1. Peipei Li, Tapan Mukerji
Annual Meeting 2014
Stanford Center for Reservoir Forecasting
Sensitivity analysis of pre-stack seismic inversion on facies classification
using statistical rock physics
Peipei Li, Tapan Mukerji

2. Motivation Estimate P-wave impedance (Zp) and S-wave impedance (Zs)
Zp & Zs used for facies classification combining with statistical rock physics
Large uncertainties in inversion as well as facies classification results
Understand the impact of each parameter to inversion and facies classification

3. Geological Background and Data
North Sea turbidite system
Target zone:
Heimdal Formation (Sand and shale)
Horizon: Top Heimdal
Two seismic partial stacks:
near offset (8 degrees) & far offset (26 degrees)
Two wells: well A (type well) & well B

4. Pre-stack seismic inversion - Theory
Hampson and Russell’s pre-stack inversion algorithm
𝑆 𝜃 = 𝑐 1 𝑊 𝜃 𝐷 𝐿 𝑃 + 𝑐 2 𝑊 𝜃 𝐷∆ 𝐿 𝑆 + 𝑐 3 𝑊 𝜃 𝐷 ∆𝐿 𝐷
Linear relationship assumption:
𝐿 𝑠 = 𝑘 𝐿 𝑝 + 𝑘 𝑐 +∆ 𝐿 𝑠
𝐿 𝐷 = 𝑚 𝐿 𝑝 + 𝑚 𝑐 +∆ 𝐿 𝐷

5. Input and Output Parameters for Sensitivity Analysis
Parameters to study:
𝑾 𝜽 Angle dependent wavelet
𝒄 𝟏 Zp-Zs relationship
𝒄 𝟐 Zp-Density relationship
𝒄 𝟑 Vs/Vp ratio
Initial guess Background model
5. Wells used to build the model
6. Highcut model frequency
Output response:
Pre-stack seismic inversion Seismic residual
Facies classification results Oil sand probability

6. Correlation coefficient between observed seismic and synthetic seismic
Wavelet Extraction
Ricker wavelet
Amplitude
Phase (degrees)
Amplitude
Phase (degrees)
Phase
Correlation coefficient between observed seismic and synthetic seismic
at well locations
Frequency (Hz)
Frequency (Hz)
Near offset
Far offset
Wavelet extracted from seismic using two wells
Amplitude
Phase (degrees)
Amplitude
Phase (degrees)
Frequency (Hz)
Frequency (Hz)
Near offset
Far offset

7. Zp-Zs Relationship Linear regression: ln⁡( 𝑍 𝑆 )=k ln 𝑍 𝑃 + 𝑘 𝑐
Depth(m)
ln⁡( 𝑍 𝑠 )
ln⁡( 𝑍 𝑠 )
ln⁡( 𝑍 𝑝 )
ln⁡( 𝑍 𝑝 )
K= kc=
K= kc=
Zp-Zs Relationship 1: Auto fit
Zp-Zs Relationship 2: User defined

8. Zp-Density Relationship
Linear regression:
ln⁡(𝜌)=m ln( 𝑍 𝑃 ) + 𝑚 𝑐
Depth (m)
ln⁡(𝜌)
ln⁡(𝜌)
ln⁡( 𝑍 𝑝 )
ln⁡( 𝑍 𝑝 )
m= mc=
m= mc=
Zp-Density Rlationship1: Well A
Zp-Density Rlationship2: Well A + Well B

9. Vs/Vp Ratio Default value: Vs/Vp=0.5 Median from well A : Vs/Vp =0.43
Histogram of Vs/Vp ratio of well A

10. Background Geological Model
Wells used to build the background geological model
Only well A
Both well A and well B
Vs Estimation for well B: sand and shale intervals separately
Highcut model frequency
Lower highcut frequency: 5HZ
Higher highcut frequency: 10HZ

11. Inversion Result – one example
Inverted Zp
P-Impedance
((m/s)*(g/cc))
Inverted Zs
S-Impedance
((m/s)*(g/cc))

12. Facies Classification using Statistical Rock Physics
6 parameters & 2 sets of value for each parameter
Pre-stack seismic inversion
2 6 = 64 inversion runs
Statistical rock physics
Most likely facies
Facies classification
Probability cubes
of each facies

13. Facies Identification
Depth (m)
IIb
IIc
IIa IV V
III
Gamma ray
Vp(km/s)
Vs(km/s)
Density(g/cm3)
Six facies:
IIa: Cemented clean sandstones
IIb: Uncemented clean sands
IIc: Plane-laminated sands
III: Interbedded sands and shales
IV: Silty and silt-laminated shales
V: Pure, massive shales
Three groups:
Shale
Brine sand
Oil sand

14. Building Training Data and Facies Classification
Quadratic discriminant analysis
Mahalanobis distance:
M 2 = x− μ i T ∑ −1 x− μ i Zs
X : sample vector [Zp; Zs]
μ𝒊 : vectors of means of facies i
∑ : training data covariance matrix Zp
Rock physics model used for
facies classification

15. Classification Result - one example
Facies classification at well A
Facies classification at well B
Shale overlying Heimdal formation
Heimdal top oil sand
Misclassification
shale brine sand oil sand
shale brine sand oil sand
inline
xline
Well B
Well A
Average oil sand probability over interest interval

16. Sensitivity Analysis Inverted ZP & ZS Seismic Inversion
Experimental design
Sensitivity Analysis
Statistical rock physics
64 runs
Facies Classification
Facies classification results

17. Sensitivity Analysis Result on Seismic Inversion
L1 norm of seismic residual
Zp-Zs Zp-Zs 2
Zp-ρ Zp-ρ 2
Ricker
wavelet
Extracted
Vs/Vp=0.5 Vs/Vp=0.43
Model 1 Model 2
Higher
frequency
Lower

18. Sensitivity Analysis Result on Facies Classification
L1 norm of oil sand probability
Zp-Zs Zp-Zs 2
Zp-ρ Zp-ρ 2
Ricker
wavelet
Extracted
Vs/Vp=0.5 Vs/Vp=0.43
Model 1 Model 2
Higher
frequency
Lower

19. Conclusion and Discussion
Pre-stack seismic inversion combing statistical rock physics
--- a good method for facies classification
--- large uncertainties
Seismic inversion -- most sensitive to seismic wavelet
Facies classification -- most sensitive to background model
Limitation: different parameters in other algorithms

20. Acknowledgement SCRF for supporting my research
Hampson - Russell software
Thank you for the attention

21. Inversion Result Well-inverted seismic trace comparison Well A Well B
Time (ms)
Filtered well log
Inverted seismic trace Zp Zs Zp Zs

22. Background Model- Wells used to build the geological model
Only well A is used to build geological models
Both well A and well B are used to build geological models
Estimate Vs from Vp Vs Vp Vp
Sand : Vs=0.771*Vp
Shale: Vs=0.876*Vp

23. Background Model- Highcut frequency
Lower frequency:5Hz
P-Impdeance
((m/s)*(g/cc))
Higher frequency:10Hz