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 Computer Research and Modeling, 2017, Volume 9, Issue 5, Pages 761–771 (Mi crm97)

MODELS IN PHYSICS AND TECHNOLOGY

About applying Rayleigh formula based on the Kirchhoff integral equations for the seismic exploration problems

A. V. Favorskayaab, V. I. Golubevba

a Moscow Institute of Physics and Technology, Institytsky Pereylok 9, Dolgoprudny, Moscow Region, 141700, Russia
b Scientific Research Institute for System Studies of the Russian Academy of Sciences, Nahimovskij av. 36/1, Moscow, 117218, Russia

Abstract: In this paper we present Rayleigh formulas obtained from Kirchhoff integral formulas, which can later be used to obtain migration images. The relevance of the studies conducted in the work is due to the widespread use of migration in the interests of seismic oil and gas seismic exploration. A special feature of the work is the use of an elastic approximation to describe the dynamic behaviour of a geological environment, in contrast to the wide-spread acoustic approximation. The proposed approach will significantly improve the quality of seismic exploration in complex cases, such as permafrost and shelf zones of the southern and northern seas. The complexity of applying a system of equations describing the state of a linear-elastic medium to obtain Rayleigh formulas and algorithms based on them is a significant increase in the number of computations, the mathematical and analytical complexity of the resulting algorithms in comparison with the case of an acoustic medium. Therefore in industrial seismic surveys migration algorithms for the case of elastic waves are not currently used, which creates certain difficulties, since the acoustic approximation describes only longitudinal seismic waves in geological environments. This article presents the final analytical expressions that can be used to develop software systems using the description of elastic seismic waves: longitudinal and transverse, thereby covering the entire range of seismic waves: longitudinal reflected PP-waves, longitudinal reflected SP-waves, transverse reflected PS-waves and transverse reflected SS-waves. Also, the results of comparison of numerical solutions obtained on the basis of Rayleigh formulas with numerical solutions obtained by the grid-characteristic method are presented. The value of this comparison is due to the fact that the method based on Rayleigh integrals is based on analytical expressions, while the grid-characteristic method is a method of numerical integration of solutions based on a calculated grid. In the comparison, different types of sources were considered: a point source model widely used in marine and terrestrial seismic surveying and a flat wave model, which is also sometimes used in field studies.

Keywords: seismic survey process, hydrocarbons, Kirchhoff formula, acoustic waves, elastic waves, numerical simulation.

 Funding Agency Grant Number Grant of the President of the Russian Federation for State Support of Young Russian Scientists --- Candidates of Science ÌÊ-1831.2017.9 The work was supported by the grant of the President of Russian Federation MK-1831.2017.9.

DOI: https://doi.org/10.20537/2076-7633-2017-9-5-761-771

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UDC: 519.63
Revised: 18.09.2017
Accepted:29.09.2017

Citation: A. V. Favorskaya, V. I. Golubev, “About applying Rayleigh formula based on the Kirchhoff integral equations for the seismic exploration problems”, Computer Research and Modeling, 9:5 (2017), 761–771

Citation in format AMSBIB
\Bibitem{FavGol17} \by A.~V.~Favorskaya, V.~I.~Golubev \paper About applying Rayleigh formula based on the Kirchhoff integral equations for the seismic exploration problems \jour Computer Research and Modeling \yr 2017 \vol 9 \issue 5 \pages 761--771 \mathnet{http://mi.mathnet.ru/crm97} \crossref{https://doi.org/10.20537/2076-7633-2017-9-5-761-771}