m at altitudes of 43–30 km. It is shown that the anisotropy increases from about 10 to 50 with increasing vertical scales.
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Lubkov, M. V. "Application of the finite element-differences method for modeling of anisotropic filtration processes." Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics, no. 3 (2021): 63–66. http://dx.doi.org/10.17721/1812-5409.2021/3.10.
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We consider modeling and geophysical interpretation of the obtained results in the oil and gas production problems in anisotropic reservoirs. For solving these practical problems, we use combined finite element-differences method of resolving anisotropic piezoconductivity problem with calculation of heterogeneous filtration parameters distribution of oil and gas productive reservoirs and oil-gas penetration conditions in the borders of investigating areas. We have defined that the anisotropy of oil and gas permeability in the far zone of the well has a greater effect on the filtration processes around the well and, accordingly, on the producing of the raw materials than the anisotropy of permeability in the near zone of the well. We have shown that the intensity of filtration processes in anisotropic reservoirs near the acting well depends significantly on the shear permeability and to a lesser extent on the axial permeability of the corresponding phase. Therefore, for the effective using of anisotropic reservoirs, it is necessary to place production wells in local areas with relatively low anisotropy of permeability of the reservoir, especially to avoid places with shear anisotropy.
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Zhu, Tieyuan. "Numerical simulation of seismic wave propagation in viscoelastic-anisotropic media using frequency-independent Q wave equation." GEOPHYSICS 82, no. 4 (July 1, 2017): WA1—WA10. http://dx.doi.org/10.1190/geo2016-0635.1.
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Seismic anisotropy is the fundamental phenomenon of wave propagation in the earth’s interior. Numerical modeling of wave behavior is critical for exploration and global seismology studies. The full elastic (anisotropy) wave equation is often used to model the complexity of velocity anisotropy, but it ignores attenuation anisotropy. I have presented a time-domain displacement-stress formulation of the anisotropic-viscoelastic wave equation, which holds for arbitrarily anisotropic velocity and attenuation [Formula: see text]. The frequency-independent [Formula: see text] model is considered in the seismic frequency band; thus, anisotropic attenuation is mathematically expressed by way of fractional time derivatives, which are solved using the truncated Grünwald-Letnikov approximation. I evaluate the accuracy of numerical solutions in a homogeneous transversely isotropic (TI) medium by comparing with theoretical [Formula: see text] and [Formula: see text] values calculated from the Christoffel equation. Numerical modeling results show that the anisotropic attenuation is angle dependent and significantly different from the isotropic attenuation. In synthetic examples, I have proved its generality and feasibility by modeling wave propagation in a 2D TI inhomogeneous medium and a 3D orthorhombic inhomogeneous medium.
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Kong, Wenxin, Changhong Lin, Handong Tan, Miao Peng, Tuo Tong, and Mao Wang. "The Effects of 3D Electrical Anisotropy on Magnetotelluric Responses: Synthetic Case Studies." Journal of Environmental and Engineering Geophysics 23, no. 1 (March 2018): 61–75. http://dx.doi.org/10.2113/jeeg23.1.61.
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Using the staggered-grid finite difference method, a numerical modeling algorithm for a 3D arbitrary anisotropic Earth is implemented based on magnetotelluric (MT) theory. After the validation of this algorithm and comparison with predecessors, it was applied to several qualitative and quantitative analyses containing electrical anisotropy and a simple 3D prism model. It was found that anisotropic parameters for ρ 1 , ρ 2 , and ρ 3 play almost the same role in affecting 3D MT responses as in 1D and 2D without considering three Euler's angles α S , α D , and α L . Significant differences appear between the off-diagonal components of the apparent resistivity tensor and also between the diagonal components in their values and distributing features under the influence of 3D anisotropy, which in turn help to identify whether the MT data are generated from 3D anisotropic earth. Considering the deflecting effects arising from the inconsistency between the anisotropy axes and the measuring axes, some strategies are also provided to estimate the deflecting angles associated with anisotropy strike α S or dip α D , which may be used as initial values for the 3D anisotropy inversion. [Figure: see text]
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Sams, Mark, Annushia Annamalai, and Jeremy Gallop. "Seismic amplitude variation with offset inversion in a vertical transverse isotropy medium." Interpretation 7, no. 3 (August 1, 2019): T581—T593. http://dx.doi.org/10.1190/int-2018-0137.1.
