# geometrical attributes

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Seismic Attribute Mapping of Structure and StratigraphyKurt J. Marfurt (University of Oklahoma)

Geometric Attributes

5-1

Course OutlineIntroduction Complex Trace, Horizon, and Formation Attributes Multiattribute Display Spectral Decomposition Geometric Attributes Attribute Expression of Geology Impact of Acquisition and Processing on Attributes Attributes Applied to Offset- and Azimuth-Limited Volumes Structure-Oriented Filtering and Image Enhancement Inversion for Acoustic and Elastic Impedance Multiattribute Analysis Tools Reservoir Characterization Workflows 3D Texture Analysis5-2

Volumetric dip and azimuthAfter this section you will be able to: Evaluate alternative algorithms to calculate volumetric dip and azimuth in terms of accuracy and lateral resolution, Interpret shaded relief and apparent dip images to delineate subtle structural features, and Apply composite dip/azimuth/seismic images to determine how a given reflector dips in and out of the plane of view.

5-3

Definition of reflector dipz

(dip magnitude) (dip azimuth) n a x (inline dip) y (crossline dip)

x5-4

(strike)

y

(Marfurt, 2006)

Alternative volumetric measures of reflector dip1. 3-D Complex trace analysis 2. Gradient Structure Tensor (GST) 3. Discrete scans for dip of most coherent reflector Cross correlation Semblance (variance) Eigenstructure (principal components)

5-5

1. 3-D Complex Trace Analysis (Instantaneous Dip/Azimuth)Instantaneous phase Instantaneous frequency = tan1

(d

H

Hilbert transform/d)

H d d d d t t = 2 = 2 f = 2 2 t d2 + dH

H

( )

Instantaneous in line wavenumber Instantaneous cross line wavenumber Instantaneous apparent dips5-6

kx

H d d d d x x = = 2 x d2 + dH

H

( )

ky =

= y

H d d d d y y d2 + d ky

H

( )

H 2

p =

kx

;q =

Seismic data7.5 km 1500Amp pos

Depth (m)

0

neg

4500 Vertical slice Depth slice

5-7

(Barnes, 2000)

Instantaneous Dip Magnitude7.5 km 1500Dip (deg) high

Depth (m)

0

4500 Vertical slice Depth slice

5-8

(Barnes, 2000)

The analytic traceEnvelope Quadrature Original (imaginary data (real component component) )

e(t) = {[d(t)] + [d (t)] } d(t)

2

H

2

1/2

d (t)+180

H

Phase

0 -180

(t) = tan [d (t)/d(t)]

-1

H

Frequency

Weighted average frequency

f(t) = d(t) /dt

5-9

(Taner et al, 1979)

Instantaneous Dip Magnitude (sensitive to errors in , kx and ky!)7.5 km 1500Dip (deg) high

Depth (m)

0

4500 Vertical slice Depth slice

5-10

(Barnes, 2000)

Weighted average dip(5 crossline by 5 inline by 7 sample window) 7.5 km 1500Dip (deg) high

Depth (m)

0

4500 Vertical slice Depth slice

5-11

(Barnes, 2000)

Instantaneous Azimuth7.5 km 1500Azim (deg) 360

Depth (m)

180

0

4500 Vertical slice Depth slice

5-12

(Barnes, 2000)

Weighted average azimuth(5 crossline by 5 inline by 7 sample window) 7.5 km 1500Azim (deg) 360

Depth (m)

180

0

4500 Vertical slice Depth slice

5-13

(Barnes, 2000)

2. Gradient Structure Tensor (GST) = u x u x u x u x u y u z u y u y u y u x u y u z u z u z u z u x u y u z

TGS

The eigenvector of the TGS matrix points in the direction of the maximum amplitude gradient

5-14

(Bakker et al, 2003)

3. Discrete scans for dip of most coherent reflectorMinimum dip tested (-200)

Dip with maximum coherence (+50)

Analysis Point

Maximum dip tested (+200)

Instantaneous dip = dip with highest coherence5-15

(Marfurt et al, 1998)

3-D estimate of coherence and dip/azimuth

5-16

(Marfurt et al, 1998)

Searching for dip in the presence of faultsAmp pos

Time (s)

CSingle window search

L

0

Rneg

Multi-window search

5-17

(Marfurt, 2006)

Search for the most coherent window containing the analysis point

inline crossline5-18

(Marfurt, 2006)

Search for the most coherent window containing the analysis pointcrossline Time (s)

5-19

(Marfurt, 2006)

