Lippmann-Schwinger积分方程广义超松弛迭代解法及其收敛特性

为克服Born级数只适用于弱散射和短程传播的弱点,从光学散射理论中引入了针对强光学散射问题的Lippmann-Schwinger方程广义超松弛迭代解法,并对这种方法在反射地震条件下的算法表现、收敛特点、计算效率以及计算精度等问题进行了分析和讨论.理论分析和数值计算结果均表明:(1)与散射级数重整化相比,超松弛法具有更坚实的数学基础;(2)超松弛法可以有效地克服Born级数的弱点,得到与有限差分相当的数值模拟结果;(3)在反射地震条件下LS方程超松弛法表现优异,完全可以解决反射地震数值模拟中的强散射问题.

The generalized over-relaxation iterative method for Lippmann-Schwinger equation and its convergence

To overcome the shortcomings of the traditional Born scattering series, which is only applicable to weak scattering and short-range propagation, we introduce a generalized over-relaxation iterative method for the Lippmann-Schwinger equation from the optical theory. It is a numerical simulation method for strong scattering to solve forward modeling and inversion problems of strong optical scattering. The applicability and convergence characteristics of the over-relaxation method under the condition of seismic reflection were analyzed in this work. Results show that (1) compared with scattering series renormalisation, the over-relaxation method has a more solid mathematics basis. (2) The over-relaxation method can effectively overcome the shortcomings of the Born series and obtain numerical simulation results equivalent to that of the finite-difference method. And (3) under the condition of seismic reflection, the over-relaxation method can be used to fully solve the problem of strong scattering.