Volume 23 Number 1
  • E-ISSN: 1365-2478



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.


Article metrics loading...

Loading full text...

Full text loading...


  1. Agarwal, B. N. P. and Lal, T., 1971, Application of rational approximation in calculation of the second derivative of the gravity field, Geophysics36, 571–581.
    [Google Scholar]
  2. Elkins, T. A., 1952, The effect of random errors in gravity data on second derivative values, Geophysics17, 70–88.
    [Google Scholar]
  3. Fajklewicz, Z. J., 1965, Fictitious, anomalies of higher vertical derivatives of gravity, Geophysics30, 1094–1107.
    [Google Scholar]
  • Article Type: Research Article
This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error