A damped forward EMI model for a horizontally stratified earth

If a magnetic dipole is placed above the surface of the earth, the electromagnetic induction (EMI) effect, encoded in Maxwell's equations, causes eddy currents in the soil which, on their turn, induce response electromagnetic fields. The magnetic field can be measured in geophysical surveys to determine the conductivity profile of the ground in a non-destructive manner. The forward model used in the inversion of experimental data usually consists of a set of horizontal homogeneous layers. A frequently used analytical model, proposed by McNeill, does not include the interaction between the eddy currents and therefore fails for larger conductivities. In this paper, we construct a new forward, analytical, model to estimate the magnetic field caused by a horizontally stratified earth which approximates the interaction between eddy currents. This makes it valid for a broader range of parameters than the current state of the art. Furthermore, the error with the (numerically obtainable) exact result is substantially decreased. We also calculate the vertical sensitivity ("depth of exploration") of the model and observe that it is in good agreement with the values obtained from the exact model.