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Vertical transverse isotropy (VTI) will affect seismic inversion, but it is not possible to solve for the full set of anisotropic elastic parameters from amplitude variation with offset inversion because there exists an isotropic solution to every VTI problem. We can easily approximate the pseudoisotropic properties that result from the isotropic solution to the anisotropic problem for well-log data. We can then use these well-log properties to provide a low-frequency model for inversion and/or a framework for interpreting either absolute or relative inversion results. This, however, requires prior knowledge of the anisotropic properties, which are often unavailable or poorly constrained. If we ignore anisotropy and assume that the amplitude variations caused by VTI are going to be accounted for by effective wavelets, the inversion results would be in error: The impact of anisotropy is not merely a case of linear scaling of seismic amplitudes for any particular angle range. Ignoring VTI does not affect the prediction of acoustic impedance, but it does affect predictions of [Formula: see text] and density. For realistic values of anisotropy, these errors can be significant, such as predicting oil instead of brine. If the anisotropy of the rocks is known, then we can invert for the true vertical elastic properties using the known anisotropy coefficients through a facies-based inversion. This can produce a more accurate result than solving for pseudoelastic properties, and it can take advantage of the sometimes increased separation of isotropic and anisotropic rocks in the pseudoisotropic elastic domain. Because the effect of anisotropy will vary depending on the strength of the anisotropy and the distribution of the rocks, we strongly recommend forward modeling for each case prior to inversion to understand the potential impact on the study objectives.
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Soda, Jiro. "Statistical anisotropy from anisotropic inflation." Classical and Quantum Gravity 29, no. 8 (March 15, 2012): 083001. http://dx.doi.org/10.1088/0264-9381/29/8/083001.
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Hu, Yunyun, and Qingtao Sun. "Modeling of triaxial induction logging responses in multilayered anisotropic formations." GEOPHYSICS 86, no. 4 (July 1, 2021): E305—E314. http://dx.doi.org/10.1190/geo2020-0475.1.
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Triaxial induction logging tools have been widely applied to formation characterization due to their sensitivity to electric anisotropy. To model triaxial induction logs in multilayered general anisotropic formations, where the anisotropy can be arbitrary, an analytical method is applied to compute the tool responses. For the analytical method, Maxwell’s equations in the spectral domain are written into a compact first-order differential equation. The equation is solved to obtain the spectral-domain fields, which are transformed to the spatial domain through the inverse Fourier transform. The singular issue for the tool located in highly deviated wells is handled by subtracting the singular term in the spectral domain. The singularity treatment makes the integrands in the inverse Fourier transform decay faster, thus making the infinite integration computation faster. Formations with isotropic, transversely isotropic, biaxially anisotropic, and general anisotropic conductivity are modeled and compared to investigate the effects of anisotropy on the tool responses. For a tool in a general anisotropic formation, all of the [Formula: see text] components are nonzero. For a tool in a vertical well in transversely isotropic and biaxially anisotropic formations, only the diagonal components of [Formula: see text] are nonzero. For a tool located in a deviated well, the effects of tool deviation and electric anisotropy are coupled. The diagonal components are more sensitive to the electric anisotropy than the off-diagonal components, and the off-diagonal ones can clearly indicate bed boundaries.
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Alkhalifah, Tariq. "Transformation to zero offset in transversely isotropic media." GEOPHYSICS 61, no. 4 (July 1996): 947–63. http://dx.doi.org/10.1190/1.1444044.
