Modeling the Mogi magma source centre of the Santorini (Thera) volcano, Aegean Sea, Greece, 1994-1999, based on a numerical-topological approach

The aim of this study is the refinement of the dynamics of a recent (1994-1999) minor, slow-inflation episode of the Santorini (Thera) volcano, famous for the Minoan (similar to 3600 B.C.) eruption and the identification of the parameters of the magmatic source responsible for the inflation. Based on the Mogi source equations, on geodetic observations of base-line changes, on a topological, grid-search approach and on the reasonable assumption that the magma source remained practically stable in map view during the inflation period, we have been able to refine the location and depth (approximately 2.7 km) of the magma center. A tendency for increase of the magma pressure with time, roughly corresponding to a sphere with radius between 30 and 60 in, and a short deflation interval were also documented. The overall modeling was based on a topological method of inversion in two steps and for a selected 4-D grid. At a first step the system of Mogi-source equations was approximated by the intersection of the 4-D sub-spaces (defined by sets of grid points) each satisfying one observation equation on the basis of a grid-search procedure. At a second step, the best estimate of the Mogi source solution and its full variance-covariance matrix were defined using a common stochastic approach. The overall approach leads to a solution of a system of equations focusing on a 4-D space bounding significant minima in the misfits between model and observed values, and not on solutions focusing on single points, usually trapped in local minima. This study is important to understand a new phase of volcanic unrest since January 2011, while the proposed methodology, inspired from traditional navigation methods may be useful for other inversion problems leading to redundant systems of highly non-linear equations with n unknowns (i.e. topological solutions in the n-D space).