In one-dimensional magnetotelluric modelling the standard deviation E is often used as an indicator of the degree of fit between the field measurements and the calculated model response. The topography of E in the space of the model parameters has been studied and found to be rather simpler than expected. The absolute minimum seems to be quite isolated from other minima. In general no such other local minima were found. To find the minimum it was not necessary, therefore, to look for a computing routine capable of jumping out of localized minima. But the search routine had to be capable of moving along a valley with an exceedingly level floor, as the minimum is often at large distances from the initial model. In this respect it was important to work with logarithmic coordinates.can be found, it often becomes possible to split € , , , i n into three separate components: (1) the scatter of the original field data, (2) the departure of these data from one-dimensionality and (3) a component that will occur if one attempts to model the data with a structure comprising too few layers. Knowing this last contribution it becomes easy to decide which is the smallest number of layers necessary to model a given data set.Since the absolute minimum

FISCHER, G., LE QUANG, B.V., MULLER, I., 1983, VLF Ground Surveys, a Powerful Tool for the Study of Shallow Two-Dimensional Structures, Geophysical Prospecting, 31, 977-991.The suitability of VLF ground surveys in the investigation of shallow two-dimensional structures is analyzed. For such structures the polar formalism is derived, necessary in practice since the transmitters are generally not in the structural strike or profile. A simple vertical dike is considered to demonstrate the striking anisotropy which can be expected over such a structure, in particular the high apparent resistivity along the direction of a well-conducting dike and the low resistivity across it. The theory is then confronted with the practical example of an asymmetrical vertical dike resulting from a strike-slip fault. Modelling of the survey results is very successful and yields good confirmation of the polar behaviour. VLF ground surveys thus provide a quick and powerful tool for the study of geological accidents within about 100 m of the surface.

A number of analytical inversion schemes of the one-dimensional magnetotelluric response Z ( T ) = &w.L~~,(T)/T exp i [n/4 -@(T)] require input data in the form of smooth single-valued functions of apparent resistivity pa and phase Q, versus the period 2' . It is generally assumed that one-dimensionality is guaranteed if the observed surface impedance Z ( T ) reduces to a complex scalar, rather than a tensor, and if the derivatives of pa@) and $(T) and the value of @(T) remain within certain bounds. This is not sufficient, however, since apparent resistivity and phase are related through integral dispersion relations similar to those which in optics connect modulus and argument of the complex reflection coefficient. Inversion schemes operating on data which do not satisfy the dispersion relations can never lead to model structures of which the computed response function agrees with the original input data. But since real field data always exhibit a certain amount of scatter, the dispersion relations may profitably be used to construct pa@) and @(T) functions compatible both with these relations and with the scattering range of the field data. In the present paper the assumption is made that measurements of pa( 2' ) are usually more reliable than those of @(T); a method is therefore described with which to compute @(T) from a smoothed single-valued function pa(T). This calculated phase, and its corresponding apparent resistivity, are thus compatible with a tabular structure and suitable as input for one-dimensional inversion schemes that need both p a ( T ) and $ ( T ) data. Such schemes are usually more efficient than those working only with the apparent resistivity. The same dispersion relations are also shown to connect amplitude and argument of the principal impedances of two-dimensional structures.

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.

A conducting slab of finite thickness divided into three segments of different conductivities and overlying a perfect conductor is proposed as a suitable two-dimensional 'control' model for testing the accuracy of the various numerical modelling programs that are available for calculating the fields induced in the Earth by an external, time-varying magnetic source. An analytic solution is obtained for this control model for the case of the magnetic field everywhere parallel to the conductivity boundaries (B-polarization). Values of the field given by this solution for a particular set of model parameters are calculated at selected points on the surface and on a horizontal plane inside the conductor, and are tabulated to three figure accuracy for reference. They are used to check the accuracy of the results given by the finite difference program of Brewitt-Taylor & Weaver and the finite element program of Kisak & Silvester for the same model. Improved formulae for calculating the derived electric field components in B-polarization are first developed for incorporation in the finite difference program, and these give s u r f x e electric fields within 1 per cent of the analytic values, while all three field components inside the conductor are calculated t o better than 96 per cent accuracy by the finite difference program. The results given by the finite element program are not quite so satisfactory. Errors somewhat greater than 10 per cent are present and although the program requires much less disk space it takes rather more CPU time to complete the calculations.