Download - Geometrical Attributes
5-1
Seismic Attribute Mapping of Structure Seismic Attribute Mapping of Structure
and Stratigraphy and Stratigraphy
Geometric AttributesGeometric Attributes
Kurt J. Marfurt (University of Oklahoma)Kurt J. Marfurt (University of Oklahoma)
5-2
Course OutlineCourse Outline
IntroductionIntroduction
Complex Trace, Horizon, and Formation AttributesComplex Trace, Horizon, and Formation Attributes
Multiattribute DisplayMultiattribute Display
Spectral DecompositionSpectral Decomposition
Geometric AttributesGeometric Attributes
Attribute Expression of GeologyAttribute Expression of Geology
Impact of Acquisition and Processing on AttributesImpact of Acquisition and Processing on Attributes
Attributes Applied to OffsetAttributes Applied to Offset-- and Azimuthand Azimuth--Limited VolumesLimited Volumes
StructureStructure--Oriented Filtering and Image EnhancementOriented Filtering and Image Enhancement
Inversion for Acoustic and Elastic ImpedanceInversion for Acoustic and Elastic Impedance
Multiattribute Analysis ToolsMultiattribute Analysis Tools
Reservoir Characterization WorkflowsReservoir Characterization Workflows
3D Texture Analysis3D Texture Analysis
5-3
Volumetric dip and azimuthVolumetric 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.
5-4
y
z
x
θθθθy
(crossline dip)θθθθx
(inline dip)
a
φφφφ (dip azimuth)
θθθθ (dip magnitude)
ψ(strike)
n
Definition of reflector dipDefinition of reflector dip
(Marfurt, 2006)
5-5
Alternative volumetric measures of Alternative volumetric measures of
reflector dipreflector dip
1. 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)
5-6
1. 31. 3--D Complex Trace Analysis D Complex Trace Analysis
(Instantaneous Dip/Azimuth)(Instantaneous Dip/Azimuth)
( )
( )
( )
ωω
φ
φ
πφ
ππω
φ
yx
H
HH
y
H
HH
x
H
HH
H
kq
kp
dd
dy
dd
y
d
yk
dd
dx
dd
x
d
xk
dd
dt
dd
t
d
tf
dd
==
+
∂
∂−
∂
∂
=∂
∂=
+
∂
∂−
∂
∂
=∂
∂=
+
∂
∂−
∂
∂
=∂
∂==
= −
;
222
)/(tan
22
22
22
1Instantaneous phase
Instantaneous frequency
Instantaneous in line wavenumber
Instantaneous cross line wavenumber
Instantaneous apparent dips
Hilbert transform
5-7 (Barnes, 2000)
Seismic dataSeismic data
1500
4500
De
pth
(m
)
neg
pos
Amp
0
7.5 km
Vertical slice Depth slice
5-8 (Barnes, 2000)
Instantaneous Dip MagnitudeInstantaneous Dip Magnitude
1500
4500
De
pth
(m
)
7.5 km
Vertical slice Depth slice
0
high
Dip (deg)
5-9 (Taner et al, 1979)
The analytic traceThe analytic traceO
rig
ina
l d
ata
(re
al
co
mp
on
en
t)F
req
ue
nc
y
Qu
ad
ratu
re
(im
ag
ina
ry
co
mp
on
en
t)
Ph
as
e
-180
+180
0
Weighted average
frequency
Envelope
d(t)
f(t) = dφφφφ(t) /dt
dH(t)
e(t) = {[d(t)]2
+ [dH(t)]
2}
1/2
φφφφ(t) = tan-1
[dH(t)/d(t)]
5-10 (Barnes, 2000)
Instantaneous Dip MagnitudeInstantaneous Dip Magnitude
(sensitive to errors in (sensitive to errors in ωωωωωωωω, k, kxx and and kkyy!)!)
