TEM simulation with topography using boundary-fitted grid

Finite-Difference Time-Domain (FDTD) method has been successfully used in transient electromagnetic (TEM) simulation. Until recently, however, topography seems to be commonly neglected. To assess the topographic effect in TEM, some authors used a staircase approximation to the earth-air interface. But this approach might have two problems: first, its error might be very large; second, since air layer is explicitly included in FDTD computation, a very small time step is necessary to maintain the stability condition, which makes it inefficient. Another method to account for the tomography is using a non-Cartesian grid which is conformed to the boundary. In fact such boundary-fitted grids have been widely used in computational fluid dynamics to approximate the irregular boundary. In this study, we use a FDTD method combining boundary-fitted grids with the classical staggered grid, unconditional stable DuFort-Frankel scheme to discrete the quasi-static Maxwell equation. Since TEM simulation needs to step to a very late time, air layer had better not be included in FDTD computation. Instead, the boundary condition at the earth-air interface is handled via upward continuation. As the interface is generally not flat, the traditional FFT approach in upward continuation needs some modification. We use a method similar to the equivalent source method in gravity upward continuation, which required several FFT iterations to refine the results. We will report the preliminary results of our method and test its accuracy and efficiency with other methods.