The role of topographic - isostatic effects on smoothing of the gravity anomaly

The gravity field effects of topography-isostasic masses are one of the most source variations in gravity observations. The removal of the gravitational effect of topography on gravity anomaly is the important task in geodesy and geophysics. In geodesy, the topographical effect is used to make a harmonic gravity space in solving the GBVP. In geophysics, the topographic effect is applied to better detection of anomalous subsurface densities. In addition, in the removing of the topographic effect, the reduced signal is so smooth that it provides the perdition or approximation with higher accuracy.
The removal effect of topography mass will produce a large effect on potential and gravity so called indirect effect. This implies that the effect of topography is compensated by an isostasy mechanism. Therefore, far two well-known ideal models, i.e., Pratt and Airy, were frequently used in local and regional gravity field modeling. Naturally, the effect of isostatic mass is related to the medium wavelength corresponded to the regional scale such as 100 km. The present study aimed to evaluate the various topographic/isostatic models success in smoothing gravity anomaly signal. In addition, the Veining Meinesz-Moritz (VMM) model and Bouguer anomalies are compared with Pratt and Airy. It is tried to find an answer for the three following questions: 1- Are the isostatic anomalies smoother than Bouguer ones? 2- What is the wavelength of the gravitational effect of isostatic masses? 3- Does the VMM isostatic model succeed in smoothing gravity anomalies with respect to ideal models of Pratt and Airy?
To answer these questions, the numerical assessment was done on about 27000 points observed gravity in Colorado, USA. The topographic and isostatic effects are evaluated by the numerical integration using the 90 meters SRTM DEM. The VMM isostatic effect is computed with respect to Moho, computed by gravity inversion using Sjoberg’s method. The global gravity model, EGM08 and the harmonic topography model, DTM2006 are used to the computation of the Moho depth in the test area.
2D Least square spectral analysis (LSSA) method was used for a detailed examination of the calculated signal anomalies smoothness. For better detection of high frequencies, first, wavelengths greater than different radius 10, 100 and 200 km are filtered out from the data using a Gaussian filter in the spatial domain. The LSSA spectrum of reduced signals indicates that Pratt and Airy models compared to the Bouguer have more oscillations in high frequencies. Besides, the spectral content of Bouguer and VMM signals are very similar in high frequency. The results show that the isostasy has no effect on the local smoothness of the Bouguer gravity anomaly signal. Moreover, the numerical results indicate that the gravitational effect of all isostatic models does not affect the wavelength below 50 km