Deformation-Induced Topographic Effects in Interpretation of Spatiotemporal Gravity Changes: Review of Approaches and New Insights

We investigate the origin and implications of deformation-induced gravitational effects in interpretation of spatiotemporal gravity changes. We review the traditional approaches to handling the attraction of subsurface and surface deformations. These effects are relevant when inferring magmatic processes in volcano geodetic studies. We focus on the surface constituent, the deformation-induced topographic effect (DITE), which consists of a gradient effect called the free-air effect (FAE) and an attraction effect referred here as the topographic deformation effect. We present defining, alternate, as well as approximate expressions for evaluating the DITE. The alternate expressions shed light on the physical nature of DITE. By simulating numerically synthetic displacement fields of diverse shapes and areal extents imposed over terrain of various relief shapes in a referential volcanic area of prominent and rugged topographic relief, we assess the suitability and accuracy of the various approximations of DITE. Synthetic case studies are carried out using a high-resolution high-accuracy DEM and the Toposk software for evaluation of topographic attraction terms. We discuss the particularities and complications in numerical evaluation of each of the DITE expressions. We close with a conclusion that the best numerical prescription for accurate evaluation of DITE is Eq. (18) derived herein. Its numerical realization requires the knowledge of the deformation field in areal form. If the vertical displacements are known only at benchmarks, two approximations of DITE are at hand that can be numerically evaluated: the normal-FAE approximation (nFAE-DITE) and the planar Bouguer approximation (BCFAG-DITE). Based on synthetic simulations, we specify under what circumstances which approximation performs better.