Time-lapse filtering and improved repeatability with automatic factorial co-kriging. Thierry Coléou CGG Reservoir Services Massy

Transcription

1 Time-lapse filtering and improved repeatability with automatic factorial co-kriging. Thierry Coléou CGG Reservoir Services Massy 1

2 Outline Introduction Variogram and Autocorrelation Factorial Kriging Factorial Co-kriging Standard approach An automatic approach Application of Factorial Kriging to 3-D seismic Filtering acquisition and processing imprints Application of Factorial Co-kriging to 4-D seismic Filtering 3-D velocity cubes Pre-stack filtering for amplitude balancing 2

3 Applications of geostatistics Interpolation Building 2-D or 3-D models from wells using Kriging Integrating heterogeneous measurements Integration of well and seismic data using Co-kriging, External drift kriging, Bayesian kriging, Collocated co-kriging Reproducing spatial behaviour Stochastic modelling for uncertainty analysis and flow simulation input Filtering Factorial kriging Factorial co-kriging for multivariate spatial filtering of regularly sampled 3-D seismic data, automated for time-lapse. 3

4 Variogram and Autocorrelation Variogram Covariance 1 γ(h) = Σ[Z(x)-Z(x+h)] 2 2N 1 C(h) = Σ[(Z(x)-m)(Z(x+h)-m)] N -h 0 σ 2 γ(h) h Variance σ 2 1 = Σ[Z(x)-m] 2 N Variogram C(h) = σ 2 - γ(h) σ 2 Autocorrelation 1 A(h) = Σ[Z(x).Z(x+h)] N C(h) C(h) = m 2 +A(h) -h 0 h Covariance 4

5 1-D variogram Measure of the variability with distance average squared difference between points at a certain distance same dimension as the statistical variance related to autocorrelation Model parameters Sill (overall variability) Range (correlation length) Nugget (noise level) 5

6 2-D variogram or variogram map Measure of variability along different directions on a grid, computed along all possible directions Data 2-D variogram 1-D variograms 6

7 Outline Introduction Variogram and Autocorrelation Factorial Kriging Factorial Co-kriging Standard approach An automatic approach Application of Factorial Kriging to 3-D seismic Filtering acquisition and processing imprints Application of Factorial Co-kriging to 4-D seismic Filtering 3-D velocity cubes Pre-stack filtering for amplitude balancing 7

8 Factorial kriging: a synthetic case Geology + Stripes + Noise = a survey 1 - Variogram computation Statistically identical distributions: Same average, variance and histogram 8

9 Factorial kriging: a synthetic case Geology + Stripes + Noise = a survey 1 - Variogram computation 2 - Variogram modelling + + = 9

10 Factorial kriging: a synthetic case Geology + Stripes + Noise = a survey 1 - Variogram computation 2 - Variogram modelling 3 - Decomposition using Factorial Kriging Component 1 Component 2 Component 3 10

11 Factorial kriging Kriging point x using points α Simple kriging system Z * (x) = Σλ α Z(α) (C(αβ) )(λ α ) = (C(αx)) Factorial kriging system for component c i Similar to a Wiener filter (C(αβ) )(λ α ) = (c i (αx)) 11

12 Outline Introduction Variogram and Autocorrelation Factorial Kriging Factorial Co-kriging Standard approach An automatic approach Application of Factorial Kriging to 3-D seismic Filtering acquisition and processing imprints Application of Factorial Co-kriging to 4-D seismic Filtering 3-D velocity cubes Pre-stack filtering for amplitude balancing 12

13 A 4D synthetic example Geology + Stripes + Noise = Survey #1 Geology + Stripes + Noise = Survey #2 13

14 Standard filtering moving average Survey #1 Parallel processing Survey #2 Smears the acquisition imprint: visible on 4D differences 14

15 Factorial kriging Survey #1 Parallel processing Variogram 1 modelling Variogram 2 modelling Survey #2 15

16 Factorial co-kriging Survey #1 Joint processing Variograms 1&2 modelling Cross variogram modelling Survey #2 Efficient removal of acquisition imprints 16

17 Automatic factorial co-kriging Survey #1 Processing-friendly no modelling no parameters Survey #2 Common part automatically extracted from both surveys 17

18 Automatic factorial co-kriging γ 12 Survey #1 γ 1 γ 2 γ 1 - γ 12 γ 2 - γ 12 Processing-friendly no modelling no parameters Survey #2 Stripes are spatially uncorrelated. 18

19 Automatic factorial co-kriging Co-kriging point x using points α Z * (x) = Σλ 1α Z 1 (α) + Σλ 2α Z 2 (α) Factorial co-kriging system for common component ( C 11 )( )=( ) (αβ) C 12 (αβ) λ 1α C 12 (αx) C 12 (αβ) C 22 (αβ) λ 2α C 12 (αx) 19

20 Seismic vs. Geology Original measurement vs. known feature 20

21 Seismic vs. Geology Standard filtering 21

22 Seismic vs. Geology Factorial kriging (one survey) 22

23 Seismic vs. Geology Factorial co-kriging (two surveys) 23

24 Outline Introduction Variogram and Autocorrelation Factorial Kriging Factorial Co-kriging Standard approach An automatic approach Application of Factorial Kriging to 3-D seismic Filtering acquisition and processing imprints Application of Factorial Co-kriging to 4-D seismic Filtering 3-D velocity cubes Pre-stack filtering for amplitude balancing 24

25 3-D land acquisition imprints RMS amplitude map over a time window 25

26 3-D marine data: input section 26

27 3-D marine data: output section 27

28 Outline Introduction Variogram and Autocorrelation Factorial Kriging Factorial Co-kriging Standard approach An automatic approach Application of Factorial Kriging to 3-D seismic Filtering acquisition and processing imprints Application of Factorial Co-kriging to 4-D seismic Filtering 3-D velocity cubes Pre-stack filtering for amplitude balancing 28

29 3-D velocity co-filtering Survey 1 Common part Survey 2 29

30 Pre-stack factorial co-kriging offset 01 offset 03 30

31 Pre-stack filtering for time-lapse From RMS amplitude map over a time window for one offset Variograms cross 98-cross Not to scale 01-cross Not to scale 31

32 Pre-stack filtering for time-lapse Correlation between surveys vs. offset Correlation between surveys 0,80 Correlation Coefficient 0,75 0,70 0,65 0,60 0,55 0, Offset Rho 32

33 Pre-stack filtering for time-lapse RMS amplitude variation coefficient (dispersion) vs. offset 0,35 Variation Coefficient 0,25 0,15 0, Offset Survey1 Survey2 AFACK 33

34 What happens to 4-D signature? Post-stack automatic Factorial Co-kriging. RMS amplitude and Time filtering. Difference before Difference after 34

35 Conclusions Balancing surveys Extraction of a common part, a better candidate for a reference than any of the surveys Removing spatially uncorrelated variations Reducing random noise and organised noise level Removing spatially organised but uncorrelated variations Providing spatial repeatability measurement An efficient algorithm Automated, applicable to large pre-stack data sets Not limited to 2-D maps (e.g. 3-D velocity cubes) Not limited to 2 vintages A CGG patented process targeted to 4-D 35