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.

A Fast and Efficient Method for 3-D Transient Electromagnetic Modeling Considering IP Effect

“…The region containing the chargeable body is discretized with 10 ×10 ×10m uniform grids. The decay curve calculated by our SOE-BEDS algorithm and by [28] are shown in Figure 6, and the two decay curves agree well. The sign reversal caused by the IP effect can be clearly seen in both curves.…”

“…Cai et al [27] developed a method to select the center point and orders for Padé series expansion adaptively during the time-stepping process, which improve the applicability of the algorithm. Ji et al [28] used a frequency-domain rational approximation method and the linear programming technique to convert the fractional order system into an integer order one. However, the limitation is that the coefficients and relaxation times of approximation functions depend on CCM exponent.…”

Feature Extraction and Intelligent Identification of Induced Polarization Effects in 1D Time-Domain Electromagnetic Data Based on PMI-FSVM Algorithm

“…Actually, from the analysis of the decay curves, we know that the slopes and sign reversals are the crucial IP characteristics. Thus, apart from the characteristic parameters about sign reversals such as time of sign reversal, the maximum absolute value of negative responses [7], [10], and the duration of negative values, we also need to pay attention to the slopes of curves.…”

“…An overall analysis reported the influences of the polarization parameters, size, and buried depth of the target on the negative responses. They also demonstrated that only moderately sized, highly-polarizable media in a shallow layer could generally be detected [10].…”

Research on 3D SIP Conjugate Gradient Inversion Algorithm with Parameter Range Constraints

“…For the past few years, the SIP forward and inversion method, taking the frequency domain Maxwell equation and Cole-Cole model as basis, or to say, taking both electromagnetic effect and IP effect into account, has deepened the research and understanding on the electromagnetic effect by leaps and bounds [2][3][4]. Nevertheless, difficulties still exist in both theoretical study and practical application, of which the electromagnetic effect and 3D inversion are of the greatest concern [5][6][7].…”