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The third and final discriminant between crosstalk and signal exploits the
inherent predictability of the crosstalk to suppress it. If we have an estimate
of the signal, we can directly model the expected crosstalk events on each
, and construct a model-space weighting function to penalize
crosstalk. Unfortunately, unless we employ a nonlinear iteration (see section
), we do not, a priori, have this signal estimate.
However, between the seabed reflection and the onset of its first multiple, the
recorded data contains only primaries (inter-bed multiples and locally-converted
shear waves are generally weak), and it is these strong, shallow events that
often spawn the most troublesome crosstalk events. Therefore, we can directly
model any pegleg multiple arising from a multiple generator with traveltime less
than that of the first seabed multiple.
If we define as an operator that applies a flat mute below twice the
zero-offset traveltime of the seabed, and as a similar operator that
mutes above the zero-offset traveltime of the multiple generator,
then

| |
(9) |

is a model of the leg of the order multiple from the
multiple generator. Each in equation
() should ideally contain only the leg of the
-order multiple from the multiple generator - all other
energy is crosstalk. To simulate crosstalk noise in , we apply
to all multiple model panels (except
) and sum:
| |
(10) |

is a kinematic model of crosstalk for . It
could be used as a traditional multiple model (see section )
and subtracted from the data, but I instead convert each into a
weighting function by taking the absolute value. We can write the model residual
corresponding to the third model regularization operator:
| |
(11) |

Although the crosstalk weights will likely overlap (and damage) signal to some
extent, the signal's flatness and self-consistency between images ensures that
regularization operators () and () will
``spread'' redundant information about the primaries from other
and other offsets to compensate for any losses. Figure
illustrates the application of the crosstalk weights for the primary image and a
multiple image. On panel (a), the primary image, the crosstalk is the obviously
curving events. On panel (c), the seabed pegleg image, the crosstalk events are
multiples from other multiple generators (e.g., R1M and R2M). Notice that in
both cases the unwanted multiples are picked cleanly out of the data, leaving
the underlying signal intact.
**crosstalk.gulf
**

Figure 2 Application of crosstalk weights to real CMP
after prestack imaging. Panel (a): primary image, . Panel (b): weighted primary image, . Panel
(c): seabed pegleg image, . Panel (d): weighted
seabed pegleg image, .
in this case. Prominent crosstalk events are labeled on the
various panels.

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Stanford Exploration Project

5/30/2004