A one-dimensional system of the Hopf-type equations is considered. Axial solutions to problems in the field of modeling two-fluid interactions are sought. A nonlinear system of ordinary differential equations is obtained. Direct and inverse problems for the obtained ODE are considered. A theorem on local solvability is proven.

The studying the regions of global seismic belts, to which giant impact structures belong, confirms the hypothesis of the possible attachment to the Earth of its satellite at the Cretaceous-Paleogene boundary and the coincidence of these belts and structures to the routes of its tangent flight along the Med-Eocene position...

The Cauchy problem for a one-dimensional homogeneous system of the Hopf-type equations arising in a two-fluid medium is considered. It is believed that energy dissipation occurs only due to the friction coefficient (analogous to Darcy) and the Cauchy data are given in the form of a finite trigonometric Fourier series...

A hypothesis is formulated about the formation of Kolpanskoye Lake, located in the vicinity of the city of Gatchina (near St. Petersburg, Russia) as a result of a meteorite fall. An approximate calculation of meteorite characteristics was performed using the energy model of the meteorite/ground dynamic system and nonlinear programming...

A study to identify the spatio-temporal relationship between strong
*MS* ≥ 7 seismic shocks and the preceding moderate mid-depth seismicity has led
to the need to consider territories that go far beyond the area of preparation of
its individual foci. First, there are the areas along the global seismolineaments...

A dynamic inverse problem for a one-dimensional system of the Hopf-type equations is considered. A theorem on local solvability in the class of functions
analytic in the variable *x* is proved.

The application of a hydrodynamic model of the two-velocity media flow of to non-stationary problems of the heterophase flows motion in channels is considered. Various flow regimes of such media are studied for given penetration rates for initially inhomogeneous flow at various values of channel inclination.

The presented mathematical model...

The paper is devoted to modeling the solvent and solute transfer in a chemically inert elastically deformable rock, the model takes into account only the variation in stress and pore pressure. Chemical effects are taken into account by changing the pore pressure and deformation of rocks in the transport equations...

The process of capturing wave energy by a round-shaped island with a conical relief for the surrounding bottom is studied in this work. The kinematics of the tsunami wave having initially straight front near such an island was investigated by the method of step-by-step orthogonal advancement of wave front. An...

A study was continued to identify the spatial-temporal relationship
between strong crustal earthquakes and moderate intermediate-depth seismicity
preceding them. In the field of preparation of these shocks, a pattern of direct
correlation of graphs *MS(t)* and *Cr(t)* has been revealed, testifying creation the
conditions for strictly deterministic influence...

The impact theory of mass extinction for Earth's biota has not yet received either its final confirmation or complete rejection and remains a working hypothesis, often explaining what is not explicable by other theories. Among all the five mass extinctions recorded in the stratigraphic annals of the Earth, only the...

Inverse dynamic problems for a one-dimensional system of Hopf-type equations are considered. Theorems on the solvability of the considered problems in the class of analytic functions are proved.

The paper considers applications of a two-velocity model of hydrody- namics for a two-phase medium for describing natural geological systems, such as movement of magma melts in magma channels, the flow of a river and the erosion of an unfixed sandy river bottom. The study deals with a test problem...

The paper investigates a mathematical model of a two-phase medium under the assumption that the phases are in equilibrium with respect to pressure and temperature. Dissipative effects are determined by interfacial friction. In the one-dimensional case, a group analysis of the dissipative system of equations for a two-phase medium is...

Two-velocity models of suspension hydrodynamics are considered, using the equality condition for chemical potentials of the phases or without this condition. The model equations are obtained by the conservation law method and are thermodynamically consistent under the assumption of one pressure or two pressure systems. Models are compared numerically on...

*MS*and depth

*H*are used, as well as one of the characteristics of the seismic regime — creepex Cr

*Ncat*, included in the complex of the...

The paper illustrates the applicability of the Laguerre spectral method to solving a one-dimensional problem of the dynamics of a saturated porous medium. A one-dimensional non-stationary problem of a pulsed action on a saturated porous medium is investigated taking into account the effects of electromagnetoacoustics. The features of the acoustic...

The paper explores the possibility of modifying the creepex (creep and
explosion) parameter, an increase in its informativeness and applicability of using
public catalogs by the GIS-ENDDB geoinformation system. Instead of the canonical
form of the creepex (Cr = *MS - kmb - l*), the introduced normalized...

Application of the variation method to simulate tsunami wave rays and to estimate the wave travel times corresponding is studied. In some cases, the wave ray determined by this method, connecting two points of the water area, may not present the global extreme, which provides the shortest tsunami travel time...

In order to explain the process of forming the outer rings of an impact crater, a model of an underground explosion of an impactor penetrating into the target is proposed. Intense crushing of the surface rocks is explained by the effect of the primary compression wave if it propagates from...

The paper studies the flow of a two-phase medium in a gravity field channel. The thermodynamically consistent equations of the mathematical model of the dynamics of a two-velocity medium with an admixture were developed within the framework of the method of conservation laws. Its numerical implementation was carried out based...

The paper considers a system of equations of motion of a two-phase medium with phase equilibrium in terms of pressure and temperature. The spectral analysis of the system was carried out for a one-dimensional case. Approximate numerical solutions of the Riemann problem about the decay of an arbitrary discontinuity were...

A chemically inert deformable rock is considered, taking into account only changes in stress and pore pressure: the chemistry of a porous fluid has no direct effect on deformation. Accounting the chemical effects leads to changes in the pore pressure and in the strain of rocks. This theory is applied...

On many territories of the Earth, the unnaturally at extended surface areas are observed that are geomorphologically expressed relative to the adjacent areas and resembling a pattern of a planed-down tree in satellite images. A new hypothesis is proposed, explaining the formation of such a pattern due to the Earth...

