When linear traveltime interpolation（LTI） method is used in the three-dimensional ray tracing

the minimum equation employed in forward processing is a transcendental equation

thus the analytic solution can not been given.Though the approximate solution can be obtained by using the grid division method

the more precision of the grid division

the more accurate calculations

the calculating works in forward processing will be increased by the orders of N3 together with the increasing partition accuracy of the grid interface

consequently reducing the calculation efficiency.In this paper

the steepest descent method is introduced in the forward processing of LTI ray tracing and a fast algorithms for solving the three-dimensional LTI transcendental equation is put forward

The method is not an exact solution

but along the negative gradient direction continuous approximation to the true solution.The results show that this algorithm improves the calculation efficiency taking into account the accuracy of ray tracing at the same time

computational speed is faster more than three times at least.