0 A 2 km Time (s) 1 2 3 4 0 1 Time (s) 2 seismic

A

A

A Comparison of dip estimates on vertical slice

inst. Inline dip

dip (s/m) +.2 0

35-20

4

smoothed inst. Inline dip

multi-window inline dip scan

-.2 (Marfurt, 2006)

2 km Comparison of dip estimates on time slice (t=1.0 s) A seismic A inst.dip dip (s/m) +.2 0 -.2 smoothed inst. dip multi-window dip scan

5-21

(Marfurt, 2006)

Vertical Slice through Seismic5 km 0.25 0.500

B

B

Amp neg

0.75pos

Time (s)

1.00

1.25 Ellenburger 1.50 Basement? 1.755-22

Time/structure of Caddo horizon5 km B Time (s)0.70 0.75

0.80 0.85

B5-23

Dip magnitude from picked horizon5 km B Dip (s/km) 0.00

0.06

5-24

B

5 km

NS dip from picked horizonB Dip (s/km) +0.06

0.00

-0.06

5-25

B

NS dip from multi-window scan5 km B

Dip (deg) +2

0

-2

5-26

B

5 km

EW dip from picked horizonB Dip (s/km) +0.06

0.00

-0.06

5-27

B

EW dip from multi-window scan5 km B

Dip (deg) +2

0

-2

5-28

B

on a surface

on a time slice through dip and azimuth volumes

5-29

(after Barnes, 2002)

Time slices through apparent dip (t=0.8s)Dip (deg) +2

0

-2

=30 =00 0 0 =150 =120 =90 =605-30

Time slices through apparent dip (t=1.2s)

Dip (deg) +2

0

-2

=90 =60 =00 =15000 =120 =3005-31

Volumetric visualization of reflector dip and azimuthDip Azimuth Hue High Dip Magnitude Saturation 0 180 360

N

0 N

s) e( Tim

1.2 W 1.4 E

S (c)

5-32

Volumetric visualization of reflector dip and azimuthDip Azimuth Hue High1 .2s) Time (

0

180

360

1. 4

Dip Magnitude Saturation

Transparent0 NN

W

Transparent

E

S

5-33

0.0

t (s)

Towards 3-D seismic stratigraphy

divergent

convergent

divergent 1.5

convergent

5-34

(Barnes, 2002)

Volumetric Dip and AzimuthIn Summary: Dip and azimuth cubes only show relative changes in dip and azimuth, since we do not in general have an accurate time to depth conversion Dip and azimuth estimated using a vertical window in general provide more robust estimates than those based on picked horizons Dip and azimuth volumes form the basis for volumetric curvature, coherence, amplitude gradients, seismic textures, and structurally-oriented filtering Dip and azimuth will be one of the key components for future computeraided 3-D seismic stratigraphy

5-35

CoherenceAfter this section you will be able to: Summarize the physical and mathematical basis of currently available seismic coherence algorithms, Evaluate the impact of spatial and temporal analysis window size on the resolution of geologic features, Recognize artifacts due to structural leakage and seismic zero crossings, and Apply best practices for structural and stratigraphic interpretation.

5-36

Seismic Time Slice

5 km

5-37

(Bahorich and Farmer, 1995)

Coherence Time Slice

salt

5 km

5-38

(Bahorich and Farmer, 1995)

Coherence compares the waveforms of neighboring traceslin e os s cr os s lin e

inline

cr

inline

5-39

Cross correlation of 2 tracesTrace #1 lag: Shifted windows of Trace #2 -4 -2 0 +2 +4 Cross correlation

40 ms

Maximum coherence

5-40

AAA high

Time slice through average absolute amplitude

0

coh

high

Time slice through coherence (early algorithm)

low

5-41

(Bahorich and Farmer, 1995)

A

A

amp pos

Vertical slice through seismic

0

neg

Acoh high

Time slice through coherence (later algorithm)

low

5-42

A

Appearance faults perpendicular and parallel to strikeN

3 km

5-43

coherence

seismic

Alternative measures of waveform similarity cross correlation semblance, variance, and Manhattan distance eigenstructure Gradient Structural Tensors (GST)

5-44

Semblance estimate of coherenceenergy of average traces 5. coherence energy of input traces 1. Calculate energy of input traces 2. Calculate the average wavelet within the analysis window. Analysis window

t-Kt dip

3. Estimate coherent traces by their average 4. Calculate energy of average traces5-45

t+Kt

The Manhattan Distance: r=|x-x0|+|y-y0|

5-46

The as the crow flies (or Pythagorian) distance r=[(x-x0)2+(y-y0)2]/1/2

New York City Archives

Pitfall: Banding artifacts near zero crossings

8 ms

5-47

Solution: calculate coherence on the analytic trace

Coherence of real trace5-4

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