Journal articles on the topic 'Anisotropic heterogeneous parameters'
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1
Ivanov, Yuriy, and Alexey Stovas. "Upscaling in orthorhombic media: Behavior of elastic parameters in heterogeneous fractured earth." GEOPHYSICS 81, no. 3 (May 2016): C113—C126. http://dx.doi.org/10.1190/geo2015-0392.1.
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A stack of horizontal homogeneous elastic arbitrary anisotropic layers in welded contact in the long-wavelength limit is equivalent to an elastic anisotropic homogeneous medium. Such a medium is characterized by an effective average description adhering to previously derived closed-form formalism. We have used this formalism to study three different inhomogeneous orthorhombic (ORT) models that could represent real geologic scenarios. We have determined that a stack of thin orthorhombic layers with arbitrary azimuths of vertical symmetry planes can be approximated by an effective orthorhombic medium. The most suitable approach for this is to minimize the misfit between the effective anisotropic medium, monoclinic in that case, and the desirable orthorhombic medium. The second model is an interbedding of VTI (transversely isotropic with a vertical symmetry axis) layers with the same layers containing vertical fractures (shales are intrinsically anisotropic and often fractured). We have derived a weak-anisotropy approximation for important P-wave processing parameters as a function of the relative amount of the fractured lithology. To accurately characterize fractures, inversion for the fracture parameters should use a priori information on the relative amount of a fractured medium. However, we have determined that the cracks’ fluid saturation can be estimated without prior knowledge of the relative amount of the fractured layer. We have used field well-log data to demonstrate how fractures can be included in the interval of interest during upscaling. Finally, the third model that we have considered is a useful representation of tilted orthorhombic medium in the case of two-way propagation of seismic waves through it. We have derived a weak anisotropy approximation for traveltime parameters of the reflected P-wave that propagates through a stack of thin beds of tilted orthorhombic symmetry. The tilt of symmetry planes in an orthorhombic medium significantly affects the kinematics of the reflected P-wave and should be properly accounted for to avoid mispositioning of geologic structures in seismic imaging.
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Ruan, Huai Ning, Di Wang, and J. W. Ju. "A Failure Model for Heterogeneous Nonlinear Anisotropic Geomaterials." Advanced Materials Research 594-597 (November 2012): 472–81. http://dx.doi.org/10.4028/www.scientific.net/amr.594-597.472.
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In designing earth structures, various kinds of complex soils and rocks are constantly encountered. These geomaterials exhibit heterogeneous, nonlinear, and anisotropic behavior. A failure criterion for such complicated materials is proposed. This model is highly comprehensive. It characterizes heterogeneity, nonlinearity, and anisotropy simultaneously in one equation. Many classical failure criteria employed in geomechanics and plasticity are its special cases. The material parameters in the proposed criterion may be determined from tests of unconfined compression, uniaxial tension, biaxial compression, and direct shear. The case study illustrates the potential of the proposed model in engineering application.
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Lubkov, M., and O. Zaharchuk. "MODELING OF DISPLACEMENT PROCESSES IN HETEROGENEOUS ANISOTROPIC GAS RESERVOIRS." Visnyk of Taras Shevchenko National University of Kyiv. Geology, no. 2 (93) (2021): 94–99. http://dx.doi.org/10.17721/1728-2713.93.11.
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Nowadays there are important problems of increasing efficiency of development and exploitation of gas deposits. There are problems associated with the growth of gas production in heterogeneous anisotropic reservoirs, increasing gas recovery, achieving economic efficiency and so on. In this situation, there are popular methods of computer modeling of gas productive reservoirs, because they allow getting information of the structure and characteristics of the gas reservoir, the distribution parameters of permeability and other important factors in it. They also allow evaluating and calculating uncertainty arising from the lack of information about the gas reservoir properties outside the well. Currently there are many methods of computer modeling, allowing solving various practical problems. From another hand there are some problems related to the accuracy and adequacy of simulation of heterogeneous anisotropic permeable collector systems in real conditions of gas deposits exploitation. On the base of combined finite-element-difference method for solving the nonstationary anisotropic piezoconductivity Lebenson problem, with calculating of heterogeneous distribution of permeable characteristics of the gas reservoir, we carried out modeling of filtration processes between production and injection wells. The results of computer modeling show that intensity of the filtration process between production and injection wells depends essentially on their location both in a shifting-isotropic and anisotropic gas reservoir. Therefore, for the effective using of poorly permeable shifting-isotropic gas-bearing reservoirs, it is necessary to place production and injection wells along the main anisotropy axes of the gas-bearing layers. At the placing production and injection well systems in low-permeable anisotropic reservoirs of a gas field, the most effective exchange between them will take place when the direction of increased permeability of the reservoirs coincides with the direction of the location of the wells. Obviously, the best conditions for gas production processes in any practical case can be achieved due to optimal selection of all anisotropic filtration parameters of the gas reservoir. One can use obtained results for practical geophysical works with a purpose optimizing of gas production activity in low-permeable heterogeneous anisotropic reservoirs. Presented method for more detailed investigation of low-permeable heterogeneous anisotropic gas-bearing deposits can be used.
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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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Ward, Andy L., Z. Fred Zhang, and Glendon W. Gee. "Upscaling unsaturated hydraulic parameters for flow through heterogeneous anisotropic sediments." Advances in Water Resources 29, no. 2 (February 2006): 268–80. http://dx.doi.org/10.1016/j.advwatres.2005.02.013.
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Lin, Hsien-Tsung, Yih-Chi Tan, Chu-Hui Chen, Hwa-Lung Yu, Shih-Ching Wu, and Kai-Yuan Ke. "Estimation of effective hydrogeological parameters in heterogeneous and anisotropic aquifers." Journal of Hydrology 389, no. 1-2 (July 2010): 57–68. http://dx.doi.org/10.1016/j.jhydrol.2010.05.021.
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B.N., Priyanka, and M. S. Mohan Kumar. "Three-Dimensional Modelling of Heterogeneous Coastal Aquifer: Upscaling from Local Scale." Water 11, no. 3 (February 27, 2019): 421. http://dx.doi.org/10.3390/w11030421.
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The aquifer heterogeneity is often simplified while conceptualizing numerical model due to lack of field data. Conducting field measurements to estimate all the parameters at the aquifer scale may not be feasible. Therefore, it is essential to determine the most significant parameters which require field characterization. For this purpose, the sensitivity analysis is performed on aquifer parameters, viz., anisotropic hydraulic conductivity, effective porosity and longitudinal dispersivity. The results of the sensitivity index and root mean square deviation indicated, that the longitudinal dispersivity and anisotropic hydraulic conductivity are the sensitive aquifer parameters to evaluate seawater intrusion in the study area. The sensitive parameters are further characterized at discrete points or at local scale by using regression analysis. The longitudinal dispersivity is estimated at discrete well points based on Xu and Eckstein regression formula. The anisotropic hydraulic conductivity is estimated based on established regression relationship between hydraulic conductivity and electrical resistivity with R2 of 0.924. The estimated hydraulic conductivity in x and y-direction are upscaled by considering the heterogeneous medium as statistically homogeneous at each layer. The upscaled model output is compared with the transversely isotropic model output. The bias error and root mean square error indicated that the upscaled model performed better than the transversely isotropic model. Thus, this investigation demonstrates the necessity of considering spatial heterogeneous parameters for effective modelling of the seawater intrusion in a layered coastal aquifer.
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Golikov, Pavel, and Alexey Stovas. "Traveltime parameters in tilted transversely isotropic media." GEOPHYSICS 77, no. 6 (November 1, 2012): C43—C55. http://dx.doi.org/10.1190/geo2011-0457.1.
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Traveltime parameters define the coefficients of the Taylor series for traveltime or traveltime squared as a function of offset. These parameters provide an efficient tool for analyzing the effect of the medium parameters for short- and long-offset reflection moveouts. We derive the exact equations for one-way and two-way traveltime parameters in a homogeneous transversely isotropic medium with the tilted symmetry axis (TTI). It is shown that most of the one-way traveltime parameters in TTI differ from the two-way traveltime parameters, and we observe strong dependence of all traveltime parameters on tilt. The equations for traveltime parameters are extended to a vertically heterogeneous TTI medium, and weak-anisotropy and weak-anellipticity approximations are considered. We also apply the exact and approximate equations to invert the traveltime parameters into the model parameters for different acquisition setups. Using the traveltime parameters in a weak-anisotropy approximation, our tests show that an analytical inversion is not applicable, whereas the numerical inversion with exact equations yields a good accuracy for strongly anisotropic models.
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Yan, Jia, and Paul Sava. "Elastic wave-mode separation for VTI media." GEOPHYSICS 74, no. 5 (September 2009): WB19—WB32. http://dx.doi.org/10.1190/1.3184014.
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Elastic wave propagation in anisotropic media is well represented by elastic wave equations. Modeling based on elastic wave equations characterizes both kinematics and dynamics correctly. However, because P- and S-modes are both propagated using elastic wave equations, there is a need to separate P- and S-modes to efficiently apply single-mode processing tools. In isotropic media, wave modes are usually separated using Helmholtz decomposition. However, Helmholtz decomposition using conventional divergence and curl operators in anisotropic media does not give satisfactory results and leaves the different wave modes only partially separated. The separation of anisotropic wavefields requires more sophisticated operators that depend on local material parameters. Anisotropic wavefield-separation operators are constructed using the polarization vectors evaluated at each point of the medium by solving the Christoffel equation for local medium parameters. These polarization vectors can be represented in the space domain as localized filtering operators, which resemble conventional derivative operators. The spatially variable pseudo-derivative operators perform well in heterogeneous VTI media even at places of rapid velocity/density variation. Synthetic results indicate that the operators can be used to separate wavefields for VTI media with an arbitrary degree of anisotropy.
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Zhou, Bing, and Stewart Greenhalgh. "On the computation of the Fréchet derivatives for seismic waveform inversion in 3D general anisotropic, heterogeneous media." GEOPHYSICS 74, no. 5 (September 2009): WB153—WB163. http://dx.doi.org/10.1190/1.3123766.
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We present a perturbation method and a matrix method for formulating the explicit Fréchet derivatives for seismic body-wave waveform inversion in 3D general anisotropic, heterogeneous media. Theoretically, the two methods yield the same explicit formula valid for any class of anisotropy and are completely equivalent if the model parameterization in the inversion is the same as that used in the discretization scheme (unstructured or structured mesh) for forward modeling. Explicit formulas allow various model parameterization schemes that try to match the resolution capability of the data and possibly reduce the dimensions of the Jacobian matrix. Based on the general expressions, relevant formulas for isotropic and 2.5D and 3D tilted transversely isotropic (TTI) media are derived. Two computational schemes, constant-point and constant-block parameterization, offer effective and efficient means of forming the Jacobian matrix from the explicit Fréchet derivatives. The sensitivity patterns of the displacement vector to the independent model parameters in a weakly anisotropic medium clearly convey the imaging capability possible with seismic waveform inversion in such an anisotropic medium.
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He, Chuan, Enlong Liu, and Qing Nie. "Mechanical properties and constitutive model for artificially structured soils with an initial stress-induced anisotropy." Acta Geotechnica Slovenica 17, no. 2 (2020): 46–55. http://dx.doi.org/10.18690/actageotechslov.17.2.46-55.2020.
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A series of triaxial compression tests was performed on artificially structured soil samples with an initial stress- -induced anisotropy at confining pressures of 25, 37.5, 50, 100, 200, and 400 kPa. Based on the results of these tests, a constitutive model for structured soils with initial stress-induced anisotropy was formulated. In the proposed model, the initially anisotropic structured soils are regarded as heterogeneous materials composed of bonded blocks and weaker bands. The bonded blocks (denoted as bonded elements) are described as transversely isotropic elastic– brittle materials, while the weaker bands (denoted as frictional elements) are described by the Lade–Duncan model of elastic–plastic materials. Based on the homogenization theorem for heterogeneous materials, and the introduction of structural parameters such as the breakage ratio and the local strain coefficient, the non-uniform distribution of stress and strain within a representative volume element was obtained. Finally, the parameters of the model were determined based on experimental results. The model was verified with test results, demonstrating that it can effectively capture many important features of artificially structured soils with an initial stress-induced anisotropy.
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Efendiev, Yalchin, Juan Galvis, Raytcho Lazarov, Svetozar Margenov, and Jun Ren. "Robust Two-level Domain Decomposition Preconditioners for High-contrast Anisotropic Flows in Multiscale Media." Computational Methods in Applied Mathematics 12, no. 4 (2012): 415–36. http://dx.doi.org/10.2478/cmam-2012-0031.
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AbstractIn this paper we discuss robust two-level domain decomposition preconditioners for highly anisotropic heterogeneous multiscale problems. We present a construction of several coarse spaces that employ standard finite element and multiscale basis functions and discuss techniques to reduce the dimensions of coarse spaces without sacrificing the robustness. We experimentally study the performance of the preconditioner on a variety two-dimensional test problems with channels of high anisotropy. The numerical tests confirm the robustness of the perconditioner with respect to the underlying physical parameters.
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Bai, Tong, Ilya Tsvankin, and Xinming Wu. "Waveform inversion for attenuation estimation in anisotropic media." GEOPHYSICS 82, no. 4 (July 1, 2017): WA83—WA93. http://dx.doi.org/10.1190/geo2016-0596.1.
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Robust estimation of attenuation coefficients remains a challenging problem, especially for heterogeneous anisotropic media. Here, we apply waveform inversion (WI) to perform attenuation analysis in heterogeneous VTI (transversely isotropic with a vertical symmetry axis) media. A time-domain finite-difference algorithm based on the standard linear solid model simulates nearly constant quality-factor values in a specified frequency band. We employ the adjoint-state method to derive the gradients of the objective function based on the Born approximation. Four parameters describing the attenuation coefficients of P- and SV-waves are updated simultaneously with a quasi-Newton optimization algorithm. To remove the time shifts between the modeled and observed data caused by velocity errors, we apply a local similarity technique. The inversion still requires a sufficiently accurate velocity model to minimize the trade-off between the contributions of velocity and attenuation to amplitudes. The inversion algorithm is tested on homogeneous background models with a Gaussian anomaly in one of the attenuation parameters and on a realistic heterogeneous VTI medium.
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Felício Fuck, Rodrigo, Andrey Bakulin, and Ilya Tsvankin. "Theory of traveltime shifts around compacting reservoirs: 3D solutions for heterogeneous anisotropic media." GEOPHYSICS 74, no. 1 (January 2009): D25—D36. http://dx.doi.org/10.1190/1.3033215.
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Time-lapse traveltime shifts of reflection events recorded above hydrocarbon reservoirs can be used to monitor production-related compaction and pore-pressure changes. Existing methodology, however, is limited to zero-offset rays and cannot be applied to traveltime shifts measured on prestack seismic data. We give an analytic 3D description of stress-related traveltime shifts for rays propagating along arbitrary trajectories in heterogeneous anisotropic media. The nonlinear theory of elasticity helps to express the velocity changes in and around the reservoir through the excess stresses associated with reservoir compaction. Because this stress-induced velocity field is both heterogeneous and anisotropic, it should be studied using prestack traveltimes or amplitudes. Then we obtain the traveltime shifts by first-order perturbation of traveltimes that accounts not only for the velocity changes but also for 3D deformation of reflectors. The resulting closed-form expression can be used efficiently for numerical modeling of traveltime shifts and, ultimately, for reconstructing the stress distribution around compacting reservoirs. The analytic results are applied to a 2D model of a compacting rectangular reservoir embedded in an initially homogeneous and isotropic medium. The computed velocity changes around the reservoir are caused primarily by deviatoric stresses and produce a transversely isotropic medium with a variable orientation of the symmetry axis and substantial values of the Thomsen parameters [Formula: see text] and [Formula: see text]. The offset dependence of the traveltime shifts should play a crucial role in estimating the anisotropy parameters and compaction-related deviatoric stress components.
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Maier, Ruth, Carsten Leven, Emilio Sánchez-León, Daniel Strasser, Maximilian Stoll, and Olaf A. Cirpka. "Revealing vertical aquifer heterogeneity and hydraulic anisotropy by pumping partially penetrating wells." Hydrogeology Journal 30, no. 2 (February 9, 2022): 463–77. http://dx.doi.org/10.1007/s10040-022-02458-9.
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AbstractThe stratification of sedimentary aquifers introduces spatial variability in hydraulic conductivity, primarily between individual horizontal layers. On larger scales, the vertical heterogeneity enhances hydraulic anisotropy, with the horizontal conductivity typically exceeding the vertical one. In this study, the hydraulic anisotropy of a stratified aquifer is estimated from data of hydraulic tests in which water is sequentially extracted from well sections screened at different depths, and the hydraulic response is measured at various multilevel observation wells. The applicability of the method is demonstrated by field tests in a fluvial gravel aquifer in the Upper Rhine Valley, Germany. A homogeneous anisotropic model, and models with three and five anisotropic layers, are fitted to the measured drawdowns in the steady-shape regime, in which differences in hydraulic head between observation locations do not change over time even though the head values themselves change. The position of the five horizontal layers is based on the lithology of the drilling profile at the pumping-well location. The three-layer model is achieved by merging insensitive or similar layers with sensitive layers. The fits result in estimates of the radial and vertical hydraulic conductivities for all layers of the respective models, which are upscaled to effective parameters over the entire depth in the case of the multilayer models. The homogeneous model shows significantly higher errors than those of the heterogeneous models. The heterogeneous locally anisotropic models not only reveal vertical variability of hydraulic conductivity, but also lead to a three-times larger anisotropy ratio upon upscaling.
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Wang, Xiaoxiang, and Ilya Tsvankin. "Ray-based gridded tomography for tilted transversely isotropic media." GEOPHYSICS 78, no. 1 (January 1, 2013): C11—C23. http://dx.doi.org/10.1190/geo2012-0066.1.
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Reflection tomography in the migrated domain can help reconstruct heterogeneous, anisotropic velocity fields needed for accurate depth imaging of complex geologic structures. The presence of anisotropy, however, increases the uncertainty in velocity analysis and typically requires a priori constraints on the model parameters. Here, we develop a 2D P-wave tomographic algorithm for heterogeneous transversely isotropic media with a tilted symmetry axis (TTI) and investigate the conditions necessary for stable estimation of the symmetry-direction velocity [Formula: see text] and the anisotropy parameters [Formula: see text] and [Formula: see text]. The model is divided into rectangular cells, and the parameters [Formula: see text], [Formula: see text], [Formula: see text], and the tilt [Formula: see text] of the symmetry axis are defined at the grid points. To increase the stability of the inversion, the symmetry axis is set orthogonal to the imaged reflectors, with the tilt interpolated inside each layer. The iterative migration velocity analysis involves efficient linearized parameter updating designed to minimize the residual moveout in image gathers for all available reflection events. The moveout equation in the depth-migrated domain includes a nonhyperbolic term that describes long-offset data, which are particularly sensitive to [Formula: see text]. Synthetic tests for models with a “quasi-factorized” TTI syncline (i.e., [Formula: see text] and [Formula: see text] are constant inside the anisotropic layer) and a TTI thrust sheet demonstrate that stable parameter estimation requires either strong smoothness constraints or additional information from walkaway VSP (vertical seismic profiling) traveltimes. If the model is quasi-factorized with a linear spatial variation of [Formula: see text], it may be possible to obtain the interval TTI parameters just from long-spread reflection data.
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Casado-Díaz, J., and M. Luna-Laynez. "Homogenization of the anisotropic heterogeneous linearized elasticity system in thin reticulated structures." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 134, no. 6 (December 2004): 1041–83. http://dx.doi.org/10.1017/s0308210500003620.
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The aim of this paper is to study the asymptotic behaviour of the solutions of the linearized elasticity system, posed on thin reticulated structures involving several small parameters. We show that this behaviour depends on the relative size of the parameters. In each case, we obtain a limit system where the microstructure and macrostructure appear simultaneously. From it, we get a suitable approximation in L2 of the displacements and the linearized strain tensor.
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Iversen, Einar. "Velocity rays for heterogeneous anisotropic media: Theory and implementation." GEOPHYSICS 71, no. 5 (September 2006): T117—T127. http://dx.doi.org/10.1190/1.2227525.
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The surface of equal two-way time referred to as the isochron is a fundamental concept in seismic imaging. The shape of an isochron depends on the source and receiver locations, on the wave type, and on the parameters constituting the seismic velocity model. A perturbation of a parameter of the velocity model forces the isochron points to move along trajectories called velocity rays, with the selected model parameter as the variable along the rays. Based on earlier work describing first-order approximations to velocity rays, I develop a general theory for velocity rays valid for 3D heterogeneous and anisotropic velocity models. By this theory, velocity rays can be obtained in a way similar to the way conventional rays are computed by numeric integration of a system of ordinary differential equations (ODEs). The process is organized with ODE solvers on two levels, where the upper level is model independent. The lower level includes conventional one-way kinematic and dynamic tracing of source and receiver rays, as well as calculation of ray perturbation quantities. Accurate velocity rays are expected to be useful for perturbation of reflectors mapped from the time domain to the depth domain, for remigration of seismic images in the depth domain, and for velocity model updating.
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Ságová, Zuzana, Valerii Vasilevich Tarasov, Ivana Klačková, Alexander Ivanovich Korshunov, and Milan Sága. "Study of Anisotropic Friction in Gears of Mechatronic Systems." Applied Sciences 12, no. 21 (October 31, 2022): 11021. http://dx.doi.org/10.3390/app122111021.
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The article discusses the features of anisotropic friction, which can be used to refine the calculation of the efficiency in various friction and gear drives and transmissions in mechatronic systems. Friction processes are considered that determine the level of losses in friction and gear drives, which are complex and heterogeneous in a number of parameters: the contact patch, which depends on the quality of the contacting surfaces; the direction and intensity of sliding; load distribution, etc. A more complete understanding of the features of these processes requires the use of the concept of friction anisotropy, which is well known in tribology of mechatronics systems. The anisotropy effect is caused by the difference in the characteristics of the surface microgeometry and its physical and mechanical properties in relation to the direction of the tool marks remaining on the surface after machining. In the presence of anisotropic friction, in contrast to isotropic, the body moves at a certain angle to the direction of application of the perturbing (external) force. The situation is considered in detail within the framework of the tensor model of anisotropic friction. The model and methodological approaches considered in the paper to the estimation of friction anisotropy can be used to refine the calculations of friction losses. The aim of the work is to create mechanical and analytical models of frictional anisotropy for a more complete understanding of this phenomenon in relation to various friction pairs. This article may be of interest to specialists in the field of friction gears for solving problems related to improving the accuracy of calculations and quantifying friction losses.
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Chen, Xi, Kun Zhang, and Wei Wang. "Seismic Stability Analysis of Tunnel Faces in Heterogeneous and Anisotropic Soils Using Modified Pseudodynamic Method." Sustainability 15, no. 14 (July 15, 2023): 11083. http://dx.doi.org/10.3390/su151411083.
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This work assesses the seismic stability of tunnel faces advanced in heterogeneous and anisotropic soils based on the plastic limit theorem. A discretized kinematic velocity field respecting the normal flow rule is generated via a point-to-point discretization technique. The distribution of soil parameters in the depth direction including cohesion, friction angle, and unit weight are considered by four kinds of profiles. The variation in cohesion with shear direction caused by consolidation and sedimentation is considered by including an anisotropy coefficient. The seismic acceleration is represented by the modified pseudodynamic method (MPD) rather than the conventional pseudodynamic method (CPD). Based on the energy equilibrium equation, an upper-bound solution is derived. The accuracy and rationality of the proposed procedure are substantiated by comparing with the solutions obtained by conventional log-spiral mechanism and CPD. A parametric study indicates that nonlinear profiles tend to predict a smaller required face pressure than the constant and linear profiles due to the convexity of nonlinear profiles. The over-consolidated soil is more sensitive to the anisotropy coefficient than normally consolidated soil. Moreover, the adverse effect of horizontal seismic acceleration is much greater than that of vertical acceleration, and the resonance effect is more prone to happen, especially for shallow-buried tunnels.
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Araújo, Iury, Murillo Nascimento, Jessé Costa, Alan Souza, and Jörg Schleicher. "Anisotropic Born scattering for the qP scalar wavefield using a low-rank symbol approximation." GEOPHYSICS 86, no. 5 (August 18, 2021): T337—T348. http://dx.doi.org/10.1190/geo2020-0764.1.
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We have developed a procedure to derive low-rank evolution operators in the mixed space-wavenumber domain for modeling the qP Born-scattered wavefield at perturbations of an anisotropic medium under the pseudoacoustic approximation. To approximate the full wavefield, this scattered field is then added to the reference wavefield obtained with the corresponding low-rank evolution operator in the background medium. Being built upon a Hamiltonian formulation using the dispersion relation for qP-waves, this procedure avoids pseudo-S-wave artifacts and provides a unified approach for linearizing anisotropic pseudoacoustic evolution operators. Therefore, it is immediately applicable to any arbitrary class of anisotropy. As an additional asset, the scattering operators explicitly contain the sensitivity kernels of the Born-scattered wavefield with respect to the anisotropic medium parameters. This enables direct access to important information such as its offset dependence or directional characteristics as a function of the individual parameter perturbations. For our numerical tests, we specify the operators for a mildly anisotropic tilted transversely isotropic (TTI) medium. We validate our implementation in a simple model with weak contrasts and simulate reflection data in the BP TTI model to indicate that the procedure works in a more realistic scenario. The Born-scattering results indicate that our procedure is applicable to strongly heterogeneous anisotropic media. Moreover, we use the analytical capabilities of the kernels by means of sensitivity tests to demonstrate that using two different medium parameterizations leads to different results. The mathematical formulation of the method is such that it allows for an immediate application to least-squares migration in pseudoacoustic anisotropic media.
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Schoenberg, Michael, and Francis Muir. "A calculus for finely layered anisotropic media." GEOPHYSICS 54, no. 5 (May 1989): 581–89. http://dx.doi.org/10.1190/1.1442685.
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Matrix algebra and group theory combine to offer a formalism for the simple calculation of the elastic, anisotropic, homogeneous medium which is equivalent, in the long‐wavelength limit, to a heterogeneous distribution of fine layers, each layer itself an elastic anisotropic medium. The properties of each anisotropic constituent in a set of fine layers map to an element of a commutative group. A reverse mapping returns the material properties of the constituent. Adding group elements gives the group element for the homogeneous medium equivalent to a heterogeneous set of layers. Addition of an inverse element—that is subtraction—provides the means to remove a set of layers from an anisotropic medium; then, if the remaining layer is a stable anisotropic medium, a valid decomposition of the original medium into anisotropic constituents is obtained. Within the group structure, eight subgroups corresponding to eight types of elastic symmetry systems may be identified, immediately yielding the symmetry of the equivalent medium, given the symmetry of its constituents. Sets of parallel fractures or aligned microcracks are also represented as group elements, allowing fractures and anisotropic rocks to be manipulated in a consistent and uniform manner. These group elements depend on at most six fracture parameters and are independent of the properties of the material in which the fractures are embedded. Multiple sets of fractures are easily taken into account by rotating (back in model space) a rock to a coordinate system appropriate to each fracture system, and then adding the appropriate fracture system group element.
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Voytenko, I. V. "АCCOUNTING THE SEISMIC COMPONENT OF THE LATERAL PRESSURE OF AN HETEROGENEOUS ANISOTROPIC SOIL ON MASSIVE HYDROTECHNICAL STRUCTURES." Bulletin of Odessa State Academy of Civil Engineering and Architecture, no. 80 (September 3, 2020): 132–39. http://dx.doi.org/10.31650/2415-377x-2020-80-132-139.
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Abstract. Strength anisotropy is characteristic of layered soil bases and has been confirmed by numerous tests. The relevance and novelty of this research is to study the effect of the seismic factor on the active pressure of the friable soil medium having strength anisotropy. A numerical experiment was carried out using a specially developed computer program, the algorithm of which used the method for determining the lateral pressure of a heterogeneous anisotropic soil, taking into account the seismic effect. The proposed method is based on the solutions of the classical theory of Coulomb, the seismic component is taken into account on the basis of the static theory of the earthquake stability of structures. We considered a vertically ideally smooth wall in contact with a two-layer incoherent soil medium, the anisotropy of the strength properties of which is represented by hodographs of friction angle. The layers are parallel, no surface load. A numerical research was to determine the parameters of the active pressure of the soil of the lower layer during rotation of the hodograph of friction angle with steps of 300. We used 4 hodographs: 1) φ1=150-200; 2) φ2=200-250; 3) φ3=250-300; 4) φ4=300-350 with a horizontal plane of isotropy. Seismic impact was taken into account by the seismicity coefficient, taken equal to depending on the scale 0.025 (7), 0.05 (8), 0.1 (9). The horizontal orientation of the seismic force and with an angle of 200 to the horizontal plane was set. The obtained results make it possible to evaluate the seismic effect on the lateral pressure of anisotropic soil by comparing it with the corresponding indicators obtained earlier without taking into account the seismic factor. An analysis of computer solutions indicates the increase of the active pressure in seismic conditions by 14%-45% compared with the same indicator, which was determined without taking into account the seismic factor.
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Guchhait, Shyamal, and Biswanath Banerjee. "Anisotropic linear elastic parameter estimation using error in the constitutive equation functional." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 472, no. 2192 (August 2016): 20160213. http://dx.doi.org/10.1098/rspa.2016.0213.
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A modified error in the constitutive equation-based approach for identification of heterogeneous and linear anisotropic elastic parameters involving static measurements is proposed and explored. Following an alternating minimization procedure associated with the underlying optimization problem, the new strategy results in an explicit material parameter update formula for general anisotropic material. This immediately allows us to derive the necessary constraints on measured data and thus restrictions on physical experimentation to achieve the desired reconstruction. We consider a few common materials to derive such conditions. Then, we exploit the invariant relationships of the anisotropic constitutive tensor to propose an identification procedure for space-dependent material orientations. Finally, we assess the numerical efficacy of the developed tools against a few parameter identification problems of engineering interest.
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Dmitriev, S. G. "Relations between Currents in the External Circuit and Parameters of a Diagnosed Heterogeneous Anisotropic Specimen." Journal of Communications Technology and Electronics 63, no. 10 (October 2018): 1222–25. http://dx.doi.org/10.1134/s106422691810008x.
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Chu, Chunlei, Brian K. Macy, and Phil D. Anno. "Approximation of pure acoustic seismic wave propagation in TTI media." GEOPHYSICS 76, no. 5 (September 2011): WB97—WB107. http://dx.doi.org/10.1190/geo2011-0092.1.
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Pseudoacoustic anisotropic wave equations are simplified elastic wave equations obtained by setting the S-wave velocity to zero along the anisotropy axis of symmetry. These pseudoacoustic wave equations greatly reduce the computational cost of modeling and imaging compared to the full elastic wave equation while preserving P-wave kinematics very well. For this reason, they are widely used in reverse time migration (RTM) to account for anisotropic effects. One fundamental shortcoming of this pseudoacoustic approximation is that it only prevents S-wave propagation along the symmetry axis and not in other directions. This problem leads to the presence of unwanted S-waves in P-wave simulation results and brings artifacts into P-wave RTM images. More significantly, the pseudoacoustic wave equations become unstable for anisotropy parameters [Formula: see text] and for heterogeneous models with highly varying dip and azimuth angles in tilted transversely isotropic (TTI) media. Pure acoustic anisotropic wave equations completely decouple the P-wave response from the elastic wavefield and naturally solve all the above-mentioned problems of the pseudoacoustic wave equations without significantly increasing the computational cost. In this work, we propose new pure acoustic TTI wave equations and compare them with the conventional coupled pseudoacoustic wave equations. Our equations can be directly solved using either the finite-difference method or the pseudospectral method. We give two approaches to derive these equations. One employs Taylor series expansion to approximate the pseudodifferential operator in the decoupled P-wave equation, and the other uses isotropic and elliptically anisotropic dispersion relations to reduce the temporal frequency order of the P-SV dispersion equation. We use several numerical examples to demonstrate that the newly derived pure acoustic wave equations produce highly accurate P-wave results, very close to results produced by coupled pseudoacoustic wave equations, but completely free from S-wave artifacts and instabilities.
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Takanashi, Mamoru, and Ilya Tsvankin. "Migration velocity analysis for TI media in the presence of quadratic lateral velocity variation." GEOPHYSICS 77, no. 6 (November 1, 2012): U87—U96. http://dx.doi.org/10.1190/geo2012-0032.1.
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One of the most serious problems in anisotropic velocity analysis is the trade-off between anisotropy and lateral heterogeneity, especially if velocity varies on a scale smaller than the maximum offset. We have developed a P-wave MVA (migration velocity analysis) algorithm for transversely isotropic (TI) models that include layers with small-scale lateral heterogeneity. Each layer is described by constant Thomsen parameters [Formula: see text] and [Formula: see text] and the symmetry-direction velocity [Formula: see text] that varies as a quadratic function of the distance along the layer boundaries. For tilted TI media (TTI), the symmetry axis is taken orthogonal to the reflectors. We analyzed the influence of lateral heterogeneity on image gathers obtained after prestack depth migration and found that quadratic lateral velocity variation in the overburden can significantly distort the moveout of the target reflection. Consequently, medium parameters beneath the heterogeneous layer(s) are estimated with substantial error, even when borehole information (e.g., check shots or sonic logs) is available. Because residual moveout in the image gathers is highly sensitive to lateral heterogeneity in the overburden, our algorithm simultaneously inverts for the interval parameters of all layers. Synthetic tests for models with a gently dipping overburden demonstrate that if the vertical profile of the symmetry-direction velocity [Formula: see text] is known at one location, the algorithm can reconstruct the other relevant parameters of TI models. The proposed approach helps increase the robustness of anisotropic velocity model-building and enhance image quality in the presence of small-scale lateral heterogeneity in the overburden.
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Abadi, Mohammad Tahaye. "Viscoelastic Characterization of Fiber-Reinforced Elastomeric Composites at Finite Strain." Advanced Materials Research 123-125 (August 2010): 603–6. http://dx.doi.org/10.4028/www.scientific.net/amr.123-125.603.
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A viscoelastic model is developed to describe the mechanical response of fiber-reinforced elastomeric composites at large deformation. A continuum approach is used to model the macroscopic mechanical behavior of elastomeric materials reinforced with unidirectional fibers, in which the resin and fibers are regarded as a single homogenized anisotropic material. The anisotropic viscoelastic constitutive model is developed considering transient reversible network theory. An efficient computational algorithm based on micromechanical modeling is proposed to relate the material parameters of constitutive model to the mechanical properties of composite constituents at finite strain. The microstructure is identified by a representative volume element (RVE) and it is subjected to large deformation with considering the conformity of opposite boundaries. The material parameters of the viscoelastic constitutive law are determined based on the response of heterogeneous microstructure which is examined under different loading conditions.
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Stunff, Yves Le, Vladimir Grechka, and Ilya Tsvankin. "Depth‐domain velocity analysis in VTI media using surface P-wave data: Is it feasible?" GEOPHYSICS 66, no. 3 (May 2001): 897–903. http://dx.doi.org/10.1190/1.1444979.
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The main difficulties in anisotropic velocity analysis and inversion using surface seismic data are associated with the multiparameter nature of the problem and inherent trade‐offs between the model parameters. For the most common anisotropic model, transverse isotropy with a vertical symmetry axis (VTI media), P-wave kinematic signatures are controlled by the vertical velocity V0 and the anisotropic parameters ε and δ. However, only two combinations of these parameters—NMO velocity from a horizontal reflector Vnmo(0) and the anellipticity coefficient η—can be determined from P-wave reflection traveltimes if the medium above the reflector is laterally homogeneous. While Vnmo(0) and η are sufficient for time‐domain imaging in VTI media, they cannot be used to resolve the vertical velocity and build velocity models needed for depth migration. Here, we demonstrate that P-wave reflection data can be inverted for all three relevant VTI parameters (V0, ε and δ) if the model contains nonhorizontal intermediate interfaces. Using anisotropic reflection tomography, we carry out parameter estimation for a two‐layer medium with a curved intermediate interface and reconstruct the correct anisotropic depth model. To explain the success of this inversion procedure, we present an analytic study of reflection traveltimes for this model and show that the information about the vertical velocity and reflector depth was contained in the reflected rays which crossed the dipping intermediate interface. The results of this work are especially encouraging because the need for depth imaging (such as prestack depth migration) arises mostly in laterally heterogeneous media. Still, we restricted this study to a relatively simple model and constrained the inversion by assuming that one of the layers is isotropic. In general, although lateral heterogeneity does create a dependence of P-wave reflection traveltimes on the vertical velocity, there is no guarantee that for more complicated models all anisotropic parameters can be resolved in a unique fashion.
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Kakar, Rajneesh. "SH-wave velocity in a fiber-reinforced anisotropic layer overlying a gravitational heterogeneous half-space." Multidiscipline Modeling in Materials and Structures 11, no. 3 (October 12, 2015): 386–400. http://dx.doi.org/10.1108/mmms-01-2015-0002.
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Purpose – The purpose of this paper is to investigate the existence of SH-waves in fiber-reinforced layer placed over a heterogeneous elastic half-space. Design/methodology/approach – The heterogeneity of the elastic half-space is caused by the exponential variations of density and rigidity. As a special case when both the layers are homogeneous, the derived equation is in agreement with the general equation of Love wave. Findings – Numerically, it is observed that the velocity of SH-waves decreases with the increase of heterogeneity and reinforced parameters. The dimensionless phase velocity of SH-waves increases with the decreases of dimensionless wave number and shown through figures. Originality/value – In this work, SH-wave in a fiber-reinforced anisotropic medium overlying a heterogeneous gravitational half-space has been investigated analytically and numerically. The dispersion equation for the propagation of SH-waves has been observed in terms of Whittaker function and its derivative of second degree order. It has been observed that on the removal of heterogeneity of half-space, and reinforced parameters of the layer, the derived dispersion equation reduces to Love wave dispersion equation thereby validates the solution of the problem. The equation of propagation of Love wave in fiber-reinforced medium over a heterogeneous half-space given by relevant authors is also reduced from the obtained dispersion relation under the considered geometry.
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Atici, Umit. "Modelling of the Elasticity Modulus for Rock Using Genetic Expression Programming." Advances in Materials Science and Engineering 2016 (2016): 1–8. http://dx.doi.org/10.1155/2016/2063987.
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In rock engineering projects, statically determined parameters are more reflective of actual load conditions than dynamic parameters. This study reports a new and efficient approach to the formulation of the static modulus of elasticityEsapplying gene expression programming (GEP) with nondestructive testing (NDT) methods. The results obtained using GEP are compared with the results of multivariable linear regression analysis (MRA), univariate nonlinear regression analysis (URA), and the dynamic elasticity modulus (Ed). The GEP model was found to produce the most accurate calculation ofEs. The proposed approach is a simple, nondestructive, and practical way to determineEsfor anisotropic and heterogeneous rocks.
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Hammer, Markus, and Wolfhart Seidel. "Helium Atom Scattering from C2H6, F2HCCH3, F3CCH2F and C2F6 in Crossed Molecular Beams." Zeitschrift für Naturforschung A 52, no. 10 (October 1, 1997): 695–701. http://dx.doi.org/10.1515/zna-1997-1002.
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Abstract Rotationally unresolved differential cross sections were measured in crossed molecular beam experiments by scattering Helium atoms from Ethane, 1,1-Difluoroethane, 1,1,1,2-Tetrafluoroethane and Hexafluoroethane. The damping of observed diffraction oscillations was used to extract anisotropic interaction potentials for these scattering systems applying the infinite order sudden approximation (IOSA). Binary macroscopic parameters such as second heterogeneous virial coefficients and the coefficients of diffusion and viscosity were computed from these potentials and compared to results from macroscopic experiments.
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Guruprasad, Thimmappa Shetty, Vincent Keryvin, and Alain Bourmaud. "ESTIMATION OF ANISOTROPIC ELASTIC PROPERTIES OF CARBON FIBERS USING NANOINDENTATION." Acta Polytechnica CTU Proceedings 27 (June 11, 2020): 107–11. http://dx.doi.org/10.14311/app.2020.27.0107.
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Understanding the mechanical behavior of carbon fiber reinforced polymers requires knowledge on the deformation behavior of carbon fibers, they are highly anisotropic and heterogeneous. Nanoindentation is an efficient method for determining the mechanical properties in small volumes of materials. For isotropic materials, a single nanoindentation test can evaluate an elastic properties of the material. But for anisotropic material, the difficulty increases since measured indentation modulus depends on five elastic parameters (El,Et,Glt, νlt,and νtt) of the material. Nanoindentation experiments are performed on carbon fibers orientated between 0° to 90° at ten different orientations to the fiber axis. From theoretical models given by Vlassak et al. and Delafargue and Ulm, the elastic constants are predicted numerically by comparing the results of indentation modulus versus orientation angle with the experiments.
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Shan, Guojian. "Optimized implicit finite-difference and Fourier finite-difference migration for VTI media." GEOPHYSICS 74, no. 6 (November 2009): WCA189—WCA197. http://dx.doi.org/10.1190/1.3202306.
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Propagation velocity of seismic waves in heterogeneous VTI media depends not only on spatial location but also on their propagation direction, which leads to a much more complex dispersion relation than in isotropic media. As a result, designing implicit finite-difference (FD) schemes for wavefield extrapolation in anisotropic media through analytic Taylor-series expansion is more difficult. Implicit FD and Fourier finite-difference (FFD) schemes are developed for vertical transversely isotropic (VTI) media based on function fitting. The dispersion relation of VTI media is approximated with a rational function and its coefficients are estimated by weighted least-squares optimization. Because these coefficients are functions of Thomsen anisotropy parameters ([Formula: see text] and [Formula: see text]) and vary laterally in heterogeneous VTI media, they are calculated before wavefield extrapolation and stored in a table. Implicit FD and FFD schemes for VTI media are almost the same as for isotropic media, except that coefficients are looked up in a precalculated table. Impulse responses and relative dispersion-relation error show that accuracy of the FD scheme for VTI media is similar to its counterpart in isotropic media. Application to a synthetic data set showed that implicit FD and FFD can handle laterally varying VTI media.
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Rice, M. E., Y. C. Okada, and C. Nicholson. "Anisotropic and heterogeneous diffusion in the turtle cerebellum: implications for volume transmission." Journal of Neurophysiology 70, no. 5 (November 1, 1993): 2035–44. http://dx.doi.org/10.1152/jn.1993.70.5.2035.
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1. Measurements of extracellular diffusion properties were made in three orthogonal axes of the molecular and granular layers of the isolated turtle cerebellum with the use of iontophoresis of tetramethylammonium (TMA+) combined with ion-selective microelectrodes. 2. Diffusion in the extracellular space of the molecular layer was anisotropic, that is, there was a different value for the tortuosity factor, lambda i, associated with each axis of that layer. The x- and y-axes lay in the plane parallel to the pial surface of this lissencephalic cerebellum with the x-axis in the direction of the parallel fibers. The z-axis was perpendicular this plane. The tortuosity values were lambda x = 1.44 +/- 0.01, lambda y = 1.95 +/- 0.02, and lambda z = 1.58 +/- 0.01 (mean +/- SE). By contrast, the granular layer was isotropic with a single tortuosity value, lambda Gr = 1.77 +/- 0.01. 3. These data confirm the applicability of appropriately extended Fickian equations to describe diffusion in anisotropic porous media, including brain tissue. 4. Heterogeneity between the molecular and granular layer was revealed by a striking difference in extracellular volume fraction, alpha, for each layer. In the molecular layer alpha = 0.31 +/- 0.01, whereas in the granular layer alpha = 0.22 +/- 0.01. 5. Volume fraction and tortuosity affected the time course and amplitude of extracellular TMA+ concentration after iontophoresis. This was modeled by the use of the average parameters determined experimentally, and the nonspherical pattern of diffusion in the molecular layer was compared with the spherical distribution in the granular layer and agarose gel by computing isoconcentration ellipsoids. 6. One functional consequence of these results was demonstrated by measuring local changes in [K+]o and [Ca2+]o after microiontophoresis of a cerebellar transmitter, glutamate. The ratios of ion shifts in the x- and y-axes in the granular layer were close to unity, with a ratio of 1.04 +/- 0.08 for the rise in [K+]o and 1.03 +/- 0.17 for the decrease in [Ca2+]o. In contrast, ion shifts in the molecular layer had an x:y ratio of 1.44 +/- 0.14 for the rise in [K+]o and 2.10 +/- 0.42 for the decrease in [Ca2+]o. 7. These data demonstrate that the structure of cellular aggregates can channel the migration of substances in the extracellular microenvironment, and this could be a mechanism for volume transmission of chemical signals. For example, the preferred diffusion direction of glutamate along the parallel fibers would help constrain an incoming excitatory stimulus to stay "on-beam."
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Rajmohan, T., R. Vinayagamoorthy, and K. Mohan. "Review on effect machining parameters on performance of natural fibre–reinforced composites (NFRCs)." Journal of Thermoplastic Composite Materials 32, no. 9 (September 5, 2018): 1282–302. http://dx.doi.org/10.1177/0892705718796541.
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In the modern years, natural fibre composites have been converted into significant materials in many industries such as automotive, aerospace and and so on. Several types of natural fibre composites, particularly plant-based fibre composites, have been developed and tested. However, their mixed nature, engineer’s requirement of experience, an understanding of machinability databases, limit setting and trouble in manufacturing are barriers to extensive use of composites. The final shape of the natural fibre–reinforced composites (NFRCs) are obtained by conventional and unconventional machining. Machining of these composites generates confront due to the heterogeneous and anisotropic nature. Different methodologies and tools are intended to overcome the machining defects. In this article, a wide range of literature review on machining of NFRCs is examined with focus on conventional and unconventional machining operation. This article also discusses the influences of machining parameters and optimum conditions for machining of NFRCs.
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Grechka, Vladimir Y. "Transverse isotropy versus lateral heterogeneity in the inversion of P-wave reflection traveltimes." GEOPHYSICS 63, no. 1 (January 1998): 204–12. http://dx.doi.org/10.1190/1.1444314.
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Nonelliptic transverse isotropy may cause pronounced nonhyperbolic moveout of long‐spread P-wave reflection data. Lateral heterogeneity may alter the moveout in much the same way, and one can expect that a given P-wave reflection moveout may be interpreted equally well in terms of parameters of homogeneous transversely isotropic (TI) or laterally heterogeneous (LH) isotropic models. Here, the common‐midpoint (CMP) moveout of a P-wave reflected from a horizontal interface beneath a weakly laterally heterogeneous medium that is also weakly transversely isotropic is represented analytically in the form similar to that in homogeneous TI media. Both the normal‐moveout (NMO) velocity and the quartic moveout coefficient contain derivatives of the zero‐ offset traveltime t0 and the NMO velocity Vnmo with respect to the lateral coordinate. Despite the presence of heterogeneity, nonhyperbolic velocity analysis can be performed in the same way as in homogeneous TI models. If all parameters of the medium are linear functions of the lateral coordinate, heterogeneity does not influence the results of inversion for the anisotropic parameter η. However, to find η in the case of general lateral heterogeneity, the second derivative of Vnmo and the fourth derivative of t0 are needed. Since these high‐order derivatives are calculated from the data measured at discrete points by numerical differentiation, stability of η estimation is further reduced as compared to that in homogeneous TI media. Consequently, the trade‐off between anisotropy and heterogeneity significantly complicates the inversion of P-wave reflection traveltimes, even in the simplest model of a single plane layer.
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Pech, Andres, Ilya Tsvankin, and Vladimir Grechka. "Quartic moveout coefficient: 3D description and application to tilted TI media." GEOPHYSICS 68, no. 5 (September 2003): 1600–1610. http://dx.doi.org/10.1190/1.1620634.
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Nonhyperbolic (long‐spread) moveout provides essential information for a number of seismic inversion/processing applications, particularly for parameter estimation in anisotropic media. Here, we present an analytic expression for the quartic moveout coefficient A4 that controls the magnitude of nonhyperbolic moveout of pure (nonconverted) modes. Our result takes into account reflection‐point dispersal on irregular interfaces and is valid for arbitrarily anisotropic, heterogeneous media. All quantities needed to compute A4 can be evaluated during the tracing of the zero‐offset ray, so long‐spread moveout can be modeled without time‐consuming multioffset, multiazimuth ray tracing. The general equation for the quartic coefficient is then used to study azimuthally varying nonhyperbolic moveout of P‐waves in a dipping transversely isotropic (TI) layer with an arbitrary tilt ν of the symmetry axis. Assuming that the symmetry axis is confined to the dip plane, we employed the weak‐anisotropy approximation to analyze the dependence of A4 on the anisotropic parameters. The linearized expression for A4 is proportional to the anellipticity coefficient η ≈ ε − δ and does not depend on the individual values of the Thomsen parameters. Typically, the magnitude of nonhyperbolic moveout in tilted TI media above a dipping reflector is highest near the reflector strike, whereas deviations from hyperbolic moveout on the dip line are substantial only for mild dips. The azimuthal variation of the quartic coefficient is governed by the tilt ν and reflector dip φ and has a much more complicated character than the NMO–velocity ellipse. For example, if the symmetry axis is vertical (VTI media, ν = 0) and the dip φ < 30°, A4 goes to zero on two lines with different azimuths where it changes sign. If the symmetry axis is orthogonal to the reflector (this model is typical for thrust‐and‐fold belts), the strike‐line quartic coefficient is defined by the well‐known expression for a horizontal VTI layer (i.e., it is independent of dip), while the dip‐line A4 is proportional to cos4 φ and rapidly decreases with dip. The high sensitivity of the quartic moveout coefficient to the parameter η and the tilt of the symmetry axis can be exploited in the inversion of wide‐azimuth, long‐spread P‐wave data for the parameters of TI media.
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Kamath, Nishant, and Ilya Tsvankin. "Full-waveform inversion of multicomponent data for horizontally layered VTI media." GEOPHYSICS 78, no. 5 (September 1, 2013): WC113—WC121. http://dx.doi.org/10.1190/geo2012-0415.1.
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Although full-waveform inversion (FWI) has shown significant promise in reconstructing heterogeneous velocity fields, most existing methodologies are limited to acoustic models. We extend FWI to multicomponent (PP and PS) data from anisotropic media, with the current implementation limited to a stack of horizontal, homogeneous VTI (transversely isotropic with a vertical symmetry axis) layers. The algorithm is designed to estimate the interval vertical P- and S-wave velocities ([Formula: see text] and [Formula: see text]) and Thomsen parameters [Formula: see text] and [Formula: see text] from long-spread PP and PSV reflections. The forward-modeling operator is based on the anisotropic reflectivity technique, and the inversion is performed in the time domain using the gradient (Gauss-Newton) method. We employ nonhyperbolic semblance analysis and Dix-type equations to build the initial model. To identify the medium parameters constrained by the data, we perform eigenvalue/eigenvector decomposition of the approximate Hessian matrix for a VTI layer embedded between isotropic media. Analysis of the eigenvectors shows that the parameters [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] (density is assumed to be known) can be resolved not only by joint inversion of PP and PS data, but also with PP reflections alone. Although the inversion becomes more stable with increasing spreadlength-to-depth ([Formula: see text]) ratio, the parameters of the three-layer model are constrained even by PP data acquired on conventional spreads ([Formula: see text]). For multilayered VTI media, the sensitivity of the objective function to the interval parameters decreases with depth. Still, it is possible to resolve [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] for the deeper layers using PP-waves, if the ratio [Formula: see text] for the bottom of the layer reaches two. Mode-converted waves provide useful additional constraints for FWI, which become essential for smaller spreads. The insights gained here by examining horizontally layered models should help guide the inversion for heterogeneous TI media.
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Amra, C., D. Petiteau, M. Zerrad, S. Guenneau, G. Soriano, B. Gralak, M. Bellieud, D. Veynante, and N. Rolland. "Analogies between optical propagation and heat diffusion: applications to microcavities, gratings and cloaks." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471, no. 2183 (November 2015): 20150143. http://dx.doi.org/10.1098/rspa.2015.0143.
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A new analogy between optical propagation and heat diffusion in heterogeneous anisotropic media has been proposed recently by three of the present authors. A detailed derivation of this unconventional correspondence is presented and developed. In time harmonic regime, all thermal parameters are related to optical ones in artificial metallic media, thus making possible to use numerical codes developed for optics. Then, the optical admittance formalism is extended to heat conduction in multilayered structures. The concepts of planar microcavities, diffraction gratings and planar transformation optics for heat conduction are addressed. Results and limitations of the analogy are emphasized.
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Salibindla, Ashwanth K. R., Rabin Subedi, Victor C. Shen, Ashik U. M. Masuk, and Rui Ni. "Dissolution-driven convection in a heterogeneous porous medium." Journal of Fluid Mechanics 857 (October 15, 2018): 61–79. http://dx.doi.org/10.1017/jfm.2018.732.
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Motivated by subsurface carbon sequestration, an experimental investigation of dissolution-driven Rayleigh–Darcy convection using two miscible fluids in a Hele-Shaw cell is conducted. A thin horizontal layer of circular impermeable discs is inserted to create an environment with heterogeneous and anisotropic permeability. The Sherwood number that measures the convective mass transfer rate between two fluids at the interface is linked to different parameters of the disc layer, including the disc size, spacing, layer permeability and its relative height with respect to the fluid interface. It is surprising that the convective mass transfer rate in our configuration is dominated by the disc spacing, but almost independent of either the disc size or the mean permeability of the layer. To explain this dependence, the convective mass transfer rate is decomposed into the number, velocity and density contrast of fingers travelling through the disc layer. Both the number and density contrast of fingers show dependences on the disc layer permeability, even though the product of them, the mass transfer rate, does not. In addition, the density contrast also shows a non-monotonic dependence on the disc spacing. The transition point is at a spacing that is close to the finger width. Based on this observation, a simple model based on mixing and scale competition is proposed, and it shows an excellent agreement with the experimental results.
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Sarkar, Debashish, and Ilya Tsvankin. "Migration velocity analysis in factorized VTI media." GEOPHYSICS 69, no. 3 (May 2004): 708–18. http://dx.doi.org/10.1190/1.1759457.
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One of the main challenges in anisotropic velocity analysis and imaging is simultaneous estimation of velocity gradients and anisotropic parameters from reflection data. Approximating the subsurface by a factorized VTI (transversely isotropic with a vertical symmetry axis) medium provides a convenient way of building vertically and laterally heterogeneous anisotropic models for prestack depthmigration. The algorithm for P‐wave migration velocity analysis (MVA) introduced here is designed for models composed of factorized VTI layers or blocks with constant vertical and lateral gradients in the vertical velocity VP0. The anisotropic MVA method is implemented as an iterative two‐step procedure that includes prestack depth migration (imaging step) followed by an update of the medium parameters (velocity‐analysis step). The residual moveout of the migrated events, which is minimized during the parameter updates, is described by a nonhyperbolic equation whose coefficients are determined by 2D semblance scanning. For piecewise‐factorized VTI media without significant dips in the overburden, the residual moveout of P‐wave events in image gathers is governed by four effective quantities in each block: (1) the normal‐moveout velocity Vnmo at a certain point within the block, (2) the vertical velocity gradient kz, (3) the combination kx[Formula: see text] of the lateral velocity gradient kx and the anisotropic parameter δ, and (4) the anellipticity parameter η. We show that all four parameters can be estimated from the residual moveout for at least two reflectors within a block sufficiently separated in depth. Inversion for the parameter η also requires using either long‐spread data (with the maximum offset‐to‐depth ratio no less than two) from horizontal interfaces or reflections from dipping interfaces. To find the depth scale of the section and build a model for prestack depth migration using the MVA results, the vertical velocity VP0 needs to be specified for at least a single point in each block. When no borehole information about VP0 is available, a well‐focused image can often be obtained by assuming that the vertical‐velocity field is continuous across layer boundaries. A synthetic test for a three‐layer model with a syncline structure confirms the accuracy of our MVA algorithm in estimating the interval parameters Vnmo, kz, kx, and η and illustrates the influence of errors in the vertical velocity on the image quality.
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GHOSH, SOMNATH, D. M. VALIVETI, CHAO HU, and JIE BAI. "A MULTISCALE FRAMEWORK FOR CHARACTERIZATION AND MODELING DUCTILE FRACTURE IN HETEROGENEOUS ALUMINUM ALLOYS." Journal of Multiscale Modelling 01, no. 01 (January 2009): 21–55. http://dx.doi.org/10.1142/s1756973709000050.
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This paper develops three components contributing to the overall framework of multiscale modeling of ductile fracture in aluminum alloys. The first module is morphology-based domain partitioning (MDP) as a pre-processor to the multiscale modeling. This module delineates regions of statistical homogeneity and inhomogeneity with a systematic three-step process that is based on geometric features of morphology. The second module is detailed micromechanical analysis of particle fragmentation and matrix cracking of heterogeneous microstructures. A locally enriched VCFEM or LE-VCFEM is developed to incorporate ductile failure through matrix cracking in the form of void growth and coalescence using nonlocal Gurson–Tvergaard–Needleman (GTN) model. The third module develops a homogenized anisotropic plasticity-damage model in the form of GTN model for macroscopic analysis. Parameters in this GTN model are calibrated from results of homogenization of microstructural variables obtained from microstructural RVE. Numerical examples elucidate the strength of components of the overall framework.
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Grechka, Vladimir, and Ilya Tsvankin. "Processing‐induced anisotropy." GEOPHYSICS 67, no. 6 (November 2002): 1920–28. http://dx.doi.org/10.1190/1.1527092.
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Processing of seismic data is often performed under the assumption that the velocity distribution in the subsurface can be approximated by a macromodel composed of isotropic homogeneous layers or blocks. Despite being physically unrealistic, such models are believed to be sufficient for describing the kinematics of reflection arrivals. In this paper, we examine the distortions in normal‐moveout (NMO) velocities caused by the intralayer vertical heterogeneity unaccounted for in velocity analysis. To match P‐wave moveout measurements from a horizontal or a dipping reflector overlaid by a vertically heterogeneous isotropic medium, the effective homogeneous overburden has to be anisotropic. This apparent anisotropy is caused not only by velocity monotonically increasing with depth, but also by random velocity variations similar to those routinely observed in well logs. Assuming that the effective homogeneous medium is transversely isotropic with a vertical symmetry axis (VTI), we express the VTI parameters through the actual depth‐dependent isotropic velocity function. If the reflector is horizontal, combining the NMO and vertical velocities always results in nonnegative values of Thomsen's coefficient δ. For a dipping reflector, the inversion of the P‐wave NMO ellipse yields a nonnegative Alkhalifah‐Tsvankin coefficient η that increases with dip. The values of η obtained by two other methods (2‐D dip‐moveout inversion and nonhyperbolic moveout analysis) are also nonnegative but generally differ from that needed to fit the NMO ellipse. For truly anisotropic (VTI) media, the influence of vertical heterogeneity above the reflector can lead to a bias toward positive δ and η estimates in velocity analysis.
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Gosselin, Jeremy M., Pascal Audet, Andrew J. Schaeffer, Fiona A. Darbyshire, and Clément Estève. "Azimuthal anisotropy in Bayesian surface wave tomography: application to northern Cascadia and Haida Gwaii, British Columbia." Geophysical Journal International 224, no. 3 (November 20, 2020): 1724–41. http://dx.doi.org/10.1093/gji/ggaa561.
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SUMMARY Surface wave tomography is a valuable tool for constraining azimuthal anisotropy at regional scales. However, sparse and uneven coverage of dispersion measurements make meaningful uncertainty estimation challenging, especially when applying subjective model regularization. This paper considers azimuthal anisotropy constrained by measurements of surface wave dispersion data within a Bayesian trans-dimensional (trans-d) tomographic inversion. A recently proposed alternative model parametrization for trans-d inversion is implemented in order to produce more realistic models than previous studies considering trans-d surface wave tomography. The reversible-jump Markov chain Monte Carlo sampling technique is used to numerically estimate the posterior probability density of the model parameters. Isotropic and azimuthally anisotropic components of surface wave group velocity maps (and their associated uncertainties) are estimated while avoiding model regularization and allowing model complexity to be determined by the data information content. Furthermore, data errors are treated as unknown, and solved for within the inversion. The inversion method is applied to measurements of surface wave dispersion from regional earthquakes recorded over northern Cascadia and Haida Gwaii, a region of complex active tectonics but highly heterogeneous station coverage. Results for isotropic group velocity are consistent with previous studies that considered the southern part of the study region over Cascadia. Azimuthal anisotropic fast-axis directions are generally margin-parallel between Vancouver Island and Haida Gwaii, with a small change in direction and magnitude along the margin which may be attributed to the changing tectonic regime (from subduction to transform tectonics). Estimated errors on the dispersion data (solved for within the inversion) reveal a correlation between surface wave period and the dependence of data errors on travel path length. This paper demonstrates the value of considering azimuthal anisotropy within Bayesian tomographic inversions. Furthermore, this work provides structural context for future studies of tectonic structure and dynamics of northern Cascadia and Haida Gwaii, with the aim of improving our understanding of seismic and tsunami hazards.
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Mańkowski, Jarosław. "Breaking Process Modeling Using FEM – Proposition of a Method for Identification of Material Data and for Identification Features Job Contact." Advanced Materials Research 1036 (October 2014): 592–97. http://dx.doi.org/10.4028/www.scientific.net/amr.1036.592.
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Brittle materials belong to the group of brittle materials with a very complex structure. As heterogeneous and anisotropic materials, are randomly distributed discontinuity structures such as scratches, cracks, pores. One of the problems, which often occurs during the analysis, is to identify the properties of materials data and identify the characteristics of the impact of the tool on a brittle material. This paper presents a method of identification of material parameters and a method of modelling the contact problems for limestone Morawica. Tests and analyzes were performed for a roller compression test. Very good convergence of the results of analysis and of the results of an experiment performed on a real object was obtained.
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Grechka, Vladimir, and Ilya Tsvankin. "Inversion of azimuthally dependent NMO velocity in transversely isotropic media with a tilted axis of symmetry." GEOPHYSICS 65, no. 1 (January 2000): 232–46. http://dx.doi.org/10.1190/1.1444714.
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Just as the transversely isotropic model with a vertical symmetry axis (VTI media) is typical for describing horizontally layered sediments, transverse isotropy with a tilted symmetry axis (TTI) describes dipping TI layers (such as tilted shale beds near salt domes) or crack systems. P-wave kinematic signatures in TTI media are controlled by the velocity [Formula: see text] in the symmetry direction, Thomsen’s anisotropic coefficients ε and δ, and the orientation (tilt ν and azimuth β) of the symmetry axis. Here, we show that all five parameters can be obtained from azimuthally varying P-wave NMO velocities measured for two reflectors with different dips and/or azimuths (one of the reflectors can be horizontal). The shear‐wave velocity [Formula: see text] in the symmetry direction, which has negligible influence on P-wave kinematic signatures, can be found only from the moveout of shear waves. Using the exact NMO equation, we examine the propagation of errors in observed moveout velocities into estimated values of the anisotropic parameters and establish the necessary conditions for a stable inversion procedure. Since the azimuthal variation of the NMO velocity is elliptical, each reflection event provides us with up to three constraints on the model parameters. Generally, the five parameters responsible for P-wave velocity can be obtained from two P-wave NMO ellipses, but the feasibility of the moveout inversion strongly depends on the tilt ν. If the symmetry axis is close to vertical (small ν), the P-wave NMO ellipse is largely governed by the NMO velocity from a horizontal reflector Vnmo(0) and the anellipticity coefficient η. Although for mild tilts the medium parameters cannot be determined separately, the NMO-velocity inversion provides enough information for building TTI models suitable for time processing (NMO, DMO, time migration). If the tilt of the symmetry axis exceeds 30°–40° (e.g., the symmetry axis can be horizontal), it is possible to find all P-wave kinematic parameters and construct the anisotropic model in depth. Another condition required for a stable parameter estimate is that the medium be sufficiently different from elliptical (i.e., ε cannot be close to δ). This limitation, however, can be overcome by including the SV-wave NMO ellipse from a horizontal reflector in the inversion procedure. While most of the analysis is carried out for a single layer, we also extend the inversion algorithm to vertically heterogeneous TTI media above a dipping reflector using the generalized Dix equation. A synthetic example for a strongly anisotropic, stratified TTI medium demonstrates a high accuracy of the inversion (subject to the above limitations).
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Singh, Abhishek Kumar, Amrita Das, Kshitish Ch Mistri, Shreyas Nimishe, and Siddhartha Koley. "Effect of corrugation on the dispersion of Love-type wave in a layer with monoclinic symmetry, overlying an initially stressed transversely isotropic half-space." Multidiscipline Modeling in Materials and Structures 13, no. 2 (August 14, 2017): 308–25. http://dx.doi.org/10.1108/mmms-10-2016-0053.
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Purpose The purpose of this paper is to investigate the effect of corrugation, wave number, initial stress and the heterogeneity of the media on the phase velocity of the Love-type wave. Moreover, the paper aims to have a comparative study of the presence and absence of anisotropy, heterogeneity, corrugation and initial stress in the half-space, which serve as a focal theme of the study. Design/methodology/approach The present paper modelled the propagation of the Love-type wave in a corrugated heterogeneous monoclinic layer lying over an initially stressed heterogeneous transversely isotropic half-space. The method of separation of variables is used to procure the dispersion relation. Findings The closed form of dispersion relation is obtained and found to be in well agreement to the classical Love wave equation. Neglecting the corrugation at either of the boundary surfaces, expressions of the phase velocity of the Love-type wave are deduced in closed form as special cases of the problem. It is established through the numerical computation of the obtained relation that the concerned affecting parameters have significant impact on the phase velocity of the Love-type wave. Also, a comparative study shows that the anisotropic case favours more to the phase velocity as comparison to the isotropic case. Originality/value Although many attempts have been made to study the effect of corrugated boundaries on reflection and refraction of seismic waves, but the effect of corrugated boundaries on the dispersion of surface wave (which are dispersive in nature) propagating through mediums pertaining various incredible features still needs to be investigated.
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Muszyński, Lech. "Imaging wood plastic composites (WPCs): X-ray computed tomography, a few other promising techniques, and why we should pay attention." BioResources 4, no. 3 (July 28, 2009): 1210–21. http://dx.doi.org/10.15376/biores.4.3.1210-1221.
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Wood plastic composites are complex, anisotropic, and heterogeneous materials. A key to increasing the share of the WPC materials in the market is developing stronger, highly engineered WPCs characterized by greater structural performance and increased durability. These are achieved by enhanced manufacturing processes, more efficient profile designs, and new formulations providing better interaction between the wood particles and the plastic matrix. Significant progress in this area is hard to imagine without better understanding of the composite performance and internal bond durability on the micro-mechanical level, and reliable modeling based on that understanding. The objective of this paper is to present a brief review of promising material characterization techniques based on advanced imaging technologies and inverse problem methodology, which seem particularly suitable for complex heterogeneous composites. Full-field imaging techniques and specifically X-ray computed tomography (CT) combined with numerical modeling tools have a potential to advance the fundamental knowledge on the effect of manufacturing parameters on the micromechanics of such materials and their response to loads and environmental exposure.
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Wang, Shu Hong, Deng Pan Qiao, Peng Jia, and Nan Zhang. "Micromechanical Analysis of Excavation Damaged Zone in Anisotropic Rock Mass." Key Engineering Materials 324-325 (November 2006): 81–84. http://dx.doi.org/10.4028/www.scientific.net/kem.324-325.81.
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Rock is a heterogeneous and anisotropic compound material, containing many shear surfaces, cracks, weak surfaces and faults. Damage and failure in a rock mass can occur through sliding along persistent discontinuities, or fractures. A new micromechanical approach to modeling the mechanical behavior of excavation damaged or disturbed zone (EDZ) of anisotropic rock is presented based on knowledge of the inhomogeneity of rock. In this numerical model, damage is analyzed as a direct consequence of microcracks growth. A study of the effect of elastic and failure anisotropy plus inhomogeneity on the underground excavations reveals that the modes of failure can be significantly influenced by the rock structure on the small and large scales. Fractures that develop progressively around underground excavations can be simulated using a numerical code called RFPA (Realistic Failure Process Analysis). This code incorporates the microscopic inhomogeneity in Young’s modulus and strength characteristic of rock. In the numerical models of a rock mass, values of Young’s modulus and rock strength are realized according to a Weibull distribution in which the distribution parameters represent the level of inhomogeneity of the medium. Another notable feature of this code is that no a priori assumptions need to be made about where and how fracture and failure will occur – cracking can occur spontaneously and can exhibit a variety of mechanisms when certain local stress conditions are met. These unique features have made RFPA capable of simulating the whole fracturing process of initiation, propagation and coalescence of fractures around excavations under a variety of loading conditions. The results of the simulations show that the code can be used not only to produce fracturing patterns similar to those reported in previous studies, but also to predict fracturing patterns under a variety of loading conditions. The numerical model was able to reproduce the associated complex stress patterns and the microseismic emission distribution for a variety of rock structural conditions.