Modified image method: Application to the response of layered ohmic conductors to active electromagnetic sources

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Abstract
The standard image method is modified in order to extend its range of applicability to the near-space regime (h∼λ the screening length) for all electromagnetic screening phenomena in conducting matter which are governed by Helmholtz’s equation. The modified method assumes a single image of a near inducing source and that the effective location of the image plane and surface screening distribution that satisfy the electromagnetic boundary conditions is one screening length below the free surface of the conductor. For applications in which the primary source and detector distance from the conducting free surface is much greater than the appropriate screening length, the modified image method (MIM) reduces to the standard form. An additional ad hoc modification for the case of induced ohmic screening is introduced into Wait’s multilayer correction function Q which is used in the definition of the complex screening length for the MIM model. This results in an extended range of agreement (both as to amplitude and phase )between the complex image fields produced by the MIM model and the secondary field produced by induced currents in the layered conducting half-space as originally formulated by Sommerfeld. This suggests the use of MIM, at least as a first-order tool, for rapid real-time inverse calculations of the structure parameters, conductivities, and thickness of the layers. The good agreement between MIM and the standard theory for a two-layer model occurs over a range of values for the parameters that define the conducting structure and the geometry of the source and sensor coils which are relevant to airborne active electromagnetic source (AEM) coastal bathymetry, sea ice thickness measurements, and studies of salt water intrusions of river deltas and marshes. The success of this application of the MIM model in the near-field regime for ohmic screening suggests the applicability of MIM in calculating the near-field electrostatic and superconducting response of conducting matter as well.