Modeling the Deformation Sources in Volcanic Environments Through Multi-Scale Analysis of DInSAR Measurements

In this work, we propose a multi-scale approach for modeling the ground deformation field of volcanic sources. The methodology is based on the use of Multiridge and ScalFun methods to analyze the elastic deformation fields by providing source information, such as the depth, the horizontal position, and its morphological features. This strategy is alternative with respect to the classical inverse approaches since it allows overcoming some aspects of the ambiguities related to the interpretation of DInSAR measurements. Indeed, the multi-scale method does not need a priori constraints on the model parameters to achieve an unambiguous solution. First, we argue on the general physical conditions so that the deformation field, generally represented by biharmonic functions, also satisfies Laplace's equation and the law of homogeneity. This occurs in the case of sources with hydrostatic pressure-change embedded in an elastic half-space. In these conditions, the properties of harmonic and homogeneous functions can be employed to model the ground deformation fields using multi-scale procedures. Then, we demonstrate the soundness of the proposed approach through the application of Multiridge and ScalFun methods to synthetic tests. We analyze the fields generated by spherical, pipes- and sills-like sources and consider different model settings, as the layered half-space, the noisy, and the multi-source scenarios. For all these simulations, we achieve unconstrained information related to the source geometry with satisfying accuracy. Finally, in order to show the flexibility of the multi-scale approach in different volcanic environments, we use Multiridge and ScalFun methods for analyzing DInSAR measurements relevant to Uturuncu, Okmok, and Fernandina volcanoes, retrieving information about their volcanic systems. In the first case, we point out a transient source at a depth of 4.5 km b.s.l., which is activated during 2006-2007 together with the stable and well-known Altiplano Puna Magma Body (APMB); in the second one, we retrieve a concentrated body at a depth of 3.1 km b.s.l. during 2003-2004; and in the last case, we interpret the 2013 unrest episode as caused by a pipe-like source located at a depth of 1.7 km b.s.l.