Ward E. Schultz and Suresh G. Thadani
Welex, a Halliburton Company
Houston, Texas
ABSTRACT
Statistical variations are often a limiting factor in obtaining precise interpretations from nuclear logs. Digital log processing allows the application of enhanced filtering techniques. The goal is to reduce statistical fluctuations while maintaining adequate response to formation changes. Alternatively, improved faltering permits increased logging speeds without degrading log quality.
One real-time technique studied utilizes a combination of moving-average filters. One filter averages over a fairly narrow depth interval to yield good resolution of formation bedding. Another filter averages over a much wider interval and, therefore, has a smaller statistical variation. By adaptively combining the two averages, statistical fluctuations are reduced, while significant log features are retained.
The second approach considered is based on the application of optimal filtering techniques to this Nonlinear estimation problem. Specifically, the technique used is that of nonlinear Kalman filtering. This technique exploits a priori problem knowledge of the underlying noise statistics while allowing for adaptive estimation of the “mean value”of the log with adequate bed boundary resolution.
The final method presented is a two-pass implementation of nonlinear Kalman smoothing. In this technique, a forward pass is made through the data and real-time Kalman filtered estimates are computed. A backward pass is then made through the same data in an off-line mode, during which the Kalman filtered estimates and the data are used to produce improved smoothed estimates.
Examples of filtering two sets of simulated count rate logs and neutron porosity data show the improved log quality that is obtained with these new techniques. The combined moving-averages yielded better results than a conventional moving-average. Additional improvement was observed with Kalman filtering, and Kalman smoothing gave the best results. Computational requirements were found to generally increase with the amount of reduction in statistical variations.