Transient field solution for a layer of finite thickness on a resistive basement

What is it about?

A closed-form asymptotic solution is derived for the transient magnetic field of the currents induced by an airborne magnetic source in a conductive layer of finite thickness. The conductive layer rests on the top of a resistive half-space. In addition to the well-known solution found by J. C. Maxwell for a thin conductive sheet surrounded by an insulator, the new solution includes terms that depend on the layer thickness h. Similarly to Maxwell's solution, the secondary magnetic field is expressed in terms of an image source receding from the layer. It is shown that immediately after the turning on of the transmitter, the plane of the symmetry that specified the initial position of the image is located below the upper interface of the conductive layer at depth h/3. This indicates the correct position at which the equivalent thin sheet should be placed when Maxwell's solution is applied to a layer of finite thickness. Maxwell's solution is a useful approximation to the data acquired above a conductive layer of finite thickness at a late stage of the decay of the induced current. If the basement that underlies the layer is non-conductive, it can be applied with increasing accuracy at later times. When the basement is conductive, the secondary magnetic field of the currents induced in the basement eventually prevails over that of the currents in the layer. The new solution accounts for the effect of the currents in the basement as long as this effect is smaller than the effect of the currents in the layer. Compared to the classic solution, the generalized solution can be used in a wider time range h/V<t<h/V(S/S0) where V is the image recession speed; S and S0 are the layer and basement conductivities, respectively. The solution allows for a rapid estimate of the layer thickness and conductivity in addition to its conductance. It may also be used to estimate conductivity of the basement.

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