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)

Defining the tour

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? bwallet@ou.edu

http://geology.ou.edu/aaspi