| Summary: | In this study, we describe new advances in the multiscale methodology to allow a more realistic interpretation of volcanic deformation fields by investigating geometrically irregular bodies and multi-source scenarios. We propose an integrated approach to be applied to InSAR measurements, employing the Multiridge and ScalFun methods and the Total Horizontal Derivative (THD) technique: this strategy provides unconstrained information on the source geometrical parameters, such as the depth, position, shape, and horizontal extent. To do this, we start from conditions where the biharmonic deformation field satisfies Laplace’s equation and homogeneity law. We test the use of the multiscale procedures to model single and multisource scenarios with irregular geometries by retrieving satisfactory results for a set of simulated sources. Finally, we employ the proposed approach to the 2004–2009 uplift episode at the Yellowstone Caldera (U.S.) measured by ENVISAT InSAR to provide information about the volcanic plumbing system. Our results indicate a single <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>~</mo><mn>50</mn><mo>×</mo><mn>20</mn></mrow></semantics></math></inline-formula> km<sup>2</sup> extended source lying beneath the caldera at around <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>10</mn></mrow></semantics></math></inline-formula> km b.s.l. (depth to the center), which is shallower below both the resurgent domes (6–7 km b.s.l. depth to the top).
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