APPROXIMATE DEPTH AVERAGES OF ELECTRICAL-CONDUCTIVITY FROM SURFACE MAGNETOTELLURIC DATA

This paper presents a simple non-linear method of magnetotelluric inve rsion that accounts for the computation of depth averages of the elect rical conductivity profile of the Earth. The method is not exact but i t still preserves the non-linear character of the magnetotelluric inve rse problem. The basic formula for the averages is derived from the we ll-known conductance equation, but instead of following the tradition of solving directly for conductivity, a solution is sought in terms of spatial averages of the conductivity distribution. Formulas for the v ariance and the resolution are then readily derived. In terms of Backu s-Gilbert theory for linear appraisal, it is possible to inspect the c lassical trade-off curves between variance and resolution, but instead of resorting to linearized iterative methods the curves can be comput ed analytically. The stability of the averages naturally depends on th eir variance but this can be controlled at will. In general, the bette r the resolution the worse the variance. For the case of optimal resol ution and worst variance, the formula for the averages reduces to the well-known Niblett-Bostick transformation. This explains why the trans formation is unstable for noisy data. In this respect, the computation of averages leads naturally to a stable version of the Niblett-Bostic k transformation. The performance of the method is illustrated with nu merical experiments and applications to field data. These validate the formula as an approximate but useful tool for making inferences about the deep conductivity profile of the Earth, using no information or a ssumption other than the surface geophysical measurements.