Modelling Postseismic Deformation: Examples from Manyi, Tibet and L’Aquila, Italy Marcus Bell COMET Student Meeting 2010 Supervisors: B. Parsons and P. England

Why study postseismic motion? In order to have a robust model of the earthquake cycle we need to know what forces drive it For this we require a model of how the continental regions deform Currently two end-member models of continental deformation Rigid blocks Continuum mechanics Each models has different implications for how stress evolves both spatially and temporally within the lithosphere and imply a different strength profile with depth

From Thatcher and Pollitz, 2008 How strong is the continental lithosphere?

Mechanisms of Postseismic Motion Afterslip. – The stresses on/near the fault plane may be released aseismically following the event. Deformation modelled as dislocations on the fault plane and an extension of it Poroelastic Rebound. – Earthquakes can induce pore pressure gradients. Flow to re- equilibrate pore pressure results in surface deformation Viscoelastic Relaxation. – Stress changes from the earthquake induce stresses in lower layers. This stress is relaxed by viscous flow. – Requires known fault geometry and slip distribution to input to numerical modelling programs which calculate time-varying deformation.

Viscoelastic Modelling - Rheology 15km elastic viscoelastic Springs – linear elastic behaviour (Hooke’s Law) Dashpots – linear viscous behaviour (Newtonian fluid)

The 1997 (M w 7.6) Manyi Earthquake From Funning et al, 2007

Model Best fitting model using variable slip patches along the fault. Fault trace determined from optical imagery and azimuth offsets Simpler model is used to simplify the postseismic calculations. Fault Slip Distribution (Uniform patches) From Funning et al, 2007

Previous Postseismic Studies time series (755 days) 100km residuals model poor spatial fit poroelastic rebound afterslip viscoelastic relaxation from Ryder et al., mm 8.3mm Implications?

Envisat Data Corrected Algorithm makes mistakes when unwrapping Flattened To remove orbital errors Interpolated Remove small areas of incoherence Stacked To improve signal-to-noise ratio Stacking Criteria Time Perpendicular Baseline

6-8yrs 10-11yrs Magnitude of deformation similar in both scenes The deformation appears to be more localised in the later stack Red line is the fault trace, scale is same in both figures Data Stacks

Preliminary Models yr 10-11yr6-8yr

Implications No long-term strength in the viscoelastic halfspace. Require two timescales to describe the deformation, one for the short term ( 6yrs) Still significant noise in the interferograms Over flattening? Would it be more appropriate to use a more complex model setup with more then one layer over the halfspace?

Initial Afterslip Model

6-8yrs 10-11yrs errors 1sig Afterslip Modelling 6-8yrs 10-11yrs slip

Conclusions If the deformation pattern is described be solely linear viscoelastic relaxation then a Burgers Rheology would be required to match both the initial (<3 years) and late (<6 year) deformation patterns Results however may be better suited to a non-linear power-law rheology. Afterslip can provide a reasonable fit to the data but in order to match the data a (after)slip rate of >10cm/yr is required. Is this reasonable?

Future Work Compare models to data using a time series to allow for a quantitative assessment of misfit. Invert data and models taking into account orbital contributions. Network the Manyi data? Perform resolution tests on the afterslip distributions and look at more representative data sampling methods

ε = strain σ = stress η=viscosity μ=rigidity Power-law Rheology ε ∞σ n