Simple linear inversion of soil electromagnetic properties from analytical model of electromagnetic induction sensor

We present an analytical model of electromagnetic induction sensor with several receiver coils placed horizontally above a soil consisting of arbitrary number of conductive and magnetic layers. The modeled region is truncated far from the transmitter coil and the solution for its vector magnetic potential is given as a series. We linearize the model with respect to the soil electrical conductivity and magnetic susceptibility of each layer, and calculate the total contribution of all layers by superposition. We evaluate the validity of the linear approximation. Finally, we postulate the inverse problem of determination of the electromagnetic properties of the soil layers using single excitation frequency and illustrate the inversion procedure on a synthetic data set. The linear model and the inversion procedure are suitable for field deployable instrument.