Abstract
Sequence convolution formulae, based on the B-splines of I. J. Schoenberg provide simple and effective methods for smoothing and differentiating data sequences. Their time and frequency domain properties allow calculation of the degree of smoothing and noise rejection, and their z-transforms lead to the rapid calculation of formulae from a simple sequence of polynomials. As an example of their use, numerical differentiation is used to produce smooth velocity—depth profiles and to delineate major velocity discontinuities from time—depth data logged at a well.
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Jupp, D.L. B-splines for smoothing and differentiating data sequences. Mathematical Geology 8, 243–266 (1976). https://doi.org/10.1007/BF01029272
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DOI: https://doi.org/10.1007/BF01029272