3D numerical modeling of induced-polarization electromagnetic response based on the finite-difference time-domain method

Abstract

Induced-polarization (IP) effects have a significant influence on transient electromagnetic (TEM) data, which commonly manifest a reversed sign. Polarization media usually have a very high economic value. To study the IP effects, a new method for modeling the time-domain electromagnetic signals of 3D dispersive materials is developed. Due to the fractional time derivatives, two main difficulties are needed to be conquered: the derivation of Cole-Cole model impulse response function and the discrete recursion of convolution in Ohm’s law. We use a frequency-domain rational approximation method and the linear programming technique to transfer the fractional order system into an integer order system. This method enables us to achieve a relatively simple and high-precision solution of the Cole-Cole model impulse response. A discrete recursion method for Ohm’s law convolution is proposed to realize an efficient numerical simulation of 3D polarization media by eliminating the prohibitive computing demands. Comparisons with published methods demonstrate the accuracy and efficiency of our algorithm. The characteristic time constant and chargeability have monotonic influences on the IP effects, whereas the frequency dependence indicates a nonmonotonic influence on the IP effects. The negative response is more significant when the frequency dependence is in the midrange. For a 3D low-resistivity chargeable body, a larger size reduces the decay rate of the induced field, which contributes to the obscuration of the polarization field. The middle-sized chargeable body can be detected under certain conditions: high chargeability, millisecond characteristic time constant, and middle frequency dependence. Small-sized chargeable bodies cannot be recognized at all by using the current forward-modeling method and instrument, which highlights the significance of precision improvement.