Deformation induced topographic effects in inversion of temporal gravity changes: First look at Free Air and Bouguer terms

We review here the gravitational effects on the temporal (time-lapse) gravity changes induced by the surface deformation (vertical displacements). We focus on two terms, one induced by the displacement of the benchmark (gravity station) in the ambient gravity field, and the other imposed by the attraction of the masses within the topographic deformation rind. The first term, coined often the Free Air Effect (FAE), is the product of the vertical gradient of gravity (VGG) and the vertical displacement of the benchmark. We examine the use of the vertical gradient of normal gravity, typically called the theoretical or normal Free Air Gradient (normal FAG), as a replacement for the true VGG in the FAE, as well as the contribution of the topography to the VGG. We compute a topographic correction to the normal FAG, to offer a better approximation of the VGG, and evaluate its size and shape (spatial behavior) for a volcanic study area selected as the Central Volcanic Complex (CVC) on Tenerife, where this correction reaches 77% of the normal FAG and varies rapidly with terrain. The second term, imposed by the attraction of the vertically displaced topo-masses, referred to here as the Topographic Deformation Effect (TDE) must be computed by numerical evaluation of the Newton volumetric integral. As the effect wanes off quickly with distance, a high resolution DEM is required for its evaluation. In practice this effect is often approximated by the planar or spherical Bouguer deformation effect (BDE). By a synthetic simulation at the CVC of Tenerife we show the difference between the rigorously evaluated TDE and its approximation by the planar BDE. The complete effect, coined here the Deformation Induced Topographic Effect (DITE) is the sum of FAE and TDE. Next we compare by means of synthetic simulations the DITE with two approximations of DITE typically used in practice: one amounting only to the first term in which the VGG is approximated by normal FAG, the other adopting a Bouguer corrected normal FAG (BCFAG).