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5Section 3
MATHEMATICAL GEOPHYSICS
Intellectual environment for studying parameters of seismic acoustic fields
L. P. Braginskaya, T. L. Latyntseva
Institute of Computational Mathematics and Mathematical Geophysics SB RAS
Email: ludmila@opg.sscc.ru
DOI 10.24412/cl-35065-2021-1-03-00
The work analyze and structure the data that have been obtained by recording the seismic effects of the
SV-100 source and the group of seismic and hydroacoustic receivers at the Baikal Lake in March 2021. The re-
sults modeling have also been studied for these experiments.
The scientific intelligent system �Active seismology� has been arranged for storage, visualization, and nu-
merical analysis of these data
An intellectual web environment has been developed for the online investigation of the acoustic fields.
The work is supported by ICMMG SB RAS state contract (0251-2021-0004), RFBR grant 20-07-00861A.
Referencies
1. L.P. Braginskaya, A.P. Grigoriuk, and V.V. Kovalevsky. Ontology approach to the organization of the Web-
environment in active seismology // Processing of spatial data in the problems of monitoring the natural and anthropo-
genic processes (SDM-2019). 2019.P. 56-60.
2. V.V. Kovalevsky, L.P. Braginskaya, and A.P. Grigoriuk. Information and analytical system for seismic research //
Problems of Informatics. 2013. No 3. P. 22-29.
On a determination of speed and elastic parameters of a focal zone by the hodographs of earthquakes
V. V. Bogdanov, Yu. S. Volkov, E. Yu. Derevtsov
Sobolev Institute of Mathematics SB RAS
Email: bogdanov@math.nsc.ru volkov@math.nsc.ru dert@math.nsc.ru
DOI 10.24412/cl-35065-2021-1-01-00
An algorithm for solving the inverse kinematic problem of seismic with internal sources, which is based on
the method of multidimensional data approximation on chaotic grids [1], is considered. The arrival times of P
and S waves fixed by seismic stations are considered to be the most reliable kinematic data on earthquakes
occurring at great depths. The earthquake hodographs constructed by the method of multidimensional ap-
proximation make it possible to calculate the velocities Vp of longitudinal and Vs of shear waves under the as-
sumption that they obey the eikonal equation [2, 3]. The Vp/Vs ratio, which can be calculated already at any
point in the study area, determines the elastic parameters of the medium, such as Poisson's ratio, as well as
Young modulus and Lame parameters as functions considered in units of the density of the medium. The re-
sults of calculations based on real data are presented.
The work was partially supported by RFBR according to the research project RFBR-DFG No. 19-51-12008.
References
1. Volkov Yu. S., Miroshnichenko V. L. Construction of mathematical model of the hill diagram of the Francis turbine
// Sibirskii zhurnal industrial�noi matematiki. 1998. V.1. No. 1. P. 77-88 (in Russian).
2. Kravtsov Yu.A., Orlov Yu.I. Geometrical Optics of Inhomogeneous Media. Moscow: Nauka, 1980 (in Russian).
3. 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].
