基于改进高斯-牛顿优化算法的频率域海洋可控源电磁二维反演

Frequency-domain 2D marine CSEM inversion using the improved Gauss-Newton optimization algorithm

稳定、高效的反演算法是开展海洋可控源电磁(CSEM)数据解释的基础.本文实现了基于改进的高斯-牛顿优化算法的频率域海洋CSEM二维反演.基于交错网格有限差分法实现可控源电磁场2.5维正演模拟,使用直接矩阵分解算法求解差分离散方程组以实现多场源电磁响应的快速计算,并采用改进的接收点插值算法实现海底任意接收点处电磁场快速高精度计算.使用伴随法隐式求取灵敏度矩阵并基于近似二次收敛的高斯-牛顿优化算法实现反演,同时提出了一种基于灵敏度矩阵特征的正则化参数自动优化选取方法以保证反演的稳定收敛.反演算例验证了本文提出的频率域海洋CSEM二维反演算法的有效性.

A stable and fast inversion is essential for marine controlled-source electromagnetic(CSEM)data interpretation.In this paper,a 2D marine CSEM inversion algorithm based on the improved Gauss-Newton optimization algorithm is developed.For the 2.5D CSEM forward solver used in inversion,the staggered finite-difference(SFD)discretization is applied and the linear system of equations is solved by a direct matrix factorizing solver,which could solve multi-transmitter electromagnetic(EM)responses efficiently with only one time of the matrix factorization per frequency.Furthermore,the improved interpolating algorithm is applied for accurately calculating the EM fields for arbitrarily located seafloor receivers in a more efficient way.The adjoint-equation method is used for calculating the sensitivities implicitly and the Gauss-Newton optimization algorithm with quasi-quadratic convergence is applied which makes the 2D inversion developed converges in a more efficient way.A way using the sensitivity matrix is also applied for selecting the regularization parameter automatically to make the inversion converge in a more stable way.Numerical tests demonstrate the efficiency and stability of the inversion algorithm developed.