High-Resolution Radon Demultiple

Neil Hargreaves Nick Cooper Peter Whiting

Veritas DGC, UK Veritas DGC, UK Veritas DGC, Singapore
neil_hargreaves@veritasdgc.com nick_cooper@veritasdgc.com peter_whiting@veritasdgc.com

Multiples are then removed by muting those parabolas in the

Radon domain that represent the multiple curvatures.
SUMMARY
Unfortunately the conventional Radon transform has some
It is well known that conventional Radon demultiple may limitations related to its spatial aperture and spatial sampling
fail when there is limited differential moveout between which can cause mis-focusing of energy in the transform.
primaries and multiples or when the input data contain Figure 1(a) shows the conventional Radon transform of a
aliased events. These limitations can be overcome by an synthetic gather that contains a small number of horizontal
extension of the conventional Radon transform which events plus three events with exactly parabolic moveout.
uses data-derived constraints to enhance the focusing of These events are ideally suited to representation by the
energy in the transform domain. This leads to better parabolic Radon transform, but the sampling and aperture
separation of primaries and multiples and an improved limitations of the transform cause energy to be smeared rather
resistance to errors due to noise and aliasing. than focused at the correct zero-offset times and curvatures of
each event. This is true for all of the events in the gather,
Data examples show the benefits that result in practice including the horizontal events, but is particularly acute for
from this high-resolution version of the transform: the high curvature event at early times. Aliased energy from
a) Better multiple removal and signal preservation this event covers almost all the transform domain.
when primaries and multiples have small differential
moveout. The practical implication of these results is that the
b) Removal of aliased multiples without the need for conventional transform can fail to separate primaries and
pre-interpolation. multiples sufficiently for multiple removal to be fully
successful. If curvatures that are nominally associated with
c) Removal of aliased noise in the course of
multiples are removed from the data, some primary energy
demultiple processing.
may also be removed and some multiple energy may remain.

Key words: multiples, Radon, resolution, aliasing. An alternative to the standard decomposition is the high-
resolution Radon transform (Sacchi and Ulrych, 1995). This
overcomes the limitations of the standard algorithm by
INTRODUCTION constraining the algorithm so that it departs from the standard
least-squares solution. Instead it performs a sparse
Multiple reflections are a serious problem in many of decomposition of the input and represents the data by fewer
Australia’s offshore petroleum provinces. Along most of the events in the Radon domain. The constraints have the effect
western coast of Australia, shallow carbonate layers overly of moving energy towards those locations where the standard
deeper clastic sediments resulting in multiples with relatively transform has its larger amplitudes, which are predominantly
high velocity, and hence less moveout separation than is ideal. where the energy would sit if there were no sampling or
To combat this problem it is common to push demultiple aperture limitations in the input data or in the transform itself.
technology to the limit, and hence straining on the amplitude The high-resolution transform is capable, therefore, of better
preserving characteristics of the algorithms. In this paper we discriminating between primary and multiples and is also
present results from an advanced multiple attenuation resistant to spatial aliasing of the input data.
technique that has the potential to be more surgical in nature
while, at the same time, having superior amplitude Figure 1(b) shows the high-resolution transform for the same
preservation properties. synthetic as that used to generate the result in Figure 1(a). All
of the events, even the strongly aliased shallow multiple, are
In the first part of the paper we discuss the general now precisely focused at their correct curvature and zero-
characteristics of our approach and compare the conventional offset times.
Radon transform with transform results from our high-
resolution approach. In subsequent sections of the paper we RESOLVING POWER
demonstrate its application in three different data scenarios:
resolution of primaries and multiples with limited differential
Figure 2(a) shows a small portion of a synthetic gather
moveout; long-offset data containing aliased multiples, and
containing a weak primary that has a limited amount of
data containing high amplitude, strongly aliased, linear noise.
differential moveout with respect to a nearby strong multiple.
The conventional Radon demultiple result in Figure 2(b)
HIGH-RESOLUTION RADON DEMULTIPLE suffers from all of the limitations discussed above. There is
leakage of multiple energy, particularly at near offsets, into the
In its conventional form (Hampson, 1986) the Radon primary part of the Radon domain, leading to remnant
transform is used to model prestack data as a set of parabolic multiple in Figure 2(b) at near offsets. Some primary energy,
events which best fit the data in a least-squares sense. particularly at larger offsets, has leaked into the multiple part

