New Modifications of Stokes’ Integral

Abstract

In the last decades several alternative methods of modifying Stokes’ formula were developed. Here, a combination of two existing modifications from Meissl and Sjoberg is developed and presented. The latter applies a least squares method to minimize the truncation error (as well as the total error of the geoid determination), while the former forces the truncation coefficients to converge to zero more rapidly by using a continuous function. The question is whether the combined Least Squares-Meissl modification reduces the truncation and/or the total geoid determination error. To determine the modification parameters, a new system of equations satisfying simultaneously the faster convergence and minimizing the total error, are presented by using (a) Green’s second identity, which is a conventional method, and (b) a set of smoothing averaging filters. The method (b) provides further flexibility when different smoothing filters can be utilized. The new modification reduces the contribution of the inner zone error by ~1 mm of the estimated RMS error. The total error does not necessarily decrease, by using the new modification for cap sizes smaller than 3o versus the least squares modification of Sjoberg (Manusr Geod 16: 367–375, 1991).