A modified version of the linear poroelasticity theory described by three elastic parameters is applied to shale swelling with an aqueous electrolyte. It is assumed that the shale behaves as an isotropic, ideal ionic membrane, and in this case, swelling depends only on the total stress and on the chemical...

We have considered the classical solution in the half-space of the second boundary value problem for an overdetermined stationary system of second order equations arising in a two-fluid medium with phase equilibrium in pressure. The solution is constructed using the Fourier transform apparatus. The effect of the kinetic parameters of...

The new method for the numerical simulation of partial reflection of the long waves off the submerged vertical barrier was developed and tested. This method is based on the inner boundary condition which takes into account the wave energy loss due to such a kind of reflection. The method was...

A technique that allows by secondary signs finding and determining the size of impact craters with a diameter exceeding 5 kilometers, whose profile has been erased by erosion processes or hidden with sediment cover is proposed.

This paper highlights the influence of the model parametrization, including the sea level recorders localization and source discretization, on the tsunami source inversion. Modeling the initial water displacement in the tsunami source area is based on the least square inversion and a truncated singular value decomposition approach that makes possible...

This paper studies a class of second order partial differential equations *utt = f(ux)uxx + g(ut)* arising in poroelasticity theory with arbitrary functions *f(ux)* and *g(ut)*, using the group classification. It is shown that the principal Lie algebra of...

The deformation tensor *ε* in a porous medium is a function of the
stress tensor *σ* and the pore pressure *ρ*. Additional osmotic effects are present
in some rocks, such as shales. It is shown that such effects, in turn, modify the
thermodynamics of the system, namely, in terms...

In this paper, the Bernoulli equation for an incompressible two-fluid medium with equilibrium of pressure phases in the reversible hydrodynamic approximation is constructed.

In this paper, a solution to an initial boundary value problem for a one-dimensional non-local system for the destruction of rocks is constructed.

There are many methods for computing the tsunami kinematics directly and inversely. The direct detection of waves in the deep ocean makes it possible to establish the tsunami source characteristics and origin. The present study proposes a modification in the methodology of determining tsunami travel times and wave front positions...

Various endogenous, those occurring in the Earth's bowels, and exogenous, for example, impact effects, geological processes characterize the state of the art in geodynamics. In order to solve problems focused on the investigation of the cause-effect relationships of the processes influencing the regional geodynamics, the Earth's Natural Disasters Database (GIS-ENDDB)...

An application of the original numerical inversion technique to modeling the tsunami sources of the 16 September 2015 Chile tsunami is presented. The problem of recovering a tsunami source from remote measurements of the incoming wave in the deep-water tsunameters is considered as an inverse problem of mathematical physics in...

In this paper, we show one of recent GIS-ENDDB algorithms: the algorithm of building seismicity lineaments in terms of Great circles of the Earth. We also show using some other GIS-ENDDB algorithms to identify and to confirm the possibility of existence of global tectonic structures of the lineament type in...

The calculation of the Novosibirsk reservoir ows with the help of the scheme with two splitting steps and a finite element method (FEM) has been carried out. At these steps, for constructing the FEM operators different types of finite elements are used. In particular, at the step corresponding to the...

In this paper, the kinematics of the tsunami wave ray and the wave front in the area, where the depth increases proportional to the squared distance to the straight shoreline, is studied. The exact analytical solution for the wave-ray trajectory above the parabolic bottom topography has been derived. This solution...

A unit vector field *τ* in the Euclidean space *E3* is considered. Let ** P** be
the vector field from the first Aminov divergent representation

*K*= div[(

*r•τ*)

**] for the total curvature of the second kind**

*P**K*of the field

*τ*. For the field

**...**

*P*In the Euclidean space *E3*, we consider the family {*Lτ*} of the curves *Lτ*
with the tangent unit vector *τ = τ (x, y, z)* and the family {*Sτ*} of the surfaces *Sτ*
with the unit normal *τ* which are orthogonal to the curves *L...*

A family {*Sτ*} of surfaces *Sτ* with the unit normal *τ = τ (x, y, z)* in
the Euclidean space *E3* is considered. The surfaces *Sτ* continuously fill a domain *D*
in *E3*. For the family {*Sτ*} of surfaces *Sτ*, the law...

This paper presents the generalized methodology for identifying the morpho-structural features of new, supposedly, impact large-size structures. Those are the following: the presence of the bank and the central raising, the presence of the hydrocarbons deposits and the mineral resources of hydrothermal origin on the crater territory, the sharp changes...

The propagation of elastic waves in strongly heterogeneous media using subgrid modeling approach is studied. The local elastic parameters and the mass density have essential variations in some interval of scales at each spatial point. To approximate a strongly heterogeneous medium, we have started from the modified Kolmogorov theory in...

In this study, the tsunami source of the 2013 Solomon Island tsunami
event was reconstructed by the *r*-solution method. The focus of this research is
the applying the regularities obtained for a model cases to the real event. To
understand the reasonable strategy of deployment of a tsunami recorders...

We consider a one-dimensional direct initial-boundary value problem for a nonlinear system of the poroelasticity equations. The theorem of local solvability of the classical solution to the problem is proved. The Frechet differentiability of the problem operator is proved, too.

We consider a one-dimensional inverse boundary value problem for a nonlinear system of the poroelasticity equations. We obtain estimates for the conditional stability of the inverse problem.

The main object of the study in Geophysics is multi-dimensional non-linear systems, varying over a wide time range from a split second to geological epochs. The present-day mathematics does not allow a sufficiently strict description of such systems, so the problem of reliable long-term earthquake prediction is still unsolvable. The...

The grid-switching algorithm for the tsunami propagation computation from the initial source to the coastline that uses scale switching has been developed. Computations are carried out on a sequence of grids with various resolutions where one is embedded into another. Tsunami wave parameters are transferred from a larger domain to...

We study the first Darboux problem for hyperbolic equations of second order with memory and consider the solvability of this problem.

