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

Abstract

Inelastic rheological behavior, such as viscoelasticity, is increasingly utilized in the modeling 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 behavior. For the modeling 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 behavior. Viscoelastic materials exhibit additional constitutive time‐dependent behaviors, determined by the stress and strain states, that are yet to be analyzed in the context of volcanic ground deformation. By utilizing 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 behaviors from a fundamental perspective. We also investigate the differences between deformation time series resulting from a pressurization or volume change, two contrasting approaches that are assumed to be equivalent through elastic modeling. Our results illustrate that the perceived influence of viscoelasticity is dependent on the mode of deformation, with stress‐based pressurization 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 modeled to be expanding or contracting, respectively.

Ductility and Compressibility Accommodate High Magma Flux Beneath a Silicic Continental Rift Caldera: Insights From Corbetti Caldera (Ethiopia)

“…We convert the strain‐based model of a point source to a stress‐based model of a finite sphere and implement time‐dependent mechanical properties using a Standard Linear Solid (SLS) parameterization (Head et al, ), consisting of a Maxwell element (elastic spring and dashpot) and an elastic spring in parallel where the instantaneous elastic response of the medium is governed by the shear modulus G ( z ), and the viscous response by a characteristic relaxation time τ 0 = η / G ( z ). We consider the fractional components ( μ 1 and μ 0 ) of the shear moduli split equally across the two branches of the SLS, whereby μ 1 = μ 0 = 0.5. η is parameterized by the Arrhenius approximation η = A×e , where A is a constant, H is the activation energy, R is the gas constant, and T is the absolute temperature.…”

“…A new generation of numerical models aims to constrain the dynamics and evolution of sub‐volcanic reservoirs by considering the thermomechanical feedbacks between magma and crust (Degruyter & Huber, ; Gottsmann et al, ; Karakas & Dufek, ). In a suitable thermal regime, magma influx can be accommodated inelastically without significantly increasing the reservoir pressure, yet still causing surface deformation (Degruyter & Huber, ; Head et al, ; Le Mével et al, ). Thermomechanical effects may reduce the amplitude and wavelength of surface deformation causing elastic models of surface deformation to overestimate source volume changes.…”

Triggering of eruptions at Axial Seamount, Juan de Fuca Ridge

“…www.nature.com/scientificreports www.nature.com/scientificreports/ presented in the supplementary materials. For further discussion of the impact of elastic and viscoelastic properties on results of unrest models we refer the reader to Zhan et al 16 and Head et al 31 , respectively.…”

The dynamics of large silicic systems from satellite remote sensing observations: the intriguing case of Domuyo volcano, Argentina

“…The effects of viscoelastic models can either over- or under-predict surface deformation, compared to the analytical elastic solution. Compared to pressure change elastic solutions, viscoelastic models result in higher deformation, implying that the true pressure change required to fit the observed surface displacements is lower 13 . Whereas, compared to volume change analytical solutions, the viscoelastic models under-predict the deformation, implying that the actual volume change required is greater 13 .…”

“…Compared to pressure change elastic solutions, viscoelastic models result in higher deformation, implying that the true pressure change required to fit the observed surface displacements is lower 13 . Whereas, compared to volume change analytical solutions, the viscoelastic models under-predict the deformation, implying that the actual volume change required is greater 13 . Thus, for our CDM source model for volume change rate, our estimate is more likely to underestimate the true value.…”