Study Of Three-Dimensional Magnetotelluric Inversion Including Surface Topography Based On Finite-difference Method

An inversion algorithm of three-dimensional (3D) magnetotelluric(MT) inversionwith topography based on finite difference (FD) method is presented. Astaggered-mesh, finite-difference method is utilized for the3D magnetotelluricnumerical simulation with surface topography. Rectangular mesh grid is used fordiscretization to meet the plane wave assumptions in magnetotelluric forwardcalculations with topography. Magnetotelluric responses are generated with atopographic model of a hemisphere pit to compare with the analytic response,verifying the correctness and reliability of the forward code. Another topographymodel of square frustum hill is tested to compare with a previous result from finiteelement method, addingIn the inversion part, a3D MT inversion scheme with topography is developed basingon nonlinear conjugate gradient method. Different conjugate gradient search directionupdater β are tested to improve the global convergence. Explicit calculations andstorage of the Hessian matrix are avoided to save both memory storage andcomputing time. A series of forward models with surface topography is established togenerate synthetic data, which is inverted by the3D inversion method withtopography. The results are hence compared with the results from3D MT inversionwith no topography implications. Field dataset from a geothermal investigation isused to further test the reliability and stability of the inversion scheme.A Matlab based visualization package is designed and developed to support the3Dmodeling and inversion procedure and to visualize the inversion results. Thevisualization package consists of a series of data and model editing functionsincluding the import and regulation of MT data, auto meshing of the model grids, theimport of digital elevation data, as well as the edit of topography/bathymetry in themodel. To better understand the topography effects in3D, a series of complexsynthetic models with topography are designed and generated with the numericalmodeling and inversion scheme, as well as the visualization package presented here.Synthetic models with typical topography and anomaly combinations are tested withthe modeling and inversion scheme presented to provide a common guide to theinterpretation of3D and2D magnetotelluric data in cases with rugged terrain.