Topographically Predicted Vertical Gravity Gradient Field and Its Applicability in 3D and 4D Microgravimetry: Etna (Italy) Case Study PETER VAJDA, 1 PAVOL ZAHOREC, 1 JURAJ PAPC ˇ O, 2 DANIELE CARBONE, 3 FILIPPO GRECO, 3 and MASSIMO CANTARERO 3 Abstract—Some geophysical or geodynamic applications require the use of true vertical gradient of gravity (VGG). This demand may be associated with reductions of or corrections to observed gravity or its spatiotemporal changes. In the absence of in situ measured VGG values, the constant value of the theoretical (normal) free air gradient (FAG) is commonly used. We propose an alternative to this practice which may significantly reduce sys- tematic errors associated with the use of constant FAG. The true VGG appears to be better approximated, in areas with prominent and rugged topography, such as alpine or some volcanic regions, by a value based on the modelled contribution of the topographic masses to the gradient. Such prediction can be carried out with a digital elevation model (DEM) of sufficient resolution and accu- racy. Here we present the VGG field computed for Mt. Etna (Italy), one of the most active and best monitored volcanoes worldwide, to illustrate how strongly the VGG deviates spatially from constant FAG. The predicted (modelled) VGG field is verified by in situ observations. We also take a look at the sensitivity of the VGG prediction to the resolution and quality of used DEMs. We con- clude with discussing the applicability of the topo-predicted VGG field in near surface structural and volcanological micro-gravi- metric studies. Keywords: VGG, free air correction, free air effect, volcano geodesy, time-lapse gravimetry, spatiotemporal gravity change. 1. Introduction In some earth science studies or applications the true values of the vertical gradient of gravity (VGG) are needed either at gravity benchmarks (observation points) or on a grid at the topographic surface. The gradient data are used in gravimetry also for image enhancement (Tu and Zhdanov 2019) and in inver- sion/interpretation (e.g., Baniamerian et al. 2018; Fregoso et al. 2019; Lin and Zhdanov 2019; Pamukc ¸u et al. 2019). The VGGs can be observed in situ by a relative gravity meter in the so called tower mode, using a geodetic or a special-design tripod, allowing measurements at different heights above the ground (e.g., Pistorio et al. 2011; Greco et al. 2012; Zahorec et al. 2014, 2016). However, the observed values are often either too sparse, or not available at all. In case of their absence the constant value of the theoretical (normal) free air gradient (FAG = -308.6 lGal/m, 1 lGal/m = 10 -8 s -2 ) is commonly used. In many cases such replacement (approximation) may be inadequate or inaccurate (Jousset 1996) and the effect of the topographic relief must be considered (Jousset and Okada 1999). Zahorec et al. (2014) have shown that the VGG field can have a spatial variability as high as 88% in terms of its relative deviation from FAG in alpine regions such as the High Tatras of Slovakia. In spe- cial cone-shaped terrain depressions (like karst sinkholes), the VGG can even tend towards zero values (Zahorec et al. 2015). Similarly, in volcanic areas with prominent topography the VGG variability can reach 77%, as shown for the Central Volcanic Complex (CVC) on Tenerife (Zahorec et al. 2016). Here we focus on the VGG field of Etna, with the aim of analyzing its spatial variability and the size of its deviation from FAG. In each computation point at the topographic surface the VGG is computed as the sum of the theoretical FAG and of the effect of topo- graphic masses on the VGG. The topo-effect is computed by a numerical Newtonian volumetric 1 Earth Science Institute, Slovak Academy of Sciences, Du ´bravska ´ cesta 9, P.O. Box 106, 840 05 Bratislava, Slovakia. E-mail: Peter.Vajda@savba.sk 2 Department of Theoretical Geodesy, Slovak University of Technology, Bratislava, Slovakia. 3 Istituto Nazionale di Geofisica e Vulcanologia (INGV)— Sezione di Catania—Osservatorio Etneo, Catania, Italy. Pure Appl. Geophys. 177 (2020), 3315–3333 Ó 2020 Springer Nature Switzerland AG https://doi.org/10.1007/s00024-020-02435-x Pure and Applied Geophysics