1. Passive seismic imaging
Brad Artman, Deyan Draganov
SEP115 p. 391

2. The premise The power of imaging Proof of the matter Synthetics
Big test at Valhall

3. Incident plane-wave postion(m) postion(m) time(s) depth(m)

4. Ambient Noise r1 r2 r1 r2 r1 r1 r1 r2 t twt lag brad@sep.stanford.edu
1968 Jon Claerbout, Geophysics: “The reflection seismogram from a surface source and a surface receiver is one side of the autocorrelation of the seismogram from a source at depth and the same receiver.” This idea leads to the conjecture that we could create a seismic section by correlation of traces at the surface that record arrivals from a buried source. Realizing that the correlation process removes complicated source functions that may be distributed at any time through the record we hypothesize that we can record for however long our equipment allows to collect sufficient energy.
Orange on the left cartoon is energy: plane waves and rays. It is recorded by all the receivers on the surface. But receiver 2 also records a bounce from the free surface to a subsurface reflector. We don’t know when this happens, but by correlating the traces, we move the energy to zero time, and remove the complicated wave-form that was propagating through the earth. By correlating r1 w/ all others, we build hyperbolas exactly like conventional reflection seismic data. t
twt
lag

5. postion(m) offset(m) 600 1200 100 200 300 400 0.1 5 10 lag(s) time(s)
600
1200
100
200
300
400
0.1
lag(s)
time(s)
0.3
Raw modeled passive data over a two reflector model. Choosing the trace under the red line as the “shot”, we cross-correlate it with all the others to build the shot-panel on the right. Using all the traces as a “shot”, we generate n shot-gathers from n traces. While traces expand to n-squared, the time axis is drastically shortened. The shot-gathers so generated can be migrated just like conventional reflection seismic.
Faint hyperbola at 0.1 seconds is an artifact of my poor modeling. It is the correlation of the two events with themselves. There will be an internal multiple at the same time of opposite polarity in the real world that will cancel that one out. I did not model the effects of multiples. If it’s not strong enough in real life to do so, the greater the velocity or dip contrast of the two reflectors in the shot-panel, the less well the hyperbolas will correlate.

6. postion(m) offset(m) 600 1200 -100 100 200 300 0.1 5 10 lag(s) time(s)
600
1200
-100
100
200
300
0.1
lag(s)
time(s)
0.3
Raw modeled passive data over a two reflector model. Choosing the trace under the red line as the “shot”, we cross-correlate it with all the others to build the shot-panel on the right. Using all the traces as a “shot”, we generate n shot-gathers from n traces. While traces expand to n-squared, the time axis is drastically shortened. The shot-gathers so generated can be migrated just like conventional reflection seismic.
Faint hyperbola at 0.1 seconds is an artifact of my poor modeling. It is the correlation of the two events with themselves. There will be an internal multiple at the same time of opposite polarity in the real world that will cancel that one out. I did not model the effects of multiples. If it’s not strong enough in real life to do so, the greater the velocity or dip contrast of the two reflectors in the shot-panel, the less well the hyperbolas will correlate.

7. 1200 600 postion(m) 20 25 30 time(s) 5 10 offset(m) -200 -100 100 200
1200
600
postion(m)
time(s)
offset(m)
-200
-100
100
200
0.1
lag(s)
0.3
Raw modeled passive data over a two reflector model. Choosing the trace under the red line as the “shot”, we cross-correlate it with all the others to build the shot-panel on the right. Using all the traces as a “shot”, we generate n shot-gathers from n traces. While traces expand to n-squared, the time axis is drastically shortened. The shot-gathers so generated can be migrated just like conventional reflection seismic.
Faint hyperbola at 0.1 seconds is an artifact of my poor modeling. It is the correlation of the two events with themselves. There will be an internal multiple at the same time of opposite polarity in the real world that will cancel that one out. I did not model the effects of multiples. If it’s not strong enough in real life to do so, the greater the velocity or dip contrast of the two reflectors in the shot-panel, the less well the hyperbolas will correlate.

