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Various methods can be used to improve images
created with inaccurate, reference velocity models.
Residual migration
Al-Yahya (1989); Etgen (1990); Stolt (1996)
is one such option,
although we could use other methods like
residual moveout or image continuation.
If image enhancement is done with a Stolt-type
residual migration operator Sava (2000, 2003); Stolt (1996),
we can write a relation for
an improved image derived from a reference
image

| |
(18) |

where is a spatially varying scalar parameter
indicating the magnitude of residual migration
at every image point.
We can compute a linearized image perturbation by a
simple first-order expansion relative to the
parameter
| |
(19) |

from which we can compute a wavefield perturbation
using the adjoint of the imaging operator.
The operator can be computed analytically, since it only depends on
the background image, while
can be picked at every location
from a suite of images computed using different values
of Sava and Biondi (2003).
Similar formulations are possible for other
kinds of operators (e.g., normal residual moveout),
and are not restricted to residual migration, in general,
or to Stolt residual migration, in particular.

With this definition of the wavefield perturbation,
we can compute another slowness perturbation:

| |
(20) |

** Next:** Discussion
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** Previous:** Rytov image perturbation
Stanford Exploration Project

10/14/2003