In the geo-information and geological studies of the last two years we has accumulated a sufficient number of geophysical, morphological, mineralogical and petrographic materials to refer the Ladoga structure to the category of the "proven" astrobleme. The identification within the Ladoga structure of the volcano-plutonic complex, which is syngenetic to...

This paper is aimed to the improvement of the quality of the data of vibro-seismic research under the condition of the wave form preservation of a sounding signal. For this purpose, it is offered to use the order statistics filters. As seismic data are mostly harmonic or frequencymodulated (or sweep)...

Let us consider the propagation of magnetoacoustic waves in the porous media saturated with electrolyte in the case when the loss of energy occurs due to electroconductivity, intercomponental friction coefficient and electrokinetic effect.

The fundamental solution to describe the three-dimensional steady-state flows of viscous fluids of the two-velocity continuum with pressure phase equilibrium has been obtained.

This paper presents the results of experimental investigations of the original ecologically safe approach as related to the assessment of the geoecological risk from powerful mass explosions for the social and natural environment. In this approach, seismic vibrators are used as sources imitating explosions but having, in contrast to them...

The method for estimating a tsunami height using the wave front kinematics computation has been developed and tested. This method is based on an orthogonal advance of computational points located along a moving tsunami wave front line. Precise algorithms for determining these points movement direction and an addition of new...

The new meaning or a property of the Gaussian and of the mean
curvature of surfaces forming a family in terms of the vector analysis has been
discovered. The divergence representations were found for the mean curvature *H* = *H(x; y; z)* and the Gaussian curvature of *K* = *K(x; y; z)* of the...

The divergence formulas we have obtained (differential conservation
laws) of the form div * F* = 0 for an arbitrary smooth field of unit vectors

**τ**(x; y; z), for a family of spatial curves as well as {

*L*τ} for a family of surfaces {

*S*τ} continuously...

The use of the shady relief model of the ENDDB-program (the Earth's Natural Disasters Database) and the data from “Global marine gravity”, V18.1 for constructing the relief and the shaded gravity anomaly maps allows us to visually reveal the new morpho-structural elements of astroblemes or to confirm the earlier found...

This paper outlines some aspects of an approach to reconstructing an initial water elevation field that generates a tsunami. Recently, the devastating tsunamis have acutely put forward the problem for their timely warning and, as consequence, the importance of the accurate tsunami simulation. Mathematical modeling of tsunamis is to provide...

A new method of estimating the impact frequency of celestial bodies on the Earth, with corrections for the rate of crater erosion is proposed. This method is based on the content of the Expert Database on the Earth's impact structures (EDEIS) that has been developed and is being maintained in...

A regularizing algorithm of an inverse problem for a one-dimensional equation of SH waves in a fluid-saturated porous medium with energy loss under intercomponent friction is proposed.

A series of the differential identities connecting velocities, pressure and body force in the two-velocity hydrodynamics equations with equilibrium of pressure phases are found. Some of these identities have a divergent form and can be considered to be certain conservation laws. It is detected that the flow functions for the...

It is known that some of the parameters required for the direct simulation of tsunamis are the bottom relief characteristics and the initial perturbation data (a tsunami source). The seismic data about the source are usually obtained in a few tens of minutes after an event has occurred (the seismic...

We investigate the continuation problem for the elliptic equation. The continuation problem is formulated in the operator form *Aq = f*. Singular values of the operator *A* are presented and analyzed for the continuation problem for the Helmholtz equation. Results of numerical experiments are presented.

In this paper, the criteria for determining a ballistic trajectory location of the Popigai cosmic body (PCB) are revised. It is concluded that this trajectory was directed not from the NE to the SW as was believed earlier, but from the SE to the NW. With this orientation, there is...

In the paper the group of variables transformation which is allowed by the shallow-water system of differential equations is obtained. During long wave simulation in water flumes it is necessary to select of the similarity coefficients, that allow to apply the results of modeling in reduced scale to real big-size...

Zones of negative gravitational anomalies accompanying the Popigai and some other astroblemes (Puchezh-Katunki, Beyenchime-Salaatian, Janisjarvi, Kamensk, Karla, Kaluga, Kogram, El'gygytgyn, Wanapitei, Steinheim, Chicxulub) are considered. It is concluded that the formation of the "tails" of cosmogenic structures is associated with the energy influence of the asteroids.

A system of second-order differential equations for the stress tensor and pore pressure for the poroelasticity statics without mass forces and energy dissipation is obtained. The stress tensor is shown to be a biharmonic function. Integral mean value relations in the explicit form for the obtained systems of differential equations...

The authors of paper [1] refer to papers [2, 3] by Dorovsky et al. as the source of governing equations of the poroelasticity model being studied in their paper. In papers [2, 3], according to the authors' opinion, the equations of motion of saturated porous media were obtained in terms...

Recently, the theory and practice of geoelectromagnetism have been enriched with the new theoretical and experimental results that appeared in many publications. However, there are still unsolved problems in geoelectromagnetism that arose as far back as in the time of Gauss, who laid the groundwork for the physico-mathematical modeling of...

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...

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.

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...

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...

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...

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...

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...

Electromagnetic fields that are observed on the Earth with the worldwide network of magnetic observatories as well as regional means when surveying the Earth's interior are conventionally considered to be force and one-mode fields.

For the numerical modeling of electromagnetic fields observed on the Earth, a force component of Maxwell's...

Electromagnetic methods for studying the Earth, electromagnetic techniques of geophysical prospecting, in particular, are conventionally based on the fact that any electromagnetic field, either observed on the Earth or artificially excited by generators, satisfy Maxwell's equations and is analytically described by these equations.

This opinion is so popular among geophysicists...

In this paper, a high-tech expert system EEDB for solving a wide range of seismological research tasks is proposed. The logical and functional structure as well as results of the algorithms usage for the analysis of seismic processes are considered. The algorithms allow us to calculate and to visualize maps...

