Unary adaptive subtraction of joint multiple models with complex wavelet frames TaM0: Non-stationary, wavelet-based, adaptive multiple removal TaM1: “Complex” wavelet transform + simple one-tap (unary) filter TaM2: Redundancy selection: noise robustness and processing speed TaM3: Smooth adaptation to adaptive joint multiple model filtering S. Ventosa (1) , S. Le Roy, I. Huard, A. Pica (2) , H. Rabeson, L. Duval* (3) (1) IPGP, (2) CGGVeritas, (3) IFP Energies nouvelles Contacts: [email protected],[email protected] Motivation: Multiple model data Shot number Time (s) 1200 1400 1600 1800 2000 2200 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 Shot number Time (s) 1200 1400 1600 1800 2000 2200 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 Shot number Time (s) 1200 1400 1600 1800 2000 2200 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 Shot number Time (s) 1200 1400 1600 1800 2000 2200 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 Data and three multiple models, common offset plane (need for a model-based, non-stationary, adaptive multiple filtering). Complex wavelet frame decomposition • Complex Morlet wavelet definition: ψ (t)= π −1/4 e −iω 0 t e −t 2 /2 ,ω 0 : central frequency (1) • Discretized time r , octave j , voice v : ψ v r,j [n]= 1 √ 2 j +v/V ψ nT − r 2 j b 0 2 j +v/V ,b 0 : sampling at scale zero (2) • Time-scale analysis: d = d v r,j = d[n],ψ v r,j [n] = n d[n] ψ v r,j [n] (3) Time-scale data and model trace representations Time (s) Scale 2.8 3 3.2 3.4 3.6 3.8 4 4.2 2 4 8 16 0 500 1000 1500 2000 Time (s) Scale 2.8 3 3.2 3.4 3.6 3.8 4 4.2 2 4 8 16 0 500 1000 1500 2000 Time (s) Scale 2.8 3 3.2 3.4 3.6 3.8 4 4.2 2 4 8 16 0 500 1000 1500 2000 Time (s) Scale 2.8 3 3.2 3.4 3.6 3.8 4 4.2 2 4 8 16 0 500 1000 1500 2000 Data and model trace Morlet wavelet scalograms. Redundancy selection 0 0.5 1 1.5 2 2.5 3 3.5 4 Time (s) primary multiple noise sum 0 0.5 1 1.5 2 2.5 3 3.5 4 -0.1 -0.05 0 0.05 0.1 0.15 Time (s) true multiple adapted multiple Key features • fast off-line parameter selection – realistic synthetics – varying random noise realizations – SNR-based wavelet parameter selection • controllable redundancy allows: – simple stable synthesis dual frame – resistance to field noise – computational efficiency balanced • Morlet wavelet frame – approximately analytic – sliding window processing along scales 4 6 8 10 12 14 16 5 10 15 20 10 12 14 16 18 20 Redundancy S/N (dB) Median S/N adapt (dB) 10 11 12 13 14 15 16 17 18 19 Complex wavelet domain adaptation Time (s) Scale 2.8 3 3.2 3.4 3.6 3.8 4 4.2 2 4 8 16 0 500 1000 1500 2000 Time (s) Scale 2.8 3 3.2 3.4 3.6 3.8 4 4.2 2 4 8 16 0 500 1000 1500 2000 Time (s) Scale 2.8 3 3.2 3.4 3.6 3.8 4 4.2 2 4 8 16 0 500 1000 1500 2000 Time (s) Scale 2.8 3 3.2 3.4 3.6 3.8 4 4.2 2 4 8 16 0 500 1000 1500 2000 Adapted joint and individual model trace Morlet wavelet scalograms. Unary filter estimation • Windowed adaptation: complex a opt compensates local delay/amplitude mis- matches: a opt = arg min {a k }(k ∈K ) d − k a k x k 2 (4) • Vector Wiener equations for complex signals: 〈d, x m 〉 = k a k 〈x k , x m 〉 (5) • Time-scale synthesis: ˆ d[n]= r j,v ˆ d v r,j ψ v r,j [n] (6) Results: field data multiple filtering Shot number Time (s) 1200 1400 1600 1800 2000 2200 