Three-dimensional modeling of IP effects in time-domain electromagnetic data

Understanding the effects of induced-polarization (IP) effects on time-domain electromagnetic data requires the ability to simulate common survey techniques when taking chargeability into account. Most existing techniques preform this modeling in the frequency domain prior to transforming their results to the time domain. Even though this technique can allow for chargeable material to be easily incorporated, its application for some problems can be computationally limiting. We developed a new technique for forward modeling the time-domain electromagnetic response of chargeable materials in three dimensions. The frequency dependence of Ohms’ law translates to an ordinary differential equation when considered in the time domain. The system of ordinary-partial differential equations was then discretized using an implicit time-stepping algorithm, that yielded absolute stability. This approach allowed us to operate directly in the time domain and avoid frequency to time-domain transformations. Although this approach can be applied directly to materials exhibiting Debye dispersions, other Cole-Cole dispersions resulted in fractional derivatives in time. To overcome this difficulty, Pade approximations were used to represent the frequency dependence as a rational series of integer order terms. The resulting method was then simplified to generate a reduced time-domain model that can be used to forward model the IP decay curves in the absence of any electromagnetic coupling. We found numerical examples in which the method produced accurate results. The potential application of the method was demonstrated by modeling the full time-domain electromagnetic response of a gradient array IP survey, and the occurrence of negative transients in airborne time-domain electromagnetic data.