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Strain tomography of magmatic systems

Tim Davis1, Juliet Biggs1, Sylvain Barbot2

Abstract

Understanding volcanic chamber conditions using mechanical models is important for forecasting eruptions. Traditionally, we rely on kinematic models to invert surface deformation data at a given time to estimate magma chamber conditions such as size, shape, volume or pressure changes. However, it is well established that the rheology of the rock surrounding magma chambers alters the deformation signal over time, making static kinematic models unreliable for accurately estimating pressure/volume changes. Here we address the challenge of inferring the rheology of the crust surrounding magma chambers to improve the reliability of deformation-based estimates of chamber conditions. We employ strain tomography, originally designed to model asthenospheric flow following earthquakes. This approach uses a suite of solutions for the displacements and stress around distributed anelastic deformation which are superimposed to estimate the surface deformation associated with arbitrary distributions of strain. This approach allows us to invert ground deformation signals to estimate the rheology of the crust without assuming a fixed source geometry. We benchmark our new method against a synthetic test case: a 2D analytical viscoelastic shell model. We demonstrate that strain distributions inverted from snapshots of deformation can estimate the rheology of the crust in our synthetic test within an order of magnitude. Thus, we infer that inverting for the strain distributions using satellite deformation datasets from actively deforming volcanoes will provide critical insights into the mechanical properties of the rock mass.  These novel methods bridge a gap between mechanical models and readily observed signals, advancing our forecasts of temporal magmatic processes.