Model Order Reduction Method for 3-D Transient Electromagnetic Modeling With Induced Polarization Effects

The induced polarization (IP) effect is an important phenomenon in geophysical exploration. Understanding the impact of the IP effect on transient electromagnetic (TEM), it is necessary to consider chargeability during the forward modeling process. Currently, most 3-D forward modeling for the IP effect relies on frequency-to-time-domain transformation techniques, using the Cole-Cole model for frequency-domain computations. Although this method is straightforward, it has low computational efficiency. Based on this, we propose a model order reduction method based on the rational Krylov subspace to achieve rapid 3-D TEM modeling for multiple sets of IP parameters. Specifically, using the finite volume method (FVM) with Octree mesh for spatial discretization of the governing equations, we transform the equations into a transfer function independent of frequency and Cole-Cole parameters. Then, the rational Krylov subspace projection method is used for model order reduction, where the large-dimensional coefficient matrix in the transfer function is reduced to a smaller dimensional matrix, allowing for fast solution of the transfer function. This transfer function is used for modeling at different frequencies and for different Cole-Cole parameters. The accuracy of our algorithm is validated by comparing the results with analytical solutions. In addition, forward modeling analysis of multiple sets of Cole-Cole parameters demonstrates the significant computational efficiency of our algorithm, indicating its suitability for forward modeling with various sets of Cole-Cole parameters.