Bayesian deconvolution of gamma‐ray logs

Abstract

The spatial resolution of gamma‐ray logs is defined by the length 𝓁 of the gamma‐ray detector. To resolve thin beds whose thickness is less than 𝓁, it is generally desirable to deconvolve the data to reduce the averaging effect of the detector. However, inherent in the deconvolution operation is an amplification of high‐frequency noise, which can be a detriment to the intended goal of increased resolution. We propose a Bayesian statistical approach to gamma‐ray log deconvolution which is based on optimization of a probability function which takes into account the statistics of gamma‐ray log measurements as well as the empirical information derived from the data. Application of this method to simulated data and to field measurements shows that it is effective in suppressing high‐frequency noise encountered in the deconvolution of gamma‐ray logs. In particular, a comparison with the least‐squares deconvolution approach indicates that the incorporation of physical and statistical information in the Bayesian optimization process results in optimal filtering of the deconvolved results.