Random Sampling Compressive Sensing Acquisition Thomas Bianchi*, Kaelig Castor, Julien Cotton, Paul Hardouin (CGG) Ammar Gasim, Mehdi Tascher (ARGAS) SEG Workshop Muscat, OMAN Seismic with simultaneous sources: Where does the industry stand?
Compressive sensing test 800
Pseudo random carpet shooting
Receiver Geophones Production VP 25 m Grid Test VP
700
600
500
400
300
200
Blended acquisition
Sweep encoding with Serpentine sweep 3
300
400
500
600
700
800
Random Sampling
4
Random sampling X, Y
Regular grid
KX, KY
5
Random grid
Randomly decimated Regular grid
Test Geometrry
800
Receiver Geophones Production VP 25 m Grid Test VP
700
600
500
400
300
200
300
400
500
600
700
800
Receiver 250 x 50 m 6
Sources 25 x 25 m decimated by a factor 4
PSTM Orthogonal geometry 0 xline
TWT(s)
Ground-roll
Amplitude (dB)
inline
mean
Northing (Km)
Amplitude (dB)
mean
inline
P-waves
Easting (Km)
3
xline
TWT(s)
0
0
Amplitude (dB)
4
47
Example style for optional footer
Amplitude (dB)
Northing (Km)
0
Easting (Km)
3
PSTM Carpet Shooting geometry 0 xline
TWT(s)
Ground-roll
Amplitude (dB)
inline
mean
Northing (Km)
Amplitude (dB)
mean
inline
P-waves
Easting (Km)
3
xline
TWT(s)
0
0
Amplitude (dB)
4
48
Example style for optional footer
Amplitude (dB)
Northing (Km)
0
Easting (Km)
3
PSTM Random Carpet Shooting geometry 0 xline
TWT(s)
Ground-roll
Amplitude (dB)
inline
mean
Northing (Km)
Amplitude (dB)
mean
inline
P-waves
Easting (Km)
3
xline
TWT(s)
0
0
Amplitude (dB)
4
49
Example style for optional footer
Amplitude (dB)
Northing (Km)
0
Easting (Km)
3
Blended Acquisition
10
Blended common receiver 1 4 1 4
2
3
11
2
3
Deblending - Sparse Coding Recovery
12
3D common receiver gather
Classical Recovery in time domain
Recovery in 3D curvelet domain
Enforcing sparsity 12
(Lin and Herrmann, 2009) (Li et al, 2013)
Deblending Process
Forward Transform
Curvelet Model
13
L1 Minimization
.l
+
L2 Minimization
Residual of continuous
Deblending Process Curvelet Inverse Transform
Time domain Reflectivity Model
Convolution by groundforce
-
Restriction Curvelet Model
+
Curvelet Transform
14
L2 Minimization
L1 Minimization
Model update In the Time domain
Correlation by groundforce
Residual of continuous
Sweep Encoding
15
Serpentine sweeps Each vibrator has its own pilot sweep. Pilot sweep could change depending of the position and VP time
Modulation of the instantaneous frequency of a reference sweep Effect on the de-blending
16
Design of a Serpentine Sweep Small Modulation of the Instantaneous-Frequency For a [3-72Hz] 18s-sweep length, comparison between a classical EmphaSeis sweep and a Serpentine sweep designed with a 3dB-amplitude sine-function modulation on its amplitude spectrum. 58
80
Amplitude (dB)
56
Instantaneous Frequency (Hz)
Classical EmphaSeis Sweep Serpentine Sweep
54 52
+/- 1.5 dB 50 48 46 10
20
30 40 50 Frequency (Hz)
60
Classical EmphaSeis Sweep Serpentine Sweep
70 60 50 40 30 20 10 0 0
70
5
10 Time (s)
15
20
1
Amplitude
0.5 0 -0.5 -1 0
2
4
