Randomized sampling without repetition in timelapse seismic surveys

Size: px

Start display at page:

Download "Randomized sampling without repetition in timelapse seismic surveys"

Clyde Gibson
5 years ago
Views:

1 Randomized sampling without repetition in timelapse seismic surveys Felix Oghenekohwo SLIM University of British Columbia

2 Randomized sampling without repetition in timelapse seismic surveys Felix Oghenekohwo Team : Rajiv Kumar, Haneet Wason, Ernie Esser, Felix Herrmann SLIM University of British Columbia

Mosher, C. C., Keskula, E., Kaplan, S. T., Keys, R. G., Li, C., Ata, E.

In SEG Annual Meeting. Society of Exploration Geophysicists.

Deliberate*&*natural*randomness*in*acquisition*

3 Mosher, C. C., Keskula, E., Kaplan, S. T., Keys, R. G., Li, C., Ata, E. Z.,... & Sood, S. (, November). Compressive Seismic Imaging. In SEG Annual Meeting. Society of Exploration Geophysicists. Randomized undersampling examples from industry (ConocoPhilips) Deliberate*&*natural*randomness*in*acquisition* (thanks*to*chuck*mosher) Land / Node Compressive Sensing = Acquisition Efficiency Marine Designed Actually Acquired

4 Haneet Wason and Felix J. Herrmann, Time-jittered ocean bottom seismic acquisition! in SEG Technical Program Expanded Abstracts, 3, p. -6 Hassan Mansour, Haneet Wason, Tim T.Y. Lin, and Felix J. Herrmann, Randomized marine acquisition with compressive sampling matrices,! Geophysical Prospecting, vol. 6, p ,. Time-lapse seismic Current*acquisition*paradigm:* repeat*expensive*dense.acquisitions*&* independent.processing* compute*differences*between*baseline*&*monitor*survey(s)* hampered*by*practical*challenges*to*ensure*repetition

5 Haneet Wason and Felix J. Herrmann, Time-jittered ocean bottom seismic acquisition! in SEG Technical Program Expanded Abstracts, 3, p. -6 Hassan Mansour, Haneet Wason, Tim T.Y. Lin, and Felix J. Herrmann, Randomized marine acquisition with compressive sampling matrices,! Geophysical Prospecting, vol. 6, p ,. Time-lapse seismic Current*acquisition*paradigm:* repeat*expensive*dense.acquisitions*&* independent.processing* compute*differences*between*baseline*&*monitor*survey(s)* hampered*by*practical*challenges*to*ensure*repetition*! New*compressive*sampling*paradigm:* cheap+subsampled.acquisition,*e.g.*via*timemjittered*marine* undersampling+ may*offer*possibility*to*relax*insistence*on*repeatability. exploits*insights*from*distributed.*compressive*sensing

6 Framework Ax = b sampling matrix observed subsampled measurements Sparsity- promoting recovery x = arg min x kxk subject to Ax = b

7 Framework in 4-D subsampled baseline data A x = b A x = b subsampled monitor data should A = A? what if A A? what if A 6= A? Question : To repeat survey design or not

8 Idealized synthetic time-lapse data Baseline Monitor 4- D signal

9 Structure - curvelet representation

10 Observations Time-lapse data has structure - significant correlations 4-D signal has structure - increased sparsity Can we exploit the structure in the vintages and the difference simultaneously?

11 Dror Baron, Marco F. Duarte, Shriram Sarvotham, Michael B. Wakin, Richard G. Baraniuk. An Information-Theoretic Approach to Distributed Compressed Sensing (5)! vintages Distributed compressive sensing joint recovery model (JRM) x = z + z differences A z } { apple A A z z } 3{ A A z 4z z 5 = b z } { apple b baseline x = z + z b monitor common+component

12 Dror Baron, Marco F. Duarte, Shriram Sarvotham, Michael B. Wakin, Richard G. Baraniuk. An Information-Theoretic Approach to Distributed Compressed Sensing (5)! Distributed compressive sensing joint recovery model (JRM) vintages!! A z } { apple A A z z } 3{ b z } { apple b baseline x = z + z x = z + z!!! differences A A z 4z z 5 = b monitor common+component! Key+idea:+ use*the*fact*that*different*vintages*share*common*information* invert*for*common.components*&*differences*w.r.t.*the*common* components*with*sparse*recovery

