Modification of the Berezkin method for the determination of the singular points for gravity anomalies
DOI:
https://doi.org/10.15407/dopovidi2017.12.060Keywords:
analytical continuation, anomalies, Berezkin method, Fourier series, gravity, gravity gradient, Laplace equation, singular pointsAbstract
New analytical expressions of the Berezkin function are introduced in order to solve the problem of the analytical continuation for the gravity values within the stripe. These expressions are obtained with the help of the analytical transformation of a Fourier series partial sum, which approximates the values of the fundamental solution of the Laplace equation for the gravity. The decrement rate for the coefficients of the Fourier series is evaluated. By means of the differential analysis, the technique of interpolation with the given accuracy of the relevant number of Fourier series terms is substantiated. A practical algorithm for calculations of the Berezkin function with the given precision is presented. This computational technique has a numerical stability to the differentiation errors.
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