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