Segmentation of well logs by maximum-likelihood estimation

A maximum-likelihood procedure for segmenting digital well-log data is presented. The method is based on a univariate state variable model in which an observed log is treated as a time-series consisting of two terms: a Gauss-Markov signal remaining constant over a segment, and an additive Gaussian, but not necessarily stationary, noise. The signal jumps by a random amount at a segment boundary. The inverse problem of log segmentation consists of detecting the segment boundaries from a given log. The problem is solved using a Bayesian approach in which the unknown parameters, the locations of segment boundaries and the jumps in the signal value, are estimated by maximizing the likelihood function for the observed data. An algorithm based on Kalman smoothing and single most likelihood replacement (SMLR) procedure is proposed. The performance of the method is illustrated with a case study comprising of multisuite log data from an exploratory well. The method is found to be rapid and robust. The resulting segments are found to be geologically consistent.