Quantitative accuracy analysis of the discontinuous Galerkin method for seismic wave propagation

We present a quantitative accuracy analysis of the Discontinuous Galerkin Finite-Element method for the simulation of seismic wave propagation on tetrahedral meshes. Several parameters are responsible for the accuracy of results, such as the chosen approximation order, the spatial discretization, that is, number of elements per wavelength, and the propagation distance of the waves due to numerical dispersion and dissipation. As error norm we choose the time-frequency representation of the envelope and phase misfit of seismograms to assess the accuracy of the resulting seismograms since this provides the time evolution of the spectral content and allows for the clear separation of amplitude and phase errors obtained by the numerical method. Our results can be directly used to set up the necessary modelling parameters for practical applications, such as the minimum approximation order for a given mesh spacing to reach a desired accuracy. Finally, we apply our results to the well-acknowledged LOH.1 and LOH.3 problems of the SPICE Code Validation project, including heterogeneous material and the free surface boundary condition, and compare our solutions with those of other methods. In general, we want to stress the increasing importance of certain standard procedures to facilitate future code validations and comparisons of results in the community of numerical seismology.