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In the above example, the assumption that the
variance of our noise is spatially invariant
is correct. In a more general problem,
this will not be the case.
As a result, a more appropriate formulation for
our noise covariance is
| |
(11) |

In this formulation, is a description
of the relation between points. It will take
the form of a PEF or one of the other operators
described above.
The second operator will attempt
to normalize the variance of the various data
errors to the same level and should be equal
to
| |
(12) |

where *V*(*i*) is the variance at a given data location *i*.

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Stanford Exploration Project

7/8/2003