1500
4500
De
pth
(m
)
7.5 km
Vertical slice Depth slice
0
high
Dip (deg)
5-11 (Barnes, 2000)
1500
4500
De
pth
(m
)
7.5 km
Vertical slice Depth slice
0
high
Dip (deg)
Weighted average dipWeighted average dip
(5 crossline by 5 inline by 7 sample window)(5 crossline by 5 inline by 7 sample window)
5-12
0
180
360
Azim(deg)
(Barnes, 2000)
Instantaneous AzimuthInstantaneous Azimuth
1500
4500
De
pth
(m
)
7.5 km
Vertical slice Depth slice
5-13
0
180
360
Azim(deg)
(Barnes, 2000)
1500
4500
De
pth
(m
)
7.5 km
Vertical slice Depth slice
Weighted average azimuthWeighted average azimuth
(5 crossline by 5 inline by 7 sample window)(5 crossline by 5 inline by 7 sample window)
5-14
2. Gradient Structure Tensor (GST)2. Gradient Structure Tensor (GST)
(Bakker et al, 2003)
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
=
z
u
z
u
z
u
y
u
z
u
x
u
y
u
z
u
y
u
y
u
y
u
x
u
x
u
z
u
x
u
y
u
x
u
x
u
GST
The eigenvector of the TGS matrix points in the direction of the
maximum amplitude gradient
5-15
3. Discrete scans for dip of most 3. Discrete scans for dip of most
coherent reflectorcoherent reflector
Instantaneous dip = dip with highest coherenceInstantaneous dip = dip with highest coherence
(Marfurt et al, 1998)(Marfurt et al, 1998)
Analysis PointAnalysis Point
Minimum dip tested (Minimum dip tested (--202000))
Maximum dip tested (+20Maximum dip tested (+2000))
Dip with Dip with
maximum maximum
coherence coherence
(+5(+500))
5-16
33--D estimate of coherence and dip/azimuthD estimate of coherence and dip/azimuth
(Marfurt et al, 1998)
5-17
Tim
e (
s)
CL R
Searching for dip in the presence of faultsSearching for dip in the presence of faults
Single window search
Multi-window search
(Marfurt, 2006)
pos
Amp
0
neg
5-18
crossline
inlin
e
Search for the most coherent window Search for the most coherent window
containing the analysis pointcontaining the analysis point
(Marfurt, 2006)
5-19
crossline
Tim
e (
s)
Search for the most coherent window Search for the most coherent window
containing the analysis pointcontaining the analysis point
(Marfurt, 2006)
5-20
dip
(µs/m)
+.2
0
-.2
(Marfurt, 2006)
0
1
2
3
4
Tim
e (
s)
A A′
0
1
2
3
4
Tim
e (
s)
A A′
seismic inst. Inline dip
multi-window inline dip scan
smoothed inst. Inline dip
2 kmComparison Comparison
of dip of dip
estimates estimates
on vertical on vertical
sliceslice
5-21
dip
(µs/m)
+.2
0
-.2
(Marfurt, 2006)
A A′′′′
2 km
seismic inst.dip
multi-window dip scan
smoothed inst. dip
Comparison Comparison
of dip of dip
estimates on estimates on
time slicetime slice
(t=1.0 s)(t=1.0 s)
5-22
B B′′′′5 km
Caddo
Ellenburger
Basement?
