Ridge regression inversion applied to crustal resistivity sounding data from South Africa

Abstract Ridge regression inversion has been used to test the applicability of various one-dimensional crustal models to the interpretation of deep Schlumberger sounding data from southern Africa (Van Zijl and Joubert, 1975). Four main models were investigated: a simple three-layered earth, a layered earth with a transition zone exhibiting a linear decrease in log resistivity with depth, a similar earth with the transition zone determined by cubic splines, and a model having exponential resistivity behavior at depth. The last model corresponds to temperature-dependent semiconduction through solid mineral grains (Brace, 1971). It was found that all of these models are capable of fitting the sounding data from southwestern Africa, while all except the semiconduction model fit the data from southeastern Africa. One is, thereby, immediately alerted to the problem of lack of resolution in Schlumberger sounding data where geologic control is not available.A major problem with the inversion of Schlumberger data alone is that accurate information is obtainable only for the resistivity-thickness product of the resistive portion of the crust. On the other hand, magnetotelluric data, when available, tends to provide information on the thickness, but very little information on the true resistivity of the section. In order to resolve both resistivity and thickness it is possible to invert simultaneously Schlumberger and magnetotelluric (MT) data. Results obtained from the combined inversion of the African resistivity data and hypothetical MT data show that a considerable improvement in model resolution can be achieved using MT amplitude data even of poor accuracy from a relatively limited frequency range (0.1 to 100 Hz), whereas inclusion of MT phase information is of negligible additional benefit.Unfortunately, no significant test can be made, from data available at the time of our analysis, of the applicability of one-dimensional inversion in a geologic circumstance which probably demands more dimension.