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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 ,同时也为地下介质的速度分布成像提供一种新的技术
Starting from the initial and boundary value problems of two-dimensional acoustic equations, a residual weighted iterative least squares (robust iteration) is derived by introducing a generalized exponential error distribution function and Born approximation to the solution of the wave equation Lippman-Schwinger equation. Algorithm, and then realize the velocity structure inversion calculation of the underground medium profile. The simulation results show that this method has high precision and strong anti-interference ability, which is an effective method to solve the inversion problem of acoustic wave equations. It also provides a new technique for velocity distribution imaging of underground media