pos
Amp
0
neg
Tim
e (
s)
0.75
1.00
1.25
0.50
1.50
1.75
0.25
Vertical Slice through SeismicVertical Slice through Seismic
5-23
0.80
Time (s)
0.75
0.70
0.85
B
B′′′′5 kmTime/structure of Caddo horizonTime/structure of Caddo horizon
5-24
0.06
Dip (s/km)
0.00
B
B′′′′5 kmDip magnitude from picked horizonDip magnitude from picked horizon
5-25B
B′′′′5 kmNS dip from picked horizonNS dip from picked horizon
-0.06
Dip (s/km)
0.00
+0.06
5-26B
B′′′′5 km
NS dip from multiNS dip from multi--window scanwindow scan
-2
Dip (deg)
0
+2
5-27B
B′′′′5 kmEW dip from picked horizonEW dip from picked horizon
-0.06
Dip (s/km)
0.00
+0.06
5-28B
B′′′′5 km
EW dip from multiEW dip from multi--window scanwindow scan
-2
Dip (deg)
0
+2
5-29
Shaded illuminationShaded illumination
on a surface on a time slice through dip and azimuth volumes
(after Barnes, 2002)
5-30
-2
Dip (deg)
0
+2
ϕϕϕϕ=00ϕϕϕϕ=300ϕϕϕϕ=600ϕϕϕϕ=900ϕϕϕϕ=1200ϕϕϕϕ=1500
Time slices through apparent dip Time slices through apparent dip
(t=0.8s)(t=0.8s)
5-31
ϕϕϕϕ=00ϕϕϕϕ=300ϕϕϕϕ=600ϕϕϕϕ=900ϕϕϕϕ=1200ϕϕϕϕ=1500
Time slices through apparent dip Time slices through apparent dip
(t=1.2s)(t=1.2s)
-2
Dip (deg)
0
+2
5-32
Dip Azimuth
Hue
180 3600
Dip
Ma
gn
itud
e
Sa
tura
tion
0
High
N
E
S
W
(c)
Volumetric visualization of Volumetric visualization of
reflector dip and azimuthreflector dip and azimuth
1.2
1.4Tim
e (s)
N
5-33
N
E
S
W Transparent
Dip Azimuth
Hue
180 3600
Dip
Ma
gn
itud
e
Sa
tura
tion
0
High
Transparent
Volumetric visualization of Volumetric visualization of
reflector dip and azimuthreflector dip and azimuth
1.2
Tim
e (
s)
N
1.4
5-34
divergent
convergent
0.0
1.5
t (s
)
convergent
divergent
(Barnes, 2002)
Towards 3Towards 3--D D
seismic seismic
stratigraphystratigraphy……
5-35
Volumetric Dip and AzimuthVolumetric 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 computer-aided 3-D seismic stratigraphy
5-36
CoherenceCoherence
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.
5-37
Seismic Time SliceSeismic Time Slice
(Bahorich and Farmer, 1995)
5 km
5-38
Coherence Time SliceCoherence Time Slice
(Bahorich and Farmer, 1995)
saltsalt5 km
5-39
inline
cross
line
inline
cross
line
Coherence compares the waveforms of Coherence compares the waveforms of
neighboring tracesneighboring traces
5-40
40 ms
Trace #1Shifted windows
of Trace #2
Crosscorrelationlag:
Cross correlation of 2 tracesCross correlation of 2 traces
- 4 -2 0 +2 +4
Maximum coherence
5-41
Time slice through Time slice through
coherencecoherence
(early algorithm)(early algorithm)
Time slice through Time slice through
average absolute average absolute
amplitudeamplitude
(Bahorich and Farmer, 1995)
0
high
AAA
low
highcoh
5-42
Vertical slice through Vertical slice through
seismicseismic
A A′′′′
A
low
highcoh
neg
pos
0
amp
Time slice through Time slice through
coherencecoherence
(later algorithm)(later algorithm)
A′′′′ (Haskell et al. 1995)
5-43
N
3 km
coherence seismic
Appearance faultsAppearance faults perpendicular perpendicular andand parallel parallel to striketo strike
5-44
Alternative measures of waveform Alternative measures of waveform
similaritysimilarity
• cross correlation
• semblance, variance, and Manhattan distance
• eigenstructure
• Gradient Structural Tensors (GST)
5-45
An
aly
sis
w
ind
ow
dip
Semblance estimate of coherenceSemblance estimate of coherence
t+K∆∆∆∆t
t-K∆∆∆∆t
2. Calculate the average wavelet within the analysis window.
1. Calculate energy of input traces
4. Calculate energy of average traces
energy of average traces
energy of input traces5. coherence≡≡≡≡
3. Estimate coherent traces by their average
5-46
The ‘Manhattan Distance’: r=|x-x0|+|y-y0|
The ‘as the crow flies’ (or Pythagorian) distance’r=[(x-x0)
2+(y-y0)2]/1/2
New York City Archives
5-47
8 ms
Pitfall: Banding artifacts near zero crossingsPitfall: Banding artifacts near zero crossings
5-48
Solution: calculate coherence on the analytic Solution: calculate coherence on the analytic
tracetrace
Coherence of real trace Coherence of analytic trace
5-49
An
aly
sis
w
ind
ow
dip
Eigenstructure estimate of coherenceEigenstructure estimate of coherence
t+K∆∆∆∆t
t-K∆∆∆∆t
2. Calculate the wavelet that best fits the data within the
analysis window.
