ON THE APPROACH TO SOLUTION FOR DIRECT KINEMATICS PROBLEM OF SEISMOLOGY IN 3D CASE

In this paper the algorithm for the ray computation and kinematic and dynamic parameters determination along the rays in 3D case is presented. A distinguishing feature of the developed algorithm is the fact that the ray tracing is performed not by numerical solution of differential equation system, but by element division of the given medium and ray computation by explicit formulas within them. The medium is divided into tetrahedra using Delaunay triangulation in 3D case, wherein it is assumed that the velocity inside each tetrahedron is linear. For such along-the-ray parameters as time and geometric spreading, explicit formulas are derived as well. This paper deals with the ray shooting algorithm which is designed for the solution of two-point boundary value problem. It suggests the implementation of this algorithm that does not require the medium velocity model to be smooth. The paper also contains the description of the results of numerical experiments that have been performed using the model data and proved the consistency of the developed algorithm.