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Suppose that we had not gotten rid of the layered media terms.
The observations would be *u*+*w* and we would be autocorrelating that.
Both *u* and *w* have essentially the same autocorrelation,
but their cross-term is dangerous.
It has a different form (as you can verify).
This form multiplies the expectation of which might be theoretically zero
but in practice might often not be zero.
In principle we eliminate the cross term by eliminating
*u* from the observation *u*+*w*,
but in practice this difficulty remains
to haunt us
wherever we find the earth is not sufficiently horizontally layered.

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Stanford Exploration Project

4/27/2000