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Abstract:
Non-Newtonian flow occurs in crustal deformation processes on the long
timescales associated with large- scale continental deformation, and also
on the short time-scales associated with post-seismic deformation. The
co-seismic displacement is determined by the instantaneous elastic
response of the rocks on either side of the fault surface to the
distribution of slip on the surface of the fault. The post-seismic
deformation is determined by some combination of visco-elastic relaxation
of the medium and post-seismic creep on the fault. The response of the
crust may depend on elastic moduli, Poisson's ratio, temperature, pressure
and creep function parameters including stress exponent, activation
energy, activation volume and viscosity coefficient. We use the von Mises
function in describing the non-linear Maxwell visco-elastic creep models.
In this study we examine a model of a strike-slip fault crossing a 3D
block. The fault slips at time zero, and we solve for the viscoelastic
deformation field throughout the 3D volume using a 3D finite element
method. We perform parametric studies on the constitutive equation by
varying these parameters and the depth of the fault event. Our findings
are focused on the fact that the system is very sensitive to the above
mentioned parameters. In particular, the most important seems to be the
temperature profiles and stress exponent. The activation energy and the
pressure are of lower importance, however, they have their meaning. We
investigated the relaxation times and the deformation patterns. We took
the material properties as typical to dry quartzite and diabase. Depending
on the parameters the surface can be deformed permanently or the
deformation can decrease. We attempt to compare qualitatively the
calculated post-seismic response in terms of the post-seismic displacement
history of the earth's surface with InSAR patterns determined from recent
major strike-slip earthquakes. Quantitative comparison of the observations
with these numerical model results can in principle provide a better
understanding of the physical properties of the sub-surface and further
insight into the diagnostic properties of the earthquake cycles of major
fault systems.

Cite as: Author(s) (2008), Title, Eos Trans. AGU, 89(53), Fall Meet.
Suppl., Abstract T44B-07

Keywords:
rheology, crust, litosphere

Abstract:
The ground displacements measured in the vicinity of a large strike-slip earthquake are
potentially important in diagnosing the state of stress on the fault and in the medium
surrounding. The co-seismic displacement is determined by the immediate elastic response
of the medium and the slip function on the fault-surface. The post-seismic
displacement is determined by a combination of post-seismic creep on the fault, viscoelastic
relaxation in the surrounding medium, and possibly poro-elastic deformation.
There are strong indications from previous earthquake studies that the visco-elastic
relaxation involves non-linear mechanisms, which produce faster deformation in the
early stages and slower deformation in the later stages than would occur with a linear
creep mechanism. In this study we examine a simplified model of a strike-slip fault
cutting a 3D block, and compute the surface displacement versus time functions for
a range of different constitutive relations. We examine linear and non-linear Maxwell
visco-elasticity, and compare with the generalized linear Maxwell visco-elasticity. The
effect of non-linearities in the elasticity (finite strain theory) is also considered.We use
the von Mises flow function in describing the non-linear Maxwell visco-elastic creep
models in which viscous creep strain-rate is proportional to the nth power of the deviatoric
stress (formulated using the 2nd invariant of the stress tensor). We describe
analytical solutions used to validate the 3D code, and then consider the effect of the
exponent n on the time histories of the surface displacement fields above the fault.
We aim here to compare these numerical models with observations from actual fault
systems obtained using InSAR and GPS data. Among the factors affecting the surface deformation patterns are near-surface layering, and lateral variation of material
properties, as well as irregularities on the fault surface. In principle, the comparison
of observations with theory should provide a better understanding of the physical response
of the sub-surface, together with a better understanding of the earthquake cycle
as it operates on specific fault systems.

Keywords:
surface deformation, seismic cycle, visco-elasticity, numerical models

Keywords:
surface deformation, viso-elasticity, seismic cycle

Keywords:
deformation, viscosity, power law