S U M M A R YConventional least-squares inversion of geophysical observational data yields a model that fits the data best or within a specified tolerance. Due to the nature of practical data, bounding values of the optimal model parameters are often sought and routinely calculated from the covariance matrix of the least-squares solution. Jackson (1976) proposed the most-squares method as an alternative approach to determining bounding values in linear inversion. As an extension of Jackson's method, we present a stable iterative scheme for obtaining extreme parameter sets in non-linear inversion. The scheme is hybrid and combines the useful properties of the ridge regression (Marquardt 1970) and most-squares methods to solve the non-linear inverse problem. The observational errors and the inherent nonuniqueness in the inversion process are accounted for using a class of models that is consistent with the data. The method is flexible and the use of Twomey-Tikhonov type constraints also enables us to define and seek a preferred class of smooth models, especially for cases in which the sought subsurface physical properties show gradational changes. It is applied to magnetotelluric depth sounding data to demonstrate its potential as an appraisal tool for conventional least-squares models.

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Magnetotelluric measurements made at 10 locations in and around the Kenyan Rift Valley in 1973-74 have been processed to yield single station induction vectors and magnetotelluric principal impedances. Following a brief description of the field work and the data processing procedure, the results are presented and subjected to both qualitative and quantitative interpretations. The induction vector results indicate a concentration of current below the rift valley. Since the maximum impedances are along the rift for sites within the valley but at right angles to the rift outside it, the apparent resistivity results are qualitatively consistent with the existence of a good conductor there. Within the rift maximum apparent resistivities lie F m 7. The variation of maximum and minimum apparent resistivity with period: (a) KER, (b) MOL, (c) JOR and (d) MUT. The variation with period of the azimuth of the major resistivity axis: (el KER, (f) MOL, (g) JOR and (h), MUT, (i) the location of KER, MOL, JOR and MUT relative to the major faults of the rift.

Magnetotelluric measurements were made during 1978-79 at nine sites on a linear traverse across South Scotland, extending from Kinloch Rannoch in the Highlands to Borthwickbrae in the Southern Uplands. Both one-and two-dimensional modelling of the apparent resistivities and phases indicate the existence of a low resisitivity (-75 a m ) zone at 20-90 km depth beneath the Southern Uplands rising closer to the surface beneath the Midland Valley to the north. A zone of slightly higher resistivity (500s2m), but still relatively conducting compared to the surrounding structure, is shown to exist beneath the Highlands. The real part of the ratio of vertical to horizontal magnetic fields is shown to be suitably modelled by a combination of induction and conduction.

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