Theoretical development and implementation of algorithms for the inversion of airborne FDEM data to a layered earth

Abstract

Equations for determining the electromagnetic response for a dipole situated above a layered earth are derived from Maxwell's equations. The theory is then expanded to allow for a transmitter and receiver at any distance above the surface of the layered earth. Using the commercially available software "Mathcad" standard curves are calculated for two- and three layer models. Damped least squares inversion is advocated. The partial derivatives of the layered earth expression with respect to all model parameters are formulated and the Jacobian matrix is constructed. The inversion routine is tested on noise-free synthetic data and on synthetic data with noise. The study is concluded with a case history where the developed technology is applied to a DIGHEM V data set flown over the Nebo granites in the Ga-Masemola area, Limpopo Province, South Africa. Results show that although the data consists of only three co-planar frequencies, parameters such as depth to bedrock, overburden conductivity and bedrock conductivity can be recovered.