1. Calculate energy of input traces
4. Calculate energy of coherent compt of traces
energy of coherent compt
energy of input traces5. coherence ≡≡≡≡
3. Estimate coherent compt of traces
5-50
Eigenstructure coherence:Eigenstructure coherence:Time slice through seismicTime slice through seismic
5-51
Eigenstructure coherence:Eigenstructure coherence:Time slice through total energy in 9 trace, 40 ms windowTime slice through total energy in 9 trace, 40 ms window
saltsalt
scourscour
5-52
Eigenstructure coherence:Eigenstructure coherence:Time slice through coherent energy in 9 trace, 40 ms windowTime slice through coherent energy in 9 trace, 40 ms window
saltsalt
scourscour
5-53
Eigenstructure coherence:Eigenstructure coherence:Time slice through ratio of coherent to total energy Time slice through ratio of coherent to total energy
saltsalt
scourscour
faultsfaults
5-54
Canyon
Salt
Seismic Crosscorrelation
EigenstructureSemblance(Gersztenkorn and Marfurt, 1999)
Channels
Coherence Coherence
algorithm algorithm
evolutionevolution
5-55
inlin
e
slic
ec
ros
slin
e
slic
etim
e
slic
e
seismicGST
coherencedip scan
coherence
Comparison of Comparison of
Gradient Gradient
Structure Tensor Structure Tensor
and dip scan and dip scan
eigenstructureeigenstructure
coherencecoherence
(Bakker, 2003)
5-56
Coherence computed along a time slice
Coherence computed along structure
Coherence artifacts due to an Coherence artifacts due to an ‘‘efficientefficient’’
calculation without search for structurecalculation without search for structure
5-57
0.4 s
0.6 s
0.8 s
1.0 s
1.2 s
1.4 s
Seismic section
0.8
0.6
1.0
0.4
1.2
1.4
t (s
)
A A′′′′
SeismicSeismic
5-58
0.4 s
0.6 s
0.8 s
1.0 s
1.2 s
1.4 s
Coherence section
0.8
0.6
1.0
0.4
1.2
1.4
t (s
)
A A′′′′
Coherence Coherence
without dip without dip
searchsearch
5-59
0.4 s
0.6 s
0.8 s
1.0 s
1.2 s
1.4 s
Coherence section
0.8
0.6
1.0
0.4
1.2
1.4
t (s
)
A A′′′′
Coherence Coherence
with dip with dip
searchsearch
5-60
radius = 12.5 m radius = 25 m
radius = 37.5 m radius = 50 m
Impact of Impact of
lateral analysis lateral analysis
windowwindow
5-61
Temporal aperture = 8 ms
Temporal aperture = 32 ms
Temporal aperture = 8 ms
Temporal aperture = 40 ms
Impact of vertical analysis windowImpact of vertical analysis window
On a stratigraphic
target
On a structural
target
5-62
Impact of vertical analysis windowImpact of vertical analysis window(time slice at (time slice at t =t = 1.586 s)1.586 s)
+/- 24 ms+/- 12 ms+/- 6 ms
5-63
0.5
1.5
1.0
Tim
e (
s)
Fault on coherence green time slice is shifted by a stronger, deeper event
Steeply dipping faults will not only be smeared by long coherence windows, but may appear more than once!
