Transient time‐domain electromagnetics

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Abstract
For externally imposed electric and magnetic sources, the electromagnetic (EM) field equations may be derived from the symmetrical Maxwell’s equations. Two variational principles for the initial boundary‐value problem of electromagnetics are derived. The first one of the Gurtin type is deduced from the integro‐differential equations equivalent to the EM field equations, while the second one is a simplified version of the first variational principle. The variational field equations are placed in a form suitable for a finite‐element formulation in space. An explicit central‐differences scheme is then applied to the finite‐element variational equation to yield a recursive relation for time integration. The results from. Newmont electromagnetic pulse (EMP) survey done in the Mutooroo prospect in Australia are verified numerically. The finite‐element model which simulates the Mutooroo survey assumes a thin vertical dike embedded in conductive host rock that is overlain by a thick layer of conductive over‐burden. The effect of overburden on the time‐domain EM response appears first at the transmitter, continues to build up, eventually splits into two parts, and migrates away from the transmitter. As such, the effect of overburden is being migrated away, the effect of the deep‐seated dike and the host rock on the response emerges and decays. The calculated EMP anomalies due to the dike agree with the corresponding field survey results in their shapes and magnitudes. The zero crossover point of the antisymmetrical vertical magnetic component and the anomaly peak of the symmetrical horizontal magnetic component are located immediately above the dike on the surface, the magnitudes of which are quantitatively comparable. The electric field decays more slowly than the magnetic field and could provide additional information in the exploration of mineral deposits. The agreement between the finite‐element solution and the field results thus provides a means of interpreting time‐domain EM survey data.
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