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EFFECTS OF DATA ERRORS AND ACCURACY IN SECOND DERIVATIVE COMPUTATION BY RATIONAL APPROXIMATION *
Author(s) -
AGARWAL B. N. P.,
SINGH J.
Publication year - 1975
Publication title -
geophysical prospecting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.735
H-Index - 79
eISSN - 1365-2478
pISSN - 0016-8025
DOI - 10.1111/j.1365-2478.1975.tb00687.x
Subject(s) - computation , second derivative , constant (computer programming) , gravity anomaly , mathematics , gravitational field , derivative (finance) , field (mathematics) , approximation error , anomaly (physics) , residual , regional geology , mathematical analysis , physics , algorithm , geology , hydrogeology , telmatology , computer science , classical mechanics , quantum mechanics , amplitude , geotechnical engineering , financial economics , pure mathematics , economics , programming language
A bstract The effects of systematic (constant) and random errors in the observed data have been investigated analytically for rational approximation method of computing second derivative involving a summation of the products of the averages of the gravity field with the corresponding weight coefficients, both in numerator as well as in denominator. A theoretical gravity anomaly over three spheres has been analyzed to demonstrate the high accuracy in the approximation. Since the sums of the weight coefficients in numerator and denominator are zero and one respectively, the regional gravity anomaly, even though approximated by a constant value over the entire area under computation, can produce substantially large error in the calculated derivative value. This is happening because of the contribution of the regional field in the denominator. Thus, inspite of the high accuracy in rational approximation, the method has limited application to field cases where a combined gravity field consisting of regional and residual anomalies is usually used. Master curves are presented for the constant and random errors by which a rough estimate of the percentage of error in second derivative computation can be made provided one has some idea of the magnitudes of the regional field and random error.