GNGTS 2023 - Atti del 41° Convegno Nazionale

Session 1.2 GNGTS 2023 Theoretical models of deformation sources are commonly employed to investigate the surface displacements observed, for example, in volcanic areas or related to a seismic event (Fig. 1). A volcanic source can be represented by a confined part of crust with a certain shape inflating/deflating because of a change in the internal magma/gas pressure. The static seismic source is ideally represented by a tabular discontinuity in the crust undergoing relative movement of both sides. Furthermore, gas reservoir exploitation, water pumping and soil consolidation, can be represented using the same models. Most analytical deformation models approximate the local crust as homogeneous and isotropic half-spaces. The most common model for deformation due to earthquakes or aseismic slip is the “Okada” fault (Okada, 1985). It provides static elastic displacements and stresses due to a constant slip applied on a rectangular fault. The simplest model to represent the expansion of a magma chamber at depth is a point dilatation source, which is a fair approximation of a spherical overpressure source (Mogi, 1958). Approximate analytical solutions for a finite volume sphere and spheroid were developed by McTigue (1987) and Yang et al. (1988), respectively. While the spherical source may represent extended reservoirs, spheroidal volumes may approximate vertical or oblique conduits, also including the pipe-like source represented by a very low aspect ratio (ie, the ratio between minimum and maximum axes). Models of cracks and sills embedded in elastic half-spaces were developed by Fialko et al. (2001) and Okada (1985). Fig. 1. Formulation of the non-linear inverse problem of ground deformations due to volcanic and seismic sources. a) A change in the conditions in the deep reservoir causes a variation of the distribution of stress in the local crust, and surface deformation. b) Similarly, the sudden slip on the seismic fault during an earthquake causes permanent deformation of the local crust. The ground deformation is detectable by geodetic surveys (in-situ, blue triangles and by remote sensing). c) It is possible to model the observed data using a theoretical representation of the volcanic or seismic source. The inversion procedure is aimed at retrieving the parameters of the model implemented. The forward models available in VSM are, from left to right, isotropic point-source (Mogi, 1958), finite volume sphere (McTigue, 1987), penny-shaped crack (Fialko et al., 2001), arbitrarily oriented prolate spheroid (Yang et al., 1988), moment tensor point-source (Davis, 1986), and fault/dyke (Okada, 1985).