## Simultaneous identification of two coefficients in a diffusion equation

An algorithm for the simultaneous determination of *two* coefficients in an inverse problem for equations of the parabolic type is presented. The model under investigation has been proposed in the literature to describe the long-time coastal profile evolution. The iterative inversion procedure is based on the minimization of a suitable...

## Mathematical statement of the inverse kinematic problem of seismics for 3D inhomogeneous medium. Part I

The inverse kinematic problem (IKP) for 2D inhomogeneous half-plane with a 2D hodograph of refracted waves given at its boundary is reduced to the initial problem for the non-classical evolutional partial differential equation of the first order. In the present paper, the method considered earlier is extended to the 3D...

## Numerical solution to combined one-dimensional inverse problems for Maxwell's equation and equations of porous media

Combined one-dimensional inverse problems for Maxwell's equation and equations of porous media are solved numerically using the optimization approach. Representative series of numerical calculations for various models of media are given.

## Estimates of conditional stability of some combined inverse problems for Maxwell's equations and equations of porous media

A combined mathematical model of Maxwell's system of equations and a system of equations for porous media taking into account admixtures is constructed.

## On hydrodynamics equations of solutions for conducting porous media

A combined mathematical model of Maxwell's system of equations and a system of equations for porous media taking into account admixtures is constructed.

## On the diffraction of nonstationary SH-wave on semi-infinite crack in porous elastic medium

The problem of diffraction of a plane SH shock wave on a semi-infinite crack for a model of porous medium for the case of energy loss due to intercomponent friction is considered. Formulas for the scattered wave in terms of the Laplace transforms with respect to time are obtained.

## Numerical solution to the inverse problem for a system of elasticity for vertically inhomogeneous medium

In the paper, the results of numerical solution to the inverse problem for a system of elasticity for vertically inhomogeneous medium are presented. The center of compression excites the elastic oscillations in medium. This mathematical model of source does not give a decomposition of the elastic system and we need...

## Integral Laguerre transform as applied to forward seismic modeling

The paper presents some efficient algorithms based on the application of the integral Laguerre transforms for approximation of temporal derivatives. Some specific features of employing this algorithm for the first and the second order equations with respect to time are considered. A few examples of calculation of seismic fields for...

## Rules of application of algorithms for tsunami waves kinematic computations based on the Huygence principle

The process of tsunami waves propagation can be well described by the shallow-water equations. One of the corollaries of this model is the independence of a wave-front velocity from the amplitude of a tsunami wave. This velocity depends only on the depth.

Methods of wave-front computation, that are based on...## Two algorithms for calculation of theoretical seismograms for anisotropic media

Two algorithms for the numerical modeling of the elastic wave propagation in non-homogeneous anisotropic media are proposed. A common feature of both algorithms is the reduction of the 3D problem of elastic wave propagation to a series of 1D problems, by means of the finite integral Fourier transform with respect...

## Numerical modeling of seismic waves for the radial-heterogeneous spherical Earth

The paper presents an efficient algorithm based on the combination of the integral Laguerre transforms for the temporal derivatives with the Legendre transforms and finite difference method for the spatial variables. Several examples of synthetic seismograms computed for the SH waves propagating in the radial- heterogeneous spherical Earth are presented.

## Numerical implementation of wave mode of definition of bottom hole coordinates

In the present paper, within the scope of the acoustic method of the wave mode of definition of the bottom hole coordinates, the procedure of estimation of drift parameters for any number of sensors ≥ 4 is discussed. Least square methods, applied in this case, with regularization and pseudo-inversion allow us...

## Polar and azimuthal geometrical divergences in two-dimensional media with a blockwise constant gradient

The ray method has long been used to solve numerically various problems of mathematical seismics. Many papers were devoted to questions of calculation of geometrical divergence in combined two- and three-dimensional media with curvilinear interfaces. For layered and blockwise gradient media (in this paper, no distinction is made between these...

## Joint inverse dynamic problem for the 1D heterogeneous isotropic medium

The present paper deals with the "joint" inverse dynamic seismic problem. An attempt is made to increase precision of the medium structure reconstruction. The problem is solved for medium having absorption, using complementary information on real structure of the medium.