Comparison of spherical cap and rectangular harmonic analysis of airborne vector gravity data for high-resolution (1.5 km) local geopotential field models over Tanzania

Abstract

SUMMARY This study examines local geopotential field modelling over a mountainous region in Tanzania using vector airborne gravity data. We use the adjusted spherical cap and rectangular harmonic analyses. Both methods are based on expansion of gravitational potential into a series of orthogonal harmonic basis functions of local support in such a way that the expansion coefficients are determined by gravity observations. All three components of gravity vector are simultaneously inverted to derive the geopotential coefficients. In order to evaluate the accuracy of the local models, independent checkpoints are selected within the study region and around its boundary and the computed gravity vectors are compared with the independent gravity observations. The results show an excellent agreement with root mean square error (RMSE) of < 1.6 mGal over the study area. On the contrary, the RMSEs of global geopotential models against the checkpoints data are 7 mGal for the models up to the maximum degree of 2190 (a resolution of ∼9.1 km) and 5 mGal to 5399 (∼3.7 km). Our local models are significantly more accurate than the state-of-the-art global models and fully exploit the airborne vector data with the measurement error of ∼1 mGal. We also present the regional models constrained only by radial (vertical) or by lateral (horizontal) gravity observations. Those models are considerably less accurate than the one from 3-D gravity data inversion. Lastly, the regional models are validated against topography data. It is found that the gravity–topography correlation is 0.8–0.9 at 100 km, 0.5 at 20 km and higher than the correlations of the global models at all frequencies. The gravity–topography admittances estimated from our regional models indicate ∼130 mGal km−1 and imply the effective density of 2500 kg m−3 for topographical mass.