Open Session - SWISS GEOSCIENCE MEETINGs

1.21
Stress and strength of the continental lithosphere.
Kaus Boris*,**
*Geophysical Fluid Dynamics, Department of Earth Sciences, Schaffmattstrasse 30, CH-8093 Zurich (boris.kaus@erdw.ethz.ch)
**University of Southern California, Los Angeles, USA.
The processes that generate stress in the lithosphere are incompletely understood. Whereas it is obvious that lithospheric
deformation (and topography) is ultimately caused by cooling of the Earth from the time of formation, it is less clear how
lithospheric deformation is coupled to mantle flow and how this affect stresses. Part of this is due to the somewhat complicated
rheology of the lithosphere, which varies from brittle (elastoplastic) to ductile (viscous). In addition, vertical layering
of the lithosphere may give rise to instabilities which affect its dynamics and stress evolution in a non-trivial manner.
Obtaining a better insight in these processes thus requires numerical tools that can model the mantle-lithosphere system in
a self-consistent manner (i.e. in a single computational domain) including topographic effects (i.e. free surface) and viscoelasto-plastic
rheologies.
Recently, a number of modelling techniques have been developed that have the above-mentioned features and that are useful
to model long-term tectonic scenarios (on a Myrs) timescale. A problem, however, with many of these long-term tectonic simulations
is that they are computationally expensive and that the parameter space is too wide to sample with brute-force
forward simulations. For this reason, I take a different approach and use the numerical technique to obtain insight in the
most likely present-day rheological stratification of the lithosphere. The advantage of such quasi-instantaneous lithospheric
models is that they require only a few timesteps per simulations and can therefore cover a wider parameter space. Moreover,
they take relatively well-constraint geophysical data such as Moho depth, topography, GPS velocity and earthquake locations
as input.
Model results, applied to the India-Asia collision zone and to Taiwan demonstrate that the approach gives constraints on the
effective viscosity and rheological stratification of the lithosphere. They also show that the distribution of high effective
viscosities, representing the strength distribution in the ductilly and plastically deforming areas of the lithosphere, does not
necessaily correspond to the distribution of high differential stresses, presumably representing the areas of high earthquake
activity. The reason is that strain rates are not necessarily constant with depth in continental collision zones, as assumed in
constructing yield strength envelopes (‚Christmas trees‘) and thin-sheet models. A direct transformation from stress to
strength (i.e. effective viscosity) in the lithosphere is not possible without knowledge of the strain rate distribution.
Consequently, the analogy of lithospheric areas with high earthquake activity and lithospheric areas with high mechanical
strength is questionable for continental collision zones.
In the case of the India/Asia collision, results show that differential stresses in the mantle lithosphere underneath the
Himalaya and Tibet are small even if it is strong (i.e. has a large effective viscosity). The scarcity of large earthquakes underneath
the Moho in this region can thus not be used as evidence for a weak (or water-rich) mantle lithosphere.
1.22
Implementation and geodynamical application of iterative and multigrid
solvers for 2D finite-element Stokes flow
Keller Tobias*, Kaus Boris*
*Geophysikalisches Institut, Schafmattstrasse 30, CH-8093 Zürich
The standard approach to solve problems with the finite element method usually involves the use of a direct solver. To do
so, the global stiffness matrix L is assembled to bring the problem into the well known and useful form Lx = R. To solve this
system of equations in a direct way, a large number of methods including sophisticated elimination schemes, preconditioning
or matrix decomposition methods have already been tested against each other, e.g. (May & Moresi 2008). One approach
that is used less frequently, is to solve the set of equations with an iterative scheme. This scheme is relatively easy to implement,
but requires many iterations per timestep. To overcome the weakness of iterative solvers, a multigrid solver can be
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Symposium 1: Structural Geology, Tectonics and Geodynamics