Seismic observations in the Altai-Sayansk region, one of seismic-prone zones in Russia, are a part of the federal observations over natural and man-caused factors. The territory of the region in question makes more than 1.5 ∙ 106 km2 includes 13 subjects of the Russian Federation and three border areas...

The form of the equation of motion of porous media in terms of velocities, stresses and pressure as a symmetric t-hyperbolic system has been obtained.

Mean value relations for a vector of displacement of an elastic porous body and a pore pressure for a poroelastic static system, when mass forces and energy dissipation are absent, are obtained.

A developed toolkit (parallel programs and visualization tools) for the numerical simulation of the elastic wave propagation in 3D and 2D nonhomogeneous elastic media, comprising cavernous inclusions applicable to the on-site inspection, is described. According to the results obtained, groups of waves were identified, and synthetic data reflecting the influence...

An Expert Database on the Earth Impact Structures (EDEIS) has been compiled and is being maintained in the Tsunami Laboratory of the Institute of Computational Mathematics and Mathematical Geophysics of SB RAS in Novosibirsk. The database has been developed on the basis of the catalog of Earth impact structures that...

A new method for the tsunami wave ray construction is proposed. It is based on isochrones that are built with the use of the wave travel times to a tsunami source. The wave ray approximation is determined as a broken line passing through intersection points of identical time isochrones from...

In a subduction zone, a tsunami source is usually situated above the continental bottom slope. Due to the wave refraction, the opposite slope of a deep water trench works like an optical lens for tsunami waves. The tsunami propagation process is studied using the wave-ray approximation. The tsunami amplitude reduction...

Methods for computing wave kinematics are wide-spread for studying the wave propagation in non-homogeneous media. Exact analytical solutions for nontrivial media are needed for testing such methods. The formula describing the wave-front shape has been found for some media with a power dependence of conductivity on only one spatial coordinate...

A brief review of the author's catalog of the Earth's Impact structures, presented on the site of ICM&MG, is given in this paper. For the research into general laws of distribution with space of the impact structures compiling the catalog and for the analysis of their parameters it is offered...

The inverse problem to infer the initial water displacement is treated as an ill-posed problem of the hydrodynamic inversion of tsunami tide gauge records. To this end, we have developed a technique based on the least square inversion and a truncated SVD approach. The proposed filtering technique essentially improves the...

In the Kerch-Tamagne areas, mud volcanoes and associated "pressed synclines" are evolving. The problem of genesis of mud volcanoes is debated; researchers of mud volcanoes do not have a common opinion about the mechanism of their formation. The necessity of studying the mud volcanoes structures is also connected with the...

The 1996 experiment performed at the Physico-Technical Federal Board (Physikalisch-Technische Bundesanstalt, PTB) provided a value of the Newtonian gravitational constant that exceeds the standard value by ~ 0.6 %. In this paper, it is shown that this anomaly does not result from neglecting the Earth's shielding effect.

One of the methods used to monitor the developing geodynamic processes in seismic-prone zones is based on the regular sounding of a medium by powerful seismic vibrators, with a subsequent analysis of the time dynamics of the seismic field parameters.

Such a monitoring is accompanied by certain nonlinear processes taking...

In this paper, to solve the problem of active vibroseismic monitoring of the processes of fracturing and dilatancy in seismic- and volcano-prone zones, we take into account the dynamic characteristics of the wave field, in addition to a tracking change in the coefficients of medium anisotropy and propagation velocities of...

The problem of the tsunami wave generation by the submarine landslide, which is moving along the bottom slope, is studied. A number of numerical experiments were carried out for a model submarine landslide. A maximum amplitude and the wavelength were defined for various landslide profiles and their moving rates. As...

This study deals with technique of interpretation of harbingers of strong earthquakes aimed at operative forecast of seismic danger. Geomonitoring data of a natural impulse of the Earth's electromagnetic field (NIEEMF) together with seismic monitoring data are analyzed. As an instrument for the analysis of a non-homogenous structure, the wavelet...

The present paper deals with the dynamic problem of linearly de-formable elastic media with an arbitrary anisotropy, containing flat parallel cavities-cracks – the so-called viruses of vibration strength of class 2. The new method with allowance for specific features of integrand functions is used for calculation of multi-dimensional inverse Fourier...

In this paper, we describe a 64 bit version of the visualization system for seismic fields. The system supports well-known SEG-Y, SDS-3, SDS-5 file formats or their scientifically adapted versions without headers. This system is used for several years as a part of industrial seismic data processing system in the...

This paper studies the importance of spatial distribution of the sea-level monitoring stations for the accuracy of restoration of a tsunami source. The ill-posed inverse restoration problem is regularized by means of the least squares inversion using a truncated SVD approach. The wave propagation is described by linearized shallow-water equations...

Methods of active geophysical monitoring with the use of powerful seismic vibrators play an important role in the investigation of changes in the stressed-deformed state of a medium in seismic prone zones for problems of the seismic hazard prediction. During the last three decades, this scientific field has been actively...

Inverse problems of the plane waves scattering of inclined incidence of the SH type by an inhomogeneous half-space (in particular, by a transition layer) or by an inhomogeneous layer with a free boundary are considered. The characteristics of an inhomogeneous elastic medium, i.e., the wave propagation velocity *υ(z)* and the...

A scheme for the automated tsunami source reconstruction on the basis of deep-ocean tsunami wave recordings was developed. The initial water displacement in the source area is represented as a linear superposition of several "unit" sources. The initial value problem for the tsunami waves propagation from each of the unit...

It is shown that seismic prospecting as regards endogenous microseismic waves gives much promise, which is confirmed by graviprospecting practice. It was found that the spring gravimeter has some properties of a high-quality resonant microseismometer not taken into account earlier. These properties are used non-deliberately in highly effective empirical gravimethod...

Now about 700 volcanoes are believed to be active in the world. In this paper, both theoretical and experimental grounds of the monitoring system of living volcanoes with the use of powerful vibroseismic sources are considered. A method to calculate Green's function for inhomogeneous models of media with employment of...