Impact of vertical analysis windowImpact of vertical analysis window
5-64
5 km
Coherence Coherence
horizon slicehorizon slice
(better for (better for
stratigraphic stratigraphic
analysis)analysis)
Coherence time Coherence time
sliceslice
(better for fault (better for fault
and salt analysis)and salt analysis)
Time Time
slices vs. slices vs.
horizon horizon
slicesslices
Figure 3.45b
salt
5-65
00+8+8
+24+24+16+16
+32+32
--88--1616--2424--3232
tim
e (
ms
)ti
me
(m
s)
analysis windowanalysis window
5 km
Figure 3.46
Impact of Impact of
height of height of
analysis analysis
windowwindow
5 km
00+8+8
+24+24+16+16
+32+32
--88--1616--2424--3232
tim
e (
ms
)ti
me
(m
s)
analysis window
5-66
CoherenceCoherence
In summary, 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: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.
5-67
Volumetric curvature and reflector shapeVolumetric 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.
5-68
Statistical measures based on vector dipStatistical 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
5-69
Sign convention for 3Sign convention for 3--D curvature attributes:D curvature attributes:Anticlinal: k > 0Planar: k = 0Synclinal: k < 0
(Roberts, 2001)
5-70
3D Curvature and Topographic Mapping3D Curvature and Topographic Mapping
(http://www.srs.fs.usda.gov/bentcreek)
5-71
3D Curvature and Molecular Docking3D Curvature and Molecular Docking
(http://en.wikipedia.org/wiki/Molecular_docking)
5-72
3D Curvature 3D Curvature
and Biometric and Biometric
Identification Identification
of Suspiciousof Suspicious
TravelersTravelerskpos> 0
kneg > 0kneg < 0
kpos < 0
kpos > 0
kneg = 0
5-73
kpos < 0 kpos = 0 kpos > 0
kneg = 0
kneg > 0
kneg < 0bowl
plane
synform
saddle
antiform
dome
(Bergbauer et al., 2003)
Geometries of folded surfacesGeometries of folded surfaces
5-74
A multiplicity of curvature attributes!A multiplicity of curvature attributes!
1. Mean Curvature2. Gaussian Curvature3. Rotation4. Maximum curvature5. Minimum curvature6. Most positive curvature7. Most negative Curvature8. Dip curvature9. Strike curvature10.Shape index11.Curvedness12.Shape index modulated by curvedness
See Roberts (2001) for definitions!
Most useful for structural interpretation
Established use in fracture prediction
Established use in biometric ID and molecular docking
Mathematical Basis
Measures validity of quadratic surface
5-75
Curvature of picked horizonsCurvature of picked horizons
5-76
The horizon exhibits different scale structures such as domes and basins
on the broad-scale, faults on the intermediate-scale, and smaller scale undulations.
Seismic horizon
(Bergbauer et al, 2003)
x (m)
5000
1000
0
0
y
0
5000
-200
+200
0
z (
m)
kx-ky spectrum
kx (cycles/m)
ky
(cyc
les
/m)
0.00
-0.02
+0.02+0.00 +0.02-0.02
po
we
r
0
high
Footprint!
kxkx--ky transform of time picksky transform of time picks
Long wavelength
Short wavelength
5-77 (Bergbauer et al, 2003)kx (cycles/m)
ky
(cyc
les
/m)
0.00
-0.02
+0.02
+0.00 +0.02-0.02
Po
wer
0
high
kxkx--ky transform of time picks after bandpass filterky transform of time picks after bandpass filter
Long wavelength
Short wavelength Short wavelength
Short wavelength Short wavelength
5-78
Maximum curvature after kMaximum curvature after kxx--kkyy bandpass filterbandpass filter
(Bergbauer et al, 2003)
x (m)
0 100005000
0
5000
y (
m)
kmax
-5
+5
0
Contours
Faults
5-79
Typical workflow for curvature Typical workflow for curvature
calculated along picked horizonscalculated along picked horizons
1. 1. pick horizonpick horizon
2. smooth horizon2. smooth horizon
3. calculate curvature on tight grid for short 3. calculate curvature on tight grid for short
wavelength estimateswavelength estimates
4. smooth horizon some more4. smooth horizon some more
5. calculate curvature on coarse grid for 5. calculate curvature on coarse grid for
long wavelength estimateslong wavelength estimates
5-80
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?
