Finite difference time domain modeling of cross-hole electromagnetic survey data

Cross-borehole electromagnetic (EM) surveying is an emerging technology in the mining industry that can offer resolution of geoelectric structures superior to that from other EM methods. However, existing interpretation techniques often employ physical models of electromagnetic wave propagation that are inappropriate for the instrument parameters and electrical properties commonly encountered in the metalliferous mining environment. Lacking appropriate numerical models, we are unable to properly assess imaging methods or to design and interpret surveys. In this thesis, I address such issues relating to the delineation of massive sulfide mineralization using cross-borehole EM techniques. Specifically, I discuss the use of the finite-difference time-domain (FDTD) method in modeling the cross-borehole electromagnetic response of a perfect electric conductor (PEC), which is a good approximation to a target of high conductivity. This model type has particular application to massive nickel sulphide ore bodies, such as those found in the Kambalda, Sudbury Basin, Norilsk, and Victoria Island regions. A key development of the thesis is the implementation of perfectly matched layer (PML) absorbing boundary conditions in a Yee FDTD algorithm. This revised algorithm permits the realistic modeling of the electromagnetic response of conductors in the frequency range transitional between the diffusion and wave domains. Such modeling reveals diffraction phenomena that are not included in attenuation-based interpretation schemes commonly used in Radio Imaging Method (RIM) interpretation. These phenomena can be expected to lead to artifacts in ray theory interpretations. Proper placement and frequency of transmitters and receivers are issues that need to be rigorously examined prior and subsequent to any cross-borehole EM experiment. Using plate type models, we illustrate how the sensitivity of receivers to perturbations in the vertical and lateral extent of the plates is a function of the receiver placement and frequency of excitation. Of particular interest here is how rapidly sensitivities can vary with spatial position and frequency. For this examination, we used the FDTD code to calculate data sensitivity maps for perturbations to three-dimensional (3D) models, and an analytic solution for the fields due to a perfectly conducting half-plane developed by Weidelt to estimate parameter uncertainties for noisy 2.5D model data generated using an array of transmitters. The thesis concludes with a discussion of weighting of transmitters to optimize resolution of a perturbation about an a priori model. For the test case, the optimal weights improve the resolution of the top edge of the half-plane by 20%. The theory could also be used to design a phased array device optimized for high resolution studies. The Weidelt code was also used in this study. Despite advances in the development of absorbing boundary conditions, the FDTD method is still an expensive solution to the 3D EM modeling problem. Such was the rationale for using a fast analytic solution to the 2.5D half-plane induction problem to orient survey design methods.