Multiple attenuation is one of the greatest challenges in seismic processing. Due to the high cross-correlation between primaries and multiples, attenuating the latter without distorting the former is a complicated problem. We propose here a joint multiple model-based adaptive subtraction, using single-sample unary filters' estimation in a complex wavelet transformed domain. The method offers more robustness to incoherent noise through redundant decomposition. It is first tested on synthetic data, then applied on real-field data, with a single-model adaptation and a combination of several multiple models. Read More: http://library.seg.org/doi/abs/10.1190/segam2012-0440.1

1. Unary adaptive subtraction of joint multiple models with complex wavelet frames
S. Ventosa (1), S. Le Roy, I. Huard, A. Pica(2), H. Rabeson, L. Duval* (3) TaM0: Non-stationary, wavelet-based, adaptive multiple removal
(1)IPGP, (2)CGGVeritas, (3)IFP Energies nouvelles TaM1: “Complex” wavelet transform + simple one-tap (unary) filter
Contacts: ventosa@ipgp.fr,laurent.duval@ifpen.fr TaM2: Redundancy selection: noise robustness and processing speed
TaM3: Smooth adaptation to adaptive joint multiple model filtering
Results: field data multiple filtering
Motivation: Multiple model data Redundancy selection
Shot number Shot number
primary
0.15
true multiple
Shot number
2200 2000 1800 1600 1400 1200 2200 2000 1800 1600 1400 1200 multiple adapted multiple
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noise 0.1 1.8
sum
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−0.05
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Time (s) Time (s) 2.6
3 3
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Key features
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Shot number Shot number • fast off-line parameter selection
2200 2000 1800 1600 1400 1200 2200 2000 1800 1600 1400 1200 3.2
1.8 1.8
19
– realistic synthetics
20 18 – varying random noise realizations 3.4
Median S/Nadapt (dB)
2 2
18 17
2.2 2.2
– SNR-based wavelet parameter selection Shot number
16 16
2200 2000 1800 1600 1400 1200
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15 • controllable redundancy allows: 1.8
Time (s)
Time (s)
14
2.6 2.6
12
13
– simple stable synthesis dual frame 2
10
2.8 2.8
20
16
12 – resistance to field noise
15 14 11
2.2
10
8
10
12
10
– computational efficiency balanced
3 3 6
5 4
S/N (dB) Redundancy • Morlet wavelet frame 2.4
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Time (s)
– approximately analytic
3.4 3.4 2.6
– sliding window processing along scales
Data and three multiple models, common offset plane (need for a model-based, non-stationary, adaptive multiple filtering). 2.8
Complex wavelet frame decomposition Unary filter estimation 3
• Complex Morlet wavelet definition: • Windowed adaptation: complex aopt compensates local delay/amplitude mis- 3.2
−1/4 −iω0t −t2/2
matches: 2 3.4
ψ(t) = π e e , ω0: central frequency (1)
aopt = arg min d − ak x k (4) Subtraction results: (top) model 3 (bottom) joint multi-model multiple removal.
Some multiples better attenuated around 3s, random noises reduced.
• Discretized time r, octave j, voice v: {ak }(k∈K) k
nT − r2j b0 1 • Vector Wiener equations for complex signals:
v
ψr,j [n] = √ ψ j+v/V
, b0: sampling at scale zero (2) References
2j+v/V 2 d, xm = ak x k , x m (5)
[1] Herrmann, F. J. and D. Wang and D. J. Verschuur, 2008, Adaptive curvelet-domain
• Time-scale analysis: k primary-multiple separation: Geophysics, 73, A17–A21.
[2] Donno, D., H. Chauris, and M. Noble, 2010, Curvelet-based multiple prediction: Geo-
v v v • Time-scale synthesis:
d = dr,j = d[n], ψr,j [n] = d[n]ψr,j [n] (3) ˆ ˆ v
physics, 75, WB255–WB263.
d[n] = dv ψr,j [n]
r,j (6) [3] Neelamani, R., A. Baumstein, and W. S. Ross, 2010, Adaptive subtraction using
n
r j,v complex-valued curvelet transforms: Geophysics, 75, V51–V60.
´
[4] Jacques, L., L. Duval, C. Chaux, and G. Peyre, 2011, A panorama on multiscale geo-
Time-scale data and model trace representations Complex wavelet domain adaptation metric representations, intertwining spatial, directional and frequency selectivity: Signal
2 2 2 2 Process., 91, 2699–2730.
2000 2000 2000 2000
4 4 4 4 [5] Ventosa, S., H. Rabeson, P. Ricarte, and L. Duval, 2011, Complex wavelet adaptive
1500 1500 1500 1500
Scale
Scale
Scale
Scale
8 8 8 8
multiple subtraction with unary filters: Proc. EAGE Conf. Tech. Exhib.
1000 1000 1000 1000
16 500 16 500 16 500 16 500
[6] Ventosa, S., S. Le Roy, I. Huard, A. Pica, H. Rabeson, P. Ricarte, and L. Duval, 2012,
0 0 0 0
Adaptive multiple subtraction with wavelet-based complex unary Wiener filters: Geo-
2.8 3 3.2 3.4
Time (s)
3.6 3.8 4 4.2 2.8 3 3.2 3.4
Time (s)
3.6 3.8 4 4.2 2.8 3 3.2 3.4
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3.6 3.8 4 4.2 2.8 3 3.2 3.4
Time (s)
3.6 3.8 4 4.2 physics, 77, V183–V192.
2 2 2 2
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4 4 4 4
1500 1500 1500 1500
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0 0 0 0
2.8 3 3.2 3.4 3.6 3.8 4 4.2 2.8 3 3.2 3.4 3.6 3.8 4 4.2 2.8 3 3.2 3.4 3.6 3.8 4 4.2 2.8 3 3.2 3.4 3.6 3.8 4 4.2
Time (s) Time (s) Time (s) Time (s)
Data and model trace Morlet wavelet scalograms. Adapted joint and individual model trace Morlet wavelet scalograms. SEG Annual Meeting, Las Vegas, Nevada, USA, 4-9 November 2012