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.

The Moho depth can be determined using seismic and/or gravimetric methods. These methods will not yield the same result as they are based on different hypotheses as well as different types, qualities and distributions of data. Here we present a new global model for the Moho computed based on a stochastic combination of seismic and gravimetric Moho models. This method employs condition equations in the spectral domain for the seismic and gravimetric models as well as degree-order variance component estimation to optimally weight the corresponding harmonics in the combination. The preliminary data for the modelling are the seismic model CRUST2.0 and a new gravimetric Moho model based on the inverse solution of the Vening Meinez-Moritz isostatic hypothesis and the global Earth Gravitational Model EGM08. Numerical results show that this method of stochastic combination agrees better with the seismic Moho model (3.6 km rms difference) than the gravimetric one. The model should be a candidate for dandifying the frequently sparsely data CRUST2.0. We expect that this way of combining seismic and gravimetric data would be even more fruitful in a regional study.

In precise geoid modelling the combination of terrestrial gravity data and an Earth Gravitational Model (EGM) is standard. The proper combination of these data sets is of great importance, and spectral combination is one alternative utilized here. In this method data from satellite gravity gradiometry (SGG), terrestrial gravity and an EGM are combined in a least squares sense by minimizing the expected global mean square error. The spectral filtering process also allows the SGG data to be downward continued to the Earth’s surface without solving a system of equations, which is likely to be ill-conditioned. Each practical formula is presented as a combination of one or two integral formulas and the harmonic series of the EGM.Numerical studies show that the kernels of the integral part of the geoid and gravity anomaly estimators approach zero at a spherical distance of about 5°. Also shown (by the expected root mean square errors) is the necessity to combine EGM08 with local data, such as terrestrial gravimetric data, and/or SGG data to attain the 1-cm accuracy in local geoid determination.