PRINZIPIELLE BEMERKUNGEN ZU THEORIE UND PRAXIS DER METHODE DER ZWEITEN ABLEITUNG BEI DER INTERPRETATION GRAVIMETRISCHER MESSERGEBNISSE

The first part of the paper deals with theoretical considerations concerning the arithmetic mean of gravity values and its use with regard to the derivation of approximation formulae for the second derivative. In order to calculate the second derivative in practice the arithmetic mean. ḡ(r) of a continuum of gravity values on a circle of radius r is approximated by a Taylor polynomial and then replaced by the arithmetic mean g n ( r ) of n discrete gravity values. Because of the invariance of ġ( r ) with regard to rotations of the coordinate system in the horizontal datum plane there exists a lower limit for the number n; this lower limit depends on the degree of the Taylor polynomial used in the formula for g zz . The general results of the first part yield routine formulae for the special case of a regular hexagonal grid; these formulae are given and discussed in the second part of the paper. Three formulae are applied to the gravity data of the Los Angeles Basin. Some remarks concerning the comparability of different approximation formulae and some hints with regard to routine calculations conclude the paper.