Geometrical Attributes

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

Geometric Attributes

5-1

Course Outline Introduction 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 Analysis 5-2

Volumetric dip and azimuth After 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 dip z

θ (dip magnitude) φ (dip azimuth) n a θx (inline dip)

x 5-4

θy (crossline dip)

ψ (strike)

y

(Marfurt, 2006)

Alternative volumetric measures of reflector dip 1. 3-D Complex trace analysis 2. Gradient Structure Tensor (GST) 3. Discrete scans for dip of most coherent reflector

5-5

•

Cross correlation

•

Semblance (variance)

•

Eigenstructure (principal components)

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

Instantaneous in line wavenumber Instantaneous cross line wavenumber Instantaneous apparent dips 5-6

φ = tan

−1

(d

Hilbert transform

H

/d)

∂H d ∂d d − d ∂φ t t ∂ ∂ = 2π ω = 2π f = 2π 2 ∂t d2 + dH

( )

kx

∂H d ∂d d − d ∂φ x x ∂ ∂ = = 2 ∂x d2 + dH

ky =

p =

H

( )

∂φ = ∂y

kx

ω

∂H d ∂d d − d ∂y ∂y

;q =

( )

d2 + d ky

ω

H 2

H

H

Seismic data 7.5 km 1500

Amp

Depth (m)

pos

0

neg

4500 Vertical slice

5-7

Depth slice

(Barnes, 2000)

Instantaneous Dip Magnitude 7.5 km 1500

Depth (m)

Dip (deg) high

0

4500 Vertical slice

5-8

Depth slice

(Barnes, 2000)

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

Envelope

2

H

2

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

1/2

d(t)

H

d (t)

Phase

+180 -1

H

φ(t) = tan [d (t)/d(t)]

0

Frequency

-180

5-9

Weighted average frequency

f(t) = dφ(t) /dt

(Taner et al, 1979)

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

Depth (m)

Dip (deg) high

0

4500 Vertical slice

5-10

Depth slice

(Barnes, 2000)

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

Depth (m)

Dip (deg) high

0

4500 Vertical slice

5-11

Depth slice

(Barnes, 2000)

Instantaneous Azimuth 7.5 km 1500

Depth (m)

Azim (deg) 360

180

0

4500 Vertical slice

5-12

Depth slice

(Barnes, 2000)

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

Depth (m)

Azim (deg) 360

180

0

4500 Vertical slice

5-13

Depth slice

(Barnes, 2000)

2. Gradient Structure Tensor (GST)

TGS

    =    

∂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

        

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 reflector Minimum dip tested (-200)

Dip with maximum coherence (+50)

Analysis Point

Maximum dip tested (+200)

Instantaneous dip = dip with highest coherence 5-15

(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 faults

Time (s)

Amp pos

C

L

0

R neg

Single window search

5-17

Multi-window search

(Marfurt, 2006)

inline

Search for the most coherent window containing the analysis point

crossline 5-18

(Marfurt, 2006)

Search for the most coherent window containing the analysis point

Time (s)

crossline

5-19

(Marfurt, 2006)

A′

0 A 2 km

A

A′ Comparison of dip estimates on vertical slice

Time (s)

1 2 3 4 0

seismic

inst. Inline dip

dip (µs/m) +.2

Time (s)

1 2

0 3

5-20

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′′

A seismic

inst.dip

dip (µs/m) +.2 0 -.2

5-21

smoothed inst. dip

multi-window dip scan

(Marfurt, 2006)

Vertical Slice through Seismic 5 km 0.25

B

B′′

Amp neg

0.50 0

0.75 Time (s)

pos

1.00

Caddo

1.25 Ellenburger 1.50 Basement? 1.75 5-22

Time/structure of Caddo horizon 5 km

B′′ Time (s) 0.70 0.75

0.80 0.85

B 5-23

Dip magnitude from picked horizon 5 km

B′′ Dip (s/km) 0.00

0.06

5-24

B

5 km

NS dip from picked horizon B′′

Dip (s/km) +0.06

0.00

-0.06

5-25

B

NS dip from multi-window scan 5 km

B′′

Dip (deg) +2

0

-2

5-26

B

5 km

EW dip from picked horizon B′′

Dip (s/km) +0.06

0.00

-0.06

5-27

B

EW dip from multi-window scan 5 km

B′′

Dip (deg) +2

0

-2

5-28

B

Shaded illumination

on a surface

5-29

on a time slice through dip and azimuth volumes

(after Barnes, 2002)

