History-dependent volcano deformation, frequency-dependent reservoir geometry, and other implications of broad-spectrum viscoelastic rheology around magma chambers

Time-dependent ground deformation is a key observable in active magmatic systems, but is challenging to characterize and connect to underlying processes. We have developed a frequency-domain approach for modeling viscoelastic deformation around magma reservoirs to identify relationships between input and output signals of interest. Typically in volcano geodesy these signals are reservoir pressure timeseries and some component of surface displacement but the approach, involving transfer functions that connect forcing at depth and surface observables, is generalizable to any inputs and outputs of a linear time invariant viscoelastic model. We present a robust numerical framework using the open-source multiphysics library NGSolve for solving axisymmetric magma chamber problems, and an analytic approximation for thermoviscoelastic deformation in a halfspace that provides insight into the regimes of possible viscoelastic response in long-term deformation timeseries. Using this modeling framework we identify several novel characteristics of time-dependent viscoelastic material response in magmatic systems. First, the spectral approach implies that different viscoelastic constitutive models, reservoir geometries, and temperature fields may be distinguishable via their deformation patterns in the frequency domain at periods where geodetic observations are routinely made. Then, using simplified descriptions of both periodic and broadband non-periodic forcing functions, we identify history dependence in sequences of reservoir pressurization episodes that have implications for volcano monitoring and eruption forecasting. Finally, by considering long period pressurization episodes of tens to hundreds of years we show that the spatial extent of the viscoelastic region varies significantly as a function of frequency, which suggests that transcrustal magma transport network structure at long-lived volcanic centers should be characterized in terms of the timescale of observations being made.