In this paper, we present and discuss the results of modeling of the transient induction processes observed at different distances from the center of a transmitter loop in studies of a two-layer earth in which the magnetic susceptibility of the top layer or the base depends on frequency. Profiling graphs (the offset is plotted on the abscissa, and the EMF induced in the receiver coil at a fixed time is plotted on the ordinate) show that the polarity of the EMF changes as the offset increases. For the model with a magnetic layer of any thickness, the polarity of the EMF reverses immediately after the receiver crosses the loop wire. For the model with a magnetic base, the offset at which the EMF polarity reversal occurs is the larger the greater the thickness of the layer. For both models, the EMF at a fixed time depends on the thickness of the layer and the offset. Particularly strong dependence of the EMF on layer thickness or offset is observed near the loop side. Therefore, measurements near the wire make it possible to determine the thickness of the layer in the case where it is much less than the length of the loop side. The overall effect of magnetic relaxation and transient eddy currents leads to the fact that small changes in the layer thickness or offset can lead to a dramatic change in the transient response.