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Nearly all dip‐moveout correction (DMO) implementations to date assume isotropic homogeneous media. Usually, this has been acceptable considering the tremendous cost savings of homogeneous isotropic DMO and considering the difficulty of obtaining the anisotropy parameters required for effective implementation. In the presence of typical anisotropy, however, ignoring the anisotropy can yield inadequate results. Since anisotropy may introduce large deviations from hyperbolic moveout, accurate transformation to zero‐offset in anisotropic media should address such nonhyperbolic moveout behavior of reflections. Artley and Hale’s v(z) ray‐tracing‐based DMO, developed for isotropic media, provides an attractive approach to treating such problems. By using a ray‐tracing procedure crafted for anisotropic media, I modify some aspects of their DMO so that it can work for v(z) anisotropic media. DMO impulse responses in typical transversely isotropic (TI) models (such as those associated with shales) deviate substantially from the familiar elliptical shape associated with responses in homogeneous isotropic media (to the extent that triplications arise even where the medium is homogeneous). Such deviations can exceed those caused by vertical inhomogeneity, thus emphasizing the importance of taking anisotropy into account in DMO processing. For isotropic or elliptically anisotropic media, the impulse response is an ellipse; but as the key anisotropy parameter η varies, the shape of the response differs substantially from elliptical. For typical η > 0, the impulse response in TI media tends to broaden compared to the response in an isotropic homogeneous medium, a behavior opposite to that encountered in typical v(z) isotropic media, where the response tends to be squeezed. Furthermore, the amplitude distribution along the DMO operator differs significantly from that for isotropic media. Application of this anisotropic DMO to data from offshore Africa resulted in a considerably better alignment of reflections from horizontal and dipping reflectors in common‐midpoint gather than that obtained using an isotropic DMO. Even the presence of vertical inhomogeneity in this medium could not eliminate the importance of considering the shale‐induced anisotropy.
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Han, S.-M., and J.-Y. Rho. "Dependence of broadband ultrasound attenuation on the elastic anisotropy of trabecular bone." Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine 212, no. 3 (March 1, 1998): 223–26. http://dx.doi.org/10.1243/0954411981534006.
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The effect of trabecular elastic anisotropy on broadband ultrasound attenuation (BUA) and bone mineral density (BMD) was investigated with human and bovine cubic cancellous bones. Ultrasonic parameters describing trabecular anisotropy were found from the three orthogonal ultrasound velocities. BMD was measured using quantitative computed tomography. Three elastic anisotropy ratios were compared to BUA in all three directions and to BMD. The combined effect of anisotropic characteristics and BMD was also correlated with BUA. The results showed that the anisotropy ratios were significantly related to BUA (p<0.05). There was, however, no correlation between BMD and the elastic anisotropy ratios. The combination of BMD and the anisotropy produced a significantly enhanced relationship with BUA.
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Daghash, Shaden, Phillip Servio, and Alejandro Rey. "First-Principles Elastic and Anisotropic Characteristics of Structure-H Gas Hydrate under Pressure." Crystals 11, no. 5 (April 24, 2021): 477. http://dx.doi.org/10.3390/cryst11050477.
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Evaluating gas hydrates properties contributes valuably to their large-scale management and utilization in fundamental science and applications. Noteworthy, structure-H (sH) gas hydrate lacks a comprehensive characterization of its structural, mechanical, and anisotropic properties. Anisotropic and pressure dependent properties are crucial for gas hydrates’ detection and recovery studies. The objective of this work is the determination of pressure-dependent elastic constants and mechanical properties and the direction-dependent moduli of sH gas hydrates as a function of guest composition. First-principles DFT computations are used to evaluate the mechanical properties, anisotropy, and angular moduli of different sH gas hydrates under pressure. Some elastic constants and moduli increase more significantly with pressure than others. This introduces variations in sH gas hydrate’s incompressibility, elastic and shear resistance, and moduli anisotropy. Young’s modulus of sH gas hydrate is more anisotropic than its shear modulus. The anisotropy of sH gas hydrates is characterized using the unit cell elastic constants, anisotropy factors, and the angular dependent moduli. Structure-properties composition correlations are established as a function of pressure. It is found that compressing filled sH gas hydrates increases their moduli anisotropy. Differences in atomic bonding across a crystal’s planes can be expected in anisotropic structures. Taken together the DFT-based structure–properties–composition relations for sH gas hydrates provide novel and significant material physics results for technological applications.
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Castro, Caio Leandro Perdigão, José Jadsom Sampaio de Figueiredo, and Isadora Augusta Soares de Macedo. "COMPARING TWO APPROACHES ON THE ESTIMATIVE ANISOTROPIC PARAMETERSFROM WELL LOGS: AN APPLICATION ON THE NORNE FIELD DATASET." Revista Brasileira de Geofísica 36, no. 4 (December 21, 2018): 1. http://dx.doi.org/10.22564/rbgf.v36i4.1971.
