Near real-time monitoring of volcanic surface deformation from Finite Element models

Trabajo presentado en el XXV CEDYA (Congreso de Ecuaciones Diferenciales y Aplicaciones) + XV CMA (Congreso de Matemática Aplicada), celebrado en Cartagena (España), del 26 al 30 de junio de 2017Volcanic eruptions affect the society and environment around hazardous rural and urban areas. Improvement of the hazard assessment is critical for the development of a resilient and wealthy society. Nowadays, multivariate collected data and robust mathematical models at volcano observatories are becoming crucial for providing effective volcano monitoring, early warnings to civil authorities and eruption forecast. Nevertheless, the forecast of volcanic eruptions is notoriously difficult. One of the most promising methods to evaluate the volcano hazard is the use of surface ground deformation since it is a proxy of magma transport through the crust [1]. Therefore, deformation is informative of where and how much magma could be eruptible. To this end, in the last decades many developments in the field of deformation modelling and their applications have been achieved [2]. A number of mathematical models of volcano deformation can be used to infer source location, depth and volume changes. Analytical deformation models limit the problem to rough approximations of the source and media although they may be useful in applications where priority is given to the fast computation of inverse solutions. In contrast, numerical modelling allows realistic media features such as topography and crustal heterogeneities to be included although it is still very time-consuming to solve the inverse problem for the real-time monitoring purposes. Here, we present a method that can be effiently used to estimate the location and evolution of magmatic sources base on real-time surface deformation data and Finite Element models that consider realistic media features. Generally, the search for the best-fitting magmatic (point) source(s) is conducted for an array of 3-D locations extending below a predefined volume region and the Green functions for all the array components have to be pre-computed. We propose a Finite Element model for the calculation of Green functions in a mechanically heterogeneous domain which eventually will lead to better description of the status of a volcanic area. The pre-computed Green functions are reduced here to the number of observational points by using their reciprocity relationship. We present and test this methodology with an optimization method base on a Genetic Algorithm for modelling data associated with volcanic deformation. Following synthetic and sensitivity tests, we apply the improved tool for tracking magma position during the June 2007 Kilauea Volcano intrusion and eruption. We show how data inversion with numerical models can speed up the source parameters estimation for a given volcano showing signs of unrest.Research supported by CGL2014-58821-C-1-R projectPeer reviewe