GNGTS 2018 - 37° Convegno Nazionale

GNGTS 2018 S essione 3.3 727 MULTIRIDGE METHOD FOR THE GEOMETRIC MODELING OF GEODETIC SOURCES: APPLICATION TO THE VOLCANIC DEFORMATION A. Barone 1,2 , R. Castaldo 2 , M. Fedi 1 , P. Tizzani 2 1 Department of Earth, Environmental and Resources Science, University of Naples “Federico II” - Naples, Italy 2 National Research Council (CNR), Institute for the Electromagnetic Sensing of the Environment (IREA) - Naples, Italy Introduction . Volcanic phenomena are currently monitored by the detection of physical and chemical observations. Generally, the ground deformation field is the most relevant shallow expression of the geometric and physical parameters variations in the magmatic reservoir. In particular, the accumulation processes of shallow magma in the crust often cause slight movements at the surface, which can be measured using standard land-surveying techniques (leveling) or satellite geodesy methodologies (e.g., GPS and DInSAR). In this study, we propose a novel method for the direct estimation of the geometric parameters of sources responsible for volcanic ground deformation detected via the SBAS- DInSAR technique, which provides a large number of deformation points (Tizzani et al., 2007). Starting with the biharmonic properties of the deformation field (Love, 1906), we study the conditions under which the theory of the deformation field reduces to the Potential Field Theory (PFT), satisfying the Laplace’s equation (Blakely, 1996). Thus, we define an approach based on the Multiridge (Fedi et al., 2009 ) and ScalFun (Fedi, 2007) methods to achieve relevant information about both the positions and shapes of active sources. Finally, we apply the proposed methodology to the real case of the Okmok volcano ground deformation pattern retrieved by the DInSAR analysis. Potential Theory for the deformation field. The interpretation of the ground deformation field via the PFT-based methods derives from Love’s theory on the elasticity (Love, 1906). When the modeled deformation field is not caused by a source shape-change, the deformation field can be represented by the coefficients of the partial differential equation (PDE), with respect to the coordinates of a single scalar function ( φ ): (1) The displacement potential φ is a biharmonic function since φ satisfies (Sadd, 2005): (2) By considering the Mogi source, we show how the modeled ground deformation field encompasses the harmonic properties. The deformation field modeled by a hydrostatic pressure change within a spherical cavity embedded in an elastic half-space, with a radius much smaller than its depth, is given by (Mogi, 1958): (3) where ( x 0 , y 0 , z 0 ) represents the coordinates for the position of the source center, a the radius of the sphere, ΔP the variation in pressure, z 0 the depth of the source from the center of the sphere, μ the shear modulus, ν the Poisson ratio and It is simple to argue that u is the gradient of the Newtonian potential in the form 1/ r , which is a harmonic function (Blakely, 1996). Therefore, all components of the deformation field u are also harmonic.