Analytical volcano deformation modelling: A new and fast generalized point-source approach with application to the 2015 Calbuco eruption

Abstract:

Ground deformation at active volcanoes is one of the key precursors of volcanic unrest, monitored by InSAR and GPS techniques at high spatial and temporal resolution, respectively. Modelling of the observed displacements establishes the link between them and the underlying subsurface processes and volume change. The so-called Mogi model and the rectangular dislocation are two commonly applied analytical solutions that allow for quick interpretations based on the location, depth and volume change of pressurized spherical cavities and planar intrusions, respectively. Geological observations worldwide, however, suggest elongated, tabular or other non-equidimensional geometries for the magma chambers. How can these be modelled? Generalized models such as the Davis’s point ellipsoidal cavity or the rectangular dislocation solutions, are geometrically limited and could barely improve the interpretation of data.

We develop a new analytical artefact-free solution for a rectangular dislocation, which also possesses full rotational degrees of freedom. We construct a kinematic model in terms of three pairwise-perpendicular rectangular dislocations with a prescribed opening only. This model represents a generalized point source in the far field, and also performs as a finite dislocation model for planar intrusions in the near field. We show that through calculating the Eshelby’s shape tensor the far-field displacements and stresses of any arbitrary triaxial ellipsoidal cavity can be reproduced by using this model. Regardless of its aspect ratios, the volume change of this model is simply the sum of the volume change of the individual dislocations. Our model can be integrated in any inversion scheme as simply as the Mogi model, profiting at the same time from the advantages of a generalized point source.

After evaluating our model by using a boundary element method code, we apply it to ground displacements of the 2015 Calbuco eruption, Chile, observed by the Sentinel-1 satellite. We infer the parameters of a deflating elongated source located beneath Calbuco, and find significant differences to Mogi type solutions. The results imply that interpretations based on our model may help us better understand source characteristics, and in the case of Calubuco volcano infer a volcano-tectonic coupling mechanism.