E. Gomeztrevino, APPROXIMATE DEPTH AVERAGES OF ELECTRICAL-CONDUCTIVITY FROM SURFACE MAGNETOTELLURIC DATA, Geophysical journal international, 127(3), 1996, pp. 762-772
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.