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Given a seismic event at ( *x*_{0} , *t*_{0} ) with a slope ,let us determine its position ( *x*_{m} , *t*_{m} ) after migration.
Consider a planar wavefront at angle to the earth's surface
traveling a distance *dx* in a time *dt*.
Assuming a velocity *v* we have
the wave angle in terms of measurable quantities.

| |
(3) |

The vertical travel path is less than the angled path by
| |
(4) |

A travel time *t*_{0} and
a horizontal component of velocity gives
the lateral location after migration:
| |
(5) |

Consideration of a hyperbola migrating towards its apex shows
why (5) contains a minus sign.
Equations (4) and (5) are the basic equations
for manual migration of reflection seismic data.
They tell you where the point migrates,
but they do not tell you how the slope *p* will change.

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** Up:** EXPLODING REFLECTORS
** Previous:** An impulse in the
Stanford Exploration Project

10/31/1997