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Poster Abstracts | Group 2 – FARM
2-063
NEW COMPUTATIONAL APPROACH TO NONPLANAR ELASTODYANIC
RUPTURES Coon ET, Shaw BE, and Spiegelman M
We present a new approach to modeling dynamic ruptures on nonplanar faults. A fundamental
challenge for modeling rupture dynamics on complicated fault networks using current techniques
is dealing with the computational mesh. Generation of a mesh that is both faithful to the
underlying fault structure and suitable for efficient computation is an open problem. Here, we test
the possibility of using an extended finite element method, XFEM, (e.g. [Dolbow, Moes, and
Belytschko, 2001]) for problems of repeated rupture.
This method is mesh-independent -- the fault need not lie on mesh edges -- drastically reducing the
requirements for suitable compuational meshes. We extend the method to include elastodynamics,
and demonstrate the feasibility of XFEM by modeling long-time series of ruptures on complicated,
two-dimensional fault networks. While the problems and geometries we solve are feasible with
existing methods, this demonstration indicates that XFEM should prove useful for the solution of
problems limited by mesh generation.
Using XFEM, sequences of elastodynamic earthquake events on networks of faults, including
branching, are generated. Efficient solution via XFEM enables the study of statistics of populations
of events and the effects of variation of geometry. As varying geometry is handled easily by the
method, we study the resulting variation in event populations. Distributions of event rupture
length, magnitude, epicenter location, and other statistical measures are presented and compared
as a function of geometry. Results for flat fault are shown to be consistent with previous results on
flat faults using other computational approaches. New results for complicated geometries are
presented, and compared with those for flat faults.
2-064
AN EFFICIENT-FEM IMPLEMENTATION OF THE SMOOTH-TSN ALGORITHM FOR
NUMERICAL MODELING OF RUPTURE PROPAGATION Moczo P, Gális M, Kristek J,
and Kristeková M
The Traction-at-Split-Node (TSN) algorithm developed independently by J. D. Andrews and S. M.
Day is so far probably the most accurate way to simulate dynamic rupture propagation in the
numerical-modeling methods in which the computational domain is covered by a grid of discrete
points. We implemented the TSN algorithm in our efficient formulation of the finite-element
method (FEM). The FEM formulation requires less computer memory because it makes use of the
global restoring-force vector instead of the global stiffness matrix. The formulation reduces
considerably the computational time (compared to the standard restoring-force formulation)
because it uses e-invariants (Moczo et al. 2007) in calculation of the restoring force.
Despite its superior accuracy, the standard TSN algorithm is not free from high-frequency
oscillations in the slip-rate time histories in the models with the linear slip-weakening friction law.
The oscillations are due to discretization of the field variables in time and space, and due to the
dynamic boundary condition on the fault. The artificial Kelvin-Voigt damping or perfectly matched
layers have been applied to suppress the oscillations.
In our implementation we do not apply either of the two tools. Instead we apply 2D spatial moving
weighted averaging separately to each of the trial traction components. The weighted averaging
combines a Gaussian-filtered with unfiltered values. We performed extensive numerical
simulations in order to select the best smoothing algorithm. The examined algorithms included the
174 | Southern California Earthquake Center