Accuracy of the linear filter coefficients determined by the iteration of the least‐squares method

Abstract

The linear filter method is a powerful tool for the estimation of some convolution integrals which are encountered in many aspects of geophysical problems. The accuracy of the method is affected by two factors, apart from the sampling interval. Because of the slowly decaying oscillations in the filter tail, the tail must be truncated at some point. Because of the extensive numerical calculations required for the determination of the filter coefficients, the resultant filter cannot be free from round‐off errors. The Wiener filter analogy, pointed out by Koefoed and Dirks (1979), gives a straightforward and efficient answer to this problem. We show that the Wiener filter technique with the iterative application of the Levinson’s algorithm not only enhances the accuracy of the filter coefficients, but also greatly reduces the oscillations in the filter tail. Because of the very rapid decay of the filter tail, there is no need to truncate it.