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This paper proposes the application of the hybrid boundary element method (HBEM) for analysis of bi-isotropic media of Tellegen type. In previous applications of this method it was possible to analyze only the electromagnetic problems in isotropic media. The main contribution of this paper is the modification of the method itself, in order to solve a large scale of quasi-static TEM problems in bi-isotropic media. Detailed theoretical analysis and HBEM procedure are described and applied. Characteristic parameters of a microstrip line with bi-isotropic substrate are analyzed. Obtained results have been compared with available numerical and software simulation results. A close results match can be noticed.

Elastic reverse-time migration (ERTM), which utilizes the advantages of both P- and S-wave modes, is a widely used application for imaging in 3D anisotropic media. However, crosstalk due to intrinsically coupled P- and S-wavefields may degrade the image quality. To solve this problem, this study presents an effective vector P- and S-wavefield decomposition scheme in ERTM that can improve the images of 3D transversely isotropic (TI) media. The proposed method consists of four steps: (1) rotating the observation coordinate system to align its vertical axis with the symmetry axis of 3D TI media; (2) deriving the formulations of the 3D TI decomposition operator by applying the VTI P/S wave-mode decomposition strategy based on eigenform analysis in the new coordinate system; (3) implementing vector P- and S-wavefield decomposition by constructing the 3D TI Poisson equation, and introducing a novel and efficient method based on the first-order Taylor expansion to accelerate the computational efficiency of the decomposition; and (4) applying a vector-based dot-product imaging condition to generate PP and PS images. Compared with previous studies, the algorithm of our proposed method in 3D TI media is both numerically stable and computationally efficient. The 3D TI decomposition operator generates vector P- and S-wavefields showing the correct amplitude/phase with the input ones. Several numerical examples illustrate the satisfactory performance of the proposed 3D TI decomposition operator and the effective image improvement.

In VTI media, the conventional inversion methods based on the existing approximation formulas are difficult to accurately estimate the anisotropic parameters of reservoirs, even more so for unconventional reservoirs with strong seismic anisotropy. Theoretically, the above problems can be solved by utilizing the exact reflection coefficients equations. However, their complicated expression increases the difficulty in calculating the Jacobian matrix when applying them to the Bayesian deterministic inversion. Therefore, the new reduced approximation equations starting from the exact equations are derived here by linearizing the slowness expressions. The relatively simple form and satisfactory calculation accuracy make the reduced equations easy to apply for inversion while ensuring the accuracy of the inversion results. In addition, the blockiness constraint, which follows the differentiable Laplace distribution, is added to the prior model to improve contrasts between layers. Then, the concept of GLI and an iterative reweighted least-squares algorithm is combined to solve the objective function. Lastly, we obtain the iterative solution expression of the elastic parameters and anisotropy parameters and achieve nonlinear AVA inversion based on the reduced equations. The test results of synthetic data and field data show that the proposed method can accurately obtain the VTI parameters from prestack AVA seismic data.

This paper develops a novel set of displacement temperature potential functions to solve the thermoelastodynamic problems in functionally graded transversely isotropic media subjected to thermal source. For this purpose, three-dimensional heat and wave equations are considered to obtain the displacement temperature equations of motion for functionally graded materials. In the present study, a systematic method is used to decouple the elasticity and heat equations. Hence one sixth-order differential equation and two second-order differential equations are obtained. Completeness of the solution is proved using a retarded logarithmic Newtonian potential function for functionally graded transversely isotropic domain. To verify the obtained solution, in a simpler case, potential functions are generated for homogeneous transversely isotropic media that coincide with respective equations. Presented potential functions can be used to solve the problems in various media like infinite and semi-infinite space, beams and columns, plates, shells, etc., with arbitrary boundary conditions and subjected to arbitrary mechanical and thermal loads.

Elastic least-squares reverse time migration (ELSRTM) has the potential to provide higher-quality migration images related to the lithology and fluid by imaging multi-component seismic data than conventional elastic reverse time migration (ERTM). Oil and gas are widely stored in fractures and sedimentary rocks. The sedimentary rocks and the rocks with fractures will produce anisotropy. The anisotropy effect should be corrected in migration. In order to correct the anisotropic effect to the images of ELSRTM, a new anisotropic ELSRTM scheme is developed to image the multi-component seismic data in vertical transverse isotropic (VTI) media. This new ELSRTM method can invert high-quality images and correct the anisotropic effect in VTI media. Many ELSRTM methods assume that the density is constant. However, the constant-density assumption will generate false migration results when the density of media is variation. We derive the elastic VTI de-migration operator in the media with density variations based on Born approximation. The adjoint state equations and gradient formulas with respect to medium images in VTI media with density variations are also derived by the adjoint state method. Using the new elastic de-migration operator, adjoint state equations, and gradients in VTI media with density variations, we can produce high-resolution subsurface elastic reflectivity images. Numerical examples from the graben VTI model and modified HESS VTI model demonstrate that the proposed ELSRTM can not only generate the images with high quality but also correct the anisotropic effect in VTI media with density variations.

