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At the reflector point *R*, the ray must obey Snell's law. In other words,
the angle of incidence must equal the angle of reflection. In terms of
ray paths, fixes the position of the reflection plane,
and and account for the angles of incidence and
reflection. Since and have equal lengths
1/*v*, Snell's law can be expressed in the following vectorial form:
| |
(9) |

where is a coefficient of proportionality. The first
two coordinates are the ray parameter components, which have
the following relation:
| |
(10) |

The third coordinate of the ray path vectors can be expressed
as a function of the inclination angle and the vector length,
1/*v*, as follows:
| |
(11) |

where is the table of angles along a ray of
parameter *p* and time *t*. Then, after simplification of
the 1/*v* factors (the velocity is the same for all rays
at the reflector point), the third equation of
relation (9) becomes
| |
(12) |

Substituting equation (12) into relation (10),
we can eliminate the proportionality factor to obtain
the following relation:
| |
(13) |

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** Up:** DERIVING THE SYSTEM OF
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Stanford Exploration Project

11/17/1997