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

0

-2

000 =30 ϕ=150 =0 =60 =90 =120 5-30

Time slices through apparent dip (t=1.2s)

Dip (deg) +2

0

-2

0 0 00 ϕϕ=150 =30 =60 =90 =0 =120 5-31

Volumetric visualization of reflector dip and azimuth Dip Azimuth Hue

N

0

180

360

Dip Magnitude Saturation

High

0 N

(s) e Tim

1.2 E

W 1.4

S (c)

5-32

Volumetric visualization of reflector dip and azimuth Dip Azimuth Hue

1 .2 s) Time (

0

180

360

Dip Magnitude Saturation

High

1. 4

Transparent 0 N N

W

Transparent

S

5-33

E

0.0

divergent

t (s)

Towards 3-D seismic stratigraphy…

convergent

divergent 1.5

convergent

5-34

(Barnes, 2002)

Volumetric Dip and Azimuth In 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

Coherence After 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

5-38

5 km

(Bahorich and Farmer, 1995)

cr

cr

os s

os s

lin e

lin e

Coherence compares the waveforms of neighboring traces

inline

5-39

inline

Cross correlation of 2 traces Trace #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′′

Vertical slice through seismic

amp pos

0

neg

A coh

high

Time slice through coherence (later algorithm)

low

5-42

A′′

(Haskell et al. 1995)

Appearance faults perpendicular and parallel to strike N

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 coherence

Analysis window

energy of average traces 5. coherence≡ ≡ energy of input traces 1. Calculate energy of input traces 2. Calculate the average wavelet within the analysis window.

t-K∆t dip

3. Estimate coherent traces by their average 4. Calculate energy of average traces 5-45

t+K∆t

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 trace 5-48

Coherence of analytic trace

Eigenstructure estimate of coherence energy of coherent compt 5. coherence ≡ energy of input traces

Analysis window

2. Calculate the wavelet that 1. Calculate energy of input traces best fits the data within the analysis window.

t-K∆t dip

3. Estimate coherent compt of traces 4. Calculate energy of coherent compt of traces 5-49

t+K∆t

Eigenstructure coherence: Time slice through seismic

5-50

Eigenstructure coherence: Time slice through total energy in 9 trace, 40 ms window

scour

salt

5-51

Eigenstructure coherence: Time slice through coherent energy in 9 trace, 40 ms window

scour

salt

5-52

Eigenstructure coherence: Time slice through ratio of coherent to total energy

faults scour

salt

5-53

Coherence algorithm evolution

Seismic

Crosscorrelation Canyon

Salt

Channels

Semblance 5-54

Eigenstructure (Gersztenkorn and Marfurt, 1999)

seismic

dip scan coherence inline slice crossline slice

Comparison of Gradient Structure Tensor and dip scan eigenstructure coherence

GST coherence

time slice

5-55

(Bakker, 2003)

Coherence artifacts due to an ‘efficient’ calculation without search for structure

Coherence computed along a time slice 5-56

Coherence computed along structure

0.4 s

Seismic

0.6 s A

A′′

t (s)

0.4 0.6 0.8 0.8 s

1.0 1.2 1.4 Seismic section

1.0 s

1.2 s

5-57

1.4 s

0.4 s

Coherence without dip search

0.6 s A

A′′

t (s)

0.4 0.6 0.8 0.8 s

1.0 1.2 1.4 Coherence section

1.0 s

1.2 s

5-58

1.4 s

0.4 s

Coherence with dip search

0.6 s A

A′′

t (s)

