Dissertation for the Degree of Doctor of Philosophy in Mineralogy, Petrology,
and Tectonics presented at Uppsala University in 1998
ABSTRACT
Medvedev, S.
Thin Sheet Approximations for Geodynamic Applications
Thin sheet approximations
are widely used in geodynamics because of their potential for fast computing
of 3D lithospheric deformations using simple numerical techniques. However,
this simplicity imposes limits to boundary conditions, rheological settings
and accuracy of results.
The thesis argued here is
that thin sheet approximations are powerful tools in geodynamic modelling
and their current limitations are not necessary. To support this thesis
the following theoretical investigations are provided:
* previous approximations are classified and their restrictions and
advantages are discussed;
* scaling analysis of balance of forces is performed for application
of an asymptotic technique based on the thickness/width ratio;
* two steps in the asymptotic analysis results in exact balance of
forces integrated through the thickness of the thin sheet;
* the model is based on creep rheology although rheological variations
are possible.
Fundamental rebuilding of thin
sheet approximation on the basis of higher order analysis expands the low
order asymptotic background of previous approaches and results in the new
Extended Thin Sheet Approximation (ETSA). This ETSA includes a set of 2D
equations expre-ssing the integrated balance of forces and rules for reconstruction
of 3D stresses and velocities. The new approach retains the simplicity
of numerical techniques required for thin sheet appro-ximations, while
broadening their geodynamic applications because of the following points:
* special investigations found no limitations to possible boundary
conditions;
* the unification behind ETSA allows significant rheological stratification
in thin sheets;
* ETSA demonstrated it's potential by modelling the development of
lithospheric instabilities in conditions that were not tractable to previous
thin sheet approximations;
* comparisons with exact analytical solutions demonstrate high accuracy
of ETSA.
These conclusions are supported
by examples of analytical investigations based on the ETSA and analyses
of analogue models and field observations. The new computer code, SIMPLE,
based on the ETSA, was designed using the simplest numerical techniques
to model deformations in a lithosphere with strong rheological layering.
(c) Sergei Medvedev 1998