What is a Standard Gravity Formula?

Abstract

Scandinavian region is uplifting and Indian region is a stable shield area, so we may expect negative gravity anomaly in the former region and no systematic anomaly in the latter. Against these expectations, we have no systematic negative anomaly in Scandinavia and negative anomaly in India, if the anomalies are calculated basing upon the standard gravity formula including only (l=2 and 4, m=0) term in the spherical harmonic expansion. It may be, however, that processes responsible to the Scandinavian uplift and the Indian geology occur in shallower depth (probably in the C layer, asthenosphere) and that mass anomaly responsible to the anomaly of rather longer wave length (or smaller wave numbers l and m) exists deep (probably in the C and D layers, mesosphere) within the earth. If such is the case, in order to get gravity anomaly closely related to geology, we must take as the standard gravity not only (l=2 and 4, m=0) term but also higher order terms in the spherical harmonic expansion. In short we must choose the standard gravity formula so as to get gravity anomaly which is agreeable with other geophysical and geological observations.
Studies are made from the above point of view. Gaposchkin and Lambeck's data on the spherical harmonic expansion of geoidal undulations are used. It is our tentative conclusion that by including terms up to (l=8, m=8) we get anomalies which are more agreeable with geology than the standard gravity formula.