Application of perfectly matched layers to the transient modeling of subsurface EM problems

Abstract

magnetic field for a pulsed horizontal magnetic dipole embedded in a resistive whole space. The conductivity of the whole space is 0.001 S/m, the relative electric permittivity and relative magnetic permeability are equal to one. The x-directed dipole moment varies in time as where c ϭ 2f max and f max is 300 kHz. These model parameters are chosen to simulate a radio imaging method (RIM)-type transmitter with one or more horizontal wire loops lowered down the boreholes for transmission, reception, or both, operating in a moderately resistive host rock. The x-directed dipole transmitter is placed at the center of a 50 ϫ 50 ϫ 50 cell mesh. The mesh resolution ⌬x is 5 m. For comparison, an analytical solution is obtained by convolving the quasi-static impulse response [8] with the transmitter moment waveform. The model parameters are chosen such that the quasi-static assumption is a good approximation for this case. The comparison of the analytical solution and FDTD solution for the fields as they vary as a function of distance from the source is shown in Figure 1. Moderate agreement is obtained very near the source (1-5 cells), and excellent agreement is obtained further away. This is expected, as the linear representation of the fields in the FDTD algorithm is not consistent with the second-or thirdorder physical variation of the fields very near the source. Although this is a limitation to be noted, it is not a limitation for typical cross-bore surveys, where the transmitters are generally placed further from the target to increase the response they obtain from the target rock. These results are also consistent with those observed in [6] for infinitesimal electric dipoles. DISCUSSION AND CONCLUSIONSSelection and design of accurate numerical modeling techniques is a prerequisite for survey design and for other steps in the interpretation process. A method of accurately simulating the magnetic loop sources that are routinely used in cross-bore EM survey techniques was developed by adapting the standard FDTD algorithm following the method of Buechler et al. [6]. The method was validated by comparison with analytical results for a magnetic source in a resistive whole space. Further validation of the accuracy of the code was demonstrated for PEC plates exposed to realistic cross-bore EM survey tools in a moderately conducting host in [9]. This method was applied to optimization of the designs of well surveys in [9], and the accurate modeling of the sources was critical to the success of the optimization. ACKNOWLEDGMENTSThe authors thank Om Gandhi, Department of Electrical Engineering, University of Utah, for the use of software previously developed under several of his bioelectromagnetic research grants. LARGE-SIGNAL MODELING OF FREQUENCY-DISPERSION EFFECTS IN SUBMICRON MOSFET DEVICES

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