6
8
10 Time (s)
12
14
16
18
Design of a Serpentine Sweep Small Modulation of the Instantaneous-Frequency 18s, Classical EmphaSeis, S1
18s, Serpentine Sweep, S2 0
50 40
40 5
30 20 10
10
Time (s)
Time (s)
5
20
40 60 Frequency (Hz)
-10
15
0
Auto-Correlation (S1, S1)
7.5 5 8
105 105 100 100
109
0
95 95
9.5
90 90
10 15
85 85
9
110 0
20 40 20Frequency 40 (Hz) Frequency (Hz)
60 60
40 60 Frequency (Hz)
80
80 80
0 -9
110 110
7.5 5 8
105 105
7
Time (s) Time (s)
Time (s) Time (s)
110 110
10.5
20
Cross-Correlation (S1, S2)
-97
8.5
-0.5 -0.5 0 -1 0 -1 -10
-20
80
0
0 0
0
-10
20
0.5 0.5
10
10
-20 0
1 1
30
0 15
1.5 1.5
50
100 100
8.5
109
0
95 95
9.5
90 90
10 15
85 85
10.5
9
110 0
20 40 20Frequency 40(Hz) Frequency (Hz)
60 60
80 80
Amplitude (dB)
0
-10 -1.5 -20 -1.5 -10 -2 -30 -20
Auto-Corr(S1, S1) Auto-Corr(S1, Auto-Corr(S1, S1) Cross-Corr(S2, S1) S1) Cross-Corr(S2, S1) Cross-Corr(S2, S1)
-5 -1
0 0
5 1
10 2
-40 -30 -50 -40 -60 -50 -70 -60 -80 -10 -3
AutoCorr S1 CrossCorr(S2,S1) -2 -5 -1 0 Time (s)
1
5
2
10 3
CleanSweep on Serpentine Customs
Amplitude Spectrum
Reducing Harmonic Noise in the Sweep Bandwidth by doing 30 vibrations on a static position to reach convergence
Time vs Frequency
Zoom onTime signal 19
CleanSweep on Serpentine Customs
Amplitude Spectrum
Reducing Harmonic Noise in the Sweep Bandwidth by doing 30 vibrations on a static position to reach convergence
Time vs Frequency
Zoom onTime signal 20
CleanSweep on Serpentine Customs
Amplitude Spectrum
Reducing Harmonic Noise in the Sweep Bandwidth by doing 30 vibrations on a static position to reach convergence
Time vs Frequency
Zoom onTime signal 21
Effect of Curvelet Transform + Thresholding on Synthetic Gathers using Same Sweeps Thresholded Signal
Initial Signal
Initial Blending Noise
Thresholded Blending Noise
Same Sweeps
1% of curvelets
22
1% of curvelets
Effect of Curvelet Transform + Thresholding on Synthetic Gathers using Different Sweeps Thresholded Signal
Initial Signal
Initial Blending Noise
Thresholded Blending Noise
Different Sweeps
1% of curvelets
23
1% of curvelets
Rejected curvelet Same Sweep
Serpentine Sweep
1%
24
1%
Effect of Curvelet Transform + Thresholding on Synthetic Gathers using Same Sweeps and Different Sweeps Initial Blended Data SNR = 0 dB
Thresholded Data SNR = 5 dB
Same Sweeps
1% of curvelets
25
Thresholded Data SNR = 13 dB
Initial Blended Data SNR = 0 dB
Different Sweeps
1% of curvelets
Results
26
Data overview : blended 0
TWT(s)
2
3
4
27
Data overview : de-blended 0
TWT(s)
2
3
4
28
Data overview : Linear Noise Attenuation FK 0
TWT(s)
2
3
4
29
Single Decon
30
Deblending with 5 seconds model
31
Deblending with 10 seconds model
32
PSTM Orthogonal
33
PSTM Random sampling
34
Faults
2 x Faster
35
Conclusion Random sampling helps de-blending but adds complexity in the field Encoding Sweeps helps Random sampling should help in processing but not proven We are ready to acquire and process compressive sensing data
Faster, Better and Chea… 36
