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The linearized model accurately predicts only precritical primary
reflections. For layered media, precritical reflections have downgoing
incident rays. Along downgoing rays, time is an increasing function
of depth. It follows that if *t*_{0} is to be a depth variable, then *T*
must be an increasing function of *t*_{0}. This is generally true only
in a subset of the *t*,*x* plane, i.e. only part of this plane contains
data accurately modeled by linearized acoustics. Therefore the rest of
the data must be muted out.
Define the *stretch factor*

Then the condition that *T*(*t*_{0},*x*) be monotone increasing as a
function of *t*_{0} is equivalent to demanding that for large enough *t*
where is a user-specified parameter larger than one.
Define (the *mute boundary*)
to be the infimum of all *t* for which the
above inequality is satisfied on the interval . Then
the support of the mute function should be contained in the
set .
Define a corresponding *t*_{0},*x* domain mute by .

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Stanford Exploration Project

4/20/1999