Abstract

Long-duration, continuous geodetic timeseries suggest that volcanoes exhibit a wide range of deformation patterns that vary between episodes of unrest. Viscoelastic deformation around crustal magma storage zones is an expected contributor to such observations, but is challenging to characterize robustly. Here we present an analytic approach for modeling crustal deformation around magma reservoirs that highlights frequency-domain signatures of viscoelastic response for temperature-dependent crustal rheology. We develop a transfer function that links frequency spectra of chamber pressure to surface displacement, finding that properties of the magmatic system are encoded at periods where geodetic observations are routinely made. Inhomogeneous viscoelastic response is characterized by a frequency-dependent elastic-viscous transition around the reservoir. We explore the consequences of this frequency dependence by examining broadband forcing consisting of multiple impulsive pressurization episodes, and identify a history dependence of volcano deformation in which past activity influences the stress state and surface deformation of future episodes.