Regular versus irregular meshing for complicated models and their effect on synthetic seismograms

• Published in: Geophysical journal international 2010-11, Vol.183 (2), p.1031-1051
• Main Authors: Pelties, Christian, Käser, Martin, Hermann, Verena, Castro, Cristóbal E.
• Format: Article
• Language: English
• Subjects: Acceptability; Alignment; Computational seismology; Finite element method; Mathematical analysis; Mathematical models; Meshing; Numerical approximations and analysis; Seismograms; Staircases; Wave propagation; Wave scattering and diffraction
• ISSN: 0956-540X; 1365-246X
• DOI: 10.1111/j.1365-246X.2010.04777.x

We present a detailed study on the numerical effects due to staircase approximations of non-planar material interfaces and the importance of mesh alignment to such material boundaries using the discontinuous Galerkin finite element method. Our aim is to define clear rules that have to be adhered to guarantee acceptable synthetic data in seismic forward modelling for the cases where material contrasts occurring along curved interfaces are discretized with regular meshes. To this end, we compare results of structured staircase approximations with reference results obtained by unstructured triangular meshes that can be aligned to non-planar interfaces. We investigate different mesh spacings, wave frequencies, and material contrasts to cover various parameter ranges that allow us to measure their influence on the accuracy of the resulting waveforms. Our results show that acceptable synthetic results strongly depend on the material contrast and we give a quantitative estimate of the required mesh resolution in the sense of numbers of elements per shortest dominant wavelength to obtain satisfying seismograms even if the material interfaces are not respected by the mesh. We apply our rules to two different test cases including a multilayered model and a basin structure, both with non-planar interfaces of small and large material contrasts to confirm the validity of our study. We finally conclude that for moderate material contrasts regular meshing can be beneficial due to its simple mesh generation process and typically superior computational efficiency compared to unstructured meshes, however, the correct frequency- and material-dependent mesh resolution has to be chosen.