This work is a continuation of the authors’ research on solving inverse problems of mathematical geophysics in a linear formulation. Unlike previous works, where the solution was built on the basis of volumetric integral equations, boundary integral representations and emerging boundary integral equations are used here to solve the inverse coefficient problem of geoelectrics to find the constant electrical conductivity of a local isotropic inclusion, located in a piecewise-constant electrical conductivity isotropic enclosing medium.

Modeling of a light pulse propagating in optical fiber where the core is bi-isotropic non-reciprocal achiral media (i.e., Tellegen media) with Kerr effect is studied. The two constitutive equations approach for nonlinear bi-isotropic media are proposed to highlight nonlinear effect, which is due to the magnetization vector under the influence of a strong electric field. According to this approach, nonlinear parameter of magnetization vector is illustrated; it is the important factors to estimate bi-isotropic optical fiber dispersion and nonlinearity. Split-step Fourier method is used to simulate and solve the nonlinear Schrödinger equation.

A passive solid cannot do work on its surroundings through any quasistatic cycle of deformations. This property places strong constraints on the allowed elastic moduli. In this Article, we show that static elastic moduli altogether absent in passive elasticity can arise from active, non-conservative microscopic interactions. These active moduli enter the antisymmetric (or odd) part of the static elastic modulus tensor and quantify the amount of work extracted along quasistatic strain cycles. In two-dimensional isotropic media, two chiral odd-elastic moduli emerge in addition to the bulk and shear moduli. We discuss microscopic realizations that include networks of Hookean springs augmented with active transverse forces and non-reciprocal active hinges. Using coarse-grained microscopic models, numerical simulations and continuum equations, we uncover phenomena ranging from auxetic behaviour induced by odd moduli to elastic wave propagation in overdamped media enabled by self-sustained active strain cycles. Our work sheds light on the non-Hermitian mechanics of two- and three-dimensional active solids that conserve linear momentum but exhibit a non-reciprocal linear response. Active, non-conservative interactions can give rise to elastic moduli that are forbidden in equilibrium and enter the antisymmetric part of the stiffness tensor. The resulting solids function as distributed elastic engines that can perform work on their surroundings through quasistatic strain cycles.

Refraction between isotropic media is characterized by light bending towards the normal to the boundary when passing from a low- to a high-refractive-index medium. However, refraction between anisotropic media is a more exotic phenomenon which remains barely investigated, particularly at the nanoscale. Here, we visualize and comprehensively study the general case of refraction of electromagnetic waves between two strongly anisotropic (hyperbolic) media, and we do it with the use of nanoscale-confined polaritons in a natural medium: α-MoO 3 . The refracted polaritons exhibit non-intuitive directions of propagation as they traverse planar nanoprisms, enabling to unveil an exotic optical effect: bending-free refraction. Furthermore, we develop an in-plane refractive hyperlens, yielding foci as small as λ p /6, being λ p the polariton wavelength (λ 0 /50 compared to the wavelength of free-space light). Our results set the grounds for planar nano-optics in strongly anisotropic media, with potential for effective control of the flow of energy at the nanoscale. Refraction between anisotropic media is still an unexplored phenomenon. Here, the authors investigate the propagation of hyperbolic phonon polaritons traversing α-MoO3 nanoprisms, showing a bending-free refraction effect and sub-diffractional focusing with foci size as small as 1/50 of the light wavelength in free space.

We examine the momentum and angular momentum (AM) properties of monochromatic optical fields in dispersive and inhomogeneous isotropic media, using the Abraham- and Minkowski-type approaches, as well as the kinetic (Poynting-like) and canonical (with separate spin and orbital degrees of freedom) pictures. While the kinetic Abraham-Poynting momentum describes the energy flux and the group velocity of the wave, the Minkowski-type quantities, with proper dispersion corrections, describe the actual momentum and AM carried by the wave. The kinetic Minkowski-type momentum and AM densities agree with phenomenological results derived by Philbin. Using the canonical spin-orbital decomposition, previously used for free-space fields, we find the corresponding canonical momentum, spin and orbital AM of light in a dispersive inhomogeneous medium. These acquire a very natural form analogous to the Brillouin energy density and are valid for arbitrary structured fields. The general theory is applied to a non-trivial example of a surface plasmon-polariton (SPP) wave at a metal-vacuum interface. We show that the integral momentum of the SPP per particle corresponds to the SPP wave vector, and hence exceeds the momentum of a photon in the vacuum. We also provide the first accurate calculation of the transverse spin and orbital AM of the SPP. While the intrinsic orbital AM vanishes, the transverse spin can change its sign depending on the SPP frequency. Importantly, we present both macroscopic and microscopic calculations, thereby proving the validity of the general phenomenological results. The microscopic theory also predicts a transverse magnetization in the metal (i.e. a magnetic moment for the SPP) as well as the corresponding direct magnetization current, which provides the difference between the Abraham and Minkowski momenta.