### Abstract

The Maslov technique provides a means of constructing uniform asymptotic solutions to the wave equation under conditions in which variables do not separate. This technique is useful whenever a body‐wave description of wave propagation in laterally heterogeneous environments is appropriate. We exploit the assumption that there is a preferred direction of propagation to simplify the presentation of Maslov asymptotic theory given by Chapman & Drummond (1982). The one‐way assumption allows all intermediate quantities of interest to be interpreted geometrically; the Lagrangian manifold plays a central role. It is shown, for instance, that in the geometric limit the wavefield and its Radon transform are projections of the Lagrangian manifold onto the depth (the transverse spatial coordinate) and slowness axes, respectively. The final one‐way wavefield representation is easy to implement numerically, offering several advantages over the Chapman & Drummond formulation. Using the one‐way formulation, all quantities required to compute the wavefield at all depths at a fixed range (the preferred propagation direction) are computed concurrently; the technique is thus particularly well suited to the modelling of wavefields which are sampled using a multi‐element vertical array (e.g. in a borehole).

Original language | English (US) |
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Pages (from-to) | 513-526 |

Number of pages | 14 |

Journal | Geophysical Journal International |

Volume | 116 |

Issue number | 3 |

DOIs | |

State | Published - Mar 1994 |

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### Keywords

- Lagrangian manifold
- Maslov theory
- chaos
- phase space
- ray theory
- wave propagation

### ASJC Scopus subject areas

- Geophysics
- Geochemistry and Petrology