### Abstract

The second-order formulation of the wave equation is often used for spectral-element discretizations. For some applications, however, a first-order formulation may be desirable. It can, in theory, provide much better accuracy in terms of numerical dispersion if the consistent mass matrix is used and the degree of the polynomial basis functions is odd. However, we find in the 1-D case that the eigenvector errors for elements of degree higher than one are larger for the first-order than for the second-order formulation. These errors measure the unwanted cross talk between the different eigenmodes. Since they are absent for the lowest degree, that linear element may perform better in the first-order formulation if the consistent mass matrix is inverted. The latter may be avoided by using one or two defect-correction iterations. Numerical experiments on triangles confirm the superior accuracy of the first-order formulation. However, with a delta-function point source, a large amount of numerical noise is generated. Although this can be avoided by a smoother source representation, its higher cost and the increased susceptibility to numerical noise make the second-order formulation more attractive.

Original language | English |
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Title of host publication | 78th EAGE Conference and Exhibition 2016 |

Subtitle of host publication | Vienna, Austria |

Publisher | EAGE |

Pages | 1-5 |

Number of pages | 5 |

DOIs | |

Publication status | Published - 2016 |

Event | 78th EAGE Conference and Exhibition 2016 - Messe Wien, Exhibition and Congress Center, Vienna, Austria Duration: 30 May 2016 → 2 Jun 2016 Conference number: 78 http://www.eage.org/sitecore/content/events/home/2016/78th-eage-conference-and-exhibition-vienna-2016?sc_lang=en |

### Conference

Conference | 78th EAGE Conference and Exhibition 2016 |
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Abbreviated title | EAGE 2016 |

Country | Austria |

City | Vienna |

Period | 30/05/16 → 2/06/16 |

Internet address |

## Fingerprint Dive into the research topics of 'Should We Use the First- or Second-order Formulation with Spectral Elements for Seismic Modelling?'. Together they form a unique fingerprint.

## Cite this

Shamasundar, R., & Mulder, W. (2016). Should We Use the First- or Second-order Formulation with Spectral Elements for Seismic Modelling? In

*78th EAGE Conference and Exhibition 2016: Vienna, Austria*(pp. 1-5). [We P4 16] EAGE. https://doi.org/10.3997/2214-4609.201601058