【摘要】 线性走时插值(LTI)算法应用于三维射线追踪时,其向前处理过程中的极小值方程是超越方程,无法求出解析解.虽然可以采用网格剖分方式近似求解,网格剖分精度越大,计算结果越精确,但随着剖分精度的提高,向前处理的计算量会以N3的阶次增加,从而导致计算效率的降低.本文将最速下降法引入到LTI射线追踪算法的向前处理,提出了一种求解三维LTI超越方程的快速数值解法,该方法也不是一种精确求解方法,而是沿着负梯度方向不断逼近真实解.计算结果表明,该算法在兼顾射线追踪精度的同时能有效提高计算效率,计算速度快了3倍以上.更多还原

【Abstract】 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.更多还原