8. 1200 600 postion(m) 20 25 30 time(s) 5 10 offset(m) -300 -200 -100 100
1200
600
postion(m)
time(s)
offset(m)
-300
-200
-100
100
0.1
lag(s)
0.3
Raw modeled passive data over a two reflector model. Choosing the trace under the red line as the “shot”, we cross-correlate it with all the others to build the shot-panel on the right. Using all the traces as a “shot”, we generate n shot-gathers from n traces. While traces expand to n-squared, the time axis is drastically shortened. The shot-gathers so generated can be migrated just like conventional reflection seismic.
Faint hyperbola at 0.1 seconds is an artifact of my poor modeling. It is the correlation of the two events with themselves. There will be an internal multiple at the same time of opposite polarity in the real world that will cancel that one out. I did not model the effects of multiples. If it’s not strong enough in real life to do so, the greater the velocity or dip contrast of the two reflectors in the shot-panel, the less well the hyperbolas will correlate.

9. The premise The power of imaging Proof of the matter Synthetics
Big test at Valhall

10. Shot-Profile Migration
I (x,s)=Σ U (w,x,s) D (w,x,s) * z z z ω
D= Source wavefield (down-going)
U= Receiver wavefield (up-going)
I= Image
Brad’s conjecture: The correlation in the imaging condition of SP migration may satisfy the correlation needed for building the shot-gathers, and thus obviating that first step. Also, the wave-equation can propagate long weird source functions just as well as short impulsive ones. So let it go, and avoid mistakes in the correlation process.
Since all geophones record the up-coming (U) and down-going (D) wave-fields, I’ll use the raw passive data for both U and D.
Down side = no reduction of time axis from the correlation process, and needs independent method to find a velocity model.
Up side= many fewer FFT’s and faster migrating 1 shot w/ n traces rather than n shots with n traces.

11. Passive Migration I (x,s)=Σ T (w,x,s) T (w,x,s)- + * z z z ω
T= Transmission (down-going)
T= Transmission (up-going) + -
I = Image
Brad’s conjecture: The correlation in the imaging condition of SP migration may satisfy the correlation needed for building the shot-gathers, and thus obviating that first step. Also, the wave-equation can propagate long weird source functions just as well as short impulsive ones. So let it go, and avoid mistakes in the correlation process.
Since all geophones record the up-coming (U) and down-going (D) wave-fields, I’ll use the raw passive data for both U and D.
Down side = no reduction of time axis from the correlation process, and needs independent method to find a velocity model.
Up side= many fewer FFT’s and faster migrating 1 shot w/ n traces rather than n shots with n traces.

12. S/N enhancement

13. The premise The power of imaging Proof of the matter Synthetics
Big test at Valhall

14. Flow model R U D T T R T= Transmssion wavefield
SP Migration
SR Migration
Passive Migration R z + U z D
z+1 + - T z T
z+1 + - R
z+1
T= Transmssion wavefield
D= Source wavefield (down-going)
U= Receiver wavefield (up-going)
R= Total refection data

15. Shot-profile datuming analogy
R = U D
R = R e
R = U D e
= U e (D e ) 1 *
+i Kz Dz
+i Kz(U) Dz + i Kz(D) Dz
+i Kz(U) Dz
-i Kz(D) Dz

16. Delft datuming

17. The premise The power of imaging Proof of the matter Synthetics
Big test at Valhall

18. S/N enhancement

19. Different runs yield slightly different illuminations sometimes if the magnitude of the sources varies a lot.
Only one reference velocity was used: notice poor focus of syncline.

20. depth
offset
position

21. The premise The power of imaging Proof of the matter Synthetics
Big test at Valhall

22. Valhall Top reservoir ~ 2500 m Water Depth ~ 70 m Area ~ 55km
OWC
2500m
12000m
Top reservoir ~ 2500 m
Water Depth ~ m 2
Area ~ km
100+ wells
Reservoir compaction
due to depletion
4.5m seafloor
since 1982

23. Receiver layout ~ 2300 4C receivers 50m x 300m spacing 35 km 2

24. Data Tide and wave-height monitoring at rig
Drill/operations noise (SWD)
Continuous recording via disc flip-flop

25. Direct migration of passive data
Rigorous foundation
Signal/noise improvement
Big test at hand: Valhall
Land test next