This paper considers some aspects of modeling non-stationary electromagnetic fields for the 3D domains, including inhomogeneous conducting media. The source of such fields is an underground power line. To describe the fields in conducting media, a vector magnetic potential and a scalar electric potential are used, while a magnetic field...

The paper considers the estimation of sensitivity of the method of active monitoring of changes in the elastic characteristics in the Earth's interior crust zone. The model of the Earth's crust-mantle system in the form of a layer in a half-space with different velocity values of elastic waves is presented...

Unlike common approaches this paper does not rely on results for 3D problems. Degeneration of the operator on a part of the border requires the use of the corresponding weight functional spaces to analyze a variational statement to build a difference scheme and to prove the convergence. A result of...

In this paper, fundamental solutions of a wave operator in an inhomogeneous medium having the properties of advanced (anti-causal) type are analyzed. These are such functions that act for the future when the field is calculated at the present time. It is shown that the use of this anti-causal property...

The inversion problem to infer the initial sea perturbation is considered as a usual ill-posed problem of the hydrodynamic inversion of tsunami tide-gage records. The ill-posed inverse reconstruction problem is regularized by means of the least square inversion using the truncated SVD approach. Numerical experiments are presented for the model...

The paper considers theory, methods and experiments aimed at creation of a monitoring system of active volcanos with the use of powerful vibroseismic sources. We propose a concept of creation of a system for studying the geometry of magma chambers, deep faults in the neighborhood of volcanos, dynamics of eruption...

One of essential attributes of the method of electromagnetic monitoring of geodynamic processes is that under the action of tectonic processes, electrical properties of a geological structure change. Electrical logging data give a large body of information for the study of rocks composing a section of formations of the Earth's...

In the given paper, a mathematical model for layered porous media is constructed. A series of numerical experiments is carried out. There is observed a weak dependence of the filtration velocity on the physical properties of a medium as compared to the boundary pressure value.

Nonlinear wave processes of radiation and propagation of elastic oscillations in complex subsurface geometries are analyzed in terms of their role in improving the quality of seismic monitoring of geodynamic processes. The efficiency of this approach is illustrated by measuring parameters of seismic waves and analyzing their temporal dynamics with...

The basic steps of the method of automatic location of borehole sources have been developed. This has been done by measuring the initial wave characteristics used to solve the inverse problem of determining the source coordinates and velocities of near-borehole media.

The problem of simulation of an industrial explosion for a vertically inhomogeneous medium has been considered in a general form. An algorithm to transform a wave field to a pulsed form, which uses a priori information about the space distribution of charges and delay times in a quarry explosion, is...

In non-homogeneous media with a variable wave propagation velocity it is not so easy to solve the boundary wave ray problem, i.e., to define a wave-ray, which connects two given points of the area. In this paper, an effective method for the wave-rays definition is proposed. The method does not...

A new attempt to the detection of the impact craters and other morphologic structures on the Earth's surface was made using high-tech computational methods. For detection and allocation of such structures, the fast two-dimensional wavelet transformation and the fast nonlinear multiparameter regression analysis for the digital elevation (DEM) data subsets...

The pulsed action on fluid-saturated nonlinearly deformed porous media is considered. A mathematical model of a nonlinear two-velocity medium was obtained on the basis of the method of conservation laws. The model is thermodynamically consistent and hyperbolic in the reversible approximation. The numerical model is based on Godunov's explicit scheme...

The inverse problem of wave scattering for a system of data collected at the observation surface with multiple coverage of sources and receivers is considered. It is shown that this redundant data system is equivalent to the configuration studied previously, in which the receiver point coincides with the source point...

A comparative analysis of the group aero- and armor ballistics of the ancient and modern poly-wedge arrows is made. The idea formulated is to use these arrows as components of warheads of the carrier rockets for the anti-asteroid defence of the Earth and the orbital stations.

We discuss a specific nature of the phase-synchronized-weighted (Synphase-Weighted) Median Filters when processing frequency-modulated (possibly, swip) signals recorded at a discrete time. It is shown that the response of the Synphase-Weighted Median Filters weaker depends on the filter length than the response of conventional median filters. The conclusions obtained are...

The present monograph is devoted to the theoretical and numerical study of the interaction of electromagnetic fields with deformable media. The models considered are based on different combination of the Lam´e and Maxwell equations. Several direct and associated with them inverse problems are studied. Then speaking about inverse problems, electromagnetic...

The problem of inhomogeneity of the observation system in the Common Depth Point Method (CDPM) was considered by authors earlier. It results from the following. At the construction of the CDP seismograms by using the data obtained by the method of multiple overlaps (MMO), there appear the CDP configurations whose...

Basic principles and engineering solutions of the AXON`s user interface are described in this paper. The software AXON is a part of the mobile geophysical data gathering systems "Rosa-D", "Rosa-N", "VIRS-M" developed in the ICM&MG. AXON provides the automatic and manual (human supervised) modes and contains a kit of tools...

Modern technology of seismic survey is based on assumptions about the use of sounding signals distinguished by their characteristics. Thus, the experimentally obtained seismograms have a different form, which appears to be an objective hindrance when comparing and interpreting the obtained seismograms. An invariant seismic experiment is understood as seismic...

The automized technology of location of a different types of seismic sources - industrial explosions, vibrators, etc., - against the noise is proposed. The efficiency of the proposed approach is illustrated on a series of examples.

One of the possible statements of a boundary value problem for a system of equations of porous media is considered. The Carleman formula for the solution of this problem is obtained.

Formulas for the modified Darcy and Ohm laws are obtained. The diffusion coefficient is shown to be a function of the conductivity of the liquid, elastic porous body, and electrokinetic coefficient. A formula for the determination of porosity is obtained.

