ÉTUDE DE L'ATTÉNUATION DE L'INFLUENCE DES ANOMALIES SUPERFICIELLES DANS LE CALCUL DE LA DÉRIVÉE SECONDE DE LA GRAVITÉ*)

In order to eliminate the effect of smoothing due to the use of a finite number of grid points, the second derivative is computed by integrating the product of g with a convenient continuous function, which yields the second derivative to the extent to which the first terms of the Taylor expansion of g represent its value correctly. By applying this method to the anomaly caused by an isolated mass, and to that caused by a homogeneous half plane, it is shown that, if the result obtained is interpreted as if it really were a second derivative, erroneous values for the depth and the mass are obtained. If the real depth of the mass is small, a too large apparent depth is obtained. In the case of a half plane the use of a system of grid points gives the same result. These considerations permit the rational choice of the method of computing the second derivative, such that the effects of too shallow mass irregularities are attenuated.