Выпуск 26

A model based on a smoothed interpretation of seismicity is presented here. We assign to a population of earthquakes a real valued function, which we call seismic flux. We considered 15 regions in the Northwest Pacific and find an evident correlation between premonitory flux anomalies and subsequent major earthquakes.

The 1979–1992 earthquake catalog issued by Department of Observatories, Institute of Physics of the Earth, Paris, provides an opportunity for intermediate-term prediction of earthquakes with magnitude M\geqslant 5.5 in the Lesser Antilles arc. The CN algorithm, when applied to this catalog identified two Times of Increased Probability (TIP) of such earthquakes; one TIP precedes the only large earthquake (3.16.1985, Ml=6.2, which occurred during the period considered; the second TIP is an alarm still in force. During both TIPs the seismic activity increased above 40 km depth and decreased below it.

We suggest a multifractal approach to describe seismicity and study self-similarity properties of clustering in space and time. We construct models (synthetic catalogs), two fractal and two multifractal, and compare them with four real subcatalogs from southern California. The parameters of the models are found by fitting generalized dimensions. Relations are shown between the models and real catalogs.

The migration of epicentral regions of great (M\geqslant 6) earthquakes in the western and central Caspian Sea is examined by analysis of catalogs of major earthquakes in the periods 1930–1990. The analysis indicates the southeast direction of migration of the seismic activity in the region. The average migration velocity is found to be approximately 6 km per year. An attempt is made to predict earthquakes using models of tectonic stress waves due to migration of deformation in the crust and the upper mantle. These waves, appearing after events, can trigger new events in other regions. A mathematical model describing propagation of stress in the lithosphere is studied. Analytical and numerical methods indicate the variation of the migration velocity with the lithosphere thickness and effective asthenosphere viscosity. That velocity varies from 1 to 100 km per year for reasonable values of the parameters.

The purpose of this paper is to analyze the time variation of seismicity with the help of a nonstationary self-exciting point process model. The model parameters are evaluated in a moving time window under the condition that each window contains the same number of events (thus the time length of the window varies). From each window a parameter vector is obtained, and so a “cloud” of parameter vectors for a seismic region to be considered. This “cloud” is analyzed with a view to detecting anomalies and different “modes” of seismicity. The results of processing the seismic catalog of the western USA (1963–1990) for various subregions are presented.

A method of statistical estimation of power \alpha of low-frequency spectrum asymptotics f(\lambda)\thicksim c/\lambda^\alpha for Gaussian and point processes is presented. The method is applied to several geophysical processes: Earth’s nutation, atmospheric pressure and regional seismicity.

The activation theory of fracture is used to construct a numerical model of a solid body. The behavior of the model demonstrates creep, the existence of lower and upper yield points, strain hardening, dilatancy, the growth of elactic anisotropy, and drop of the velocity ratio \nu_p/\nu_s under loading.

Two one-dimensional models of an earthquake fault studied here are constructed as systems of blocks residing in one of three (the first model) or five states (the second model). Certain transition rules are included, which specify the interaction of blocks. We obtain a magnitude-frequency relation similar to that in the model of Burridge and Knopoff. We also study the evolution of large events and show that the behavior the model can be described by information effectively contracted by the multifractal technique.

The systematic deviation of the magnitude of a single earthquake from the linear orthogonal regression between local magnitude M_L and coda duration magnitude M_d, calculated for the whole region in used as a measure of the frequency content of Italian earthquakes. Predominantly high-frequency events are found in two areas of Quaternary tectonic shortening, in northern Central Italy and in the Calabrian arc. This result, confirmed by two independent statistical tests, is in agreement with the global creepex pattern obtained from a study of the regression between body-wave magnitude, m_b, and surface-wave magnitude M_S: there is a systematic shift to higher frequencies in the seismic energy release for subduction zones and to lower frequencies in spreading zones.

Creepex which is the difference between M_S magnitude and the orthogonal regression of M_S on m_b is used as a spectral characteristic of seismic sources. Estimation of creepex precision is made on EDR bulletin data. The statistical significance of the difference between the source spectrums of subduction and spreading zones is demonstrated using the data of A.M. Dziewonski’s CMT catalog. The spectrum are different also for two continuous zones with different spreading rates. Creepex in relation to a parameter of source mechanism – null axis plunge – is studied for spreading and subduction zones.

We present an algorithm for numerical modeling of three-dimensional viscous flows governed by Stokes’, continuity, and thermoconvection equations in a rectangular three-dimensional region. We apply the finite-difference technique to these equations written in terms of natural variables, that is, velocity components, pressure, and temperature. At each time step we solve one parabolic and five elliptic equations, one after another. Lithospheric pates are assumed to be thin and perfectly rigid, drifting on the surface of a viscous fluid. The thermomechanical coupling between the flow and the plates is introduced through boundary conditions representing no-slip and zero heat flux conditions at the bottom of the plates. The translatory and rotary motions of the plates depend on the velocity of mantle flows and on mechanical interaction between the plates. We calculated movements of Laurasia and Gondwana supercontinents, including formation and breakup of Pangaea. Initially, steady convection is assumed in a three-dimensional rectangular 3×3×1 box. The initial positions of the continents are taken from geological reconstruction data for one billion years ago. Numerical results show that the continents approach each other and converge into Pangea covering the descending mantle flow. Then the convection pattern changes due to thermal insulation at the boundary. An ascending flow forms in place of the formerly descending flow, which leads to the breakup of Pangea after several hundred million years.

