A Data-Based Minimal Model of Episodic Inflation Events at Volcanoes - Walwer, Damian; Ghil, Michael; Calais, Eric (Frontiers in Earth Science, 2022)
Space geodetic time series, be they ground-based or space-based, have increased in length and accuracy. These series can now be mined for information on the qualitative dynamics of volcanic systems directly from surface deformation data. Here, we study three volcanoes that are continuously monitored by the Global Positioning System (GPS) and apply Multichannel Singular Spectrum Analysis (M-SSA) to identify common stair step--shaped inflation cycles referred to as ``episodic inflation events.'' M-SSA is a data-adaptive, non-parametric time series analysis methodology that allows for (i) the reliable detection and extraction of such patterns even when the corresponding signal lies close to, or even below, the data scatter; and (ii) the extraction of information relevant to the underlying qualitative dynamics without a priori assumptions on the underlying physical mechanisms. For our three volcanoes, we find that the inflation cycles resemble the relaxation oscillations of a simple oscillator that involves a nonlinear dissipative mechanism. This finding provides important guidelines for physics-based models of episodic inflation cycles. In fact, the three volcanoes share a plumbing system composed of several interconnected storage bodies. Guided by the qualitative M-SSA--inferred dynamics, we build a simple physical model of two magma bodies connected by a conduit in which the viscosity of the fluid varies with temperature or magma crystallization. We show that such a model possesses internal relaxation oscillations similar to those of a simple oscillator, with no need for a time-dependent magma flux into or out of the system. We also show that the model's number of degrees of freedom is consistent with the amount of information extracted from M-SSA data analysis. % with the M-SSA.