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ASEG 15 Geophysical Conference and Exhibition, August 2001, Brisbane. Extended Abstracts
High-Resolution Radon Transform Hargreaves, Cooper and Whiting

of the transform and is removed by the demultiple, leading to demonstrates that it can potentially be obtained without the
weakening of primary amplitudes at far offsets. There is also additional cost and delays of pre-stack trace interpolation.
some high frequency noise in the output that is caused by
leakage of aliased energy into the primary part of the ALIASED NOISE
transform.
In shallow hard water-bottom areas it is possible for high
Figure 2(c) shows the demultiple result produced by the high- amplitude, steeply-dipping, refracted noise to contaminate
resolution transform. The multiple removal is more complete significant portions of pre-stack seismic gathers. Whilst it
at near offsets than with the conventional transform and the may be possible to remove this type of noise by muting the
primary amplitude preservation is superior at far offsets. There gathers, this can severely limit the useable offset range after
is also less background aliasing noise. the mute.

Figure 3 shows peak amplitude estimates for these events When conventional Radon demultiple is applied to data
before and after demultiple obtained from a small window containing such noise there will be smearing of the noise
centred on the primary event. The amplitude estimate at near energy throughout the transform, in a similar manner to the
offsets before demultiple is contaminated by the nearby smearing of the steeply curved event at shallow times in
multiple. The amplitude is still contaminated by the multiple Figure 1. The noise can interfere with the least-squares
after the conventional Radon demultiple, and is also weakened decomposition of the data and degrade the demultiple
at large offsets. The amplitude estimate at both near and far processing and the primary amplitude preservation. When the
offsets is more accurate after the high-resolution demultiple noise is strong it is difficult to overcome these limitations by
because of its more complete multiple removal and better pre-conditioning using trace interpolation.
amplitude preservation.
The high-resolution transform, because of its ability to resist
LONG-OFFSETS aliasing in the input data, is able to correctly position the noise
in the transform domain and avoid the noise-related errors that
Figure 4 shows a portion of long-offset data containing aliased cause difficulties for the conventional approach. Once the
deep-water multiples predominantly on the near offset traces, noise is positioned correctly it becomes possible to remove the
where they overlay the primaries. Hyperbolic NMO has been noise in the course of the demultiple processing.
applied to the data using primary velocities, and the over-
correction of the primaries at large offsets is possible evidence Figures 5(a) and 5(b) show a gather of data containing high
of either anistropic moveout or strong vertical velocity amplitude, aliased, linear noise, before and after demultiple
variations. The objective for demultiple processing is to processing using the high-resolution Radon transform. The
remove the moderately aliased multiple energy on near offsets transform curvature limits were chosen to model the noise as
with minimum damage to primary amplitudes on larger well as the multiples, and a portion of the transform that
offsets, so that pre-stack attributes can be derived from the contains some of the noise is shown in Figure 5(c). Despite
data after demultiple processing. being strongly aliased, the noise is focused in the correct part
of the transform, and since most of the noise is at curvature
Conventional Radon demultiple without any pre-interpolation values above the cut-off between primaries and multiples, the
gives the result shown in Figure 4(b). Much of the multiple demultiple processing removes both the noise and the
energy has been removed but there is a significant degradation multiples from the data.
of primary amplitudes at far offsets.