As can be seen from the seismicity of the last decade a continuous seismic belt bounds the Bering sea on the west. Hence the Bering sea region is surrounded by seismic belts, thus identifying the present-day Beringia plate. Alternative hypotheses of the South Koryakiya seismicity origin are discussed. These hypotheses are tested using data for the largest Koryakiya earthquake. Estimates of this earthquake focal mechanism and source spatio-temporal integral parameters were obtained from long period surface wave records. Seismogenic strain fields have been reconstructed from aftershock data. A qualitative model of the source evolution was developed. The relation of the source processes to the recent tectonics of South Koryakiya is demonstrated. The present-day evolution of the plate boundary was compared with past tectonic processes in the region. A rough model of Beringia plate motion was developed.

A nonlinear integral rheological model is proposed to describe the rheology of the earth’s mantle. For constant stress the model behaves like a power-law non-Newtonian fluid. However, the model differs significantly if stress changes with time, because it has a memory, in contrast with the power-law fluid model. The proposed model is applied to linear stability analysis of large-scale convective circulation in the mantle. The Lorenz equations, a three-mode spatial Fourier expansion of the non-linear thermal convection equations are generalized for non-Newtonian fluid models. In the proposed rheological model, the instability of the lower thermal boundary layer of a whole mantle convective circulation is oscillatory. The period of the boundary layer convective oscillation is about 6×10⁷ years.

We present a sedimentary basin formation mechanism based on the subsidence of an eclogite lens in the upper mantle. After the extension of the lithosphere a hot asthenospheric component is advected to the base of the lithosphere into the space created by that process. If the lithosphere/asthenosphere boundary prevents further magma uplift a magmatic lens concentrates due to its buoyancy at the roof of the asthenospheric bulge. We assume that basalt melt in the asthenospheric bulge has not been transported onto the surface and stays in the magmatic lens. According to experimental data, basalt melts turn into eclogite of an increased density during the process of general cooling and crystalization at pressures of 18–22 Kb and temperatures of 1000–1200°C (at 60–80 km depth). Hence the eclogite lens causes crustal subsidence resulting in sedimentary basin formation. A bicubic spline finite element method is used for a quantitative analysis of the proposed subsidence mechanism. The model region comprises a cross section through the lithosphere and the upper part of the asthenosphere. We assume the Newtonian rheology with variable density and viscosity. An approximate topography is calculated from the normal stress at the free-slip surface boundary for several sample models. The model can be applied to study intracratonic sedimentary basin evolution.

Even the simplest cases of rotating fluids in a sphere or a spherical shell, as in the earth’s core, are not yet completely studied; in particular, this is the case of Poincare’s operator. Namely, the following problem arises: To choose most smooth, or least oscillatory, fields from a family of vector or tensor fields in some space. We consider Dirichlet’s integral as a functional defined on normalized fields and use it to compare their smoothness. Particularly, we used this functional to classify known principal modes of Poincare’s operator in a sphere. It is also possible to use the functional in a more complicated problem where a spherical shell is taken instead of a sphere; it is possible to choose a basis, ordered in smoothness, in the space of smooth solenoidal fields, and to construct successive Galerkin’s subspaces in this basis.

In this article the procedure to solve the inverse scattering problem for two-dimensional acoustic equation is proposed. The method to construct a scatterer with the given scattering amplitude at fixed frequency \omega is presented. The hypothesis about convergence for \omega \rightarrow \infty is proposed.

Rayleigh-type vibrations are usually studied in geophysics for various cases of plane-stratified media. However, such vibrations exist in elastic media with other types of symmetry, as in cylindrical axially symmetric bodies with properties varying with radius. This type of symmetry is typical of well logging measurements and can often be found in engineering problems, such as the ultrasonic nondestructive testing of cables, pipes, and optical fibers. We show here that vibrations in a cylindrical body can be described by solutions of a matrix Sturm–Liouville problem. The matrix potential in such problem has the same structure as in the case of usual Rayleigh waves in a plane-stratified body. The two cases differ in the analytical form of the symmetric matrices D specifying the potentials and in the boundary conditions at the surface. We derive the matrix D and the boundary conditions for the case of the cylindrical symmetry.

A complete mathematical study is presented for an extremum problem that has arisen in the development of the fast search algorithm yielding the widest waveguide.

We describe a method providing 10 to 30 times cuts in computation time of synthetic seismograms for gradient media as compared with the standard Thomson–Haskell algorithm. The speed is achieved by using specific, so-called D-constant, gradient media for approximation. The analytical solution of equations for Rayleigh surface waves in such media is simpler than in homogeneous media.

The approach developed earlier for solving 2D tomography problem is extended for joint estimation of lateral velocity variations and azimuthal anisotropy. The solution satisfies a’priori assumption on smoothness of unknown functions. Numerical examples demonstrate efficiency of the method. The method was applied for estimation of azimuthal anisotropy of Rayleigh wave velocities in southeastern Europe. A strong azimuthal anisotropy was found in the solution. However, the analysis of resolution indicated that the anisotropy resulted from lateral heterogeneity.

We study Rayleigh waves in a heterogeneous elastic half-space whose density and Lame’s parameters are proportional and increase exponentially with depth. The Rayleigh waves do not propagate at a frequency lower than a critical one. We show the cutoff frequency depends on Lame’s parameters and density, and derive in a parametric form the Rayleigh wave phase velocity as a function of frequency.

A geologic structure with several waveguides is used to illustrate the determination of SH velocity from Love modes excited by a low frequency monochromatic surface source. The velocity distribution in a waveguide becomes available through the technique, though in a smoothed form, if the thickness of waveguide lid is less than wavelength of the monochromatic signal.