The process of radiation of seismic wave fields generated by powerful seismic vibrators is accompanied by a number of physical phenomena taking place in the vicinity of a source and having continuation at significant distances from it. The present paper is dealt with the analysis of these phenomena and the...

The paper deals with mathematical problems of physical phenomena, connected with generation, long-distance propagation, and interaction of the acoustic and the seismic waves from powerful vibrational sources operating on the interface of the elastic Earth-atmosphere. Three problems of mathematical modeling are considered: modeling of acoustic waves radiation of a vibrational...

In this paper, the process of tsunami wave propagation along the waveguide with flat sloping sides is studied using the wave-ray method. When propagating along the waveguide, a single tsunami wave transforms into the wave train. The expression for the propagation velocities of the fastest and slowest signals is defined...

In this paper, the formulas of digital recursive filters for the long-period deconvolution, which are successfully tested on real records of seismic events, are deduced.

The possibilities of obtaining numerical estimations of the time of wave propagation and parameters to describe the form of recorded wave impulses, with the use of a sequence of sessions of the monochromatic radiation on various frequencies are investigated. The monochromatic signals are invariant in their form when propagating in...

The method of filtration of monochromatic vibroseismic signals is offered. The proposed method is based on the application of the operation resulting in the compression of a frequency characteristic of the passband filter with the centre of compression assigned to a basic signal. The coefficient of compression of the frequency...

The statements of inverse problems of two types are considered within the framework of the scalar wave equation. The inverse problems include the reconstruction of sources of the wave field (the right-hand side of the equation) and the determination of the unknown coefficient (wave velocity). In spite of some difference...

The object of the research is a travel time curve (the second term is a hodograph) which is obtained by profiling. In this paper, an attempt is made to offer a model of the hodograph as well as some ways of its analysis.

Reception and recording systems called VIRS-M and ROSA developed at the Institute of Computational Mathematics and Mathematical Geophysics (ICM&MG), SB RAS, are considered in this paper. They are designed for scientific investigations of vibroseismic fields and calibration of seismic stations and seismic traces with the use of powerful seismic vibrators.

The paper is dealt with a brief statement of a basis of the theory of optimal planning of seismic networks. Some concepts of such a planning of seismic networks are given. Some specific formulations of problems of planning of seismic networks are presented. A numerical algorithm of constructing discrete optimal...

It is known that a key to efficiency of functioning of the International Seismic Monitoring System (ISMS) is the definition of the location and identification of a source of seismic waves. The priority issues are those of increasing the accuracy of solving these problems. Here errors in the determination of...

It is well known that the self-contained deep-water stations (ADS) are widely accepted in the tasks of the World Ocean monitoring. Various information about physical fields is collected via the ADS network, distributed throughout the ocean floor. The information from each ADS is clocked with its internal clock having a...

The paper presents the results of mathematical modeling of superpower vibrational sources for the global tomography of the Earth. A hydroresonance scheme of a seismovibrator is considered, in which an oscillating in the vertical shaft liquid column with the mass of several tens thousands tons serves a seismic waves source...

Realization of the Wave Analog of the Common Depth Point Method (WCDP) is described. This method is one of numerous employed in seismic data processing and is based on the "rigorous" mathematical solution of the inverse scattering problem in linear approximation by multiple overlapping data. The WCDP method is tested...

A variant of modified training functional that allows considering fuzzy input data is suggested. A limiting case when a part of input data is completely undefined, and, therefore, a problem of reconstruction of hidden parameters should be solved, is also considered. Some numerical experiments are presented. The suggested approach yields...

Optimization methods of the solution of inverse kinematic problems, have gained importance in the last few years. Such methods demand fast algorithms of ray tracing from a given position of the source to a given series of the points, forming a set (generally speaking, two-dimensional) of the receivers on the...

The paper deals with the reconstruction of the original tsunami waveform in the source area records from the waves observed on a set of the coastal wave gauges. The wave propagation is described by the linearized shallow-water equations when depth depends on one variable. The direct problem is approximated by...

The paper deals with the statement of mathematical problems and the analysis of experimental data of physical phenomena, connected with generation, long-distance propagation and interaction of the acoustic and the seismic waves from powerful vibrational sources working on the interface of the elastic Earth - atmosphere. This phenomena were observed...

The paper describes the results of the application of the "client–server" technology for the development of the Web version of the Historical Tsunami Database for the Pacific. The database consists of two main parts: the catalog of tsunamigenic events in the Pacific with their basis source parameters and the catalog...

Currently, vibroseismic method for the Earth’s Sounding (VES) is in most common use in solution of a great number of the geophysical tasks, such as vibroseismic monitoring of seismic-prone zones, seismic tomography, calibration sounding of seismic traces and seismic stations for increasing of the accuracy of definition of the coordinates...

The wave propagation in real media can be described within the framework of the theory of linear viscoelasticity. The presence of convolutional integral in Boltzmann' superposition principle poses the main difficulties in implementing the direct numerical methods in time domain. The paper presents an efficient algorithm, based on the application...

The paper deals with the modeling of the resonant vibrational source of the acoustic waves of infrasonic frequency range for the Earth's global tomography problems. The model of the hydroacoustic vibrational source includes a gasfilled resonance radiator operated under the free surface of the liquid. It is shown that for...

We present a subgrid model for the flow of incompressible fluid through fractal porous rocks. Using the scaling hypothesis for the latter, we derive an expression for the effective permeability.

The equations of motion of a two-component isothermal viscous fluid for two cases are considered, when 1) velocity-pressure and 2) stream function - vortex are taken as unknown variables. Such equations can, in particular, be used for the mathematical simulation of some geodynamic processes. The algorithm of numerical solution of...

On the basis of group bundle of the eikonal equation the new equations, estimates and formulas are obtained which give a new description of the direct and inverse kinematic seismic problem (geometrical optics). The paper given is the summary of these results. They make it possible to reduce the direct...

