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
Outline
• Seismic data • Seismic attributes • PCA • Image grand tour • Non-linear methods • Conclusions • Acknowledgements
Outline
• Seismic data • Seismic attributes • PCA • Image grand tour • Non-linear methods • Conclusions • Acknowledgements
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
Seismic shot
Courtesy of Bin Lyu
Common midpoint gather
Migration
Convolutional model
Velocity Density Impedance
= x Shale
Sand
Shale
Sand
Shale
Lithology Reflection Coefficients
⇒ * ⇒
Wavelet
Seismic data
(Elebiju et al., 2009)
Outline
• Seismic data • Seismic attributes • PCA • Image grand tour • Non-linear methods • Conclusions • Acknowledgements
These are features
From one comes many Seismic data
Attribute 2 Attribute 3 Attribute 4 Attribute 5 Attribute 6 Attribute 7 Attribute 8 Attribute 1
Coherence
inline inline
Seismic
(Bahorich and Farmer, 1995)
5 km
Coherence
(Bahorich and Farmer, 1995)
salt 5 km
1.0
0.6
Coh
Spectral decomposition Synthetic Reflectivity CWT Magnitude Voices
CWT magnitude
0
pos
(Matos and Marfurt, 2011)
Σ
Le Nozze di Figaro
Spectral decomposition
(Laughlin et al., 2002)
A
A′
15 Hz Map
A′
A
30 Hz Map
30 Hz 15 Hz A A′
Tim
e (s
)
Spectral decomposition
18 Hz Red 24 Hz Green 36 Hz Blue
(Bahorich et al., 2002)
Dip attributes
y
z
x
θy (crossline dip) θx
(inline dip)
a
φ (dip azimuth) θ (dip magnitude)
ψ (strike)
n
(Marfurt, 2006)
Dip attributes
Instantaneous dip = dip with highest coherence (Marfurt et al, 1998)
Analysis Point
Minimum dip tested (-200)
Maximum dip tested (+200)
Dip with maximum
coherence (+50)
Dip attributes Dip Azimuth Hue
180 360 0
Dip
Mag
nitu
de
Sat
urat
ion
0
High
N
E
S
W
(c)
1.2
1.4
(Guo et al., 2008)
How do we “assimilate” all these attributes?
Outline
• Seismic data • Seismic attributes • PCA • Image grand tour • Non-linear methods • Conclusions • Acknowledgements
PCA
• Rotates attribute space • New dimensions are called principal components • Var(pc1) > Var(pc2) > … > Var(pc d) • Defines variance as information
PCA
(Wikapedia)
Watonga survey
Complex PCA
Complex PCA
PCA
PCA
PCA
Outline
• Seismic data • Seismic attributes • PCA • Image grand tour • Non-linear methods • Conclusions • Acknowledgements
Linear projections
Poorly separated Somewhat separated
∑=
=d
iiiproj
1)( ξαξ
Well separated
The Grand Tour (1750-1880’s)
Image Grand Tour 7.005 10.95 -6.215
View Locked Color IGT
Outline
• Seismic data • Seismic attributes • PCA • Image grand tour • Non-linear methods • Conclusions • Acknowledgements
Latent spaces
a)
b)
N
Cartoon illustration of GTM
Generative topographical maps
Canterbury Basin, offshore New Zealand
170°
30’
E
173°
00’
E
45° 30’ S
46° 30’ S
(Figure by Origin Energy) (Modified from Mitchell and Neil, 2012)
Waka 3D
36
Seismic
Peak Frequency
38
Peak spectral magnitude
39
Curvedness
40
GLCM homogeneity
41
Co-rendering
GTM
Waveforms as attributes
(Wallet et al, 2009)
Watonga revisited
(Wallet et al, 2009)
Diffusion maps
Form n-by-n similarity matrix
Normalize rows to sum to 1
Perform PCA on diffusion matrix
Diffusion maps
Advantages • Closed form solution • Direct calculation of inter-point
distances • Not tied to a Euclidean space • Eigenvalues
Disadvantages • Computationally intractable for
reasonable sized data sets • Out of training set data are not
defined in mapping
Diffusion maps
Outline
• Seismic data • Seismic attributes • PCA • Image grand tour • Non-linear methods • Conclusions • Acknowledgements
Conclusions
• The human is still the best interpreter we have • Attribute overload can overwhelm interpeters • Dimensionality reduction produces highly interpretable images
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
Acknowledgments
Questions? [email protected]
http://geology.ou.edu/aaspi