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

100%
Bogdanov V., Karsten W., Miroshnichenko V., Volkov Y.
Open Mathematics
|
2013
|
tom 11
|
nr 4
779-786
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.
2
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Obtaining a banded system of equations in complete spline interpolation problem via B-spline basis

100%
Volkov Y.
Open Mathematics
|
2012
|
tom 10
|
nr 1
352-356
EN
We study the problem of interpolation by a complete spline of 2n − 1 degree given in B-spline representation. Explicit formulas for the first nand the last ncoefficients of B-spline decomposition are found. It is shown that other B-spline coefficients can be computed as a solution of a banded system of an equitype linear equations.
3
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An extended Prony’s interpolation scheme on an equispaced grid

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Karalienė D., Navickas Z., Čiegis R., Ragulskis M.
Open Mathematics
|
2015
|
tom 13
|
nr 1
EN
An interpolation scheme on an equispaced grid based on the concept of the minimal order of the linear recurrent sequence is proposed in this paper. This interpolation scheme is exact when the number of nodes corresponds to the order of the linear recurrent function. It is shown that it is still possible to construct a nearest mimicking algebraic interpolant if the order of the linear recurrent function does not exist. The proposed interpolation technique can be considered as the extension of the Prony method and can be useful for describing noisy and defected signals.
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