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A B S T R A C TAn edge finite-element method has been applied to compute magnetotelluric (MT) responses to three-dimensional (3D) earth topography. The finite-element algorithm uses a single edge shape function at each edge of hexahedral elements, guaranteeing the continuity of the tangential electric field while conserving the continuity of magnetic flux at boundaries. We solve the resulting system of equations using the biconjugate gradient method with a Jacobian preconditioner. The solution gives electric fields parallel to the slope of a surface relief that is often encountered in MT surveys. The algorithm is successfully verified by comparison with other numerical solutions for a 3D-2 model for comparison of modelling methods for EM induction and a ridge model. We use a 3D trapezoidal-hill model to investigate 3D topographic effects, which are caused mainly by galvanic effects, not only in the Zxy mode but also in the Zyx mode. If a 3D topography were approximated by a two-dimensional topography therefore errors occurring in the transverse electric mode would be more serious than those in the transverse magnetic mode.

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S U M M A R YA method for accurately approximating sensitivities is introduced for the efficient 3-D inversion of static-shifted magnetotelluric (MT) data. Approximate sensitivities are derived by replacing adjoint secondary electric fields with those computed in the previous iteration. These sensitivities can reduce the computation time, without significant loss of accuracy when constructing a full sensitivity matrix for 3-D inversion, based on the Gauss-Newton method. Additional reduction of computational cost can be attained by modifying the inversion scheme to run on a parallel computing platform. The effectiveness of approximate sensitivities is tested by inverting both synthetic and field data obtained in Pohang, Korea, and Bajawa, Indonesia. The accuracy of approximate sensitivities is validated by sensitivity analysis of synthetic data. To make the inversion of static-shifted MT data more stable, a weighting coefficient for static-shift parameters is added to the objective function and is updated at each iteration. Approximate sensitivities are calculated much faster than exact sensitivities, and are accurate enough to drive an iterative inversion algorithm.

S U M M A R YTopographic effects due to irregular surface terrain may prevent accurate interpretation of magnetotelluric (MT) data. Three-dimensional (3-D) topographic effects have been investigated for a trapezoidal hill model using an edge finite-element method. The 3-D topography generates significant MT anomalies, and has both galvanic and inductive effects in any polarization. This paper presents two different correction algorithms, which are applied to the impedance tensor and to both electric and magnetic fields, respectively, to reduce topographic effects on MT data. The correction procedures using a homogeneous background resistivity derived from a simple averaging method effectively decrease distortions caused by surface topography, and improve the quality of subsurface interpretation. Nonlinear least-squares inversion of topography-corrected data successfully recovers most of structures including a conductive or resistive dyke.