History‐Dependent Volcanic Ground Deformation From Broad‐Spectrum Viscoelastic Rheology Around Magma Reservoirs

Abstract

Geodetic timeseries suggest that volcanoes exhibit a wide range of deformation patterns. Viscoelastic deformation around crustal magma storage zones is an expected contributor to such observations, but is challenging to characterize robustly. Here we present a novel approach to modeling crustal deformation around magma reservoirs that identifies frequency‐domain signatures of viscoelastic response for temperature‐dependent crustal rheology. We develop a transfer function that links unsteady reservoir pressure forcing to surface displacement, finding that thermomechanical properties and geometry of the magmatic system are encoded in viscoelastic response on timescales where geodetic observations are routinely made. Inhomogeneous viscoelasticity is reflected by spatially variable relaxation of host rocks that results in a viscous aureole whose size depends on the frequency spectrum of forcing. We explore viscoelastic signatures of broadband pressurization episodes, identifying a history dependence of volcano deformation in which past activity influences the stress state and surface deformation patterns of future episodes.

Transport of melt, pressure and heat through a magma mush

“…For the 1D crystal mush problem, a Fouriertransform-based approach has some advantages: first, there are evidence suggesting that some magmatic signals are cyclic/periodic in nature, hence would be easily represented by a superposition of one or multiple harmonic functions (Murphy et al, 2000;Rout et al, 2021); second, a frequency-domain approach could potentially predict characteristics of frequency spectra for key quantities, hence allowing observational data (time series) to be examined under new lenses. Overall, Fourier transform and Laplace transform do not contradict but complement each other, and have been shown to have converging results (Liao et al, 2023).…”

“…The resulting frequencydomain solutions are then inverted by a numerical discrete Inverse Fourier Transform code to produce time sequence of the outputs. This frequency-domain approach has been applied in a couple of recent works and shown to be efficient in computational time and a powerful alternative method for time-domain approach (Rucker et al, 2022;Liao et al, 2023).…”