13 Sparsity-promoting recovery Joint recovery model (JRM) z = arg min z kzk subject to Az = b Independent reconstruction x i = arg min x i kx i k subject to A i x i = b i, for i =,

14 Interpretation of the model w/ & w/o repetition! In+an+ideal+world+ (A = A ) JRM*simplifies*to*recovering*the*difference*from* expect*good*recovery*when*difference*is*sparse* but*relies*on* exact *repeatability... (b b )=A (x x )

15 Interpretation of the model w/ & w/o repetition! In+an+ideal+world+ (A = A ) JRM*simplifies*to*recovering*the*difference*from* expect*good*recovery*when*difference*is*sparse* but*relies*on* exact *repeatability...* (b b )=A (x x )! In+the+real+world++ (A 6= A ) no*absolute*control*on*surveys* calibration*errors* noise...

16 Stylized Examples

17 Sparse baseline, monitor and time-lapse signals z common component z difference z difference x baseline x monitor x x time- lapse Signal length N = 5

18 Stylized experiments! Conduct*many*CS*experiments*to*compare* joint*vs*parallel.recovery*of*signals*and*the*difference* recovery*with*completely*independent** A, A random*acquisition*with*different*numbers*of*samples**

19 Stylized experiments! Conduct*many*CS*experiments*to*compare* joint*vs*parallel.recovery*of*signals*and*the*difference* recovery*with*completely*independent** A, A random*acquisition*with*different*numbers*of*samples** A A n = n n N N b = A x b = A x

20 Stylized experiments! Conduct*many*CS*experiments*to*compare* joint*vs*parallel.recovery*of*signals*and*the*difference* recovery*with*completely*independent** A, A random*acquisition*with*different*numbers*of*samples** A A n = n n N N b = A x b = A x Run different experiments Compute Probability of recovery

21 Results: independent versus joint recovery Recovery of vintages Recovery of difference

22 Observations Joint recovery is better than independent Improved recovery of the vintages and the difference Requires fewer samples

23 With exact repetition A = A A n = A n n N N b = A x b = A x Run**different*experiments REPEAT EXPERIMENT AS BEFORE Compute*Probability*of*recovery

24 Results: independent versus joint recovery Recovery of vintages Recovery of difference

25 WITH Repetition Recovery of vintages Recovery of vintages Recovery of difference Recovery of difference

26 WITHOUT Repetition Recovery of difference Recovery of vintages Recovery of difference

27 Observations Recovery*of*vintages*themselves*improves*without+repetition. Recovery*of*difference*improves*with+repetition.because. difference.is*sparse*compared*to*sparsity*of*vintages. does*not*recover*the*vintages*themselves

28 Observations Recovery*of*vintages*themselves*improves*without+repetition. Recovery*of*difference*improves*with+repetition.because. difference.is*sparse*compared*to*sparsity*of*vintages. does*not*recover*the*vintages*themselves.! Do5the5acquisitions5really5have5to5overlap?

29 Observations Recovery*of*vintages*themselves*improves*without+repetition. Recovery*of*difference*improves*with+repetition.because. difference.is*sparse*compared*to*sparsity*of*vintages. does*not*recover*the*vintages*themselves.! Do5the5acquisitions5really5have5to5overlap? A A Overlap 4% n REPEAT EXPERIMENT AS BEFORE

30 Results: recovery and overlap dependency Recovery of vintages Recovery of difference

31 Interpretation from the stylized example Joint.recovery.model.(JRM).is.always.superior.to.the.independent.or. parallel.method.! As.the.degree.of.overlap.between.the.sampling.increases,.the. recovery.of.the.signals.gets.worse..! TimeGlapse.signal.recovery.benefits.from.some.overlap

32 Seismic example Time-jittered source in marine

z (m) 5 5 Baseline Model baseline z (m) 5 5 Monitor Model monitor Method Velocity*and*density*model* provided*by*bg,*taken*as*baseline* High*permeability*zone*identified* at*a*depth*of*~*3m*

33 z (m) 5 5 Baseline Model baseline z (m) 5 5 Monitor Model monitor Method Velocity*and*density*model* provided*by*bg,*taken*as*baseline* High*permeability*zone*identified* at*a*depth*of*~*3m* Fluid*substitution*(gas/oil*replaced* with*brine)*simulated*to*derive* monitor*velocity*model* Wavefield*simulation*to*generate* synthetic*timemlapse*data x (m) x (m) Velocity (m/s) baseline monitor 4D (difference) z (m) 3 z (m) 3 z (m) x (m) x (m) x (m)

sampling time: 4. ms receiver:.5 m source:.

