Deformation-induced Topographic Effect Due to Shallow Dyke: Etna December 2018 Fissure Eruption Case Study

Gravitational effect of surface deformation is in 4D microgravimetry treated as the deformation-induced topographic effect (DITE). The DITE field is computed using Newtonian volumetric integration which requires high resolution digital elevation model (DEM) and vertical displacement field in areal form. If only elevation changes on benchmarks of the gravimetric network are available, instead of the vertical displacement field, the DITE on benchmarks can be evaluated only approximately, using a planar Bouguer or a normal free-air-effect (nFAE) approximation. Here we analyze the adequacy and accuracy of these two approximations in a case study for the December 2018 fissure eruption on Etna accompanied by significant surface deformation caused primarily by a relatively shallow dyke. The outcome is that in volcanic areas of similar morphology as that over the Etna summit area, and for surface deformation fields due to relatively shallow dykes, neither the Bouguer nor the nFAE approximation of the DITE is accurate enough. In such situations the residual gravity changes should be computed with both the Bouguer and nFAE corrections and interpreted as two marginal cases. In addition we analyze also a correction for the effect of benchmark elevation change based on the topographically modelled (predicted) vertical gradient of gravity (VGG) meant to approximate the in-situ VGG values at benchmarks. This correction does not appear suitable to approximate the DITE in conditions of our case study or in broader sense.