3-D Time-Domain Airborne EM Forward Modeling With IP Effect Based on Implicit Difference Discretization of Caputo Operator

As an efficient geophysical exploration method, the time-domain airborne electromagnetic (AEM) data often show sign reversal in late-time channels due to induced polarization (IP) effect. The traditional imaging and inversion methods without considering the IP effect cannot recover the true electrical structure of the earth, so it is necessary to develop 3-D electromagnetic (EM) forward modeling and inversion techniques with IP effect. In this article, we propose a 3-D forward modeling method for time-domain AEM with IP effect based on unstructured finite-element (FE) method. To describe the IP effect of a medium, we introduce the Cole–Cole model and transform it into fractional derivative form using frequency–time conversion. Then, we discretize it using the difference discretization format of Caputo fractional derivative. Finally, we use the vector FE method based on unstructured tetrahedral mesh and unconditionally stable second-order backward Euler’s scheme to discretize Maxwell’s equations in space and time. In this way, we can solve the 3-D forward modeling problem for AEM with IP effect in time domain. We verify the accuracy of our algorithm by comparing it with the 1-D semi-analytical solution for a half-space model and then calculate EM responses for typical abnormal models and analyze the characteristics of IP effect.