Principles of probability tomography for natural‐source electromagnetic induction fields

Abstract

The 3-D interpretation problem of natural‐source electromagnetic (EM) induction field data collected over a flat air‐earth boundary is dealt with using the concept of probability tomography. This paper presents a method to recognize the most probable localization of the induced electric charge accumulations across resistivity discontinuities and current channeling inside conductive bodies. We begin by writing the solutions for the electric (magnetic) ground surface EM field components in the frequency domain as a sum of elementary contributions, each resulting from a single induced‐charge (dipole) element. Then we express the total electric (magnetic) power associated with each EM field component as a sum of crosscorrelation integrals between the measured component and the homologous synthetic expression resulting from each causative induced‐charge (dipole) element. The synthetic component takes the key role of scanner function in the new imaging procedure. Moreover, using the crosscorrelation bounding inequality we introduce the concept of EM induction occurrence probability as a suitable parameter for the tomographic representation of the induced‐charge and dipole distributions underground. For each electric and magnetic surface component we define the corresponding occurrence probability function as the crosscorrelation product of the observed component and the relative scanning function, divided by the square root of the product of the respective variances. In the space domain, the 3-D tomographic procedure consists of scanning the half‐space below the survey area by the unit strength charge or dipole element, which is given a regular grid of space coordinates within the volume. At each node of the grid, the occurrence probability function is calculated. We use the complete set of calculated grid values to single out the zones of highest occurrence probability of electric charge accumulations and current channeling elements. The physical reliability of the proposed tomography is tested on synthetic and field examples.