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On the Determination of the Velocity and Elastic Parameters of a Medium in the Focal Zone from Earthquake Hodographs

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Abstract

We consider the inverse kinematic problem of seismics (IKPS) with internal sources. It consists in determining the velocities of the longitudinal and transverse waves by the travel times from earthquake sources in the focal zone to a group of seismic stations. We propose an algorithm for the numerical solution of the problem which bases on the eikonal equation and the technology of smoothing multidimensional splines, which give an approximation of the velocity structure of the focal zone. The paper presents some theoretical results that substantiate the algorithm for solving the problem by approximation methods on using smoothing with multidimensional splines from data on irregular grids. We describe the results of the numerical solution of the problem, the calculations with real data on earthquakes in the focal zone, and give the estimates of the velocity and elastic parameters of a medium.

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Funding

The authors were supported within the framework of the State Contract of the Sobolev Institute of Mathematics (projects Nos. 0314–2019–0011 and 0314–2019–0013) and partially by the Russian Foundation for Basic Research (RFBR) and the German Science Foundation (DFG) (joint German–Russian research project 19–51–12008).

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, 630090, Russia

    Yu. E. Anikonov, V. V. Bogdanov, Yu. S. Volkov & E. Yu. Derevtsov

Authors
  1. Yu. E. Anikonov
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  2. V. V. Bogdanov
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  3. Yu. S. Volkov
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  4. E. Yu. Derevtsov
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Corresponding authors

Correspondence to Yu. E. Anikonov, V. V. Bogdanov, Yu. S. Volkov or E. Yu. Derevtsov.

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Anikonov, Y.E., Bogdanov, V.V., Volkov, Y.S. et al. On the Determination of the Velocity and Elastic Parameters of a Medium in the Focal Zone from Earthquake Hodographs. J. Appl. Ind. Math. 15, 569–585 (2021). https://doi.org/10.1134/S1990478921040013

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  • DOI: https://doi.org/10.1134/S1990478921040013

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