基于有限差分正演的带地形三维大地电磁反演方法

本研究实现了一套基于有限差分（FD）方法的大地电磁测深数据带地形三维反演算法及代码.其中，在大地电磁场正演数值模拟方面，开发了起伏地形条件下基于交错网格剖分、有限差分方法的大地电磁测深三维正演代码；在满足平面波场假设的前提下，使用长方体网格剖分模拟三维起伏地形，实现了带地形三维正演计算；并设计理论模型进行试算，经试算结果与前人的有限元法计算结果对比，验证了所研发的带地形三维正演计算的正确性与可靠性.在反演方面，本研究基于非线性共轭梯度方法编写了大地电磁测深带地形三维反演代码，试验了不同的共轭梯度搜索因子β，避免了目标函数对海森矩阵（参数二次导数矩阵）的显式计算和存储，初步实现了大地电磁资料的带地形三维反演.最后，对一系列理论模型进行正演计算，利用其生成的合成数据模拟实测数据进行反演，并与现有的不带地形大地电磁测深三维反演结果比较，检验了所研发的带地形三维反演计算的可靠性与稳定性.

Study of Three-dimensional magnetotelluric inversion including surface topography based on Finite-difference method

An algorithm of three-dimensional (3D) magenetotlluric inversion with topography based on finite difference (FD) method is presented. A staggered-mesh, finite-difference method is utilized for the 3D magnetotelluric numerical simulation with surface topography. Cuboid mesh grid is used for discretization to meet the plane wave assumptions in magnetotelluric forward calculations with topography.Magnetotelluric responses are generated utilizing a topography model of square frustum hill to compare with previous result from finite element method, verifying the correctness and reliability of the forward code. In the inversion part, a 3D inversion scheme with topography is developed based on nonlinear conjugate gradient method.Different conjugate gradient search direction updater β are tested to improve the global convergence. Explicit calculations and storage of the Hessian matrix are avoided. Finally, a series of forward models with topography is established to generate synthetic data, which is inverted by the 3D inversion method with topography. The results are hence compared with the results from 3D MT inversion with no topography implications.The reliability and stability of the three-dimensional inversion is tested.