遗传算法和多重网格在两步线性反演中的应用

基于扩展玻恩近似和电场积分方程,建立起非线性反演方程,然后应用两步线性反演方法进行迭代反演.在反演过程中,采用多重网格技术将待反演区域的离散网格从粗网格逐渐推演到细网格.在迭代前期,待反演区被离散为粗网格,利用实数编码的遗传算法对病态方程进行优化反演,并将其迭代反演结果作为迭代后期的初始值.在迭代后期,待反演区被离散成细网格,则采用共轭梯度(CG)法求解未知量较多的矩阵方程.二维轴对称非均匀介质剖面分布的反演结果表明,本文方法可反演高对比度的散射目标,具有较好的稳定性.

Genetic algorithm and multi-grid technique applied to two-step linear inversion method

The nonlinear inversion equation based on the extended Born approximation was derived, the two-step inverse method for reconstructing the conductivity profile was presented. The discretization grid size of the inhomogeneous object domain was reduced gradually by using the multi-grid technique in the inversion procedure. In the previous inversion procedure, the discretization grid size was big, the ill-posed equation was solved by the real-coded genetic algorithm. The previous inversion result was used as the initial value of the later inversion. In the later inversion procedure, the discretization grid size was small, the matrix equation was solved by the conjugate-gradient method. The numerical simulation has shown that this method works well at a high contrast and has good stability.