An optimal Savitzky-Golay derivative filter with geophysical applications: an example of self-potential data

We propose a strategy in designing an optimal set of filter parameters, such as the order of interpolating polynomial and the filter length for a Savitzky-Golay derivative filter. The proposed strategy is based on the 'principle of parsimony' while satisfying the optimality conditions. The optimality conditions are based on the Durbin-Watson lag-1 test statistic and the Derringer-Suich desirability function. While the former checks for an appropriate data fitting, the latter, on the other hand, ensures minimal shape distortion of the reconstructed response. The proposed strategy of designing filter parameters is developed and validated through numerical experiments using Gaussian pulse as a test function which is contaminated with additive white Gaussian noise. In the numerical tests, the polynomial orders used were 3, 5 and 7, but the filter length for each polynomial was varying until the optimality conditions were satisfied. The Savitzky-Golay derivative filtering is used in obtaining the robust reconstruction of noisy geophysical anomaly and the robust estimation of its first- and second-order derivatives. We validated the proposed technique on the published self-potential anomaly data using a data-based interpretation technique where the reconstructed anomaly and its first- and second-order derivatives were used in estimating model parameters. The data-based interpretation using the proposed technique of Savitzky-Golay derivative filtering provides a close agreement with the published results.