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63. Anikonov Yu.E., Bogdanov V.V., Derevtsov E.Yu., Miroshnichenko V.L., Pivovarova N.B., Slavina L.B. Some
approaches to a numerical solution for the multidimensional inverse kinematic problem of seismics with inner sources //
J. Inv. Ill-Posed Problems. 2009. V. 17, No. 3. P. 209-238.
Spectral portraits in tasks of recognition of moving objects
V. I. Dobrorodny
Tyumen Higher Military Engineering Command School named after Marshal of the Engineering Troops
A. I. Proshlyakov
Email: Dobrorodny@bk.ru
DOI 10.24412/cl-35065-2021-1-02-92
The paper presents the consideration of tasks of passive geometric environmental monitoring associated
with seismic and acoustic detection of man-made noise sources affecting the deterioration of the surrounding
environmental background. Another task is related to the problem of automatic classification of noise sources
by dividing them into disjoint sets in the space of their corresponding informative parameters. Obtaining in-
formation about the object of radiation of the wave field is effectively solved by methods of spectral analysis.
Spectral analysis is the most informative method for analyzing various seismic and acoustic processes, includ-
ing those caused by moving sources. However, in the case of a moving source, a complex spectral picture aris-
es, connected with the peculiarity of the radiation of a particular object in various modes of its operation.
The classification problem based on spectral analysis requires a priori information about the object. With
this approach, it is effective to analyze the features of the wave field of the radiation object and present the
information obtained in the form of spectral portraits. In this case, spectral portraits mean the projection of a
three-dimensional frequency-time function onto a two-dimensional plane �frequency-time�. This projection
allows to select the time-frequency windows that characterize the analyzed seismic and acoustic vibrations.
The latter are used to construct clusters displaying the position of individual objects in the space of informa-
tive parameters of moving objects. On the basis of experimental data, the paper presents the consideration
and results of the listed stages of solving the problems of passive geophysical monitoring.
3D ray shooting algorithm in heterogeneous isotropic media
A. A. Galaktionova1,2, A. S. Belonosov1,2
1Institute of Computational Mathematics and Mathematical Geophysics SB RAS
2Novosibirsk State University
Email: a.galaktionova@g.nsu.ru
DOI 10.24412/cl-35065-2021-1-01-01
The problem of numerical modeling of seismic waves propagation in three-dimensional heterogeneous
isotropic media is of practical interest in seismic imaging and seismic exploration [1]. We solve this problem by
the ray tracing method [2]. The purpose of the work is to develop effective algorithms and programs for calcu-
lating the times and directions of arrival of seismic waves in a given 3D grid of receivers.
An algorithm for 3D ray shooting has been developed. This algorithm can be applied for a point source and
also for a more general case when the initial position of the wave front is given as a surface. The algorithm re-
quires a velocity to be a smooth function. As far as this requirement is limitative we use smoothing algorithm
based on a spatial low-pass filtering. We use an operator which describes the operation of a digital-to-analog
converter (DAC), well known in digital signal processing theory [3].
The cases of different velocity structure of the medium are considered: homogeneous, gradient, etc., as
well as various types of the initial wave front position surface. The results of numerical experiments are pre-
sented.
References
1. Gjoystdal H., Iversen E., Laurain R. et al. Review of ray theory applications in modelling and imaging of seismic data
// Stud. Geoph. Geod. 2002. V. 46. P. 113-164.
2. Cerveny V. Seismic Ray Theory. New York: Cambridge University Press, 2001.
3. Rabiner L. R., Gold B. Theory and Application of Digital Signal Processing. Prentice Hall Inc, 1975. Ch. 5. P. 300-302.
Exact Navier � Stokes solutions for oil and gas problems
V. A. Galkin1,2, A. O. Dubovik1,2
1Surgut Branch of Scientific Research Institute for System Analysis RAS
2Surgut State University
Email: alldubovik@gmail.com
DOI 10.24412/cl-35065-2021-1-01-02
The system of Navier-Stokes equations is considered, which describes the flow of a viscous incompressible
fluid in a porous medium. The simplest model of a porous medium consists of a discrete set of points - grid
nodes, which is the boundary of the flow region, in which the adhesion boundary condition is satisfied. Classes
of exact solutions corresponding to vortex flow are presented [1]. The study of exact solutions is necessary for
the development of a core simulator and simulation of fluid dynamics in a porous medium, its response to dy-
namic effects of various types and the creation of a domestic technology "digital field" [2].
This work was supported by the Russian Foundation for Basic Research (grants 18-01-00343, 18-47-860005).
References
1. Betelin V.B., Galkin V.A., Dubovik A.O. Exact Solutions of Incompressible Navier�Stokes Equations in the Case of Oil
and Gas Industrial Problems // Doklady Mathematics. 2020. V.102. No 3. pp.456�459. DOI: 10.1134/S1064562420060071.
2. Betelin V.B., Galkin V.A. Control of Incompressible Fluid Parameters in the Case of Time-Varying Flow Geometry//
Doklady Mathematics. 2015. V. 92. No 1. pp. 511-513. DOI: 10.1134/S1064562415040067.
Investigation of the propagation of nonlinear waves in a two-fluid medium caused by an analogue
of the Darcy coefficient
B. Kh. Imomnazarov1, B. B. Khudainazarov2
1Novosibirsk State University
2National University of Uzbekistan named after Mirzo Ulugbek
Email: imom@omzg.sscc.ru
DOI 10.24412/cl-35065-2021-1-01-03
The extreme difficulty of analyzing nonlinear waves, especially strong turbulence, led to another tendency
in the development of their theory - the transition from complex equations of nonlinear random waves to
simpler model equations [1, 2]. In this paper, a system of quasi-linear equations of hyperbolic type is obtained
from a system of non-stationary equations of two-velocity hydrodynamics [3-5]. It is believed that the energy
dissipation occurs due to the analogue of the Darcy. We study the Cauchy problem for a given system of equa-
tions in the class of bounded measurable functions based on the Kruzhkov method.
The support of the Russian Science Foundation under grant � 21-51-15002 is gratefully acknowledged.
