Integrated Multi-scale approach for constraining source parameters responsible of deformation field in volcanic framework.
Authors: Barone Andrea , Fedi Maurizio , Pepe Antonio , Pepe Susi , Solaro Giuseppe , Tizzani Pietro , Castaldo Raffaele 
Published: March 2022

&lt;p&gt;The monitoring and characterization of volcanic systems are performed through measurements of different nature; among these, the development of the remote sensing technologies has supported the analysis and interpretation of the ground deformation field, for which the Differential SAR Interferometry (DInSAR) technique provides a large amount of densely sampled measurements over space and time (Dzurisin, 2007). The modeling of these datasets leads to understand the changes of physical and geometrical parameters of deep and/or shallow volcanic reservoirs by using different strategies, such as the forward (Lu et al., 1998), the parametric (Battaglia et al., 2013) and tomographic (Camacho et al., 2020) inverse modeling. Unfortunately, these methods could bring to ambiguous interpretation of deformation measurements because of ambiguities of inherent, theoretical, algebraic, instrumental/experimental nature.&lt;/p&gt;&lt;p&gt;Here, we model the deformation field in volcanic framework through a different approach, which is mainly based on harmonic elastic fields satisfying the homogeneity laws; in particular, we use multi-scale procedures, such as the Multiridge (Fedi et al., 2009) and ScalFun (Fedi et al., 2007) methods, and boundary analysis technique, such as the Total Horizontal Derivative (THD) (Blakely, 1996), for unambiguous estimate of the geometrical parameters of the deformation sources, which are the depth, the horizontal position, the shape and the horizontal extent.&lt;/p&gt;&lt;p&gt;Starting from the harmonic solutions of the Navier&amp;#8217;s equation, Castaldo et al. (2018) and Barone et al. (2019) have shown that multi-scale methods are valid tools to study simple field sources as the Mogi one, according to the homogeneity law and the Euler&amp;#8217;s equation. To generalize this approach, we show the use of multi-scale methods to model sources with any geometry, also irregular. We test our methodology, which is an integration of multi-scale techniques, on Finite Element synthetic deformation field generated through Comsol Multiphysics software package; we consider both regular and irregular geometry cases by analysing different deformation component estimating the source geometry without any reference model.&lt;/p&gt;&lt;p&gt;Finally, we use the proposed approach to investigate the ground deformation pattern of the 2004 &amp;#8211; 2010 uplift episode occurred at Yellowstone caldera resurgent domes area and the 2013 unrest event at Fernandina volcano (Galapagos Archipelago, Ecuador); in the first case, we use the vertical component and the integrated multi-scale approach to highlight the geometrical irregularities of the retrieved sill-like intrusion; in the second case, we analyse the E-W component retrieving a &amp;#8776; 1.5 km b.s.l. deep pipe-like source.&lt;/p&gt;&lt;p&gt;We conclude that our approach is crucial for retrieving an unconstrained geometrical model of the deformation source.&lt;/p&gt;