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.
@article{bwmeta1.element.doi-10_2478_s11533-012-0158-8,
author = {Vladimir Bogdanov and Wladimir Karsten and Valeriy Miroshnichenko and Yuriy Volkov},
title = {Application of splines for determining the velocity characteristic of a medium from a vertical seismic survey},
journal = {Open Mathematics},
volume = {11},
year = {2013},
pages = {779-786},
zbl = {1260.86013},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0158-8}
}
Vladimir Bogdanov; Wladimir Karsten; Valeriy Miroshnichenko; Yuriy Volkov. Application of splines for determining the velocity characteristic of a medium from a vertical seismic survey. Open Mathematics, Tome 11 (2013) pp. 779-786. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0158-8/
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