Page 392 - Acquisition and Processing of Marine Seismic Data

7.4 RADON VELOCITY FILTER 383

increases, and therefore α must be modified as higher the residual moveout, the more effective
the p value changes during the computations, the method in multiple elimination. This prereq-
while n is kept constant. The α value as a func- uisite requires long offset seismic data to be col-
tion of p is given by lected, and therefore the method is generally
almost ineffective on the data collected with a
q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2
α p ¼ α 0 1 p V 2 (7.3) short streamer cable. In addition, since the
M
method is based on the moveout differences
where α 0 is the prediction distance at p ¼ 0, and after NMO correction, it also requires a careful
V M is the propagation velocity of the multiples. velocity analysis.
The data examples given here, however, are The amplitudes in the CDP gathers are
computed for constant α and n parameters. mapped into different areas in the τ-p domain,
Fig. 7.18 shows an application of the τ-p depending on their curvature controlled by their
domain predictive deconvolution to a marine
residual moveout times since the horizontal axis
shot gather. Prediction lag is determined as
of the τ-p gather corresponds to residual move-
160 ms, being equal to the length of the first tran-
outs. Providing an accurate velocity field, the
sient package in the autocorrelograms, and then
multiple reflections are still hyperbolic while
different operator lengths are tested. Deconvo-
the primary reflections are flattened following
lution with an operator length smaller than
the NMO correction. This difference results
n ¼ 100 ms cannot suppress the multiple, and
in the amplitudes of primaries and the multiples
the efficiency of the deconvolution increases as
being mapped in different areas in the τ-p
the operator length increases. The optimal
domain, in which the amplitudes of the multi-
parameters for this shot are α ¼ 160 ms and
ples are muted out (Landa et al., 1999). The
n ¼ 240 ms. Fig. 7.19 shows the τ-p domain pre-
important point here is the correct picking of this
dictive deconvolution results on a brute stack
mute zone, which discriminates the primary and
section using the parameters given here. multiple amplitudes in the τ-p domain. The
method involves following steps which are sche-
matically shown in Fig. 7.20.
7.4 RADON VELOCITY FILTER
i. NMO correction with velocities of primary
reflections is applied to input CDP.
Long period multiples can be suppressed by
parabolic Radon transform based on the move- ii. CDP gather is transferred into the τ-p
out differences between primary and multiple domain by Radon transform.
reflection hyperbolas in CDP gathers. The iii. The area comprising the multiple
method was first proposed by Hampson (1986) amplitudes in τ-p domain is muted out.
and it is accomplished by an application of the iv. CDP is transferred back into the time-
distance domain by inverse Radon
τ-p transform to NMO-corrected CDPs. The
transform.
most important advantage of the method is that
v. If required, an inverse NMO is applied to
it does not require information on the formation
obtain original CDP gather.
mechanism of the multiples. Practical applica-
tions indicate that the Radon velocity filters Fig. 7.20A schematically shows reflection
are effective in suppressing the long period mul- hyperbolas representing the arrival times of
tiples, especially at far offsets. However, for five primary and three multiple reflections.
complete success, the residual moveout between If we apply an NMO correction to this CDP
primary and multiple reflections after NMO cor- gather usingprimary reflectionvelocities, hyper-
rection should be at least 30 ms. In practice, the bolas of the primary reflections are flattened.