Multispectral estimates of volumetric Multispectral estimates of volumetric
curvaturecurvature
5-81
Radius of Curvature Radius of Curvature 3 km
1.0
1.2
Tim
e (
s)
5-82 (Cooper and Cowan, 2003)
Thermal imagery with sunThermal imagery with sun--shadingshading
5-83 (Cooper and Cowan, 2003)
Fractional derivatives with sunFractional derivatives with sun--shadingshading
Red=0.75 Green=1.00Blue=1.25
5-84
2D curvature estimates from inline dip, p:2D curvature estimates from inline dip, p:
dp/dx = F-1[ ikx F(p) ]
fractional derivative(or 1st derivative followed by a low pass filter)
dααααp/dxαααα ≈≈≈≈ F-1[i(kx )αααα F(p) ]
1st derivative
(al-Dossary and Marfurt, 2006)
5-85
““FractionalFractional”” derivativesderivatives
distance in grid points
am
p
-1.0
+1.0
-20 +200
αααα=1.00
αααα=0.75
αααα=0.50
αααα=0.25
αααα=0.01
αααα=1.25
0.0
kx wavenumber (cycles/grid point) a
mp
0.0
0.5
0.00 0.500.25
αααα=1.00
αααα=0.75
αααα=0.50
αααα=0.25
αααα=0.01
αααα=1.25
convolutional operator in space
operator wavenumber spectrum
(al-Dossary and Marfurt, 2006)
5-86
Interpretation of Interpretation of ‘‘fractional derivativefractional derivative’’ as a filteras a filter
2∆
x
4∆
x
8∆
x
16
∆x
32
∆x
infin
ite
0
1
2
3
4
Wavelength, λ
Filt
er
applie
d t
o 1
stderivative
0.25
0.80
Idealiz
ed firs
t deriv
ative
Wavenumber, k
π/∆
x
π/2
∆x
π/4
∆x
π/1
6∆
x
π/8
∆x
0
1.00
(Chopra and Marfurt, 2007b)
5-87
Attributes extracted along a geological horizonAttributes extracted along a geological horizon
5-88
Caddo
Ellenburger
0.800
B B′′′′t
(s)
0.750
1.000
1.250
Vertical Slice Vertical Slice –– Fort Worth Basin, USAFort Worth Basin, USA
(al-Dossary and Marfurt, 2006)
5-89
kkmeanmean=1/2(d=1/2(d22T/dxT/dx22++dd22T/dyT/dy2)2) –– CaddoCaddo
(Horizon pick calculation)(Horizon pick calculation)
B
B′′′′
5 km
+.25
s/m2
0.0
-.25
5-90
5 km
+.25
s/m2
0.0
-.25
kkmeanmean horizon slice horizon slice –– CaddoCaddo
(volumetric calculation)(volumetric calculation)
B
B′′′′
5-91
.08
0.9
1.0
Coherence horizon slice Coherence horizon slice –– CaddoCaddo
B
B′′′′5 km
5-92
Attributes extracted along time slicesAttributes extracted along time slices
5-93
Caddo
Ellenberger
0.800
B B′′′′t
(s)
0.750
1.000
1.250
Vertical slice through seismicVertical slice through seismic
(al-Dossary and Marfurt, 2006)
5 km
5-94
Time slice through coherenceTime slice through coherence
t=0.8 st=0.8 s
1.0
0.9
0.8
(al-Dossary and Marfurt, 2006)B
B′′′′5 km
5-95
Most negative curvature (Most negative curvature (αααααααα=1.00)=1.00)
t=0.800 st=0.800 s
-.25
s/m2
0.0
+.25
αααα=1.00
5 km
(al-Dossary and Marfurt, 2006)B
B′′′′
5-96
Spectral estimates of most negative Spectral estimates of most negative
curvature t=0.8 scurvature t=0.8 s
-.25
s/m2
0.0
+.25
(al-Dossary and Marfurt, 2006)
αααα=2.00αααα=1.75αααα=1.50αααα=1.25αααα=1.00αααα=0.75αααα=0.50αααα=0.25
5 km
B
B′′′′
5-97
Principal component coherencePrincipal component coherence
t=0.8 st=0.8 s
1.0
0.9
0.8
5 km
(al-Dossary and Marfurt, 2006)B
B′′′′
5-98
