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Least-squares problems often present themselves as fitting goals such as
| |
(58) |

| (59) |

To balance our possibly contradictory goals we need weighting functions.
The quadratic form that we should minimize is
| |
(60) |

where is the inverse multivariate spectrum of the noise
(data-space residuals) and
is the inverse multivariate spectrum of the model.
In other words,
is a leveler on the data fitting error and
is a leveler on the model.
There is a curious unresolved issue:
What is the most suitable constant scaling ratio
of to ?

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Stanford Exploration Project

4/27/2004