dimensionality reduction for seismic attribute...

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