In this paper, the propagation model considers the two half-spaces as a homogeneous isotropic medium and one-dimensionally anisotropic medium. From the exact formulas for the transient field with delta-function excitation, it is obtained readily the exact formulas for the transient field excited by a horizontal electric dipole with Gaussian excitation when both the dipole point and field point ...

The soil is a heterogeneous and anisotropic medium. Hydraulic conductivity, an intrinsic property of natural alluvial deposits varies both deterministically and randomly in space and has different values in various directions. In the present study, the permeability of natural deposits and its influence on the seepage flow through a natural alluvial deposit is studied. The 2D Finite Difference c...

A Dirichlet problem is considered for the eikonal equation in an anisotropic medium. The nonlinear boundary value problem (BVP) formulated in the present work is the limit of the diffusion–reaction problem with a diffusion parameter tending to zero. To solve numerically the singularly perturbed diffusion– reaction problem, monotone approximations are employed. Numerical examples are presented f...

We show that the support of a (possibly) coated anisotropic medium is uniquely determined by the electric far-field patterns corresponding to incident time-harmonic electromagnetic plane waves with arbitrary polarization and direction. Our proof avoids the use of a fundamental solution to Maxwell’s equations in an anisotropic medium and instead relies on the well-posedness and regularity proper...

Uniqueness in inverse conductivity and scattering problems is considered. In case the medium consists of two discontinuous constant anisotropic conductive parts, the measurements of potential and induced currents on the boundary of surrounding body are enough to guarantee uniqueness to determine conductivity and region of embedded unknown material under a very weak condition. The analogous uniq...

We consider the inverse scattering problem of determining the support of an anisotropic inhomogeneous medium from a knowledge of the incident and scattered time harmonic acoustic wave at 1xed frequency. To this end, we extend the linear sampling method from the isotropic case to the case of anisotropic medium. In the case when the coe6cients are real we also show that the set of transmission ei...

The separation of wave modes from isotropic elastic wavefields is typically done 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 the use of more sophisticated opera...