RESISTIVITY INVERSION WITH RIDGE REGRESSION

Abstract

The problem of direct interpretation of apparent resistivity curves from horizontally layered earth models is solved by using the ridge regression estimator. This ridge regression estimator is more stable than the generalized linear inverse estimator that was advocated in a previous paper. The generalized linear inverse method is unstable if the problem is nearly singular. The problem of estimating the standard deviations of the estimated parameters is analyzed. In some layered models the covariance matrix is an accurate estimate of the standard deviations. However, in problems where there is high correlation between parameters, the covariance matrix is not always an accurate estimate. Confidence regions can be contoured in selected parameter spaces to give an accurate estimate of the range of possible layered models that fit the data. Five soundings were chosen to test the inversion scheme. Two of the soundings were theoretical, and the remaining three were field cases. The method works well since it is possible to find models that fit the data, indicate the accuracy of fit relative to the noise in the data, and predict the accuracy with which each parameter is estimated.