| Accurate subsurface imaging is of interest to geophysicists, having applications in geological mapping, underground void detection, ground contaminant mapping and land mine detection. The mathematical framework necessary to generate images of the subsurface from measurements of these fields describe the inverse problem, which is generally ill-posed and non-linear. Target scattering from an electromagnetic excitation results in a non-linear formulation, which is usually linearized using a weak scattering approximation.;The equivalent source inversion method, in contrast, does not rely on a weak scattering approximation. The method combines the unknown total field and permittivity contrast into a single unknown distribution of "equivalent sources". Once determined, these sources are used to obtain an estimate of the total fields within the target or scatterer. The final step in the inversion is to use these fields in obtaining the desired physical property. Excellent reconstructions are obtained when the target is illuminated using multiple look angles and frequencies. Target reconstructions are further enhanced using various iterative algorithms.;The general formulation of the method allow it to be used in conjunction with a number of geophysical applications. Specifically, the method can be applied to any geophysical technique incorporating a measured response to a known induced input. This is illustrated by formulating the method within resistivity electrical prospecting. |
