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To avoid division by zero, Claerbout and Nichols (1994) suggest
multiplying both the numerator and denominator in
equation (4) by
, and
stabilizing the division by adding a small positive number to the
denominator:
| |
(5) |

Although this does solve the problem of division by zero, the
numerator and denominator will still oscillate rapidly in amplitude
with the phase of the image.
Illumination, however, should be independent of the wavefield's
phase. Therefore, I calculate weighting functions from the ratio of
the smoothed analytic signal envelopes (denoted by <>) of the
model-space images:

| |
(6) |

where is a damping parameter that is related to the
signal-to-noise level.

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Stanford Exploration Project

4/29/2001