34 Simulated original data time-domain finite differences Baseline Monitor 4-D signal time samples: 5 receivers: sources:! sampling time: 4. ms receiver:.5 m source:.5 m Source position (m) Source position (m) Source position (m)

35 Conventional vs. time-jittered sources undersampling ratio =, source arrays conventional jittered acquisition (for baseline) jittered acquisition (for monitor) Array Array 5 Array Array 5 Array Array Recording time (s) Recording time (s) 5 3 Recording time (s) Source position (m) Source position (m) Source position (m) shorter*acquisition*time geometry*is*not*the*same

36 Measurements undersampled and blended baseline monitor Recording time (s) 9 Recording time (s) 9 5 Receiver position (m) 5 Receiver position (m)

37 Stacked sections Original baseline Original 4-D signal CMP (km) CMP (km)

38 Stacked sections Original 4-D signal Original 4-D signal CMP (km) CMP (km)

39 Stacked sections 5% overlap in acquisition matrices Parallel (9.7 db) Joint (8. db) CMP (km) CMP (km)

40 NRMS Plot

41 Seismic example An extension to model space

42 Example : Stacking b = M H N H S H C H x M midpoint- offset } observed b = Ax N normal move- out undersampled measurements S stacking C sparsifying operator m = C H x stacked section H adjoint

43 Idealized synthetic time-lapse data Baseline Monitor 4- D signal

44 Method Acquisition Subsampled baseline and monitor data, with independent and randomly missing shots Processing Independent processing of the observed data (Parallel) Joint processing (JRM)

45 Method Acquisition Subsampled baseline and monitor data, with independent and randomly missing shots Processing Independent processing of the observed data (Parallel) Joint processing (JRM) Compare Parallel versus Joint Repeat for a partial dependence in geometry

46 Baseline recovery - % overlap in acquisition matrices Parallel residual Joint (9.6 db) (.8 db) residual

47 Monitor recovery - % overlap in acquisition matrices Parallel residual Joint (.8 db) (. db) residual

48 4-D recovery - % overlap in acquisition matrices Ideal (True) Parallel Joint (3.45 db) (7.53 db)

49 Baseline recovery - 5% overlap in acquisition matrices Parallel residual Joint (9.6 db) (9.79 db) residual

50 Monitor recovery - 5% overlap in acquisition matrices Parallel residual Joint (9.69 db) (9.8 db) residual

51 4-D recovery - 5% overlap in acquisition matrices Ideal (True) Parallel Joint (7.5 db) (8.7 db)

52 Conclusions Randomized sampling techniques can be extended to time- lapse seismic surveys and processing. Process time- lapse data jointly, not independently, in order to exploit the shared information. We can work with subsampled data, and recover densely sampled vintages and time- lapse differences. Provided we understand the physics of our model, we can safely work with subsampled data from randomized sampling ideas. TAKE HOME Think randomized sampling in seismic surveys!! It saves cost!!!

53 Acknowledgements Thank you for your attention! This work was in part financially supported by the Natural Sciences and Engineering Research Council of Canada Discovery Grant (R854) and the Collaborative Research and Development Grant DNOISE II (3754-8). This research was carried out as part of the SINBAD II project with support from the following organizations: BG Group, BGP, BP, CGG, Chevron, ConocoPhillips, ION, Petrobras, PGS, Statoil, Total SA, Sub Salt Solutions, WesternGeco, and Woodside.

Time-jittered ocean bottom seismic acquisition Haneet Wason and Felix J. Herrmann

Time-jittered ocean bottom seismic acquisition Haneet Wason and Felix J. Herrmann SLIM University of British Columbia Challenges Need for full sampling - wave-equation based inversion (RTM & FWI) - SRME/EPSI