## Description

A modified version of the original Rayleigh scattering theory has been used to model transverse electric (TE) and magnetic (TM) topographic effects in magnetotellurics. The method has been evaluated by self-consistency checks and comparisons with other scattering theories. Integral equation, network analogy (finite difference), and finite element results were used for comparison. An inherent Rayleigh error restricts valid results to slopes of less than 53° for the TE mode and 26° for the TM case. Surface amplitude limitations are poorly defined and are frequency dependent. A major problem in the interpretation of magnetotelluric data has been the effects of topography and near-surface lateral inhomogeneities. Two methods have been proposed to handle this problem: the TM apparent resistivity curve can be shifted to match the TE apparent resistivity curve at high frequencies, or the impedance and tipper tensors can be "stripped." The second method requires that the source of the distortion is known. Applying the Rayleigh-FFT technique to this problem demonstrates the inadequacy of the curve shifting method. The tensor stripped method is shown to be an excellent technique for correcting the data, for an analytic model, if the distortion tensors are frequency dependent. The frequency dependent distortion tensor method was applied to data collection near Socorro, New Mexico. The topography consists of 5,400 m of relief over a distance of approximately 10 km. The result of the tensor stripping was disappointing. The tensor stripping provides a small correction, but a significant distortion remains. This may be due to the complexity of real data combined with uncertainties about the geoelectric structure. Extensive modeling with the Rayleigh-FFT technique suggests another explanation. TM topographic response is most sensitive to local surface slopes. This observation means that TM effects are as large for a 1 m high feature as for a 1 km feature if the slopes are equal. The TM mode responds to the largest slope "seen" at the skin depth. The TE mode responds to the amplitude "seen" at the skin depth. The TE effects have the characteristics of an inductive effect; they are frequency dependent. The TM effects have the characteristics of a galvanic effect; they are only slightly frequency dependent.