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Whenever
and , we find easily that
, while . In this case, *v*_{1}
and *v*_{3} are themselves the eigenvectors, while the eigenvalues are
proportional to *A*^{*}_{11} and *A*^{*}_{33}. In the quasi-isotropic
limit, *A*^{*}_{13} can vanish only if , in which
case *A*^{*}_{33} also does not depend on fluid properties. For media
differing significantly from the quasi-isotropic limit,
*A*^{*}_{13} could vanish for some physically interesting situations,
but the resulting physical constraints are too special (and
complicated) for us to consider them further here.

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** Up:** Compliance formulation
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Stanford Exploration Project

5/23/2004