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 Shot number Time (s) 1200 1400 1600 1800 2000 2200 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 Subtraction results: (top) model 3 (bottom) joint multi-model multiple removal. Some multiples better attenuated around 3s, random noises reduced. References [1] Herrmann, F. J. and D. Wang and D. J. Verschuur, 2008, Adaptive curvelet-domain primary-multiple separation: Geophysics, 73, A17–A21. [2] Donno, D., H. Chauris, and M. Noble, 2010, Curvelet-based multiple prediction: Geo- physics, 75, WB255–WB263. [3] Neelamani, R., A. Baumstein, and W. S. Ross, 2010, Adaptive subtraction using complex-valued curvelet transforms: Geophysics, 75, V51–V60. [4] Jacques, L., L. Duval, C. Chaux, and G. Peyr ´ e, 2011, A panorama on multiscale geo- metric representations, intertwining spatial, directional and frequency selectivity: Signal Process., 91, 2699–2730. [5] Ventosa, S., H. Rabeson, P. Ricarte, and L. Duval, 2011, Complex wavelet adaptive multiple subtraction with unary filters: Proc. EAGE Conf. Tech. Exhib. [6] Ventosa, S., S. Le Roy, I. Huard, A. Pica, H. Rabeson, P. Ricarte, and L. Duval, 2012, Adaptive multiple subtraction with wavelet-based complex unary Wiener filters: Geo- physics, 77, V183–V192. SEG Annual Meeting, Las Vegas, Nevada, USA, 4-9 November 2012
Unary adaptive subtraction of joint multiple models with complex wavelet frames
Jul 04, 2015
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
Read More: http://library.seg.org/doi/abs/10.1190/segam2012-0440.1
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Unary adaptive subtraction of joint multiple models with complex wavelet framesTaM0: Non-stationary, wavelet-based, adaptive multiple removalTaM1: “Complex” wavelet transform + simple one-tap (unary) filterTaM2: Redundancy selection: noise robustness and processing speedTaM3: Smooth adaptation to adaptive joint multiple model filtering
S. Ventosa(1), S. Le Roy, I. Huard, A. Pica(2), H. Rabeson, L. Duval*(3)(1)IPGP, (2)CGGVeritas, (3)IFP Energies nouvellesContacts: [email protected],[email protected]
Motivation: Multiple model dataShot number
Tim
e (s
)
1200140016001800200022001.8
2
2.2
2.4
2.6
2.8
3
3.2
3.4
Shot number
Tim
e (s
)
1200140016001800200022001.8
2
2.2
2.4
2.6
2.8
3
3.2
3.4
Shot number
Tim
e (s
)
1200140016001800200022001.8
2
2.2
2.4
2.6
2.8
3
3.2
3.4
Shot number
Tim
e (s
)
1200140016001800200022001.8
2
2.2
2.4
2.6
2.8
3
3.2
3.4
Data and three multiple models, common offset plane (need for a model-based, non-stationary, adaptive multiple filtering).
Complex wavelet frame decomposition•Complex Morlet wavelet definition:
ψ(t) = π−1/4e−iω0te−t2/2, ω0: central frequency (1)
•Discretized time r, octave j, voice v:
ψvr,j[n] =1√
2j+v/Vψ
(nT − r2jb02j+v/V
), b0: sampling at scale zero (2)
•Time-scale analysis:
d = dvr,j =⟨d[n], ψvr,j[n]
⟩=∑
n
d[n]ψvr,j[n] (3)
Time-scale data and model trace representations
Time (s)
Sca
le
2.8 3 3.2 3.4 3.6 3.8 4 4.2
2
4
8
16
0
500
1000
1500
2000
Time (s)
Sca
le
2.8 3 3.2 3.4 3.6 3.8 4 4.2
2
4
8
16
0
500
1000
1500
2000
Time (s)
Sca
le
2.8 3 3.2 3.4 3.6 3.8 4 4.2
2
4
8
16
0
500
1000
1500
2000
Time (s)
Sca
le
2.8 3 3.2 3.4 3.6 3.8 4 4.2
2
4
8
16
0
500
1000
1500
2000
Data and model trace Morlet wavelet scalograms.
