Thin sheet approximations for geodynamic applications

Sammanfattning: 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 expressing the integrated balance of forces and rules for reconstruction of 3D stresses and velocities.The new approach retains the simplicity of numerical techniques requited for thin sheet approximations, 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.