二维声波方程稳健迭代速度反演

2-D ROBUST ITERATIVE VELOCITY INVERSION OF ACOUSTIC WAVE EQUATION

从二维声波方程初、边值问题出发 ,通过引进一个广义幂指数误差分布函数 ,以及对波动方程的Lippman -Schwinger方程的解进行Born近似 ,导出一个残差加权迭代最小二乘 (稳健迭代 )算法 ,进而实现对地下介质剖面的速度结构反演计算。模拟计算表明 ,本方法具有较高的精度和较强的抗干扰能力 ,是求解声波方程反演问题的一种有效方法 。

D velocity inversion of acoustic wave equation is studied. First,starts from initial condition and boundary condition of wave equation,and adopts Born approxmiation.Then,we introduce generalized exponential error distribution function to our model,and minimize it. One anto weighted robust iterative inversion of 2-D acoustic wave equation is obtained: Iterative weighted least squares method. Further,the velocity inversion of media underground is solved. Numerical tests show that this method can give a result with accutacy and stability. lt's an effective algorithm for 2-D velocity inversion of wave equation. Meanwhile,it offers a new kind of method for tomography of velocity structure underground.