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When the velocity varies laterally, the matrix *M* in the extrapolation
operator at equation (7) has coefficients which varies along the diagonal,
but we can still derive a symmetric matrix (Godfrey et al., 1979).
The symmetry property, which will guarantee the unconditional stability,
can be obtained by putting the velocity term on both sides as follows

| |
(20) |

Now the small block matrices which are located along the diagonal in split
matrices *M*_{e} and *M*_{o} will have a symmetric form

where
and
The eigenvalues of are given by
and lie on the unit circle since *a* and *b* are imaginary,
and .It follows that the matrix norms and .To prove the unconditional stability of the algorithm we need only show that
. This follows immediately since , each of
which is unity according to the preceding argument.

** Next:** WIDE-ANGLE DEPTH MIGRATION
** Up:** 15-DEGREE DEPTH MIGRATION
** Previous:** Accuracy
Stanford Exploration Project

12/18/1997