Controlled initial-value ray tracing, able to accurately determine the boundaries between ray histories and to cover the model volume with a sufficiently dense system of rays forming ray tubes, is a by-product of the development of the shooting algorithm for boundary-value ray tracing. Considerable attention has thus been paid to the development of a new method for the computation of multivalued travel times at nodes of 3-D grids in complex 3-D structures based on the controlled initial-value ray tracing. The method is an alternative to the wavefront tracing method. It is based on construction of ray tubes, composed of ray cells, through the model volume, followed by interpolation inside individual ray cells. In contradiction to the wavefront tracing method, in which the rays are traced by parts, and interpolation is performed as soon as the wavefront reaches a gridpoint of the receiver grid, all the rays are traced during the first step and interpolation is done during the second step of the proposed method.
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