Three-Dimensional Forward Modeling for Grounded-Source Semi-Airborne Transient Electromagnetic Method With IP Effect Directly in Time Domain Based on SOE Approximation

It is very useful for the exploration of metallic sulfide deposits to simulate the induced polarization (IP) effect in semi-airborne transient electromagnetic (TEM) data and analyze its response characteristics. To improve the computational efficiency and the ability to handle the complex models, we develop a fast 3D forward modeling algorithm for semi-airborne TEM method with IP effect directly in time domain based on the sum-of-exponentials (SOE) approximation and the time-domain unstructured vector finite-element method. By adopting the SOE method to approximate the kernel function of Caputo fractional derivative, the convolution operation in the time direction is transformed into a piecewise analytical solution and a recursive relationship. This approach resolves the problem of huge storage and calculation caused by the traditional L1 approximation relying on all historical information, thereby improving the efficiency of 3D forward modeling. Meanwhile, the flexibility of the unstructured finite-element method provides our algorithm with the ability to deal with the models with undulating terrain and complex-shaped bodies. The numerical accuracy and efficiency of our method are verified by comparing it with the 1D analytical solution on a polarized half space and the L1 approximation respectively. On this basis, we analyze the influence of transmitting-waveform parameters on the IP responses on a polarizable ellipsoid model. Finally, our algorithm is applied to a polarizable model with topography to check its ability to handle the complex model. We further analyze the influence of the observation mode and the direction of the transmitter sources on the IP responses.