Quantifying thermal variability in subduction zones via data-driven reduced-order modelling

Subduction zones can give rise to severe natural hazards, e.g. earthquakes, tsunami & volcanism. Improved hazard assessment may be realised through physics based modelling. The thermal structure of a subducting plate has a first order control on many aspects of the subduction zone, including: dehydration reactions; intermediate depth seismicity; melt production; formation of arc volcanoes. Subduction zones exhibit a wide variability with respect to slab age, velocity, dip, rheology and mechanical behaviour of the overriding plate. For many subduction zones the assumption of a thermo-mechanical steady-state is reasonable, hence forward models often assume the form of a kinematically driven slab causing traction-driven mantle wedge flow. Even for this simplified forward model, our understanding of how the parameters and their uncertainties influence the thermal structure is incomplete. 

To address this uncertainty, here we use a data-driven model reduction technique, specifically the interpolated Proper Orthogonal Decomposition (iPOD), to define a fast-to-evaluate and surrogate model of a steady-state subduction zone that is valid over a high-dimensional parameter space. The accuracy of the iPOD surrogate model is controlled using a hyper-rectangle tree-based adaptive sampling strategy combined with a non-intrusive error estimator. To illustrate the applicability of the iPOD, we present examples in which reduced-order models are constructed for combinations of parameters related to the kinematics, rheology and geometry of the subduction zone. The examples will characterize the efficiency and accuracy of the iPOD reduced-order model when using parameter spaces that vary in dimension from 1 to 7.