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波速反演实际上是一种波动方程反演方法。目前所见的大部分反演方法都借助于积分方程求解。这方面的研究工作还处于探索阶段。本文以余函数为基础,给出一种新的波动方程反演方法。其基本思想是从波动方程出发,将其中波速视为参数,通过对方程进行傅里叶变换及变数变换,把波动方程化作一阶微分方程组,并对频率一波数域中非线性参数的方程实行变分,从而使方程线性化,然后利用余函数方法进行逐次迭代运算,求得速度参数的最佳估计值。此法运算过程比较简单,用理论模型试算,可得到较为满意的结果。
Wave velocity inversion is actually a wave equation inversion method. Most of the inversion methods seen so far are solved by the integral equation. Research work in this area is still in the exploratory stage. Based on the residual functions, this paper presents a new inversion method of wave equation. The basic idea is to start with the wave equation and take the wave velocity as the parameter. The wave equation is transformed into first-order differential system by Fourier transform and variable transformation of the equation, and the nonlinear parameters in the frequency-wave-number domain The equation is variational, so that the equation is linearized, and then iterative operation is performed by using the residual function method to get the best estimated value of speed parameter. This method is relatively simple operation process, with the theoretical model test, you can get more satisfactory results.