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.