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ABSTRACT. Estimating the elastic properties of the rocks in the subsurface is a task with many challenges. The main goal of this work is to estimate the Thomsen anisotropic parameters from the inversion of elastic stiffness coefficients using data from five wells of the Norne Field, located at Norway. We compare the results of these parameters with the Backus average, using Li’s empirical method. Further, aspect ratio and crack density are calculated from the results of the elastic stiffness coefficients. It is considered a transversely isotropic medium. The results from the two methods showed similarities in estimating anisotropic parameters, aspect ratio and fracture density. The anisotropy of the study area is weak with some regions with moderate anisotropy. Some patterns suggest the possibility of calculating the anisotropic parameters for the adjacent wells and interpolate values for use in seismic processing.Keywords: Transversally isotropic medium, well logs, Thomsen parameters, Backus AverageRESUMO. Estimar as propriedades elásticas das rochas em subsurperfície é uma tarefa com muitos desafios. O principal objetivo deste trabalho é estimar os parâmetros de anisotropia de Thomsen a partir da inversão dos coeficientes de rigidez elástica, utilizando dados de cinco diferentes poços do campo de Norne, localizado na Noruega. Comparamos os resultados obtidos para esses parâmetros com a média de Backus, usando o método empírico de Li. Em seguida, a razão de aspecto e a densidade de fratura foram calculadas a partir dos resultados dos coeficientes de rigidez elástica. O meio transversalmente isotrópico é considerado neste trabalho. Os resultados obtidos a partir dos dois métodos mostraram similaridades na estimativa dos parâmetros de anisotropia, razão de aspecto e densidade de fratura. A anisotropia da área de estudo é fraca com algumas regiões de anisotropia moderada. Alguns padrões encontrados sugerem a possibilidade de calcular os parâmetros de anisotropia para os poços vizinhos e interpolá-los para uso futuro no processamento sísmico.Palavras-chave: Meios transversalmente isotrópicos, perfis de poços, parâmetros de Thomsen, média de Backus 1UFPA,
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Hadden, Shaun, R. Gerhard Pratt, and Brendan Smithyman. "Anisotropic full-waveform inversion of crosshole seismic data: A vertical symmetry axis field data application." GEOPHYSICS 84, no. 1 (January 1, 2019): B15—B32. http://dx.doi.org/10.1190/geo2017-0790.1.
Full textAbstract:
Anisotropic waveform tomography (AWT) uses anisotropic traveltime tomography followed by anisotropic full-waveform inversion (FWI). Such an approach is required for FWI in cases in which the geology is likely to exhibit anisotropy. An important anisotropy class is that of transverse isotropy (TI), and the special case of TI media with a vertical symmetry axis (VTI) media is often used to represent elasticity in undeformed sedimentary layering. We have developed an approach for AWT that uses an acoustic approximation to simulate waves in VTI media, and we apply this approach to crosshole data. In our approach, the best-fitting models of seismic velocity and Thomsen VTI anisotropy parameters are initially obtained using anisotropic traveltime tomography, and they are then used as the starting models for VTI FWI within the acoustic approximation. One common problem with the acoustic approach to TI media is the generation of late-arriving (spurious) S-waves as a by-product of the equation system. We used a Laplace-Fourier approach that effectively damps the spurious S-waves to suppress artifacts that might otherwise corrupt the final inversion results. The results of applying AWT to synthetic data illustrate the trade-offs in resolution between the two parameter classes of velocity and anisotropy, and they also verify anisotropic traveltime tomography as a valid method for generating starting models for FWI. The synthetic study further indicates the importance of smoothing the anisotropy parameters before proceeding to FWI inversions of the velocity parameter. The AWT technique is applied to real crosshole field gathers from a sedimentary environment in Western Canada, and the results are compared with the results from a simpler (elliptical) anisotropy model. The transversely isotropic approach yields an FWI image of the vertical velocity that (1) exhibits a superior resolution and (2) better predicts the field data than does the elliptical approach.