Automatic model for finding the one-dimensional magnetotelluric problem

Abstract

A method is described for finding a resistivity model that fits given magnetotelluric data in the one-dimensional case. The procedure is automatic and objective in that no a priori model structure is imposed. Starting with a uniform half space derived directly from the data, the procedure gradually transforms the half space to one with a continuous and smooth resistivity distribution whose response fits the measured data. The method is illustrated b y application to two magnetotelluric data sets.

The magnetotelluric inverse problem

“…Hobbs (1982) writes: 'MT analysts are notoriously optimistic in believing the significance of the errors accompanying their data, the result being that in some cases no model exists whose response fits...'; he uses this assertion as an argument for raising experimental error estimates if he is unable to find a suitable model adopt a measure of misfit consisting of the sum of squares of differences in q~ and in in p,, each quadratic term weighted by the inverse confidence interval (not the square of the interval as traditional practice would suggest). They also propose omitting a term form the sum whenever it is less than some arbitrary amount.…”

“…One difficulty with this approach is that the particular solution obtained depends upon the starting guess; the process does not define a single result. Hobbs (1982) attempts to avoid the problem by finding models as close as he can to a uniform conductor: he introduces a bias into the data which'pulls the responses towards those of a uniform model, Gauss-Newton iteration is used to improve the misfit, then the bias is reduced and the process repeated. Neither of these methods is certain to bring the misfit down to an acceptable level, although in actual application they appear to work quite well.…”

“…This set has been the subject of many investigations (e.g. Jones and Hutton, 1979;Larsen, 1981;Fischer and LeQuang, 1981;Hobbs, 1982;Parker, 1982). I followed the assumption that p, and r are uncorrelated and calculated an approximate standard deviation for them by dividing the given confidence interval by 3.92, the number appropriate for a Gaussian distribution.…”

Combined transient electromagnetic and magnetotelluric study of the southern Kenya rift valley

“…The continuous conductivity models derived in the second category of solutions are inversion schemes that produce resistivity structure that is isotropic and a continuous function of depth (e.g. Niblett and Sayn-Wittgenstain, 1960;Parker, 1970Parker, ,1977Oldenburg, 1979;Hobbs, 1982) The non unique nature of the EM data implies that there is more than one model which satisfy the recorded data in the absence of a priori information. Random search or Monte Carlo methods can provide a partial solution to the problem and can explore the range of uniqueness of the solutions.…”

“…A great variety of 1-D modelling and inversion schemes exist (Niblett and SaynWittgenstein, 1960;Wu, 1968;Jupp and Vozoff, 1975;Jones and Hutton, 1979;Parker, 1980;Parker and Whaler, 1981;Fischer et al, 1981;Hobbs, 1982;Constable et al, 1987;Meju, 1988Meju, , 1992Meju and Hutton, 1992).…”