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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:
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,
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,
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
If we combine all these points and add in the data variance we get,
Short Note
An extension of poroelastic analysis to double-porosity materials: A
new technique in microgeomechanics
James G. Berryman
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Next: INTRODUCTION
Up: Prucha and Biondi: STANFORD
Previous: AVA analysis
Stanford Exploration Project
6/7/2002