### Abstract

A full treatment of topographic effects on the seismic wavefield requires a 3-D treatment of the topography and a 3-D calculation for the wavefield. However, such full 3-D calculations are still very expensive to perform. An economical approach, which does not require the same level of computational resources as full 3-D modelling, is to examine the 3-D response of a model in which the heterogeneity pattern is 2-D (the so-called 2.5-D problem). Such 2.5-D methods can calculate 3-D wavefields without huge computer memory requirements, since they require storage nearly equal to that of the corresponding 2-D calculations. In this paper, we consider wave propagation from a point source in the presence of 2-D irregular topography, and develop a computational method for such 2.5-D wavepropagation problems. This approach is an extension to the 2.5-D case of the discrete wavenumber-boundary integral equation method introduced by Bouchon (1985) and Gaffet & Bouchon (1989) to study 2-D topographic problems. One of the most significant advantages of the 2.5-D calculations is that calculations are performed for a point source and so it is possible for us to take into account the 3-D radiation pattern from the source. We demonstrate that this discrete wavenumber-boundary integral equation procedure, coupled with a Green's function decomposition into P-and S-wave contributions, provides a flexible and effective means of evaluating the wavefield.

Original language | English |
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Pages (from-to) | 741-755 |

Number of pages | 15 |

Journal | Geophysical Journal International |

Volume | 124 |

Issue number | 3 |

DOIs | |

Publication status | Published - Mar 1996 |

Externally published | Yes |

### Keywords

- P waves
- S waves
- Topography
- Wave propagation

### ASJC Scopus subject areas

- Geophysics
- Geochemistry and Petrology

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## Cite this

*Geophysical Journal International*,

*124*(3), 741-755. https://doi.org/10.1111/j.1365-246X.1996.tb05635.x