| Scope and method of study. A model of gamma-ray oil well logging is given which shows that Poisson noise is a major source of error. A simple synthetic log is used to evaluate the performance of the various filters. This log has uniformly distributed bed levels from 50 to 288 counts, and uniformly distributed bed widths between 5 and 10 samples. The result for the Wiener filter is given. An unattainable minimum level for noise after filtering is derived. Using Monte Carlo Simulation, various nonlinear stationary filters are evaluated on a simple scale of RMS error. These include median and recursive median filters of various lengths, linear combinations of recursive median filters and recursive median filters run in reverse. Multiple linear regression is used to show that optimal weighting yields little improvement over unweighted averages. A novel filter is then introduced, named the twin window filter. Various kernels and filter parameters are evaluated in Monte Carlo simulation. The kernels include mean, median, and maximum likelihood. The twin window filter is further evaluated on a synthetic log with slopes between beds and evaluated when followed by a recursive median filter of length 3.;Findings and conclusions. Ordinary median filters increase the RMS error. Recursive medians reduce the RMS error to as little as 73% of the original error. Linear combinations of recursive median filters achieve a 70% level, and if filtering in reverse is allowed, this can be reduced to 66%. If multiple liner regression is used for each synthetic log independently, the RMS error is reduced to 63% of its value, so very little additional improvement can be achieved by adjusting the weighting of the linear combination. The twin window filter with the average kernel achieved the best result of the novel filters: 56%. Following it with a recursive median of length 3 improves that to 53%. Attempting to further improve the filter by optimizing the filter parameter with respect to signal level yielded an improvement of only 0.003%, which while easy to implement, is unlikely to be a significant improvement. The unattainable minimum noise level is 36.5% of the original, so the twin window filters achieve significantly better results for only a slight increase in computational complexity. |
