On Gravity Inversion by No-Topography and Rigorous Isostatic Gravity Anomalies

We discuss some theoretical aspects and practical consequences of using traditional versus “new”/rigorous formulations of the Bouguer and isostatic gravity anomalies/disturbances. In principle, the differences between these two concepts are in the definition of the so-called secondary indirect topographic effect (SITE) on the gravity data. Although we follow the tradition to call this effect SITE, we show that it is formally a direct topographic effect (DITE), needed to remove all topographic signal, but in practice not regarded as such. Consequently, there is a need for a no-topography gravity anomaly, which removes all topographic effects, leaving the below-crust Earth transparent for gravity inversion. Similarly, a rigorous isostatic gravity anomaly includes also a compensation effect for the SITE. By using a simple topographic model, we confirm a theoretically found ratio of 2/(n + 1) between the magnitudes of the SITE and DITE by wavelength (spherical harmonic degree n), both for the Bouguer and isostatic gravity anomalies. Finally, global gravity inversions are applied by utilizing the Vening Meinesz-Moritz isostatic model to determine the Moho geometry using the Bouguer gravity disturbances/anomalies and the no-topography gravity anomalies, and the results are compared. The numerical results confirm our theoretical findings that the Bouguer gravity disturbances and the no-topography gravity anomalies provide very similar results. A comparison of these gravimetrically computed Moho depths with the CRUST1.0 seismic model shows rms agreements of 4.3 and 4.5 km, respectively. This is a significant improvement when compared to the Moho result obtained by using the Bouguer gravity anomalies, yielding the rms difference of 7.3 km for the CRUST1.0 model. These results confirm a theoretical deficiency of the classical definition of the Bouguer and isostatic gravity anomalies, which do not take into consideration the SITE effects on the topography and its compensation.