The mathematical models of the tsunami wave generation by an underwater landslide should include a set of the fluid flow equations and the landslide motion equations along the sloping surface taking into account the energy of the wave generation and the necessary initial and the boundary conditions. Examples of the...

Dilatancy, or increase in void volume, is typically associated with the inelastic deformation of a relatively intact rock. However, dilatancy associated with frictional sliding in laboratory samples also has been observed. At low normal stresses, dilatancy may be due to the uplift in sliding over asperity contacts. At higher normal...

The inverse problem of wave scattering on inhomogeneities of a medium within the framework of a scalar wave equation is considered. The scattered field in such a model can be described in two ways: either with the help of the surface distribution of secondary sources, or by using volume distribution...

There are grounds to consider that pattern recognition in geological sciences is a challenge to those engaged in applied mathematics, which was cast in the 50-s of the XX century by the practice of scientific investigations, to which no worth answer was found . As it seems, this is caused...

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...

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...

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.

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

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

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.

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...

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...

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 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...

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.

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...

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...

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.

An attempt is made to use the data of monitoring of electromagnetic precursors of earthquakes for reconstructing the time dynamics of some characteristics of the medium in the regions under observation. The results obtained show that, although the data are designed for statistical analysis, some parameters of the medium associated...

An inverse problem to determine the location of acting equivalent forces to geodetic data on the surface of the Earth's crust is considered within the framework of the quasistatic model for the elastic isotropic half-space with the sources of point type. It uses the data of monitoring for deformations of...

A physical-mathematical model and approaches to the measurement of the integral earthquake precursor proposed in the form of a theoretical scheme are developed by authors in previous papers. This model can probably reduce the acuteness of contradictions which often take place between precursors of different physical nature when a multidisciplinary...

The present paper is an attempt to develop a technology of fertilizer production with optimal output of nutrients (humates, macro- and microelements) on the basis of physical-mathematical simulation using vibroaction. An empirical formula relating the basic technological parameters, such as the frequency of vibroaction, time and temperature of the process...

The formulas for calculation the displacement of an elastic porous body, strains and pressure for simple forces using the Galerkin vector are obtained.

This paper describes a numerical method for the solution to the inverse problem for the equations of electromagnetoelasticity. We consider the case when electromagnetic waves are generated by elastic deformations. At the same time, we neglect the reverse influence of the electromagnetic field on the elastic oscillations.

We focus our...

In this paper, a technique for estimating diverse physical properties of bottom deposits is discussed. The methodology is based on the evaluation of reflection coefficients of stratigraphic boundaries using the amplitudes of bottom and multiple acoustic reflectors by the so-called quotient method in combination with the regression equations of Hamilton...

When solving the forward seismic problems in inhomogeneous media it appeared effective to use algorithms based on a combination of finite integral Fourier, Fourier-Bessel or Legendre transforms along one or two spatial coordinates with the finite difference technique along the remaining coordinate. The development of such an approach for vertically...

This paper is the latest version of the numerical-analytical algorithm for solving the forward seismic problem and migration. The main concept of the algorithm is in splitting of 2D and 3D seismic problems to a series of 1D problems with the help of the finite integral Fourier, Fourier-Bessel or Legendre...

The paper presents an algorithm of domain decomposition when solving the forward dynamic seismic problem in the polar coordinate system. The new algorithm is based on combination of the method of direct and of finite integral Fourier transforms. As seen from the studies conducted, if on some sites of the...

Rational utilization of raw materials and effective control of their use calls for creation of computer data banks on the state of natural resources. The necessity of creation of a data bank on peats is obvious.

First, Russia occupies a highly important place in the world's resources of peat. The...

Differences and regularities of the behavior of quartz under the action of the both methods make it possible to conclude that vibroaction is a promising and highly effective method of activation of substances. It allows (given the deformation of the structure is small without reconstruction) a considerable increase of the...

The paper is devoted to reconstruction of the movement of the ocean bottom when the water elevation is known at the finite set of points. For this ill-posed problem the technique using r-solutions is suggested; it is based on the singular value decomposition of the compact operator. The dependence of...

A new method for seismological investigation of the Earth's crust and the upper mantle, geodynamic processes and earthquake preparation zones has been developed using powerful vibrational sources of seismic waves. Since nuclear explosions have been prohibited, this method remains the only active method for deep seismic sounding of the Earth...

Efficiency of systems for monitoring of nuclear tests within the Comprehensive Test Ban Treaty (CTBT) essentially depends on accuracy in the determination of time, geographical coordinates, depth and power of explosions in accordance with the data for seismic waves recorded by seismologic stations. The purpose of the present project is...

The paper considers the results of the 1995 Russian--Japanese experiment, in which the structure of vibroseismic fields of powerful sources, as well as the relation between these fields and the tensely deformed state of the geological medium were investigated.

The raise of efficiency for information process engineerings is an actual problem. In the paper, the effective algorithm of digital handling of signals is presented. The given algorithm can be used in many applications of the spectral analysis.

The present paper is dedicated to the construction of an allocated system designed to perform vibroseismic monitoring of earthquake prone zones.

The main problem is associated with the creation of a distributed computer system providing collection, accumulation and processing of the observational data at an area of several thousands of...

The phenomenon of intensive acoustic wave excitation by surface explosion sources is known in seismology and seismic prospecting geophysics. The sound impulse from explosion propagating along the Earth's surface induces elastic surface waves. They are recorded on seismograms with arrival times equal to the travel time of acoustic wave from...

A specific character of "the wave arrival time" concept with reference to seismorecords taken from a vibrating source is considered. The arrival time is defined as the envelope maximum on the grouped waves of the corresponding convolution. The accuracy of estimation of the envelope maximum depending on the degree of...

The recently developed method of active vibroseismic monitoring is based on the sounding of a geological structure by seismic waves from artificial controlled sources-vibrators. Thus, the changes occurring in the tensely-deformed state of a medium are considered as related to changes of information parameters of wave fields that are established...

