Application of splines for determining the velocity characteristic of a medium from a vertical seismic survey

• Autorzy: Vladimir Bogdanov , Wladimir Karsten , Valeriy Miroshnichenko , Yuriy Volkov
• Języki publikacji: EN

Abstrakty

EN

A method for solving the inverse kinematic problem of determining the velocity characteristic of a medium from a vertical seismic survey, is proposed. It is based on the combined use of the eikonal equation and spline methods of approximation for multivariable functions. The problem is solved by assuming a horizontally stratified medium; no assumptions about the number of layers and their thickness are made. First, using the data of the first arrival times of the seismic signal from several shotpoints, which are registered by detectors located in the vertical borehole, a spline approximating the function of first arrival time of the signal from source points to any point in the Earth subsurface is constructed. Then with the help of the eikonal equation, the characteristic of the medium around the borehole is determined. Numerical experiments on the model and the real data show high efficiency of the proposed method.

Słowa kluczowe

EN

Velocity characteristic of a medium; Seismic survey; Eikonal equation; Traveltime of seismic waves; Vertical borehole; Spline approximation

Kategorie tematyczne

• 65D07: Splines
• 86A22: Inverse problems
• 65D15: Algorithms for functional approximation

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2013
• Tom: 11
• Numer: 4
• Strony: 779-786

Daty

wydano

2013-04-01

online

2013-01-29

Twórcy

autor

Vladimir Bogdanov

• Siberian Branch of the Russian Academy of Sciences

autor

Wladimir Karsten

• Siberian Branch of the Russian Academy of Sciences

autor

Valeriy Miroshnichenko

• Siberian Branch of the Russian Academy of Sciences

autor

Yuriy Volkov

• Siberian Branch of the Russian Academy of Sciences

Bibliografia

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• [3] Anikonov Yu.E., Bogdanov V.V., Derevtsov E.Yu., Miroshnichenko V.L., Sapozhnikova N.A., Numerical solution of an inverse kinematic seismic problem with internal sources, Sib. Zh. Ind. Mat., 2006, 9(4), 3–26 (in Russian)
• [4] Bezhaev A.Yu., Vasilenko V.A., Variational Theory of Splines, Kluwer Academic/Plenum, New York, 2001
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• [6] Miroshnichenko V.L., The approximation of functions given by values at scattered points by DMM-splines, In: Vsesibirskie Chteni’ya po Matematike i Mekhanike, 1, Matematika, Tomsk, June 17–20, 1997, Tomsk University, 1997, 211–212 (in Russian)
• [7] Sayfy A.M., Azzawi K.A., Makky S.M., Seismic inverse problems: determining seismic wave speeds using arrival times, Int. J. Comput. Math., 2006, 83(11), 797–808 http://dx.doi.org/10.1080/00207160601117123
• [8] Schaback R., Wendland H., Characterization and construction of radial basic functions, In: Multivariate Approximation and Applications, Cambridge University Press, Cambridge, 2001, 1–24 http://dx.doi.org/10.1017/CBO9780511569616.002
• [9] Volkov Yu.S., Miroshnichenko V.L., Constructing a mathematical model of a universal characteristic for a radial-axial hydroturbine, Sib. Zh. Ind. Mat., 1998, 1(1), 77–88 (in Russian)

Identyfikatory

DOI

10.2478/s11533-012-0158-8