Abstract
This study compares the efficiency of 3-D transient electromagnetic forward modeling schemes on the multi-resolution grid for various modeling scenarios. We developed time-domain finite-difference modeling based on the explicit scheme earlier. In this work, we additionally implement 3-D transient electromagnetic forward modeling using the backward Euler implicit scheme. The iterative solver is used for solving the system of equations and requires a proper initial guess that has significant effect on the convergence. The standard approach usually employs the solution of a previous time step as an initial guess, which might be too conservative. Instead, we test various initial guesses based on the linear extrapolation or linear combination of the solutions from several previous steps. We build up the implicit scheme forward modeling on the multi-resolution grid, which allows for the adjustment of the horizontal resolution with depth, hence improving the performance of the forward operator. Synthetic examples show the implicit scheme forward modeling using the linearly combined initial guess estimate on the multi-resolution grid additionally reduces the run time compared to the standard initial guess approach. The result of comparison between the implicit scheme developed here with the previously developed explicit scheme shows that the explicit scheme modeling is more efficient for more conductive background models often found in environmental studies. However, the implicit scheme modeling is more suitable for the simulation with highly resistive background models, usually occurring in mineral exploration scenarios. Thus, the inverse problem can be solved using more efficient forward solution depending on the modeling setup and background resistivity.
Highlights
The transient electromagnetic (TEM) method is widely used in many geophysical applications, including exploration for minerals [1,2,3]
We present three synthetic examples to verify the accuracy and efficiency of TEM forward modeling using the implicit scheme on the MR grid
We have found that the implicit scheme modeling using the linearly combined x0 approach with Nprev = 3 has much better performance than the other initial guess approaches
Summary
The transient electromagnetic (TEM) method is widely used in many geophysical applications, including exploration for minerals [1,2,3]. In order to fully exploit the observed data, the full 3-D quantitative data inversion is warranted. The inversion techniques rely heavily on accurate and efficient forward modeling algorithms. The TEM forward modeling can be implemented in frequency-domain and thereafter transformed to time-domain using the Fourier transform. The frequency-domain approach generally requires a sufficiently dense and wide frequency range to ensure the accuracy of the solution [4]. The simulation can be implemented directly in the time-domain so that the electromagnetic (EM) fields are recursively advanced using time-stepping [5]. The time-domain TEM modeling can be further classified into explicit and implicit schemes, depending on how the time-stepping is approached
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