Выпуск 22

Strong foreshocks within days and hours before main shocks are examined to study time variations of the b-value in the frequency-magnitude law. Analysis of the world earthquake catalog (1964–80 years, M > 4) shows that b drops by a half during several hours before main shocks. An increase in the b-value with the increase of main shock magnitude (Berg) has not been detected.

The present paper considers the diagnostics of TIPs of strong earthquakes in a densely populated megapolice – the state of New York. The results of the paper confirm similarity of earthquake flow in low and high seismicity regions.

The authors study the possibility of TIPs diagnostics of earthquakes with M ≥ 5.6 in Central Italy using a set of properties of smaller main shock flow. The identified periods precede 3 out of 5 earthquakes and take up 17% of total time.

Assuming the hypothesis of similarity in spatial distribution of earthquakes, the reoccurrence law is presented in the following form {\lg N(M,L) = A - \mathit {B}(M - 5) + C\lg L}, where {N(M, L)} is the expected annual number of mainshocks of a certain magnitude M within an area of a linear dimension L. The coefficients are estimated for the seismic regions of the USSR and other countries, as well as for the global seismic belts of the Earth.

Times of the Increased Probability («TIPs») for strong earthquakes in the Eastern Tien Shan within 1963 through 1987 are retrospectively identified by algorithm M8. TIPs were diagnosed for all 4 earthquakes with M ≥ 6.5. Additional tests confirm the stability of the results.

A model of interaction of lithospheric blocks is suggested. Dynamics of the lithosphere is described as alternation of slow deformations and ruptures («earthquakes»). A model produces an artificial catalog of seismicity. The properties of this catalog are compared with and contrasted to the properties of real seismicity catalogs. By this means it is possible to determine which properties of earthquake sequence can be derived from simple assumptions about the processes that occur in the lithosphere. We consider both the instability of the process and the possibility that strong earthquakes might be predicted.

A multiscale model of defect development kinetics is studied. Some critical effects are found. The simulation produces the phenomena that make it possible to predict the time of a «large» defect.

The system of mobile interacting disks in the crumped circumstances is regarded as a model of geophysical environment. The evolution of the system simulated as described by the solution of a set of dynamic equations. Under conditions of stationary influence, the system demonstrates a complicated behavior that combines chaotic features with the formation of structures. There is a qualitative change of energy dissipation time series when the rate of deformation varies.

The problem of gravitational instability of compressible Maxwell medium is discussed. Two half-spaces with horizontal intermediate boundary are considered with the density of the upper half-space greater than that of the lower one. Growth of small harmonic perturbations of the intermediate boundary is analyzed. This problem is reduced to determination of eigenvalues of a system of ordinary differential equations with boundary conditions. This problem in its turn is reduced to computation of zeroes of an entire function. Results of computation (graphs of eigenvalues) are given with corresponding discussion.

The results of determination of the threshold for magnetic field generation values of magnetic Reynolds number are described in the Couette—Poiseuille flow of an electrically conducting fluid between cylinders of ideal conductor case.

The results of application of asymptotical methods to the analysis of the process of magnetic field generation by the Couette—Poiseuille flow of electrically conducting fluid are described. The good accordance with the results of calculations is obtained.

Kinematic dynamo problem of magnetic field generation in a sphere by a motion v (x) of conducting medium, defined by rot v (x) = δv (x), is solved numerically by Galerkin’s method for magnetic Reynolds number of the order 10¹–10². The model manifests the properties of a fast dynamo.

Asymptotics of the eigenvalue with the maximal real part of the equation of transference and diffusion of scalar admixture on the two-dimensional torus for large Reynolds numbers is studied numerically using Galerkin’s method.

Differential equations for dynamics of layered block model are obtained. As a result, applications of the model for engineering seismology problems become possible.

The paper presents two different substitutions into the system for the Rayleigh-type vibrations reducing it to two mutually transposed Sturm–Liouville’s boundary problems in matrix form. The property is used to derive orthonormality conditions for normal modes with complex, as well as real eigenvalues. Some relations are established between the complex eigenvalues and energy of the corresponding modes. The formula of matrix Weil’s function residues is obtained from the same property of the Rayleigh system.

It is well known that if there is a waveguide the one-dimensional kinematic inverse problem has no unique solution, i.e. the velocity structure is not uniquely determined by a travel time curve. Let u (y) is a possible solution. How is one to find the others? We assume in this paper that u (y) is a velocity-depth function having exactly one waveguide. Theorems have been proved giving a constructive technique to find a wide set of velocity-depth functions u*(y) with the same travel-time curve Γ as u (y).

Necessary and sufficient conditions of Love wave existence are found. They are formulated in terms of shear wave velocities, namely, Love waves can propagate if and only if {\rm{min}\; v_s(z) \lt v_s(\infty)}. Estimates for cut off frequencies for Love waves are presented.

Formulas for calculation of the derivative of surface wave phase velocity with respect to the depth of any interface are presented. This derivative is expressed in terms of parameters of the medium, of the relevant eigenfunction and its derivative at the interface depth and of values of integrals of this eigenfunction. Formulas are given for Love and Rayleigh waves both for flat and spherical geometry.

The existence of complex wave-numbers in the problem of vibrations of a liquid layer on an elastic half-space is considered. The main result is proof of the absence of complex wave-numbers for the case of vibrations decreasing with depth in the half-space. The low-frequency asymptotics for complex wave-numbers corresponding to solutions that increase with depth in the half-space is also obtained.

The inversion of surface wave spectra is applied to the NARS array data. The shear velocity structure between the stations is given.

The model of a «short» signal is considered on the segment T. It consists of two complex harmonics with unknown amplitudes and frequencies \omega_i plus a complex white noise. It is shown that frequencies \omega_i are resolved if and only if {\mid\omega_1-\omega_2\mid T^\gamma\gg 1}, where \gamma=5/4 for harmonics with unequal initial phases and \gamma=7/6 in the opposite case. Extremal properties of the least squares method for the model are found.

The statistical properties and resolution capability of Pisarenko’s method of harmonic decomposition (PHD) is investigated theoretically. The main result is as follows: the ability of the PHD-method to resolve closely spaced features manifests itself only for «long» time T, i.e. for {\sqrt[6]{T}\mid\Delta\omega\mid\gg 1}, where \mid\omega\mid is a frequency offset.

The statistical approach to the problem of the weak seismic signals detection and estimation by using the seismic array data is considered. The optimal algorithms are proposed which generalize Capon’s optimal array filtration. The adaptive array data on-line procedure is developed based on this algorithm. This procedure was investigated by computer simulation and by processing of the NORSAR seismic noise and signal records.

Recognition of earthquake-prone areas (М ≥ 5.0) is carried out in four regions of the Mediterranean Belt: the Pyrenees, Western Alps, Great Caucasus and Italy. Intersections of morphostructural lineaments are the objects of recognition. Universal geomorphic criteria have been obtained. The criteria detect intersections of lineaments where earthquakes М ≥ 5.0 can occur.