Modelling Postseismic Deformation: Examples from Manyi, Tibet and

L’Aquila, Italy

Marcus BellCOMET 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 - Rheology15km elastic

viscoelastic

Springs – linear elastic behaviour (Hooke’s Law)

Dashpots – linear viscous behaviour (Newtonian fluid)

The 1997 (Mw 7.6) Manyi Earthquake

From Funning et al, 2007

ModelBest 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

residualsmodel

poor spatial fitporoelastic

rebound

afterslip

viscoelastic

relaxation

from Ryder et al., 2007

6.5mm

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

2004 2006 2008

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 Models4

-41

-1

0-1yr10-11yr6-8yr

Implications

•No long-term strength in the viscoelastic halfspace.

•Require two timescales to describe the deformation, one for the short term (<3yrs) and one the long 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

errors 1sig

Afterslip Modelling

6-8yrs 10-11yrs

slipslip

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 ∞σn