A new physical foundation for anomalous gravity

Abstract

The rigorous relation between the sought subsurface anomalous density distribution and the gravity anomaly, the gravity disturbance, and the geoidal height is newly reviewed. The emphasis is put on the proper treatment of the respective effects of topographical masses. The aim is to prove, that the rigorous formulation of the above mentioned relations calls for using such topographical corrections that adopt the reference ellipsoid as the lower boundary of the topography, and a reference topographical density. We base our derivations on a reference topographical density that is chosen to be globally constant. Such topographical corrections are then referred to as “No Ellipsoidal Topography of Constant Density” corrections, abbreviated as “NETC” corrections, as they differ from the commonly used Bouguer topographical corrections. We derive the NETC corrections to the disturbing potential, the gravity disturbance, the gravity anomaly, and the geoidal height. Equations are derived, that link the anomalous density, via Newton integrals with specific kernels, with the NETC gravity disturbance, the NETC gravity anomaly, and the NETC geoidal height. Prescriptions for compiling the NETC gravity disturbance, anomaly, and geoidal height from observable data are derived. It is proved, that the NETC gravity disturbance is rigorously equal to the gravitational effect (attraction) of the anomalous density distribution inside the entire earth. That is the fundamental point of the paper. The spherical complete Bouguer anomaly (SCBA) widely used in geophysical studies is then compared with the NETC gravity disturbance. The SCBA is also demonstrated to be a hybrid quantity, neither an anomaly, nor a disturbance. The systematic deviation between the SCBA and the NETC gravity disturbance is shown to be the most general form of the so called geophysical indirect effect (GIE), which is defined as the departure of the SCBA from the attraction of anomalous earth’s masses. The GIE is computed for the area of the Eastern Alps.