Excess anomalous current inversion

Consider a 3-D geoelectric model with a normal (background) complex conductivity CTfc and a local inhomogeneity D with an arbitrarily varying complex conductivity a = 5ft -f Aa. The model is excited by an electromagnetic field generated by an arbitrary source which is time harmonic as The magnetic permeability of 

The electromagnetic fields in this model can be presented as the sum of the background and anomalous fields  

According to formulae (9.40) and (9.41), the anomalous field in the frequency domain can be represented as an integral over the excess (anomalous) currents, j = A5E, in the inhomogeneous domain D  

We assume that the anomalous field E (r ) is given on some surface of observation S. The goal is to find the anomalous conductivity Act (r). 

One simple idea for linear inversion of the anomalous electric field is to solve the linear equation (10.2) with respect to excess (anomalous) currents j = ActE  

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