next up previous print clean
Next: Confusing terminology for data Up: MULTIVARIATE SPECTRUM Previous: MULTIVARIATE SPECTRUM

What should we optimize?

Least-squares problems often present themselves as fitting goals such as
\begin{eqnarray}
\bold 0 &\approx& \bold F \bold m - \bold d\\ \bold 0 &\approx& \bold m\end{eqnarray} (58)
(59)
To balance our possibly contradictory goals we need weighting functions. The quadratic form that we should minimize is
\begin{displaymath}
\min_m \quad
(\bold F \bold m - \bold d)'
\bold A'_n \bold A...
 ... F \bold m - \bold d)
 +
 \bold m' \bold A'_m \bold A_m \bold m\end{displaymath} (60)
where $\bold A'_n \bold A_n$ is the inverse multivariate spectrum of the noise (data-space residuals) and $\bold A'_m \bold A_m$ is the inverse multivariate spectrum of the model. In other words, $\bold A_n$ is a leveler on the data fitting error and $\bold A_m$ is a leveler on the model. There is a curious unresolved issue: What is the most suitable constant scaling ratio of $\bold A_n$ to $\bold A_m$?
next up previous print clean
Next: Confusing terminology for data Up: MULTIVARIATE SPECTRUM Previous: MULTIVARIATE SPECTRUM
Stanford Exploration Project
4/27/2004