Viscoelastic modelling of crustal deformation
Keywords: Santorini
Earthquake
Postseismic
Defomation
Viscoelasticity
Faulting
Numerical Modelling
Rheology

Deformation in continents is not restricted to narrow bands but is spread over great distances within their interiors. A number of lines of evidence, including the distribution of earthquakes, reveal that the strength of different continental regions varies markedly. While it is relatively easy to qualitatively map out these variations, little progress has been made in quantifying the range of strength in the continents and identifying the physical mechanisms that control these variations. I investigate crustal deformation associated with the earthquake cycle, inflation of magma chambers beneath volcanoes, and changes in surface loads. Results of these models has important implications for our understanding of large-scale continental deformation and mountain building, in addition to both seismic and volcanic hazard assessment.
Novel analytic solutions for simple shear with depth-dependent linear and non-linear viscoelastic rheologies are derived, in addition to analytical solutions for imposed harmonic tractions and displacements on an elastic layer over a Maxwell viscoelastic half space. Notably this model exhibits an effective relaxation timescale with wavenumber (k) and elastic lid thickness (de) dependence, tR = ƞ/μ[1 + coth (kde)], a result which elegantly explains observations of past earthquakes where short wavelength deformation has been observed to decay more rapidly than longer wavelengths.
The long term structural form of distributed shear beneath a strike-slip fault is investigated to determine the relative importance of physical mechanisms which may localise shear. For a depth-dependent viscosity,ƞ =ƞ0 exp (−z/z0), I find a shear zone develops with half-width δw ~ √—z0 for small z0. Including a non-linear stress-strain rate relation (Ė ∝ σn) scales δw by 1/√—n, comparable to length scales in thin viscous sheet calculations used for large-scale continental deformation calculations over geologic time scales. In contrast to previous work, this model shows for the first time that the primary control on the shear zone width is the depth-dependence of viscosity, instead of thermomechanical coupling or a non-linear rheology.
When examining post-seismic transient deformation, a purely non-linear rheology is found to rapidly cease deforming due to the implausibly high viscosities away from the fault, with deformation confined to a region half that of the depth of faulting unless I include far field loading. A full earthquake cycle model with non-linear rheology reproduces the zone of weakness observed in the viscous shear zone model. A new model is also proposed that allows for a combination rheology with dislocation and diffusion creep mechanisms. Initial analytical calculations indicate that the viscosity will then behave linearly, excepting a narrow region of reduced viscosity surrounding the fault tip.
InSAR and GPS measurements from Santorini during a recent phase of unrest led to the opportunity to model a system containing both seismic and volcanic activity. A new model for a shallow magma chamber at Santorini is proposed and demonstrates that two separate pulses of increasing pressure to a chamber, surrounded by a viscoelastic shell of constant viscosity, account for the observed cumulative volume change. The derived shell viscosity and ratio of outer-inner radius match those reported by other studies and are consistent with observations of metamorphic aureoles. Derived shuto ff times for the pressure pulses match seismicity observations and suggest that any effective increase in pressure to the shallow magma chamber ceased in early 2012.
These results suggest that combining depth-dependent viscosity and multiple creep mechanisms in a single model will reproduce observations seen across the seismic cycle and may be extended to further our understanding of magmatic processes. Previous models have often invoked heterogeneities in sub-fault properties to explain localisation of deformation at various stages of the earthquake cycle. These results reveal that localisation arises naturally from the physical processes in operation.