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Most imaging methods described in the literature involve the correlation
between scalar wavefields. An exception is the tensorial imaging
condition formulated by Karrenbach (1991):
where is the *l* component of the forward modeled shot wavefield,
and is the reverse propagated difference between the
forward modeled wavefield at the receivers and the recorded wavefield.
This process is equivalent to one step of a wavefield inversion scheme,
and can be interpreted as the estimated perturbation
in the stiffness tensor. In this sense, it can be considered as an extension
of Tarantola's (1986) elastic inversion theory to the general anisotropic
case.
Hildebrand (1987) used a variation of this principle to image
for the acoustic impedance rather than the reflection coefficient, using
reverse-time migration to extrapolate the pressure and particle-velocity
wavefields. Contrary to the above formulation, Hildebrand's approach
obtained a image of the impedance (rather than perturbations), using
a recursive depth extrapolation procedure.

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Stanford Exploration Project

11/18/1997