Principal component coherencePrincipal component coherence
t=1.2 st=1.2 s
1.0
0.9
0.8
(al-Dossary and Marfurt, 2006)
5 km
B
B′′′′
5-99
Most negative curvature (Most negative curvature (αααααααα=0.25)=0.25)
t=1.2 st=1.2 s
(al-Dossary and Marfurt, 2006)
+.25
-.25
s/m2
0.0
5 km
B
B′′′′
5-100
-.25
+.25
s/m2
0.0
Most positive curvature (Most positive curvature (αααααααα=0.25)=0.25)
t=1.2 st=1.2 s
(al-Dossary and Marfurt, 2006)
5 km
B
B′′′′
5-101
ZeroZero--crossings are less sensitive to crossings are less sensitive to
noise than peaks or troughsnoise than peaks or troughs
(Blumentritt et al., 2005)(Blumentritt et al., 2005)
pick errorpick error
noisenoise
signalsignal
signal+noisesignal+noise
pick errorpick error
pick errorpick error
pick errorpick error
pick errorpick error
5-102
AA AA’’NegNeg PosPos1240 ms1240 ms
1520 ms1520 ms
Vertical slice through seismic volume Vertical slice through seismic volume
showing faults having small displacementshowing faults having small displacement
(Alberta, Canada)(Alberta, Canada)
(Chopra and Marfurt, 2007a)
Picked horizon
5-103 (Chopra and Marfurt, 2007a)
AA
AA’’
NegNeg PosPos00
2.5 km2.5 km
AA
AA’’
Curvature computed from a picked, filtered horizonCurvature computed from a picked, filtered horizon
Most-positive Most-negative
5-104 (Chopra and Marfurt, 2007a)
AA
AA’’
NegNeg PosPos00
2.5 km2.5 km
AA
AA’’
Curvature computed from volumetric dip/azimuthCurvature computed from volumetric dip/azimuth
Most-positive Most-negative
5-105
s=-1.0
s=-0.5
s=0.0
bowl
synform
saddle
antiform
dome
(Bergbauer et al., 2003)
The shape index, s:The shape index, s:
)(2
12
12
kk
kks
−
+−= ATAN
π
21 kk ≥
s=+0.5
s=+1.0
Principal curvatures
5-106
Shape index and biometric identificationShape index and biometric identification
photographic image distance scan
Shape indices
(Woodward and Flynn, 2004)
5-107
bo
wl
sa
dd
le
rid
ge
do
me
va
lle
y
plane
Shape index
cu
rve
dn
es
s
-1.0 -0.5 0.0 +0.5 +1.00.0
0.2
2D color table2D color table
(al-Dossary and Marfurt, 2006)
5-108
Shape index modulated by curvedness Shape index modulated by curvedness
((αααααααα=0.25)=0.25)5 km
(Guo et al., 2007)
5 km
B
B’
1.2
1.4Tim
e (
s)
N
Bo
wl
Sadd
le
Rid
ge
Dom
e
Va
lley
Plane
Shape index
Cu
rve
dne
ss
-1.0
-0.5
0.0
+0
.5
+1
.0
0.0
0.2
5-109
Shape index modulated by curvedness Shape index modulated by curvedness
((αααααααα=0.25)=0.25)5 km
(Guo et al., 2007)
5 km
B
B’
1.2
1.4Tim
e (
s)
N
Bo
wl
Sadd
le
Rid
ge
Dom
e
Va
lley
Plane
Shape index
Cu
rve
dne
ss
-1.0
-0.5
0.0
+0
.5
+1
.0
0.0
0.2
Transparent
5-110
0.0
0.5
1.0
-1.0 -0.5 0.0 0.5 1.0
bow l
valley
saddle
ridge
dom e
Shape index
Filte
r re
sp
on
se
Shape Shape ‘‘componentscomponents’’ –– an attempt to provide shape an attempt to provide shape
information amenable to geostatistical analysisinformation amenable to geostatistical analysis
Figure 3.68f (al-Dossary and Marfurt, 2006)
5-111
Shape components (Shape components (αααααααα=0.25)=0.25)
t=1.2 st=1.2 s
0
high
Bowl Valley Saddle
5 km