The given work is aimed at the analysis of features of spectral-temporal functions (STF), describing vibrational seismograms from powerful vibrators in the near and far zones. The spectral characteristics of P- and S-waves in a far zone at distances of 50, 320, 355 km have been analyzed. The phenomenon of...

The paper is devoted to modeling of the acoustoseismic induction process caused by the interaction of a harmonic wave with elastic half-space. This effect was first detected in experiments with powerful vibrational sources of seismic waves, carried out at the vibroseismic test site of Siberian Branch of RAS. The 2D...

The method of\/ active vibroseismic monitoring being developed recently suggests geological medium probing by seismic waves from artificial controlled sources. Here the changes happening in the stress-deformed state of the medium and its rheologic characteristics are determined by changes in the information parameters of seismograms, i.e., by changes in the...

In the article, there resumed the results of polarization treatment of seismic fields from various types of powerful vibrators depending on temperature of surrounding air. Peculiarities of P- and S-waves in these conditions have been studied.

The main aspects of the complex amplitude method were developed for analyzing the modulated oscillations in radio engineering systems. Such signals representing the oscillations of the carrier frequency ω0 modulated by a relatively low-frequency signal Ωmax are characterized by the relationship Ωmax ≪ ω0. Most generally...

The present work deals with the problems connected with precision of measurements of vibroseismic signals and techniques of setting-up an amplification factor of the seismometric channel.

We present some definitions of the percentile filter and the weighted-order statistics. Then we offer the probability interpretation of the weighted-order statistics and the definition of the percentile filter for this case. To conclude, we give some examples of data processing, characteristic of some fields of geophysics.

It is proposed to increase the accuracy in the determination of the seismic sources’ coordinates and power, taking into account quantitatively the kinematic and dynamic anomalies of the seismic field, associated with a considerable spatial non-homogeneity of the Earth along the traces of the waves’ passage and in the places...

This paper describes a numerical method for the solution of the inverse problem of acoustics in the case of recording of the full wave field at the free surface. The solution is sought by means of minimization of the data misfit functional which is a mean square deviation of the...

The given paper considers the problem of determination of the right hand side of the high-order parabolic equation with the variable coefficients.

A vibroseismic method of studying the Earth’s deep structure has been most intensively used in the last fifteen years. Much progress has been made toward the creation of powerful seismic vibrators with precise amplitude- frequency-phase characteristics as well as toward methods and instruments for measuring the wave field parameters in...

When solving the multi-dimensional problems of theory of the seismic wave propagation, the numerical-analytical method, based on the combination of finite integral transforms with the finite-difference method is gaining in importance in the last few years. In this paper, instead of the finite difference method with respect to one spatial...

Geographic information systems (GIS) of different kinds are now widely used for numerical modeling of geophysical processes. The main idea of GIS is visualization of some kind of objects and results of mathematical modeling on a geographic map which if drawn on the screen of computer. In majority GIS during...

The induction seismomagnetic effects arising in the seismic wave motion in the Ktant Earth’s magnetic field are numerically studied in this artical. The phenomenon is described as a simultaneous solution of the system of elastic equations quasistationary Maxwell’s equations with displacement velocity components, solving the problem we use numerical-analitical algorithm...

Inverse problem for wave equation with instant, lagging source on segment of boundary y=0 is considered. The problem of determination of sound velocity, smooth depending of both spacing coordinates by response of medium on the same segment, is posed. In regularizating statement the uniqueness of problem is proved with assumption...

The article is devoted to methodological aspects of constructions of expert system to geophysical data processing. Expert system will provide a researcher-geophysicist with the powerful software tools that increase efficiency of his work while solving, prediction, analysis and interpretation of geophysical objects according to the number of features.

In the...

The paper contains the proof of theorem estimating the condition number of matrix after discretization of the integral equation of the first kind with logarithmic singularity on the closed curve by the collocation method with piecewise-linear approximation of unknown function. It is based on a new approach using convex properties...

A method for the determination of the integral critical parameter (precursor) of the rocks strength and destruction has been developed using the dilatancy physical–mathematical model for the destruction of rocks in the earthquake source. This parameter is density of cracks in the unit of the volume. It is determined on...

The paper deals with the problem of combined inversion of wave and electromagnetic fields. It is assumed that there exists the functional relation between the velocity and electric conductivity the character of which is known to us.

The distributions of velocity and conductivity in the medium under study are chosen...

The problem of the simultaneous determination of the sounding signal form and wave propagation velocity in a vertically-inhomogeneous medium is considered in the paper.

It should be noted that usually the form of the sounding signal is either unknown or given only approximately, although its accurate estimate is necessary for...

The notion of the *r*-solution for a system of linear equation in the finite dimensional Euclidean space generalizes for an equation in Hilbert space with a compact operator. The Hadamard correctness of *r*-solution is proved (i.e., its stability with respect to perturbation of right-hand side and operator).

As a result of a feasibility study, a concept and prototype of the Expert Tsunami Data Base (ETDB) was developed at the Tsunami Laboratory of the Novosibirsk Computing Center, Russian Academy of Sciences. The ETDB contains in the digital form all available information on regional earthquakes and tsunamis (source parameters...

In the paper the technology for creating detailed digital bathymetry on personal computer is given. Such data is necessary for numerical modeling of tsunami waves. Information about depth is based on bathymetry charts (on paper). Two methods of digitizing are proposed. Given examples illustrate fitness of this technology for this...

The problem to recover structure of vertically-inhomogeneous medium by VSP data with unknown source-function is considered on the basis of optimization approach. It is proved that any stationary point of the cost function provides identity of a simulated wave field with a recorded one.

A numerical algorithm to reconstruct velocity...

A number of inverse problems of oscillation processes studied in optics, acoustics, radiophysics and geophysics may be reduced to solving the integral equation of the convolution type with the special kernel. Several theorems for uniqueness solution of this integral equation are proved. These proofs are constructive and may be used...