Forward Gravity Modelling to Augment High-Resolution Combined Gravity Field Models

Abstract

During the last few years, the determination of high-resolution global gravity field has gained momentum due to high-accuracy satellite-derived observations and development of forward gravity modelling. Forward modelling computes the global gravitational field from mass distribution sources instead of actual gravity measurements and helps improving and complementing the medium to high-frequency components of the global gravity field models. In this study, we approximate the global gravity potential of the Earth's upper crust based on ellipsoidal approximation and a mass layer concept. Such an approach has an advantage of spectral methods and also avoids possible instabilities due to the use of a sequence of thin ellipsoidal shells. Lateral density within these volumetric shells bounded by confocal lower and upper shell ellipsoids is used in the computation of the ellipsoidal harmonic coefficients which are then transformed into spherical harmonic coefficients on the Earth's surface in the final step. The main outcome of this research is a spectral representation of the gravitatioal potential of the Earth's upper crust, computed up to degree and order 3660 in terms of spherical harmonic coefficients (ROLI_EllApprox_SphN_3660). We evaluate our methodology by comparing this model with other similar forward models in the literature which show sub-cm agreement in terms of geoid undulations. Finally, EIGEN-6C4 is augmented by ROLI_EllApprox_SphN_3660 and the gravity field functionals computed from the expanded model which has about 5 km half-wavelength spatial resolution are compared w.r.t. ground-truth data in different regions worldwide. Our investigations show that the contribution of the topographic model increases the agreement up to ~ 20% in the gravity value comparisons.

Topographic Gravity Field Modelling for Improving High-Resolution Global Gravity Field Models

“…Once the density is known (estimated from the combination of four layers mentioned above) for each grid point within each shell, especially over the regions of land-coast transition, ellipsoidal surface harmonic analysis of the laterally varying density values can be performed. The details of the methodology and formulae used in this paper are given in Ince et al (2020).…”

“…Starting from the lowermost ellipsoid up to the bounding ellipsoid, the calculations are defined for subsequent shells whose thickness has an important effect on the final product. Our primary focus is to advance our preliminary work (Ince et al 2020) on the reduction of the omission error and increase the resolution of the most recent high-resolution combined static global gravity field models via enhancing the spatial and spectral content of the topographic model. We also investigate the impact of the shell thickness in the computed products and determine an optimum thickness interval for the computations.…”

“…We also investigate the impact of the shell thickness in the computed products and determine an optimum thickness interval for the computations. Based on our previous study (Ince et al 2020), comparisons of an augmented (enhanced) version of EIGEN-6C4 w.r.t. external ground-truth datasets clearly indicate the improvements that are due to the contribution of the topographic model.…”

Can an Earth Gravitational Model Augmented by a Topographic Gravity Field Model Realize the International Height Reference System Accurately?

“…There are generally three types of EGMs: (1) satellite-only such as DIR-R6 (Förste et al 2019) and GOCO06s (Kvas et al 2019); (2) hybrid such as EGM2008 (Pavlis et al 2012) and EIGEN-6C4 (Förste et al 2014); and (3) topographically-augmented such as XGM2019e (Zingerle et al 2020). Type 3 combines either Type 1 or Type 2 with a Topographic Gravity Field Model (TGFM), such as Earth2014 (Rexer et al 2017) and ROLI (Ince et al 2020). The high spatial resolution of digital elevation models (DEMs) and the recent development of TGFMs allow EGMs to reach a spatial resolution of 2 0 (about 4 km), which is comparable to regional (quasi-) geoid models.…”

“…• EIGEN-6C4e (degree and order (d/o) 3660) combines EIGEN-6C4 (Förste et al 2014) and the ROLI topographic gravity field model (Ince et al 2020). The transition band merging the two models is between spherical harmonic degrees 2000 and 2100.…”