The Influence of Viscoelastic Crustal Rheologies on Volcanic Ground Deformation: Insights from Models of Pressure and Volume Change

Abstract

Inelastic rheological behaviour, such as viscoelasticity, is increasingly utilised in the modelling of volcanic ground deformation, as elevated thermal regimes induced by magmatic systems may necessitate the use of a mechanical model containing a component of time-dependent viscous behaviour. For the modelling of a given amplitude and footprint of ground deformation, incorporating a viscoelastic regime has been shown to reduce the magma reservoir overpressure requirements suggested by elastic models. This phenomenon, however, is restricted to pressure-based analyses and the associated creep behaviour. Viscoelastic materials exhibit additional constitutive time-dependent behaviours, determined by the stress and strain states, that are yet to be analysed in the context of volcanic ground deformation. By utilising a mechanically homogeneous model-space and distinct reservoir evolutions, we provide a comparison of three viscoelastic rheological models, including the commonly implemented Maxwell and Standard Linear Solid configurations, and their time-dependent behaviours from a fundamental perspective. We also investigate the differences between deformation timeseries resulting from a pressurisation or volume change; two contrasting approaches that are assumed to be equivalent through elastic modelling. Our results illustrate that the perceived influence of viscoelasticity is dependent on the mode of deformation, with stress-based pressurisation models imparting enhanced deformation relative to the elastic models, thus reducing pressure requirements. Strain-based volumetric models, however, exhibit reduced levels of deformation and may produce episodes of apparent ground subsidence induced by source inflation or vice versa, due to the relaxation of crustal stresses, dependent on whether the reservoir is modelled to be expanding or contracting, respectively.