Figure 4(c) shows the result obtained from conventional

Radon demultiple after trace interpolation prior to demultiple, REFERENCES
and then trace drop back to the original CDP fold.
Interestingly, the interpolation has helped to preserve primary Hampson, D., 1986, Inverse velocity stacking for multiple
amplitudes at large offsets, although the result still has a elimination: Journal of Canadian Society of Exploration
somewhat smeared appearance compared to the input data. Geophysics, 22, 1, 44-55.
There is also a slightly higher noise level in this result Sacchi, M.D. & Ulrych, T.J., 1995, High-resolution velocity
compared to that in Figure 4(b). This is because, after gathers and offset space reconstruction: Geophysics, 60, 4,
interpolation, the noise in the data is less aliased, and there is 1169-1177
less noise leakage into the multiple region of the Radon
domain.

Figure 4(d) shows the equivalent high-resolution demultiple

result, with no trace interpolation prior to demultiple. The
result is comparable to that in Figure 4(c) with interpolation;
multiples have been removed at near offsets and primary
amplitudes have been preserved at far offsets. Again, the
output appears slightly more noisy than in Figure 4(c),
possibly because of the ability of the high-resolution transform
to further overcome spatial aliasing of data noise.

The improved amplitude preservation of the high-resolution

result could be critical for, e.g., AVO analysis. Figure 4

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ASEG 15 Geophysical Conference and Exhibition, August 2001, Brisbane. Extended Abstracts
 High-Resolution Radon Transform Hargreaves, Cooper and Whiting
curvature
0 (residual moveout at far offset)
0

high

low

1.2 (c)
(a) (b)
Figure 1. Conventional versus high-resolution Radon transforms. Figure 1(a) shows the conventional Radon transform of a
synthetic gather containing a set of flat events and three curved events. Energy is smeared throughout the transform domain,
particularly in the case of the severely aliased (high-curvature) event at early times. With the high-resolution transform, shown
in Figure 1(b), the energy of each event is focused at its correct curvature and zero-offset time.

(a) s
Figure 2. Resolving power of high-resolution versus input 0.2
standard Radon demultiple. The synthetic input data in
Figure 2(a) contain a strong multiple with small residual
moveout adjacent to a weak primary. After standard (b)
Radon demultiple the primary is contaminated by
remnants of the multiple and by aliasing noise. The high- conventional
resolution transform removes more of the multiple
energy, with less aliasing noise, and has better (c)
preservation of the primary amplitude.

0 2 Offset (km) 4 6

0
input standard hi-res
Amp

-1
Figure 3. Amplitude preservation of high-resolution
Radon versus standard Radon demultiple. The
amplitude of the primary event in Figure 2 is
contaminated by the nearby multiple, both before
demultiple and after conventional Radon demultiple. A
more accurate measure of the true primary amplitude is
obtained after high-resolution Radon demultiple.

-2
2 Offset (km) 4 6

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ASEG 15 Geophysical Conference and Exhibition, August 2001, Brisbane. Extended Abstracts
 High-Resolution Radon Transform Hargreaves, Cooper and Whiting
4.7 km

2.4

2.8

(a) (b) (c) (d)

Figure 4. Radon demultiple and long offset data. Conventional Radon demultiple with no pre-conditioning, Figure 4(b), is
able to remove the multiple at near offsets in the input data of Figure 4(a), but does so at the cost of destroying primary
amplitudes at far offsets. This can be avoided by interpolation prior to conventional demultiple, as shown in Figure 4(c).
High-resolution Radon demultiple, Figure 4(d), can give a comparable result without the need for pre-interpolation.

1km 300 curvature 1600

0.8
” (ms at far offset)
”

1.6
(a) (b) (c)
Figure 5. Radon demultiple and aliased noise. The input gather in Figure 3(a) contains high amplitude, strongly aliased, linear noise.
This noise can cause transform errors in conventional Radon demultiple, reducing the effectiveness of the demultiple and possibly
damaging primary amplitudes. High-resolution Radon demultiple gives the result in Figure 3(b). The noise is focused in the correct
part of the transform domain, as shown in Figure 3(c), despite its strong aliasing. Since the noise sits above the cut-off between
primary and multiple curvatures both the noise and the multiples are removed when this part of the transform domain is muted for
demultiple.
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ASEG 15 Geophysical Conference and Exhibition, August 2001, Brisbane. Extended Abstracts