Journal of Conference Abstracts

Simulation of Wave Propagation on Irregular Grids with Arbitrary Boundaries

Heiner Igel (heiner@esc.cam.ac.uk)¹, Malcolm Sambridge² & Jean Braun²

¹Institute of Theoretical Geophysics, Downing Street, Cambridge, CB2 3EQ, U.K.

²Research School of Earth Sciences, ANU, Canberra, Australia

Numerical studies of wave propagation often require solutions to models with arbitrarily shaped internal interfaces and generally irregular boundaries. While in some cases it may be possible to work directly in the curved coordinate system, this may be impractible in others (e.g. wave propagating in 3-D spheres, 3-D cylinders, due to the singularities in the governing equations). An alternative is to solve the governing equations in the cartesian system on generally irregular grids. As an example we solve the elastic wave equation on arbitrary grids with local difference operators, calculated as weight factors for the natural neighbors of each grid point. In two dimensions this technique requires triangulation of the grid and search for the natural neighbours. Once the natural neighbours have been found, derivative weights can be calculated for each grid point by different techniques (e.g. finite volumes, natural neighbour coordinates). In three dimensions, the grids are discretized with tetrahedra. In both cases (2-D, 3-D) we use two seperate grids for stresses and velocities (quasi staggering). We discuss the accuracy of several methods for centered and staggered schemes. The free surface conditions are applied by rotating tensors and vectors into a local system and applying symmetry conditions. This technique is applied to wave propagation in spherical and cylindrical bodies.