An analytic one-dimensional magnetotelluric inversion scheme

Abstract

An analytic one-dimensional magnetotelluric inversion scheme is described. The main characteristics of this new scheme are its simplicity and its minimal requirements in computer time and storage space. The basic idea of the scheme is that for a given period T only the structure above a certain depth matters. The scheme therefore starts with the shortest periods of the available data set and tries to explain the observed response, specifically the apparent resistivity pa(T) and the phase @(T), in terms of a two-layer structure. Shifting successively to longer periods, discrete new layers are introduced at progressively greater depth. Some stabilizing features simultaneously keep the inversion process from diverging and hold the necessary number of layers to a minimum. The properties of the scheme are analysed by studying its performances when working on synthetic and real field data. The scheme can handle fairly scattered data and is very stable. It has, in fact, never been observed to diverge. Examples are given of how the scheme might be handled in practice, especially regarding the use of the causal dispersion relations with which it is possible to ensure that the model proposed by the inversion scheme will return a response function in agreement with the initial data.

Inversion methods applied to Dst data.

“…Global response estimates were derived from storm data analysed by MARSHALL (1980) covering the frequency range 0.07 to 2cpd. The response data were inverted to give conductivity profiles within the upper mantle using the algorithms due to BAILEY (1970aBAILEY ( , 1970b, PARKER (1980) and PARKER and WHALER (1981), and FISCHER et al (1981a. The results obtained from these inversions are consistent, and reveal two major discontinuities in conductivity of several orders of magnitude at depths between 650-750km and 950-1050km.…”

“…The inversion scheme is therefore used to derive starting structures for the modelling algorithm. For a full account of these methods the reader is referred to FISCHER et al (1981aFISCHER et al ( , 1981b.…”

“…The inversion method of FISCHER et al (1981a) uses the simple fact that only the conductivity structure above a certain depth will affect the response function above a given frequency. Therefore, starting with the high frequency values, the response data are described in terms of a two layer structure with new layers being introduced at greater depths as the lower frequency data are used.…”

“…Several methods now exist which invert a set of response data to give, whenever they exist, acceptable one dimensional conductivity profiles, e.g. BAILEY (1970), KHACHAY (1978), PARKER (1970aPARKER ( , 1970b, PARKER (1980), FISCHER et al (1981a), andBARCILON (1982). However, one outstanding topic, and perhaps the most difficult of all, still requires further development; given a finite data set, how to interpret in a geophysically satisfying way the totality of solutions that may be obtained using inverse methods, some of which yield many acceptable but diverse models.…”

A new inversion scheme for two-dimensional magnetotelluric modelling.

“…The earth model parameters at a certain depth principally influence the response function for a limited range of periods. FISCHER and SCHNEGG (1981) This procedure is repeated with increasing periods to determine the resistivities and the depths to the interface of the model layer from the top to the maximum depth. It is clear that at each step only a fraction of the parameters of a complex model is determined and only one period is involved, however all parameters of the model can be obtained through the inversion for a series of periods.…”