A Numerical Evaluation of the Limitations of the Thin-Sheet Approximation

One of the prime difficulties encountered in magnetotellurics involves adequately modeling the conducting earth when lateral conductivity variations are present. A common modeling technique that is used when the horizontal conductivity variations are of limited vertical extent is known as the thin-sheet approximation. The validity of the thin-sheet approximation is examined by comparing the surface impedance obtained for a horizontally layered earth model and its thin-sheet equivalent. Only a homogeneous thin sheet is considered; thus, the effects on the thin-sheet approximation of horizontal conductivity variations within the thin sheet are not evaluated. For the homogeneous thin sheet, it is found that generally the thinsheet approximation yields less than 10-percent error in the surface impedance for frequencies such that the thickness of the layer being modeled by the thin sheet is less than 0.3 of a skin depth in the layer, although in some instances the error approaches ten percent at larger ratios of layer thickness to layer skin depth. The presence of a shallow, highly conductive substratum does not adversely affect the validity of the approximation in many cases, contrary to what was previously believed. In those instances where the conductive substratum does have an effect, it is to reduce the ratio of layer thickness to layer skin depth at which the approximation is valid, and not to invalidate the procedure altogether.