Numerical simulation of 2D wave propagation on unstructured grids using explicit differential operators

We present a numerical method of simulating seismic wave propagation on uns tructured 2D grids. The algorithm is based on the velocity-stress formulati on of the elastic wave equation and therefore uses a staggered grid approac h. Unlike finite-element or spectral-element methods, which can also handle flexible unstructured grids, we use explicit differential operators for th e calculation of spatial derivatives in each time step. As shown in previou s work, three types of these operators are used, and their particular perfo rmance is analysed and compared with standard explicit finite-difference op erators on regular quadratic and hexagonal grids. Our investigations are es pecially focused on the influence of grid irregularity, sampling rate (i.e. gridpoints per wavelength) and numerical anisotropy on the accuracy of num erical seismograms. The results obtained from the various methods are there fore compared with analytical solutions. The algorithm is then applied to a number of models that are difficult to handle using (quasi-)regular grid m ethods. Such alternative techniques may be useful in modelling the full wav efield of bodies with complex geometries (e.g. cylindrical bore-hole sample s, 2D earth models) and, because of their local character; they are well su ited for parallelization.