Abstract: We consider a problem of determination velocity characteristics of medium by known first-arrival travel times from the earthquake sources to seismic stations. The problem is known as an inverse kinematic problem of seismic with internal sources [1]. Beginning time of earthquake and hypocenters coordinates assumed to be known. From the travel times of longitudinal and transverse waves to several seismic stations, it is required to find the velocities of these waves in the so-called focal zone, characterized by increased seismic activity, i.e. by a large number of earthquakes occurring in it. We offer a methodology for describing the features of the structure and state of the medium in focal zones. In particular, according to observations of Kamchatka seismological stations. We offer a methodology for describing the features of the structure and state of the environment in focal zones. In particular, according to observations of Kamchatka seismological stations. The technique allows one to build models of the distribution of velocities of longitudinal and transverse waves in the focal zone, and on their basis to determine such characteristics of the medium as the parameters of elasticity and deformation. The method is based on the eikonal equation and multidimensional approximation by splines [2], which allows one to use travel times data of seismic waves from hypocenters to observation stations whose location is irregular, as well as to construct a dynamic picture of the change in the environment, which is necessary for predicting dangerous or catastrophic natural phenomena such as earthquakes or tsunami waves. The authors were partially supported by the Russian Foundation for Basic Research and the German Research Foundation (project no. 19-51-12008). References 1. AnikonovYu.E., BogdanovV.V., DerevtsovE.Yu., MiroshnichenkoV.L., SapozhnikovaN.A. “Numerical solving the inverse kinematic seismic problem with internal sources”, Sib. Zh. Industr. Matematiki, 9, No.4(28), 3-26 (2006) (in Russian). 2. AnikonovYu.E., BogdanovV.V., DerevtsovE.Yu., MiroshnichenkoV.L., Pivovarova N. B., Slavina L.B. ”Some approaches to a numerical solution for the multidimensional inverse kinematic problem of seismics with inner sources”, J. Inverse Ill-Posed Problems, 17, No.3.209-238(2009).

Cite: Bogdanov V.V. , Derevtsov E.Y.
Application of splines in the problem of medium properties determination by seismic data
In compilation FRONTIER IN MATHEMATICS AND COMPUTER SCIENCE Abstracts of the International Online Conference (October 12–15, 2020,Tashkent).. – National University of Uzbekistan., 2020.

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