2. 5-D forward modeling of the frequency-domain ground-airborne electromagnetic response in areas with topographic relief

Ground-airborne frequency-domain electromagnetic method is an effective and efficient geophysical prospecting method. It usually places the controlled source on the ground and measure the electromagnetic field in the air. This method can achieve fast measurement in large scale, is especially suitable for resource exploration in rugged mountains, deserts, swamps, sea-land interaction zones and other areas with complex topography relief. However, in these areas, the topography relief is serious, so the study of the topographic effect on ground-airborne electromagnetic response is meaningful. In this paper, the 2. 5D frequency domain ground-airborne electromagnetic response of topography earth model was calculated based on the finite element method and the response characteristic is analyzed. Fourier transform was applied to the Maxwell's equations to transform a 2. 5D problem into a 2D problem, and then the discrete finite element equation was deduced using the Galerkin weighted residual method. The surveyed region is subdivided into many arbitrary quadrilateral elements with different sizes, the ones region near the source and the target have smaller size to ensure the accuracy of numerical calculation, the ones away from the target region have bigger size to simulate infinite boundary and reduce the requirements for computing resource. Interpolation is conducted in the element to transform the finite element equations to the linear system of equations. Using the total field algorithm, the pseudo-delta function with a certain area is employed to approximate the distribution of the source current, the source terms are approximately distributed at 25 nodes centered on the electric dipole source. By solving the equation, the solution of electromagnetic field in wavenumber domain was obtained, then the solution of electromagnetic field in spatial domain can be calculated by the Invers Fourier Transformation. The accuracy of our algorithm was verified by the comparison of our 2. 5D forward modeling results and the analytical results. We also compared the electromagnetic field response characteristics measured in the air and on the ground.