## Laguerre spectral method as applied to numerical solution of a two-dimensional linear dynamic seismic problem for porous media

Seismic methods based on the seismic waves propagation in an acoustic or an ideally elastic medium, were successfully applied to various geophysical problems to identify geological structures. In such studies, properties of a pore liquid such as density, the module of volumetric deformation, fluidsaturation and viscosity were generally ignored. A...

## Theorem of the mean for inhomogeneous poroelastic static system

Relations of the mean for a vector of displacement of an elastic porous body and pore pressure for an inhomogeneous poroelastic static system, when mass forces are present and energy dissipation is absent, are obtained.

## The Kuril-Kamchatka gridded digital bathymetry creation and analysis

In this paper, algorithms and an interface for creating detailed digital regular gridded bathymetry using digital sounding data are described, and examples of the data obtained for different regions of the Pacific are shown. In calculations of the depth at each grid point, the algorithm uses up to nine points...

## Divergent formulas (conservation laws) in the differential geometry of plane curves

In this paper, it is discovered that in the differential geometry of arbitrary smooth plane curves there exists a solenoidal vector field * S**, i.e., the field with a property div

**= 0 (in a certain area**

*S***D*), having the following geometric meaning. Let {

*Lτ*} be...

## Conservation laws for a time field (the eikonal equation solutions) in kinematic seismics (geometric optics)

A number of non-classical formulas of vector analysis are represented as differential identities that, on the one hand, relate the modulus to the direction of an arbitrary smooth vector field in a three- and two-dimensions. On the other hand, these formulas, in a sense, separate these characteristics. In particular, for...

## Modeling of the free convection in a viscous compressible fluid

Convection is one of the basic types of the flows used in description of processes of the Earth's interior and the Earth's atmosphere. The simulation of convection of many geological systems under the assumption of an incompressible medium in the Boussinesq approximation often appears to be poor and the model...

## Propagation of a gravity current in the atmosphere over a valley

A 2D version of a 3D nonhydrostasic meteorological model is used to simulate the effects of atmospheric front propagation over a valley. The front surface is described in the model by an equation for advection of a scalar substance, which is solved by a third-order semi-Lagrangian procedure. A leap-frog type...