A computational framework for time dependent deformation in viscoelastic magmatic systems

This is a Preprint and has not been peer reviewed. This is version 2 of this Preprint.


Download Preprint


Cody Rucker, Brittany Angela Erickson, Leif Karlstrom, Brian Lee, Jay Gopalakrishnan


Time-dependent ground deformation is a key observable inactive magmatic systems, but is challenging to characterize. Here we present a numerical framework for modeling transient deformation and stress around a subsurface, spheroidal pressurized magma reservoir within a viscoelastic half-space with variable material coefficients, utilizing a high-order finite-element method and explicit time-stepping. We derive numerically stable time steps and verify convergence, then explore the frequency dependence of surface displacement associated with cyclic pressure applied to a spherical reservoir beneath a stress-free surface. We consider a Maxwell rheology and a steady geothermal gradient, which gives rise to spatially variable viscoelastic material properties. The temporal response of the system is quantified with a transfer function that connects peak surface deformation to reservoir pressurization in the frequency domain. The amplitude and phase of this transfer function characterize the viscoelastic response of the system,and imply a framework for characterizing general deformation timeseries through superposition. Transfer function components vary with the frequency of pressure forcing and are modulated strongly by the background temperature field. The dominantly viscous region around the reservoir is also frequency dependent, through a local Deborah number that measures pressurization period against a spatially varying Maxwell relaxation time. This near-reservoir region defines a spatially complex viscous/elastic transition whose volume depends on the frequency of forcing. Our computational and transfer function analysis framework represents a general approach for studying transient viscoelastic crustal response to magmatic forcing through spectral decomposition of deformation timeseries, such as long-duration geodetic observations.




Applied Mathematics, Computer Sciences, Earth Sciences, Mathematics


viscoelasticity, magma reservoir, Finite element method


Published: 2022-04-01 14:51

Last Updated: 2022-07-18 22:50

Older Versions

CC BY Attribution 4.0 International

Additional Metadata

Conflict of interest statement:

Data Availability (Reason not available):

Add a Comment

You must log in to post a comment.


There are no comments or no comments have been made public for this article.