On the isostatic gravity anomaly and disturbance and their applications to Vening Meinesz–Moritz gravimetric inverse problem

In this study, we show that the traditionally defined Bouguer gravity anomaly needs a correction to become ‘the no-topography gravity anomaly’ and that the isostatic gravity anomaly is better defined by the latter anomaly plus a gravity anomaly compensation effect than by the Bouguer gravity anomaly plus a gravitational compensation effect. This is because only the new isostatic gravity anomaly completely removes and compensates for the topographic effect. F. A. Vening Meinesz’ inverse problem in isostasy deals with solving for the Moho depth from the known external gravity field and mean Moho depth (known, e.g. from seismic reflection data) by a regional isostatic compensation using a flat Earth approximation. H. Moritz generalized the problem to that of a global compensation with a spherical mean Earth approximation. The problem can be formulated mathematically as that of solving a non-linear Fredholm integral equation. The solutions to these problems are based on the condition of isostatic balance of the isostatic gravity anomaly, and, theoretically, this assumption cannot be met by the old definition of the isostatic gravity anomaly. We show how the Moho geometry can be solved for the gravity anomaly, gravity disturbance and disturbing potential, etc., and, from a theoretical point of view, all these solutions are the same.