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2013 | 11 | 4 | 779-786
Tytuł artykułu

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

Treść / Zawartość
Warianty tytułu
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.
Wydawca
Czasopismo
Rocznik
Tom
11
Numer
4
Strony
779-786
Opis fizyczny
Daty
wydano
2013-04-01
online
2013-01-29
Twórcy
autor
Bibliografia
  • [1] Aasen J.O., On the reduction of a symmetric matrix to tridiagonal form, Nordisk Tidskr. Informationsbehandling (BIT), 1971, 11, 233–242
  • [2] 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 seismic with inner sources, J. Inverse Ill-Posed Probl., 2009, 17(3), 209–238 http://dx.doi.org/10.1515/JIIP.2009.017
  • [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
  • [5] Hardy R.L., Theory and applications of the multiquadric-biharmonic method, 20 years of discovery 1968–1988, Comput. Math. Appl., 1990, 19(8–9), 163–208 http://dx.doi.org/10.1016/0898-1221(90)90272-L
  • [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)
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-012-0158-8
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