## Abstract

We apply the normal mode representation of tsunami waves, as introduced by WARD (1980) to the systematic study of the excitation of far-field tsunamis by both dislocation sources (represented by double-couples of moment M_{o}), and landslides (represented by single forces). Using asymptotic representations of the continuation of the tsunami eigenfunction into the solid Earth, we derive analytical expressions of the spectral amplitude generated by both systems. We show that the quadrupolar corrections defined by DAHLEN (1993) in the case of landslides can result in an increase of 1 to 2 orders of magnitude of the effective force. Even so, the spectrum of tsunami waves generated by landslides is found to be offset significantly to relatively high frequencies (10 mHz), where dispersion becomes important and eventually diminishes time-domain amplitudes. We proceed to calculate the total energy delivered into the tsunami modes by integrating the energy of multiplets for an average source geometry. In the case of dislocation sources, and taking into account the corner frequency of the source, we reproduce the scaling with M^{4/3}_{0} which was derived from purely static arguments by KAJIURA (1981). We compare the directivity patterns of far-field tsunami waves by dislocations and landslides, and conclude that the latter cannot give rise to pronounced lobes of directivity for physically acceptable values of the velocity of the slide. Directivity thus constitutes a robust discriminant of the nature of the source which, when applied to the 1946 Aleutian tsunami in the far-field, requires generation by a dislocative source.

Original language | English (US) |
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Pages (from-to) | 2189-2221 |

Number of pages | 33 |

Journal | Pure and Applied Geophysics |

Volume | 160 |

Issue number | 10-11 |

DOIs | |

State | Published - Oct 2003 |

### Funding

I thank the conveners who invited me to the Los Angeles Workshop on landslides and tsunamis in March 2000. The comments of Bob Geller on an early version of these computations are appreciated, as well as recent discussions with Steve Kirby, Homa Lee and Bill Normark. The paper was improved through the comments of an anonymous reviewer. I am grateful to my field companions, principally Costas Synolakis and George Plafker, for helping me become acquainted first hand with the awesome scale of the 1946 Aleutian tsunami, both in the near and far fields. Parts of this work were supported by the National Science Foundation.

## Keywords

- Directivity
- Landslides
- Normal modes
- Tsumani theory

## ASJC Scopus subject areas

- Geophysics
- Geochemistry and Petrology