0.4 0.6 0.8 0.8 s

1.0 1.2 1.4 Coherence section

1.0 s

1.2 s

5-59

1.4 s

Impact of lateral analysis window radius = 12.5 m

5-60

radius = 37.5 m

radius = 25 m

radius = 50 m

Impact of vertical analysis window On a stratigraphic target

Temporal aperture = 8 ms

Temporal aperture = 32 ms

On a structural target

5-61

Temporal aperture = 8 ms

Temporal aperture = 40 ms

Impact of vertical analysis window (time slice at t = 1.586 s)

+/- 6 24ms 12 ms 5-62

Impact of vertical analysis window Fault on coherence green time slice is shifted by a stronger, deeper event

Time (s)

0.5

1.0

1.5 Steeply dipping faults will not only be smeared by long coherence windows, but may appear more than once! 5-63

Time slices vs. horizon slices

Coherence time slice (better for fault and salt analysis) salt

Figure 3.45b 5 km

Coherence horizon slice (better for stratigraphic analysis) 5-64

5 km

time (ms)

Figure 3.46

Impact of height of analysis window

+32 +24 +16 +8 0 -8 -16 -24 -32

analysis window

time (ms)

5 km

5-65

+32 +24 +16 +8 0 -8 -16 -24 -32

analysis window

Coherence In summary, coherence: • Is an excellent tool for delineating geological boundaries (faults, lateral stratigraphic contacts, etc.), • Allows accelerated evaluation of large data sets, • Provides quantitative estimate of fault/fracture presence, • Often enhances stratigraphic information that is otherwise difficult to extract, • Should always be calculated along dip – either through algorithm design or by first flattening the seismic volume to be analyzed, and • Algorithms are local - Faults that have drag, are poorly migrated, or separate two similar reflectors, or otherwise do not appear locally to be discontinuous, will not show up on coherence volumes.

In general: • Stratigraphic features are best analyzed on horizon slices, • Structural features are best analyzed on time slices, and • Large vertical analysis windows can improve the resolution of vertical faults, but smears dipping faults and mixes stratigraphic features. 5-66

Volumetric curvature and reflector shape After this section you will be able to: • Use the most positive and negative curvature to map structural lineaments, • Choose the appropriate wavelength to examine rapidly varying vs. smoothly varying features of interest, • Identify domes, bowls, and other features on curvature and shape volumes, • Integrate curvature volumes with coherence and other geometric attributes, and • Choose appropriate curvature volumes for further geostatistical analysis. 5-67

Statistical measures based on vector dip • Reflector divergence and/or parallelism • angular unconformities • stratigraphic terminations? • Reflector curvature • flexures and folds • unresolved or poorly migrated faults • differential compaction • Reflector rotation • data quality • wrench faults 5-68

Sign convention for 3-D curvature attributes: Anticlinal: k > 0 Planar: k=0 Synclinal: k < 0

5-69

(Roberts, 2001)

3D Curvature and Topographic Mapping

5-70

(http://www.srs.fs.usda.gov/bentcreek)

3D Curvature and Molecular Docking

5-71

(http://en.wikipedia.org/wiki/Molecular_docking)

kneg > 0

kneg < 0 kpos < 0 kpos > 0

kpos > 0 kneg = 0

5-72

3D Curvature and Biometric Identification of Suspicious Travelers

Geometries of folded surfaces kpos < 0

kpos = 0

kpos > 0

synform

kneg < 0 saddle

bowl

antiform

kneg = 0 plane

kneg > 0 dome

5-73

(Bergbauer et al., 2003)

A multiplicity of curvature attributes! 1. Mean Curvature 2. Gaussian Curvature Measures validity of 3. Rotation quadratic surface 4. Maximum curvature Mathematical Basis Established use in 5. Minimum curvature fracture prediction 6. Most positive curvature Most useful for structural 7. Most negative Curvature interpretation 8. Dip curvature 9. Strike curvature 10. Shape index Established use in biometric 11. Curvedness ID and molecular docking 12. Shape index modulated by curvedness

See Roberts (2001) for definitions! 5-74

Curvature of picked horizons

5-75

kx-ky transform of time picks Seismic horizon -0.02

Short wavelength 50 00

x

50

(m

y

) 0 0 00 0 1

high

power

ky (cycles/m)

00 0 -2 00

Long wavelength

0

z (m)

+2

kx-ky spectrum

0.00

Footprint!

