The controlled-source electromagnetic response of two buried plates, including mutual inductance and interaction with the host medium

A solution for the response of multiple buried plates in a host medium to controlled-source electromagnetic (CSEM) stimulation has been found. This solution accounts for the interaction between the plates and the host medium. The solution for a plate in free space is well-known and analytic. However, adding a second plate or a conducting host medium increases the complexity of the solution. Time-varying currents induced by the source in the plates and the host medium introduce new magnetic flux to the system that in turn modify the currents via mutual inductance. This solution is obtained by solving the (A,φ ) potential formulation of Maxwell's equations using the finite element method. The finite element mesh generator allows for local refinement of the mesh in regions where greater resolution is desirable. This allows finer meshing in the region of the plates, which allows for more accurate modeling of the nuances in the induced currents caused by the interaction between the plates and the host medium. The effect of mutual induction and the efficacy of the locally refined finite element solution are demonstrated. The response of a model containing two plates within a host medium is compared to the sum of the responses of the two plates modeled separately. The plates are 2 m by 2 m, with a separation distance of 1 m, buried at a depth of 1 m. The plates have a conductivity of 100 S/m, and are within a host medium of conductivity 0.01 S/m. The system is excited by a source with a frequency between 1 and 100 kHz. It is shown that the model response of a two-plate system differs from the sum of the responses of two one-plate systems. The interaction between the two plates and the host medium must be properly modeled. An accurate model of the interaction of buried conductors excited by a controlled source is necessary to properly discriminate and classify buried targets. This is particularly true in the near-surface region of the earth where complex heterogeneity is common.