Redundancy selection
0 0.5 1 1.5 2 2.5 3 3.5 4Time (s)
primarymultiplenoisesum
0 0.5 1 1.5 2 2.5 3 3.5 4−0.1
−0.05
0
0.05
0.1
0.15
Time (s)
true multipleadapted multiple
Key features• fast off-line parameter selection
– realistic synthetics– varying random noise realizations– SNR-based wavelet parameter selection
• controllable redundancy allows:
– simple stable synthesis dual frame– resistance to field noise– computational efficiency balanced
•Morlet wavelet frame
– approximately analytic– sliding window processing along scales
46
810
1214
16
5
10
15
2010
12
14
16
18
20
RedundancyS/N (dB)
Med
ian
S/N
adap
t (dB
)
10
11
12
13
14
15
16
17
18
19
Complex wavelet domain adaptation
Time (s)
Sca
le
2.8 3 3.2 3.4 3.6 3.8 4 4.2
2
4
8
16
0
500
1000
1500
2000
Time (s)
Sca
le
2.8 3 3.2 3.4 3.6 3.8 4 4.2
2
4
8
16
0
500
1000
1500
2000
Time (s)
Sca
le
2.8 3 3.2 3.4 3.6 3.8 4 4.2
2
4
8
16
0
500
1000
1500
2000
Time (s)
Sca
le
2.8 3 3.2 3.4 3.6 3.8 4 4.2
2
4
8
16
0
500
1000
1500
2000
Adapted joint and individual model trace Morlet wavelet scalograms.
Unary filter estimation•Windowed adaptation: complex aopt compensates local delay/amplitude mis-
matches:
aopt = argmin{ak}(k∈K)
∥∥∥∥∥d−∑
k
akxk
∥∥∥∥∥
2
(4)
•Vector Wiener equations for complex signals:
〈d,xm〉 =∑
k
ak 〈xk,xm〉 (5)
•Time-scale synthesis:d[n] =
∑
r
∑
j,v
dvr,jψvr,j[n] (6)
Results: field data multiple filtering
Shot number
Tim
e (s
)
1200140016001800200022001.8
2
2.2
2.4
2.6
2.8
3
3.2
3.4
Shot number
Tim
e (s
)
1200140016001800200022001.8
2
2.2
2.4
2.6
2.8
3
3.2
3.4
Subtraction results: (top) model 3 (bottom) joint multi-model multiple removal.
Some multiples better attenuated around 3s, random noises reduced.
References[1] Herrmann, F. J. and D. Wang and D. J. Verschuur, 2008, Adaptive curvelet-domain
primary-multiple separation: Geophysics, 73, A17–A21.
[2] Donno, D., H. Chauris, and M. Noble, 2010, Curvelet-based multiple prediction: Geo-physics, 75, WB255–WB263.
[3] Neelamani, R., A. Baumstein, and W. S. Ross, 2010, Adaptive subtraction usingcomplex-valued curvelet transforms: Geophysics, 75, V51–V60.
[4] Jacques, L., L. Duval, C. Chaux, and G. Peyre, 2011, A panorama on multiscale geo-metric representations, intertwining spatial, directional and frequency selectivity: SignalProcess., 91, 2699–2730.
[5] Ventosa, S., H. Rabeson, P. Ricarte, and L. Duval, 2011, Complex wavelet adaptivemultiple subtraction with unary filters: Proc. EAGE Conf. Tech. Exhib.
[6] Ventosa, S., S. Le Roy, I. Huard, A. Pica, H. Rabeson, P. Ricarte, and L. Duval, 2012,Adaptive multiple subtraction with wavelet-based complex unary Wiener filters: Geo-physics, 77, V183–V192.
SEG Annual Meeting, Las Vegas, Nevada, USA, 4-9 November 2012
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