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## Relying on interpolated data?

Let us look at the issue of relying on data not paid for''. First we'll see that interpolation and extrapolation need do no harm. Conventional inversion can be expressed by minimizing the quadratic form
 (4)
where is the model vector, is the kth row of a partial derivative matrix, dk is the kth known data point, is a scalar, and to avoid clutter I have neglected the residual weighting. The missing data philosophy is to add terms involving the missing data dm, namely
 (5)
Since the missing data dm are freely adjusted variables, it is evident that the value of Q at the minimum is the same both with and without the missing data. Missing data interpolated or extrapolated in this way cannot perturb the solution .Of course there are many other ways to interpolate and extrapolate, and they are generally less sophisticated than the model-based method I am describing. How can they be of value?

Next: Rate of convergence Up: CLASH IN PHILOSOPHIES Previous: CLASH IN PHILOSOPHIES
Stanford Exploration Project
1/13/1998