00

+0.02 -0.02

+0.00 kx (cycles/m)

+0.02

0

The horizon exhibits different scale structures such as domes and basins on the broad-scale, faults on the intermediate-scale, and smaller scale undulations. 5-76

(Bergbauer et al, 2003)

kx-ky transform of time picks after bandpass filter -0.02

high

-0.02 5-77

Long wavelength

0.00

+0.02

Short wavelength

Power

ky (cycles/m)

Short wavelength

Short wavelength

Short wavelength

+0.00 kx (cycles/m)

0

+0.02 (Bergbauer et al, 2003)

Maximum curvature after kx-ky bandpass filter kmax +5 Fa ul

ts

y (m)

5000 0

Contours

-5

0 0

5-78

5000 x (m)

10000 (Bergbauer et al, 2003)

Typical workflow for curvature calculated along picked horizons 1. pick horizon 2. smooth horizon 3. calculate curvature on tight grid for short wavelength estimates 4. smooth horizon some more 5. calculate curvature on coarse grid for long wavelength estimates

5-79

Multispectral estimates of volumetric curvature

Motivation:

• Structural Geology models relate curvature to fractures • Geologic features have different spectral lengths – short wavelength faults, moderate wavelength compaction over channels, longer wavelength domes and sags • Seismic artifacts have different spectral lengths – short wavelength footprint, moderate wavelength migration smears about faults • Current horizon-based curvature calculations are both tedious to generate and overly sensitive to picking errors • We have very accurate dip and azimuth volumes – can we use them to generate more robust curvature volumes? • Can we design x-y operators to produce results similar to Bergbauer et al.’s (2003) kx-ky transforms to avoid slicing the dip and azimuth volumes? 5-80

Radius of Curvature 3 km

Time (s)

1.0

1.2 5-81

Thermal imagery with sun-shading

5-82

(Cooper and Cowan, 2003)

Fractional derivatives with sun-shading

Red=0.75 Green=1.00 Blue=1.25

5-83

(Cooper and Cowan, 2003)

2D curvature estimates from inline dip, p: 1st derivative

dp/dx = F-1[ ikx F(p) ] fractional derivative (or 1st derivative followed by a low pass filter)

dαp/dxα ≈ F-1[i(kx )α F(p) ]

5-84

(al-Dossary and Marfurt, 2006)

“Fractional” derivatives α=1.25 α=1.00

α=1.00

α=0.75

α=0.75

α=0.50

α=0.50

α=0.25

α=0.25

α=0.01

α=0.01

0.0

-1.0

0.0 -20

0

+20

distance in grid points

convolutional operator in space 5-85

α=1.25

0.5

amp

amp

+1.0

0.00

0.25

0.50

kx wavenumber (cycles/grid point)

operator wavenumber spectrum (al-Dossary and Marfurt, 2006)

Filter applied to 1st derivative

Interpretation of ‘fractional derivative’ as a filter

ize l ea d I

3

d

0.80

2

1.00

1

Wavelength, λ 2∆x

4∆x

8∆x

16∆x

Wavenumber, k π/∆x

π/2∆x

π/4∆x

π/8∆x

32∆x π/16∆x infinite 0

0

5-86

0.25

4

ive t iva r de t s fir

(Chopra and Marfurt, 2007b)

Attributes extracted along a geological horizon

5-87

Vertical Slice – Fort Worth Basin, USA B′′ B

0.750 0.800

t (s)