(al-Dossary and Marfurt, 2006)
RidgeDome
5-112
‘‘LineamentLineament’’ attribute attribute –– an attempt to use shapes to an attempt to use shapes to
accentuate linear featuresaccentuate linear features
Shape index
Filte
r re
sp
on
se
0.0
0.5
1.0
-1.00 -0.50 0.00 0.50 1.00
bo
wl
sa
dd
le
do
me
rid
ge
va
lle
y
(Guo et al., 2007)
5-113
2D color bar for lineament attribute2D color bar for lineament attribute
(strike=azimuth of minimum curvature)(strike=azimuth of minimum curvature)
(al-Dossary and Marfurt, 2006)
Lin
ea
me
nt
Strike
0 +90-90strong
weak
5-114
1.0 s0.8 s0.9 s1.0 s1.1 s1.2 s
Curvature lineaments Curvature lineaments
colored by azimuthcolored by azimuth
90-90 0 45-45
0.0
0.1
Strike
Va
lley c
om
pone
nt
5-115 (Guo et al., 2007)
N
5 km
Tim
e (
s)
0.8
1.0
1.2
Volumetric view of lineament attribute (Volumetric view of lineament attribute (αααααααα=0.25)=0.25)
Lin
eam
en
t
Strike
0 +90-90
transparent
5-116
Example: Attribute time slices through Example: Attribute time slices through
Vinton Dome, Louisiana, USAVinton Dome, Louisiana, USA
5-117
Coherence time slice at t=1.0 sCoherence time slice at t=1.0 s
1.0
0.9
0.8
Coh
2km
N
A
A’
5-118
-.25
0.0
+.25
A
A’
2km
N
Most negative curvature time slice at t=1.0 sMost negative curvature time slice at t=1.0 s
5-119
+.25
0.0
-.25
2km
A
A’
Most positive curvature time slice at t=1.0 sMost positive curvature time slice at t=1.0 s
5-120
-1.0
0.0
1.0
2km
Reflector rotation time slice at t=1.0 sReflector rotation time slice at t=1.0 s
A
A’
5-121
A A’
2km
1.0
1.5
0.5
Tim
e (
s)
Vertical seismic sliceVertical seismic slice
5-122
Computational vs. Interpretational curvatureComputational vs. Interpretational curvature
Normal fault seen by curvature
Strike slip fault not seen by curvature
5-123
Channels seen by curvature
Channel not seen by curvature
Computational vs. Interpretational curvatureComputational vs. Interpretational curvature
5-124
CurvatureCurvature
In Summary: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.
5-125
Lateral Changes in Amplitude and Pattern Lateral Changes in Amplitude and Pattern
RecognitionRecognition
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.
5-126 (Partyka, 2001)
-0.1
+0.1
0
2
env
0 50thickness (ms)
impedance
envelope
reflectivity
seismic
0
100
150
Tim
e (m
s)
50
0
100
150
Tim
e (m
s)
50
0
100
150
Tim
e (m
s)
50
0
100
150T
ime
(ms
)
50
Thin bed tuning and the wedge modelThin bed tuning and the wedge model
5-127
temporal thickness (ms)
0 10 20 30 40 50
-0.005
-0.000
-0.010
-0.015
-0.020
-0.025
am
plitu
de o
f tr
ou
gh
Tuning thickness
Temporal thickness (ms)
0 10 20 30 40 50
Tro
ug
h t
o p
eak t
hic
kn
ess (
ms)
0
10
20
30
40
50
Tuning thickness
Thin bed tuning and the wedge modelThin bed tuning and the wedge model
5-128
Sobel edge detectorSobel edge detector
(numerical approximation to first derivative)(numerical approximation to first derivative)
∆
∆−−∆+=
∂
∂
>−∆ x
xxuxxu
x
u
x 2
)()(lim
0
ERROR: stackunderflow
OFFENDING COMMAND: ~
STACK: