Homogeneous Anisotropic Medium Research Articles

A method for detecting Dyakonov surface waves at an interface of two anisotropic media

The possibility of excitation and detection of Dyakonov surface waves at the interface of two identical homogeneous anisotropic media by means of the effect of polarization conversion in reflection is investigated theoretically. Excitation of the Dyakonov wave is uniquely related to a peculiarity in the reflection coefficient near a certain incidence angle determined only by parameters of the medium. The largest effect of conversion is achieved for the crystal plane exhibiting the largest difference of refractive indices.

Upscaling in orthorhombic media: Behavior of elastic parameters in heterogeneous fractured earth

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.

Determining the source time function using the modified matrix method

The modified matrix method of construction of wavefield on the free surface of an anisotropic medium is proposed. The earthquake source represented by a randomly oriented force or a seismic moment tensor is placed on an arbitrary boundary of a layered anisotropic medium. The theory of the matrix propagator in a homogeneous anisotropic medium by introducing a “wave propagator” is presented. It is shown that the matrix propagator can be represented by a “wave propagator” in each layer for anisotropic layered medium. The matrix propagator P(z, z0=0) acts on the free surface of the layered medium and generates stress-displacement vector at depth z. The displacement field on the free surface of an anisotropic medium is obtained from the received system of equations considering the radiation condition and that the free surface is stressless. The new method determining source time function in anisotropic medium for three different types of seismic source is validated.

Optical Surface Transformation: Changing the optical surface by homogeneous optic-null medium at will.

A new theory on designing electromagnetic/optical devices is proposed, namely, an optical surface transformation (OST). One arbitrary surface can establish the corresponding relationship with another surface entirely optically with an optic-null medium (ONM), (i.e. the electromagnetic wave propagates from one surface to its equivalent surface without any phase delay). Many novel optical devices can be designed by an OST with the help of an ONM. Compared with traditional devices designed by Transformation Optics, our optical surface-reshaping devices have two main advantages. Firstly, the design process is very simple (i.e. we do not need to consider any mathematics on how to make a coordinate transformation, and what we need to do is simply to design the shapes of the input and the output surfaces of the devices). Secondly, we only need one homogeneous anisotropic medium to realize all devices designed by this method. Our method will explore a new way to design novel optical devices without considering any coordinate transformations.

Semi-analytical modeling of acoustic beam divergence in homogeneous anisotropic half-spaces

Beam divergences of acoustical fields in semi-infinite homogeneous anisotropic media are calculated based on a semi-analytical model. The model for a plane source in a semi-infinite homogeneous anisotropic medium is proposed as an extended model for a point source in an infinite medium. Beam divergences propagating along crystallographic axes 〈100〉, 〈110〉, and 〈111〉 in a cubic crystal, a single crystalline Ni-based alloy, are measured and compared to calculation results for verifying the model. The contribution of beam divergence attenuation to the total attenuation for propagating in anisotropic polycrystalline materials is quantitatively evaluated in isolation from scattering attenuation effects.

Application of a Modified Boundary-Element Method to Problems of the Elasticity Theory in Piecewise Homogeneous Anisotropic Media

UDC 539.3 We study the problem of determination of the stress-strain state of a thin elastic orthotropic plate with orthotropic inclusions of any shape under loads applied to its edges. To solve the problem, we propose a modified direct boundary-element method capable of the simultaneous determination of all necessary quantities on the contact surfaces of each inclusion with the matrix by using a two-dimensional approximation of the components of the vector of displacements and stress tensor in every element of the discretization. The governing input relations are obtained for all components of the vector of displacements and stress tensor on the boundary and at inner points of the body under consideration. Recent years are marked by the extensive application of materials and structural elements with anisotropic properties. The use of these materials makes it possible to get the required operating characteristics of strength and stiffness. For their efficient and safe application, we need the exact and reliable numerical methods aimed at the determination of their stress-strain state. The customary numerical methods based on the discretization of the domain itself (finite-element method) or its boundary (boundary-element method) exhibit high efficiency in the case where the corresponding fundamental solutions of the problem under study are available. The presence of anisotropy increases the number of elastic constants in Hooke’s law and, hence, complicates the procedure of construction of the fundamental solutions. However, the fundamental solutions of the two-dimensional problems of elasticity theory are, as a rule, available [5, 6]. The analysis of the stress-strain state for these class of problems was carried out, e.g., in [4, 7, 8]. If we use the ordinary boundary-element method, then the solution of boundary integral equations enables one to find only a part of the components of the stress tensor, namely, the components appearing in the contact conditions. To find the other components of the stress tensor, it is necessary to perform the limit transition both in the integral representations of the vector of displacements and in their differentiated representations. The two-dimensional approximation of displacements on the boundaries of inclusions [1] removes the necessity of differentiation of the representations and makes it possible to determine all components of the vector of displacements and stress tensor on the boundaries of the analyzed bodies already directly from the boundary integral equations. In what follows, we apply this approach to the construction of constitutive relations for the plane problem of elasticity for orthotropic bodies. Consider a thin elastic orthotropic plate with orthotropic inclusions of any shape. The plate suffers the action of muss forces Xi and distributed forces pi applied to its edges. Thus, it can be regarded as an elastic orthotropic matrix with elastic orthotropic inclusions.

A fine-layered medium of finite-thickness in an electromagnetic field

It is shown that the general solution of Maxwell’s equations in an inhomogeneous isotropic periodic fine-layered medium consisting of n pairs of different homogeneous isotropic plane layers coincides, as n → ∞, with the general solution of these equations in a homogeneous anisotropic medium formed by a uniaxial crystal of the same thickness as that of the initial inhomogeneous medium.

Inverse problem for the identification of a memory kernel from Maxwell’s system integro-differential equations for a homogeneous anisotropic media

We consider the problem of reconstructing the time-dependent history of electromagnetic fields from Maxwell’s system of equations for an homogeneous anisotropic medium. As additional information, the Fourier image of electric and magnetic field intensity vectors for values ν = 0 of transformation parameter are given. It is shown that if the given functions satisfy some conditions of agreement and smoothness, the solution of the posed problem is uniquely defined in a class of continuously differentiable functions.

Anisotropic wavefronts and Laguerre geometry

Motivated by the study of wavefronts in anisotropic media, we propose an incidence geometry for anisotropic spheres in a Finsler-Minkowski space. An anisotropic version of the Laguerre functional is considered. In some circumstances, this functional can be used to determine that two wavefronts observed at distinct times in a homogeneous anisotropic medium do not originate from the same source.

On the source-frequency dependence of fracture-orientation estimates from shear-wave transmission experiments

Shear-wave propagation through anisotropic fractured or cracked media can provide valuable information about these fracture swarms and their orientations. The main goal of this work is to recover information about fracture orientation based on the shear waveforms (S-waveforms). For this study, we carried out ultrasonic S-wave measurements in a synthetic physical model made of epoxy resin (isotropic matrix proxy), with small cylindrical rubber strips as inclusions (artificial cracks) inserted in it to simulate a homogeneous anisotropic medium. In these experiments, we used low, intermediate, and high frequency shear-wave sources, with frequencies 90, 431, and 840kHz. We integrated and interpreted the resulting S-wave seismograms, cross-correlation panels and anisotropic parameter-analysis curves. We were able to estimate the crack orientation in single-orientation fracture zones. The high frequency peaks associated with scattered S-waves provided interpretable information about the fracture orientations when the propagation direction was parallel to the fracture plane. The analysis was possible utilizing results from frequency-versus-polarization-angle curves. Moreover, we applied a bandpass filtering process to the intermediate and high frequency seismograms in order to obtain low frequency seismograms. A spectral analysis using frequency–wavenumber (F–K) spectra supports this filtering process. The results obtained using an analysis of cross-correlograms and the Thomsen parameter γ extracted from filtered high-frequency data were quite similar to those obtained using a low-frequency source. This highlighted the possibility of using less expensive high-frequency sources to recover information about the fracture set.

Shear-wave group-velocity surfaces in low-symmetry anisotropic media

Shear waves excited by natural sources constitute a significant part of useful energy recorded in downhole microseismic surveys. In rocks, such as fractured shales, exhibiting symmetries lower than transverse isotropy (TI), the shear wavefronts are always multivalued in certain directions, potentially complicating the data processing and analysis. This paper discusses a basic tool — the computation of the phase and group velocities of all waves propagating along a given ray — that intends to facilitate the understanding of geometries of the shear wavefronts in homogeneous anisotropic media. With this tool, arbitrarily complex group-velocity surfaces can be conveniently analyzed, providing insights into possible challenges to be faced when processing shear waves in anisotropic velocity models that have symmetries lower than TI. Among those challenges are complicated multipathing and the presence of cones of directions, known as internal refraction cones, in which no fast shear waves propagate and the entire shear portion of the body-wave seismic data consists of several branches of the slow shear wavefronts.

SURFACE TRANSFORMATION WITH HOMOGENOUS OPTIC-NULL MEDIUM

An optical surface transformation (OST) method is proposed briefly in this short paper. Compared with Transformation Optics (TO), we do not need to consider what kinds of coordinate transformation should be used when designing a novel device, but only need to choose the shapes of two end surfaces (namely, the input and output surfaces of the device), which are linked by an optic-null medium (ONM) that is a highly anisotropic homogeneous medium. All devices designed by OST can be realized by some ONM. The design process of an optical device with some pre-designed function can be converted to the simple choice of the shape and size of the optical surfaces with the OST, which will become a simple and yet innovative way to design electromagnetic/optical devices.

Mathematical and neural network prediction model of three-phase immiscible recovery process in porous media

Scaling analysis of fluids displacement in porous media is a reliable fast method to evaluate the displacement performance of different oil production processes under various conditions. This paper describes scaling of multiphase flow through permeable media with special attention to three-phase immiscible water alternating gas flooding processes. The procedure of inspectional analysis (IA) was used to determine relevant dimensionless groups. It was found that scaling immiscible water alternative gas (IWAG) displacement in a two-dimensional homogeneous anisotropic medium needs matching of seven dimensionless scaling groups. A series of numerical sensitivity studies were conducted to determine the magnitude of scaling groups and their interaction with recovery factors. None of the dimensionless groups individually could correlate the efficiency of the process in all the circumstances. Two predictor models, a mathematical model and an artificial neural network (ANN) model, were developed to map the effective combinations of the dimensionless scaling groups. For the mathematical model, a new combined dimensionless group which incorporates all the dominant scaling groups has been derived. Functional relationship between the combined group and fractional oil recovery is investigated. This relation has potential application in prediction of displacement efficiency. To prepare the ANN prediction model, scaling groups obtained from fine mesh simulation were used as input parameters. The agreement between the simulation methods and ANN model validate the applicability of the model to predict the recovery factors for the range of the groups which were not included in the simulations. The comparison study of the models showed the superior performance of ANN model compared to the mathematical model. The ANN model can be used to propose a proper development plan for a reservoir and/or to determine the optimal plan of operation.

How nonreciprocal is an effective permittivity matrix?

ABSTRACTThe property of nonreciprocity in electromagnetic structures is a pivotal feature when designing useful devices such as directional phase shifters, circulators, isolators, and gyrators. The performance of these components is judged by the “nonreciprocity index,” indicating the degree of nonreciprocity. In this work, we consider a slab filled with a homogeneous anisotropic medium with an arbitrary and full permittivity matrix. The scattering parameters of the formulated four‐port network are analytically evaluated and a “nonreciprocity index” is defined. The variations of this function with respect to the complex elements of the effective permittivity matrix are shown and general conclusions are drawn. © 2014 Wiley Periodicals, Inc. Microwave Opt Technol Lett 56:2018–2021, 2014

A method for the analytical description of coupled-field waves in various anisotropic media

The formalism of the matricant method based on constructing the optimal structure of the matrix of fundamental solutions to the governing differential equations is presented. The structures of the coefficient matrices of the governing equations and the structure of the matricant are determined for the acoustic coupled-field waves in elastic, thermoelastic, piezoelectric, and piezomagnetic anisotropic media. The analytical expressions of matricants are obtained for various homogeneous anisotropic media. The efficiency of the method is demonstrated in the case for an analysis of wave propagation in periodic structures. As examples, the secular equations for dispersive waves in layered and periodic structures are derived.

Tunnel Internal Crack in a Piecewise Homogeneous Anisotropic Space

UDC 539.3 The problem of internal tunnel crack in a piecewise homogeneous anisotropic medium is reduced to a system of three singular integral equations. We propose an efficient numerical-analytic method for the solution of the obtained system and establish the regularities of the behavior of stress intensity factors in the case where the crack approaches the plane of joint of dissimilar anisotropic half spaces.

The Modification of the Matrix Method for the Modelling of Propagation of the Body Waves

The modification of the matrix method of construction of wavefield on the free surface of an anisotropic medium is presented. The earthquake source represented by a randomly oriented force or a seismic moment tensor is placed on an arbitrary boundary of a layered anisotropic medium. The theory of the matrix propagator in a homogeneous anisotropic medium by introducing a "wave propagator" is presented. It is shown that for anisotropic layered medium the matrix propagator can be represented by a "wave propagator" in each layer. The matrix propagator P(z,z0=0) acts on the free surface of the layered medium and generates stress-displacement vector at depth z. The displacement field on the free surface of an anisotropic medium is obtained from the received system of equations considering the radiation condition and that the free surface is stressless. The approbation of the modification of the matrix method for isotropic and anisotropic media with TI symmetry is done. A comparative analysis of our results with the synthetic seismic records obtained by other methods and published in foreign papers is executed.

Reservoir fracture characterization from seismic scattered waves

Fracture characterization in an oil or gas reservoir is very important for field development and exploration because natural fracture systems can dominate the fluid drainage pattern in a reservoir. Traditional seismic methods for fracture characterization, such as amplitude variations with offset and azimuth and shear wave birefringence, are based on the equivalent medium theory with the assumption that fracture dimensions and spacing are small relative to the seismic wave length, so a fractured unit is equivalent to a homogeneous anisotropic medium. However, fractures on the order of the seismic wavelength are also very important for enhanced oil recovery, and they are one of the important subsurface scattering sources that generate scattered seismic waves. In this paper, we present an approach for detecting fracture direction through computing the fracture transfer function using surface recorded seismic scattered waves. The applicability and accuracy of this approach is validated through both laboratory experiment and numerical simulation. Our results show that fracture direction can be robustly determined by using our approach even for heterogeneous models containing complex non-periodic orthogonal fractures with varying fracture spacing and compliance.

Thermal inclusions inside a bounded medium

In the context of thermal conduction taken as a prototype of numerous transport phenomena, a general method is elaborated to study Eshelby's problem of inclusions inside a bounded homogeneous anisotropic medium. This method consists in: (i) recasting by a linear transformation the initial problem into Eshelby's problem of the transformed inclusion inside the transformed finite isotropic medium and (ii) decomposing Eshelby's problem of a thermal inclusion embedded in a finite isotropic medium into the sub-problem of the same inclusion inside the associated infinite medium and the sub-problem of the finite ambient isotropic medium including no inclusion but undergoing appropriate compensating boundary conditions. The general method is applied in the two-dimensional situation and the corresponding temperature field and Eshelby's conduction tensor are explicitly expressed in terms of some curvilinear complex integrals for the Dirichlet and Neumann boundary conditions. Thus, the difficulties owing to the unavailability or non-existence of Green's function are overcome. The general results in the two-dimensional case are finally specified and illustrated by considering a finite circular medium with circular or polygonal inclusions.

Self-Induced Torque in Hyperbolic Metamaterials

Optical forces constitute a fundamental phenomenon important in various fields of science, from astronomy to biology. Generally, intense external radiation sources are required to achieve measurable effects suitable for applications. Here we demonstrate that quantum emitters placed in a homogeneous anisotropic medium induce self-torques, aligning themselves in the well-defined direction determined by an anisotropy, in order to maximize their radiation efficiency. We develop a universal quantum-mechanical theory of self-induced torques acting on an emitter placed in a material environment. The theoretical framework is based on the radiation reaction approach utilizing the rigorous Langevin local quantization of electromagnetic excitations. We show more than 2 orders of magnitude enhancement of the self-torque by an anisotropic metamaterial with hyperbolic dispersion, having negative ratio of permittivity tensor components, in comparison with conventional anisotropic crystals with the highest naturally available anisotropy.