Caddo

1.000

1.250

5-88

Ellenburger

(al-Dossary and Marfurt, 2006)

kmean=1/2(d2T/dx2+d2T/dy2) – Caddo (Horizon pick calculation) B′′ s/m2 -.25

0.0

+.25 5 km 5-89

B

kmean horizon slice – Caddo (volumetric calculation) B′′ s/m2 -.25

0.0

+.25 5 km 5-90

B

Coherence horizon slice – Caddo 5 km

B′′

1.0

0.9

.08

5-91

B

Attributes extracted along time slices

5-92

Vertical slice through seismic B

5 km

B′′

0.750 0.800

t (s)

Caddo

1.000

1.250

5-93

Ellenberger

(al-Dossary and Marfurt, 2006)

Time slice through coherence 5 km t=0.8 s B′′

1.0

0.9

0.8

5-94

B

(al-Dossary and Marfurt, 2006)

Most negative curvature (α=1.00) 5 km t=0.800 sB′′ s/m2 +.25

0.0

-.25

α=1.00 5-95

B

(al-Dossary and Marfurt, 2006)

Spectral estimates of most negative 5 km curvatureB′′ t=0.8 s s/m2 +.25

0.0

-.25

α=0.25 =2.00 =1.75 =1.50 =1.25 =1.00 =0.75 =0.50 5-96

B

(al-Dossary and Marfurt, 2006)

Principal component coherence 5 km t=0.8 s B′′

1.0

0.9

0.8

5-97

B

(al-Dossary and Marfurt, 2006)

Principal component coherence 5 km t=1.2 s B′′

1.0

0.9

0.8 B 5-98

(al-Dossary and Marfurt, 2006)

5 km

Most negative curvature (α=0.25) t=1.2 B′′ s

s/m2 +.25

0.0

-.25 B 5-99

(al-Dossary and Marfurt, 2006)

5 km

Most positive curvature (α=0.25) t=1.2B′′s

s/m2 -.25

0.0

+.25 5-100

B

(al-Dossary and Marfurt, 2006)

Zero-crossings are less sensitive to noise than peaks or troughs

noise pick error

signal

pick error

pick error

signal+noise

pick error

pick error

5-101

(Blumentritt et al., 2005)

Vertical slice through seismic volume showing faults having small displacement (Alberta, Canada) A 1240 ms

Neg

Pos

A’

Picked horizon

1520 ms

5-102

(Chopra and Marfurt, 2007a)

Curvature computed from a picked, filtered horizon A

A 2.5 km

A’

A’

Most-positive 5-103

Neg

0

Most-negative Pos

(Chopra and Marfurt, 2007a)

Curvature computed from volumetric dip/azimuth A

A 2.5 km

A’

A’

Most-positive 5-104

Neg

0

Most-negative Pos

(Chopra and Marfurt, 2007a)

s=-1.0

The shape index, s: bowl

k 2 + k1 s = − ATAN( ) π k 2 − k1 2

synform

s=-0.5

k1 ≥ k 2

s=0.0 saddle

Principal curvatures

antiform

s=+0.5

s=+1.0 dome

5-105

(Bergbauer et al., 2003)

Shape index and biometric identification photographic image

distance scan

Shape indices

5-106

(Woodward and Flynn, 2004)

dome

ridge

curvedness

0.2

saddle

valley

bowl

2D color table

0.0 -1.0 5-107

plane -0.5

0.0 +0.5 Shape index

+1.0

(al-Dossary and Marfurt, 2006)

Shape index modulated by curvedness 5 km (α=0.25) 5 km N

B’

Dome

Ridge

1. 4

Saddle

Valley

Bowl

e (s Tim

)

1 .2

Curvedness

0.2 B

Plane

Shape index

+1.0

0.0

+0.5

5-108

-0.5

-1.0

0.0

(Guo et al., 2007)

Shape index modulated by curvedness 5 km (α=0.25) 5 km N

B’

Dome

1. 4

Ridge

Saddle

Valley

Bowl

e (s Tim

)

1 .2

Curvedness

0.2 B

Transparent Plane

Shape index

+1.0

0.0

+0.5

5-109

-0.5

-1.0

0.0

(Guo et al., 2007)

Shape ‘components’ – an attempt to provide shape information amenable to geostatistical analysis

