Combination of various observation techniques for regional modeling of the gravity field

Abstract

Modeling a very broad spectrum of the Earth's gravity field needs observations from various measurement techniques with different spectral sensitivities. Typically, high‐resolution regional gravity data are combined with low‐resolution global observations. To exploit the gravitational information as optimally as possible, we set up a regional modeling approach using radial spherical basis functions, emphasizing the strengths of various data sets by the flexible combination of high‐ and middle‐resolution terrestrial, airborne, shipborne, and altimetry measurements. The basis functions are defined and located in the region of interest in such a manner, which the highest measure of information of the input data is captured. Any functional of the Earth's gravity field can be derived, as, e.g., quasi‐geoid heights or gravity anomalies. Here we present results of a study area in Northern Germany. A comprehensive cross validation to external observation data delivers standard deviations less than 5 cm. Differences to an existing regional quasi‐geoid model count on average ±6 cm and proof the plausibility of our solution. The comparison with existing global models reaches higher standard deviations for the more sensitive gravity anomalies as for quasi‐geoid heights, showing the additional value of our solution in the high frequency domain. Covering a broad frequency spectrum, our regional models can be used as basis for various applications, such as refinement of global models, national geoid determination, and detection of mass anomalies in the Earth's interior.

On the equivalence of spherical splines with least-squares collocation and Stokes’s formula for regional geoid computation

“…The mathematical foundation of RBFs, the special RBFs known as spherical wavelets, and their application in multiscale analysis are given by, for example, , Schmidt (2001), Jekeli (2005), or Schmidt et al (2007). In later years, we have observed an increased use of RBFs for regional gravity modeling (Roland 2005;Klees et al 2008;Eicker 2008;Tenzer and Klees 2008;Wittwer 2009;Bentel 2013;Naeimi 2013;Bentel et al 2013a, b;Eicker et al 2014;Pock et al 2012;Bucha et al 2015Bucha et al , 2016Naeimi et al 2015;Farahani et al 2016;Lieb et al 2016).…”

“…There is a vast amount of RBFs to choose from, as long as they represent harmonic kernel functions. They are versatile in that their approximation characteristics and spatial distribution can be adjusted, making it possible to use them for all kinds of data sets and for combining different types of observations (e.g., Lieb et al 2016). Regional gravity field modeling with RBFs can be done using numerical integration (e.g., Freeden and Schneider 1998;Schmidt et al 2002;Liu and Sideris 2003;Roland and Denker 2005) or least-squares estimation approaches (e.g., Schmidt et al 2007;Lieb et al 2016).…”

A methodology for least-squares local quasi-geoid modelling using a noisy satellite-only gravity field model

“…Lin et al 2014). Some aspects related to the combination of data with different bandwidths have been discussed in Panet et al (2011);Naeimi (2013); Bentel and Schmidt (2016); Lieb et al (2016);Lieb (2017). However, they do not cover numerical studies about the combination of a GGM with full noise covariance matrix with high-resolution noisy datasets.…”

How to deal with the high condition number of the noise covariance matrix of gravity field functionals synthesised from a satellite-only global gravity field model?

“…The latter requires a careful choice of the functional model for both the high-resolution and the low-resolution datasets, which for broadband signals is frequently offered by a multi-scale model (e.g. Chambodut et al 2005;Lieb et al 2016). Moreover, as extensively discussed in this paper, the noise covariance matrix of the GGM dataset may be ill-conditioned.…”

“…SRBFs have been used successfully in many studies of local gravity field and (quasi-) geoid modelling (e.g. Klees et al 2008;Eicker 2008;Wittwer 2009;Bentel et al 2013;Naeimi 2013;Slobbe 2013;Lin et al 2014;Bentel and Schmidt 2016;Lieb et al 2016;Bucha et al 2016;Naeimi and Bouman 2017). The following experimental setup was chosen.…”