The dispersion relations of the magnetotelluric response and their incidence on the inversion problem

Abstract

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.

Two-dimensional resistivity modeling based on regional magnetotelluric survey in the northern Tohoku district, northeastern Japan.

“…On the other hand, phase of the total electric field is less distorted, because the phase of the galvanic charge is nearly the same as that of the primary field, if the scale of shallow localized inhomogeneity is small as compared with the skin depth. This is equivalent to the fact that phase can be derived from the derivative of log apparent resistivity with respect to log frequency (WEIDELT, 1972;FISCHER and SCHNEGG, 1980). One way to remove the static effect is spatial averaging of apparent resistivity values at each frequency over several stations.…”

Magnetotelluric observational techniques on land

“…The data is continuously checked for such things as amplifier overload and coherency, and rejected if certain criteria are not met. Additionally the system can perform rotations of the coordinate system, for example to the principal coordinates, or if the data appear to satisfy the 1-D criteria, the 1-D dispersion relations can be applied (Weidelt, 1972;Fischer and Schnegg, 1980) or a 1-D inversion carried out (Fischer, 1980, Fischer et al, 1981. Similar systems built around a Digital Equipment Corp. LSI-11/03 microcomputer have recently been reported by the Berkeley group and the Edinburgh group (Dawes, 1980).…”

The magnetotelluric inverse problem

“…Weidelt (1972) and several others (e.g. Bailey, 1970;Fischer and Schnegg, 1980) have discussed relationships between the real and imaginary parts of c and between pa and 4). In a genuine response, these pairs of functions are not independent so that, for example:…”