1.0

Filter response

bow l valle y 0.5

s addle ridge dom e

0.0 -1.0

-0.5

0.0

0.5

1.0

Shape index 5-110 Figure 3.68f

(al-Dossary and Marfurt, 2006)

Shape components (α=0.25) 5 km t=1.2 s

high

0

Ridge Dome Saddle Valley Bowl 5-111

(al-Dossary and Marfurt, 2006)

valley

‘Lineament’ attribute – an attempt to use shapes to accentuate linear features

Filter response

1.0

dome

ridge

saddle

bowl

0.5

0.0 -1.00

5-112

-0.50 0.00 Shape index

0.50

1.00

(Guo et al., 2007)

2D color bar for lineament attribute (strike=azimuth of minimum curvature) Strike 0

+90

Lineament

-90 strong

weak 5-113

(al-Dossary and Marfurt, 2006)

Valley component

Curvature lineaments colored by azimuth

-90 0.1

0.0

1.0 1.2 1.1 1.0 0.9 0.8sss s 5-114

-45

Strike 0

45

90

Volumetric view of lineament attribute (α=0.25) Strike 0

+90

Lineament

-90

transparent

5 km N

Time (s)

0.8

1.0

1.2

5-115

(Guo et al., 2007)

Example: Attribute time slices through Vinton Dome, Louisiana, USA

5-116

Coherence time slice at t=1.0 s 2km Coh 1.0

A’

0.9 N

A 5-117

0.8

Most negative curvature time slice at t=1.0 s 2km A’ +.25

0.0 N

A 5-118

-.25

Most positive curvature time slice at t=1.0 s 2km A’ -.25

0.0

A 5-119

+.25

Reflector rotation time slice at t=1.0 s 2km A’ 1.0

0.0

A 5-120

-1.0

Vertical seismic slice A

A’

0.5

Time (s)

2km

1.0

1.5 5-121

Computational vs. Interpretational curvature

Normal fault seen by curvature 5-122

Strike slip fault not seen by curvature

Computational vs. Interpretational curvature

Channel not seen by curvature Channels seen by curvature 5-123

Curvature In Summary: • Volumetric curvature extends a suite of attributes previously limited to interpreted horizons to the entire uninterpreted cube of seismic data. • The most negative and most positive curvatures appear to be the most unambiguous of the curvature images in illuminating folds and flexures. • Curvature attributes are a good indicator of paleo rather than present-day stress regimes. • Open fractures are a function of the strike of curvature lineaments and the azimuth of minimum horizontal stress. • Channels appear in curvature images if there is differential compaction. • Faults appear in curvature images if there is a change in reflector dip across the fault, reflector drag, if the fault displacement is below seismic resolution, or if the fault edge is over- or under-migrated. 5-124

Lateral Changes in Amplitude and Pattern Recognition After this section you will be able to: • Relate lateral changes in amplitude to thin bed tuning, • Identify channels and other thin stratigraphic features on amplitude gradient images, • Predict which geologic features can be seen best by amplitude gradients, textures, curvature, and coherence attributes, and • Apply best practices for stratigraphic interpretation.

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Thin bed tuning and the wedge model 0

thickness (ms)

50 0

impedance

100

Time (ms)

50

150 0 50

reflectivity

+0.1

100

Time (ms)

-0.1

150 0 50 100

Time (ms)

seismic

150

env 2

0

100 150

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Time (ms)

envelope

50

0

(Partyka, 2001)

Thin bed tuning and the wedge model

50

-0.025

40

-0.020

30 20 10 0 0

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Tuning thickness

amplitude of trough

Trough to peak thickness (ms)

Tuning thickness

10 20 30 40 50 Temporal thickness (ms)

-0.015 -0.010 -0.005 -0.000

0

10 20 30 40 50 temporal thickness (ms)

Sobel edge detector (numerical approximation to first derivative) ∂u  u ( x + ∆x) − u ( x − ∆x)  = lim   ∂x ∆x − >0  2∆x 

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