A Data-Based Minimal Model of Episodic Inflation Events at Volcanoes

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: Akutan and Okmok that are part of the Aleutian arc, and Piton de la Fournaise on la Reunion Island. All three are continuously monitored by the Global Positioning System (GPS) and exhibit common stair step–shaped inflation cycles sometimes referred to as to as “episodic inflation events”. Here we seek to characterize the corresponding dynamical regime of pressure build-up within their plumbing system. To do so, we make use of Multichannel Singular Spectrum Analysis (M-SSA), a data-adaptive, non-parametric time series analysis methodology that allows for 1) the reliable detection and extraction of such patterns even when the corresponding signal lies close to, or even below, the data scatter; and 2) 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 formulate 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. These oscillations correspond to repetitive events with sharp variations in the rate of magma transport and they can account for episodic events of pressure build-up in magma bodies, 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. The approach presented here relies on the robust statistical analysis of deformation time series to constrain the phenomenology of pressure build-up within a volcanic plumbing system; it provides a novel framework for understanding the dynamics of volcanic systems.