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Dimensionality Reduction for Seismic Attribute Analysis Bradley C. Wallet, Ph.D. University of Oklahoma ConocoPhillips School of Geology and Geophysics Where oil is first found is in the minds of men - Wallace Pratt Motivation Motivation

  1. Dimensionality Reduction for Seismic Attribute Analysis Bradley C. Wallet, Ph.D. University of Oklahoma ConocoPhillips School of Geology and Geophysics

  2. Where oil is first found is in the minds’ of men - Wallace Pratt

  3. Motivation

  4. Motivation

  5. Outline • Seismic data • Seismic attributes • PCA • Image grand tour • Non-linear methods • Conclusions • Acknowledgements

  6. Outline • Seismic data • Seismic attributes • PCA • Image grand tour • Non-linear methods • Conclusions • Acknowledgements

  7. Why care about seismic data? • Single pre-stack data sets can be 10’s – 100’s of terabytes in size • Provide good spatial coverage exploration area • Used to make high dollar decisions

  8. Seismic shot Courtesy of Bin Lyu

  9. Common midpoint gather

  10. Migration

  11. Convolutional model Reflection Lithology Velocity Density Impedance Wavelet Coefficients Shale ⇒ ⇒ Sand x = * Shale Sand Shale

  12. Seismic data (Elebiju et al., 2009)

  13. Outline • Seismic data • Seismic attributes • PCA • Image grand tour • Non-linear methods • Conclusions • Acknowledgements

  14. These are features

  15. From one comes many Seismic data Attribute 1 Attribute 2 Attribute 3 Attribute 4 Attribute 5 Attribute 6 Attribute 7 Attribute 8

  16. Coherence inline inline

  17. Seismic 5 km (Bahorich and Farmer, 1995)

  18. Coherence Coh 1.0 0.6 5 km salt (Bahorich and Farmer, 1995)

  19. Σ Spectral decomposition Reflectivity Synthetic CWT Magnitude Voices CWT magnitude pos 0 Le Nozze di Figaro (Matos and Marfurt, 2011)

  20. Spectral decomposition A ′ A Time (s) 30 Hz 15 Hz A A A ′ A ′ 30 Hz Map (Laughlin et al., 2002) 15 Hz Map

  21. Spectral decomposition 18 Hz  Red 24 Hz  Green 36 Hz  Blue (Bahorich et al., 2002)

  22. Dip attributes z θ (dip magnitude) φ (dip azimuth) n a θ y θ x (crossline dip) (inline dip) ψ y x (strike) (Marfurt, 2006)

  23. Dip attributes Minimum dip tested (-20 0 ) Dip with maximum coherence (+5 0 ) Analysis Point Maximum dip tested (+20 0 ) Instantaneous dip = dip with highest coherence (Marfurt et al, 1998)

  24. Dip attributes Dip Azimuth Hue 0 180 360 High Dip Magnitude Saturation 0 N 1.2 E W 1.4 S (c) (Guo et al., 2008)

  25. How do we “assimilate” all these attributes?

  26. Outline • Seismic data • Seismic attributes • PCA • Image grand tour • Non-linear methods • Conclusions • Acknowledgements

  27. PCA • Rotates attribute space • New dimensions are called principal components • Var(pc1) > Var(pc2) > … > Var(pc d) • Defines variance as information

  28. PCA (Wikapedia)

  29. Watonga survey

  30. Complex PCA

  31. Complex PCA

  32. PCA

  33. PCA

  34. PCA

  35. Outline • Seismic data • Seismic attributes • PCA • Image grand tour • Non-linear methods • Conclusions • Acknowledgements

  36. Linear projections Poorly separated Well separated Somewhat separated ξ d ∑ = α ξ proj ( ) i i = i 1

  37. The Grand Tour (1750-1880’s)

  38. Defining the tour

  39. Image Grand Tour 7.005 -6.215 10.95

  40. View Locked Color IGT

  41. Outline • Seismic data • Seismic attributes • PCA • Image grand tour • Non-linear methods • Conclusions • Acknowledgements

  42. Latent spaces

  43. Generative topographical maps a) N b) Cartoon illustration of GTM

  44. Waka 3D Canterbury Basin, offshore New Zealand 170° 30’ E 173° 00’ E 45° 30’ S 46° 30’ S (Modified from Mitchell and Neil, 2012) (Figure by Origin Energy)

  45. Seismic 36

  46. Peak Frequency

  47. Peak spectral magnitude 38

  48. Curvedness 39

  49. GLCM homogeneity 40

  50. Co-rendering 41

  51. GTM

  52. Waveforms as attributes (Wallet et al, 2009)

  53. Watonga revisited (Wallet et al, 2009)

  54. Diffusion maps Form n-by-n similarity matrix Normalize rows to sum to 1 Perform PCA on diffusion matrix

  55. Diffusion maps Advantages Disadvantages • Closed form solution • Computationally intractable for reasonable sized data sets • Direct calculation of inter-point distances • Out of training set data are not defined in mapping • Not tied to a Euclidean space • Eigenvalues

  56. Diffusion maps

  57. Outline • Seismic data • Seismic attributes • PCA • Image grand tour • Non-linear methods • Conclusions • Acknowledgements

  58. Conclusions • The human is still the best interpreter we have • Attribute overload can overwhelm interpeters • Dimensionality reduction produces highly interpretable images

  59. Acknowledgments • Prof. Kurt Marfurt (University of Oklahoma) • Mr. Victor Aarre (Schlumberger Norway Technology Center) • Mr. Tao Zhao (OU) • Dr. Marcilio de Matos (Petrobras) • CGG Veritas, Chesapeake Energy, Anadarko Petroleum, and the Government of New Zealand

  60. Acknowledgments

  61. Questions? bwallet@ou.edu http://geology.ou.edu/aaspi

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