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A We can follow a parallel definition for the data fitting goal in terms of the inverse noise covariance 366#366:
506#506 (211)
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 4#4 and a non-uniform function of 244#244.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 224#224 by finding the moveout parameter 66#66that best describes the moveout in migrated angle gathers. I calculate 224#224 by mapping my selected 66#66 parameter back into residual moveout and the multiplying by the local velocity. Conversely I can write my fitting goals in terms of 507#507 by introducing an operator 367#367 that maps 224#224 to 508#508,
509#509

Making the data a uniform function of space is even easier. I can easily write an operator that maps my irregular 507#507 to a regular function of 510#510 by a simple inverse interpolation operator 315#315.I then obtain a new set of fitting goals,
511#511
On this regular field the noise inverse covariance 366#366 is easier to get a handle on. We can approximate the noise inverse covariance as a chain of two operators. The first, 512#512, f a fairly traditional diagonal operator that amounts for uncertainty in our measurements. For the tomography problem this translate into the width of our semblance blob. For the second operator we can estimate a Prediction Error Filter (PEF) on 513#513 () after solving
514#514
If we combine all these points and add in the data variance we get,
515#515

bob7

 

 

Short Note
An extension of poroelastic analysis to double-porosity materials: A new technique in microgeomechanics

James G. Berryman

[1] [*] [1] [*]
516#516 (212)
x M A C D E F G K L P R S T V W Int Bdy


next up previous print clean
Next: INTRODUCTION Up: Prucha and Biondi: STANFORD Previous: AVA analysis
Stanford Exploration Project
6/7/2002