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The formulation of an optimal estimation usually consists of two steps.
The first step is to construct an objective function that depends on
the unknown parameter to be determined. This function measures the quality
of the estimation. The second step is to estimate the unknown
parameters through the extremization of the objective function,
depending on type of the quality measure.
In this section, I use dip
estimation of seismic events as an example to describe two types of
quality measures.
Let us suppose a seismic section *P*(*t*,*x*) contains events reflected
from subsurface boundaries. We want to estimate the local dips of these events.
An event with local dip *p* at point (*t*,*x*) follows the trajectory

| |
(1) |

at that point. For each point on the section, we can construct a
subsection by applying linear moveout corrections to a
window of data
| |
(2) |

where and . The symbols and are the temporal and spatial sampling intervals,
respectively. If the local dip *p* used for the linear moveout correction
is equal to the true dip at the location (*t*,*x*), then *P*_{ij} is composed
of horizontal events. Otherwise, the events in *P*_{ij} are slanted. With this
observation, we can define the objective functions.

** Next:** Error measure
** Up:** Zhang: Automatic picking
** Previous:** Introduction
Stanford Exploration Project

12/18/1997