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Claerbout (1992)
casts the problem of slope estimation as a univariate optimization problem, based
on the observation that the partial differential equation
| |
(1) |

is zero-valued if the wavefield *u*(*t*,*x*) consists only of plane waves with
time slope, or ``stepout,'' *p*. Claerbout also notes that a cascade of two
PDEs annihilates data consisting of plane waves with two slopes, *p*_{1} and *p*_{2}.
The analog to equation (1) is:
| |
(2) |

or after expansion,
| |
(3) |

** Next:** Discretizing the problem
** Up:** Brown: Slope estimation
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Stanford Exploration Project

11/11/2002