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A

We can follow a parallel definition for the data fitting goal in terms of the inverse noise covariance :

(5) |

Noise covariance for velocity estimation Using the multiple realization methodology for velocity estimation problem posed in the manner results in several difficulties. First, what I would ideally like is a model of the noise. This poses the problem of how to get the noise inverse covariance. The first obstacle is that our data is generally a uniform function of angle and a non-uniform function of .What we would really like is a uniform function of just space. We can get this by first removing the angle portion of our data.

I obtain by finding the moveout parameter that best describes the moveout in migrated angle gathers. I calculate by mapping my selected parameter back into residual moveout and the multiplying by the local velocity. Conversely I can write my fitting goals in terms of by introducing an operator that maps to ,

(6) | ||

Making the data a uniform function of space is even easier. I can easily write an operator that maps my irregular to a regular function of by a simple inverse interpolation operator .I then obtain a new set of fitting goals,

(7) | ||

(8) | ||

(9) | ||

6/8/2002