HR: 1340h
AN: S53A-0191 [Abstracts]
TI: Linearized perturbation analysis of
along-strike nonuniformity of slip in 3D fault models with
depth-variable properties
AU: * Liu, Y
EM: liu@esag.harvard.edu
AF: Department of Earth and Planetary Sciences, 29 Oxford Street, Cambridge, MA 02138
United States
AU: Rice, J R
EM: rice@esag.harvard.edu
AF: Department of Earth and Planetary Sciences, 29 Oxford Street, Cambridge, MA 02138
United States
AU: Rice, J R
EM: rice@esag.harvard.edu
AF: Division of Engineering and Applied Science, 29 Oxford Street, Cambridge, MA 02138
United States
AB:
In our three dimensional modeling [EOS, 2003; JGR submitted, 2004]
of long term loading and earthquake sequences on a shallow
subduction fault, with depth-variable rate and state friction
properties, we found the response was perturbed into a strongly
nonuniform slip mode along strike by introducing small along-strike
perturbations in friction properties. Similar results were found in
some cases of 3D strike slip modeling by Rice and Ben-Zion [PNAS,
1996]. To explore this further, we report results of linearized
perturbation analyses for two versions, ``ageing'' (or ``slowness'')
and ``slip'', of the friction laws. The 3D solution vector
$S(x,z,t)$, where $x,z$ are the respective along-strike and downdip
coordinates in the fault plane, consists of shear stress
$\tau(x,z,t)$, slip $\delta(x,z,t)$ and state variable
$\theta(x,z,t)$. It can be written as the sum of a 2D solution
vector $S_0(z,t)$, which is subject to initial conditions
$S_0(z,0)$, and an infinitesimal variation Re$[S_1(z,t) \exp(2 i \pi
x / \lambda)]$, where $\lambda$ is a perturbation wavelength. In our
case the friction properties and external driving are such that
$S_0(z,t)$ describes a sequence of earthquakes separated by long
interseismic loading intervals during which slow creep slippage
occurs, like in the Tse and Rice [JGR, 1986] type of 2D modeling.
Linearizing the governing equations in $S_1(z,t)$ (giving a
nonautonomous system, because coefficients depend on $S_0(z,t)$), we
can calculate the evolution of $S_1$ for a given unperturbed history
$S_0(z,t)$ and initial conditions $S_1(z,0)$.
For both pure thrust and pure strike-slip fault geometries, we
found that there is a critical ratio $\lambda_{crit}/h^*$, which
seems to determine the stability of along-strike response; $h^*$ is
the minimum neutrally stable downdip slip patch size, according to
rate and state stability theory for perturbation of steady slip.
When $\lambda_{crit}/h^*$ is greater than the critical value,
$\partial\delta_1(z,t)/\partial t$ and $\theta_1(z,t)$ grow to
significantly large values; when less than the critical value, the
perturbations decay with time. Our calculations give the critical
ratio around 4 to 6. Such a transition is confirmed by our fully
nonlinear 3D simulations. However, the perturbation growth history
(which is not a simple exponential in $t$) depends on the position
at depth. Fault parts which are in the well-locked seismogenic zone
have earlier rise time and faster growth rate than those in the
velocity-strengthening regions. Remarkable resistance to break up
into non-uniform strike slip was observed by Rice and Ben-Zion when
using the slip version of friction law. Linearized perturbation
analysis with that version shows, as compared to the ageing version
with the same $h^*$, that the $\lambda_{crit}$ is similar but that
the perturbation growth is much slower. This might explain why
along-strike heterogeneity of slip for that version was much less
than for the ageing version. However, for the 3D thrust fault case,
we have not found significant qualitative difference for the two
laws; both show break-up of the slip distribution along strike.
DE: 7209 Earthquake dynamics and mechanics
DE: 7215 Earthquake parameters
DE: 3210 Modeling
DE: 3220 Nonlinear dynamics
SC: Seismology [S]
MN: 2004 AGU Fall Meeting