THE NEWTON METHOD FOR SOLVING A DIRECT KI NEMATIC PROBLEM

The formulas for the second (two-point) compound derivative of the tra vel-time curve t ''(x1x2) have been obtained for two-dimensional media with smooth interfaces of layers with constant velocity gradients. A calculation scheme is proposed For the three dimensional case. Analysi s of the calculation complexity has been carried out, and two ways of solving a two-point boundary problem of ray tracing are compared: adju stment and variational methods, which both use the Newton method of de termination of nonlinear-equation roots and of function minimization. It is shown that the adjustment method gives much more information and is more efficient as compared with the variational method.