New extended thin-sheet approximation for geodynamic applications - II. Two-dimensional examples

The potential of the new extended thin-sheet approximation (ETSA) has been investigated by application to a representative range of 2-D problems. The system of governing equations presented by Medvedev & Podladchikov (1999) f or 3-D modelling was reduced to two dimensions and tested on problems invol ving one- and two-layer systems of Newtonian viscous materials. The applica tion of ETSA in each case included (1) setting boundary conditions, (2) com pletion of equations by evaluation of coefficients, (3) comparison of equat ions with governing equations of existing thin-sheet approximations, and (4 ) linear analysis of small perturbations and determination of their dominan t wavelengths. It is shown that most previous approaches can be derived by simplification of an extended system under specified boundary conditions. L inear analyses compare well with exact analytical solutions over a wide ran ge of wavelengths for modelling isostatic adjustment, Rayleigh-Taylor insta bilities and the development of instabilities due to lateral compression an d extension. These problems cannot be described by the previous generation of thin-sheet approximations. Our results suggest that the new extended thi n-sheet approximation (ETSA) will be a powerful tool for the realistic mode lling of complicated 2- and 3-D geodynamic structures.