Exploration of Galerkin methods for seismic wavefield modelling
Summary
In this thesis, we explored the impact of trial functions of Galerkin finite element methods on seismic waveform modelling. If we use linear spline functions, the modelling will be the same as second-order finite difference. Here we propose the sinc functions instead in order to reconcile with the nature of wavefield. We derive formally the errors of operators and show the potential superiority of sinc function to spline functions. We tested numerical solutions for 1D SH cases. The future work is the optimisation of these operators (Geller & Takeuchi 1995) but since there have been no systematical recipe of optimisation, we reformulate the optimisation for future automatisation.