In‐situ complex resistivity measurements over the frequency range [Formula: see text] to [Formula: see text] have been made on 26 North American massive sulfide, graphite, magnetite, pyrrhotite, and porphyry copper deposits. The results reveal significant differences between the spectral responses of massive sulfides and graphite and present encouragement for their differentiation in the field. There are also differences between the spectra of magnetite and nickeliferrous pyrrhotite mineralization, which may prove useful in attempting to distinguish between these two common IP sources in nickel sulfide exploration. Lastly, there are differences in the spectra typically arising from the economic mineralization and the barren pyrite halo in porphyry copper systems. It appears that all these differences arise mainly from mineral texture, since laboratory studies of different specific mineral‐electrolyte interfaces show relatively small variations. All of the in‐situ spectra may be described by one or two simple Cole‐Cole relaxation models. Since the frequency dependence of these models is typically only about 0.25, and the frequency dependence of inductive electromagnetic coupling is near 1.0, it is possible to recognize and to remove automatically the effects of inductive coupling from IP spectra. The spectral response of small deposits or of deeply buried deposits varies from that of the homogeneous earth response, but these variations may be readily determined from the same “dilution factor” [Formula: see text] currently used to calculate apparent IP effects.

A fast ridge regression inversion technique has been devised for the interpretation of simple two‐dimensional resistivity and induced‐polarization data. The program will determine the rectangular source under a single layer of overburden which best fits the observed data. Several advantages are derived from using the ridge regression method; they include convergence from very poor initial guesses, stability in the presence of high‐frequency geologic noise, readily obtained estimates of parameter statistics, and the ability for simultaneous inversion of multiple data sets. Unfortunately, each ridge regression inversion requires a great many forward problem evaluations; thus in order to achieve speed and reasonable cost, it is essential to reduce the calculation time for the forward problem to an absolute minimum. One method of achieving this is to store in the computer a data bank containing solutions for the entire range of expected parameter combinations. The forward problem then reduces to numerical interpolation between these precalculated data sets. For compilation of the data bank of forward solutions, two main numerical methods were investigated: the finite element and transmission‐surface algorithms. Although these algorithms are conceptually quite different, the resulting matrix equations are very similar. The efficiency of either method depends mainly on the scheme chosen for solving the resultant large system of linear equations. Once the data bank has been created, it is possible to obtain inverse solutions for less cost than the computation of one finite element or transmission‐surface forward problem. Tests on theoretical data and field data show the inversion technique to be reasonably accurate, stable, and fast. The statistics estimated by the inversion program provide additional useful information on the uncertainty in the parameters of the derived model and on high correlations between parameters. The most highly correlated parameters are, as might be anticipated, the resistivity and the width of thin conductive bodies. Two practical methods for carrying out inversion in spite of highly correlated parameters are, preferably, to add extra data sets which provide more information on some of the parameters or, alternatively, to fix some of the parameters at geologically reasonable values and invert to a more restricted model.

One hundred and twelve Schlumberger vertical electrical soundings were made as part of a hydrogeological study in the Apodi Valley, Brazil. Most of the data have been interpreted using an automatic ridge regression inversion algorithm in conjunction with a fast digital filter forward algorithm. As a result, the inversion costs are very low. The increase in speed and accuracy in the evaluation of the forward problem has also allowed calculation of the Schlumberger apparent resistivity from potential differences, instead of the electric held. Consequently, there is no diffiIlr;TRODC:CTION In February I97 I and February 1974 the Superintendencia do Desenvolvimento do Nordeste and the Universidade Federal de Pernambuco conducted resistivity soundings during an investigation of the groundwater resources of the Apodi Valley, Rio Grande do Norte, Brazil. A total of II2 Schlumberger vertical electrical soundings (VES) were made with a maximum electrode spacing (A B/2) ranging from I50 to 500 m. The objectives of the electrical survey were to determine the thicknesses of the underlying alluvial and sandstone horizons and to determine the basement topography. Instead of using time-consuming traditional methods of interpretation such as auxiliary point techniques (Zohdy, 1965) and curve-matching procedures using albums of theoretical curves (Compagnie general de Geophysique, 1973; Orellana and Mooney, 1966; Rijkwaterstaat, 1969) the data were automatically processed on a Univac 1108 computer at the University of Utah. C. FEITOSAS. AND S. Il. WARD* culty in the interpretation of data where very large receiver electrode (MN) spacings have been used or where discontinuities have been introduced by changing the MN spacing on a layered earth containing large resistivity contrasts. The soundings were conducted primarily to map the thicknesses of a known alluvial aquifer and a potential sandstone aquifer. These thicknesses have been determined to within an error of 20 percent as estimated from analysis of the parameter standard deviations and comparison with available drill hole information. There are at least two main approaches to computerized interpretations of VES data. One approach (Zohdy, 1975) assumes that nothing is known about the number of subsurface layers, their thicknesses, or resistivities. This approach has advantages when a survey is being made in areas where absolutely no geologic information is available: no initial guess is required, and the processing costs are very low (less than $1 per sounding). However, in most hydrogeological applications, at least some rudimentary geologic information is available. This may only consist of a rough idea of the layering sequence: overlying sediments, aquifer, and basement. Or, in areas where wells have been drilled, very detailed information may exist regarding the number of distinct lithological units and their thicknesses. In these situations it is usually desirable to obtain an interpretation which has the same number of layers as there are distinct lithological units, a...

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 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.

No abstract