1Sobolev Institute of Mathematics SB RAS, 630090 acad. Koptjug prosp., 4, Novosibirsk, Russia. Email: anik@math.nsc.ru
2Sobolev Institute of Mathematics SB RAS, 630090 acad. Koptjug prosp., 4, Novosibirsk, Russia. Email: bogdanov@math.nsc.ru
3Sobolev Institute of Mathematics SB RAS, 630090 acad. Koptjug prosp., 4, Novosibirsk, Russia. Email: dert@math.nsc.ru
4Sobolev Institute of Mathematics SB RAS, 630090 acad. Koptjug prosp., 4, Novosibirsk, Russia. Email: miroshn@math.nsc.ru
5Schmidt United Institute of Physics of the Earth RAS, 123995, B. Gruzinskay, 10, GSP-5, Moscow D-242, Russia. Email: pivovarova@ifz.ru
6Schmidt United Institute of Physics of the Earth RAS, 123995, B. Gruzinskay, 10, GSP-5, Moscow D-242, Russia. Email: slavina@ifz.ru
Citation Information: Journal of Inverse and Ill-posed Problems. Volume 17, Issue 3, Pages 209–238, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: 10.1515/JIIP.2009.017, April 2009
Abstract
A numerical solution for the inverse kinematic problem of seismics with inner sources is suggested. We assume the coordinates of centers and the times of beginning of earthquakes to be known in some interior area (a focal zone) of the Earth. The purpose is to determine a velocity structure of the Earth in the focal zone. For the solution of the problem, two algorithms are suggested. The first algorithm is based on the idea of inversion of the wave front and its local approximation by a plane or a sphere. Main tools of the second algorithm are the procedures of interpolation, approximation and smoothing of functions based on the modern algorithms of multidimensional splines. Properties of the algorithms by means of test media with known velocity structure are investigated.
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