Geometrical Attributes

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)

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

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.

θθθθy

(crossline dip)θθθθx

(inline dip)

φφφφ (dip azimuth)

θθθθ (dip magnitude)

ψ(strike)

Definition of reflector dipDefinition of reflector dip

(Marfurt, 2006)

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)

1. 31. 3--D Complex Trace Analysis D Complex Trace Analysis

(Instantaneous Dip/Azimuth)(Instantaneous Dip/Azimuth)

ππω

∂−

)/(tan

1Instantaneous phase

Instantaneous frequency

Instantaneous in line wavenumber

Instantaneous cross line wavenumber

Instantaneous apparent dips

Hilbert transform

5-7 (Barnes, 2000)

Seismic dataSeismic data

7.5 km

Vertical slice Depth slice

5-8 (Barnes, 2000)

Instantaneous Dip MagnitudeInstantaneous Dip Magnitude

7.5 km

Dip (deg)

5-9 (Taner et al, 1979)

The analytic traceThe analytic traceO

Weighted average

frequency

Envelope

f(t) = dφφφφ(t) /dt

e(t) = {[d(t)]2

+ [dH(t)]

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!)!)

7.5 km

Dip (deg)

5-11 (Barnes, 2000)

7.5 km

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)

Azim(deg)

(Barnes, 2000)

Instantaneous AzimuthInstantaneous Azimuth

7.5 km

Azim(deg)

(Barnes, 2000)

7.5 km

Weighted average azimuthWeighted average azimuth

(5 crossline by 5 inline by 7 sample window)(5 crossline by 5 inline by 7 sample window)

2. Gradient Structure Tensor (GST)2. Gradient Structure Tensor (GST)

(Bakker et al, 2003)

The eigenvector of the TGS matrix points in the direction of the

maximum amplitude gradient

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))

33--D estimate of coherence and dip/azimuthD estimate of coherence and dip/azimuth

(Marfurt et al, 1998)

Searching for dip in the presence of faultsSearching for dip in the presence of faults

Single window search

Multi-window search

(Marfurt, 2006)

crossline

Search for the most coherent window Search for the most coherent window

containing the analysis pointcontaining the analysis point

(Marfurt, 2006)

crossline

Search for the most coherent window Search for the most coherent window

containing the analysis pointcontaining the analysis point

(Marfurt, 2006)

(µs/m)

(Marfurt, 2006)

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

(µs/m)

(Marfurt, 2006)

A A′′′′

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)

B B′′′′5 km

Ellenburger

Basement?

Vertical Slice through SeismicVertical Slice through Seismic

Time (s)

B′′′′5 kmTime/structure of Caddo horizonTime/structure of Caddo horizon

Dip (s/km)

B′′′′5 kmDip magnitude from picked horizonDip magnitude from picked horizon

B′′′′5 kmNS dip from picked horizonNS dip from picked horizon

Dip (s/km)

B′′′′5 km

NS dip from multiNS dip from multi--window scanwindow scan

Dip (deg)

B′′′′5 kmEW dip from picked horizonEW dip from picked horizon

Dip (s/km)

B′′′′5 km

EW dip from multiEW dip from multi--window scanwindow scan

Dip (deg)

Shaded illuminationShaded illumination

on a surface on a time slice through dip and azimuth volumes

(after Barnes, 2002)

Dip (deg)

ϕϕϕϕ=00ϕϕϕϕ=300ϕϕϕϕ=600ϕϕϕϕ=900ϕϕϕϕ=1200ϕϕϕϕ=1500

Time slices through apparent dip Time slices through apparent dip

(t=0.8s)(t=0.8s)

ϕϕϕϕ=00ϕϕϕϕ=300ϕϕϕϕ=600ϕϕϕϕ=900ϕϕϕϕ=1200ϕϕϕϕ=1500

Time slices through apparent dip Time slices through apparent dip

(t=1.2s)(t=1.2s)

Dip (deg)

Dip Azimuth

180 3600

Volumetric visualization of Volumetric visualization of

reflector dip and azimuthreflector dip and azimuth

1.4Tim

W Transparent

Dip Azimuth

180 3600

Transparent

Volumetric visualization of Volumetric visualization of

reflector dip and azimuthreflector dip and azimuth

divergent

convergent

divergent

(Barnes, 2002)

Towards 3Towards 3--D D

seismic seismic

stratigraphystratigraphy……

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

CoherenceCoherence

• 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.

Seismic Time SliceSeismic Time Slice

(Bahorich and Farmer, 1995)

Coherence Time SliceCoherence Time Slice

saltsalt5 km

inline

Coherence compares the waveforms of Coherence compares the waveforms of

neighboring tracesneighboring traces

Trace #1Shifted windows

of Trace #2

Crosscorrelationlag:

Cross correlation of 2 tracesCross correlation of 2 traces

- 4 -2 0 +2 +4

Maximum coherence

Time slice through Time slice through

coherencecoherence

(early algorithm)(early algorithm)

average absolute average absolute

amplitudeamplitude

highcoh

Vertical slice through Vertical slice through

seismicseismic

A A′′′′

highcoh

coherencecoherence

(later algorithm)(later algorithm)

A′′′′ (Haskell et al. 1995)

coherence seismic

Appearance faultsAppearance faults perpendicular perpendicular andand parallel parallel to striketo strike

Alternative measures of waveform Alternative measures of waveform

similaritysimilarity

• cross correlation

• semblance, variance, and Manhattan distance

• eigenstructure

• Gradient Structural Tensors (GST)

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

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

Pitfall: Banding artifacts near zero crossingsPitfall: Banding artifacts near zero crossings

Solution: calculate coherence on the analytic Solution: calculate coherence on the analytic

tracetrace

Coherence of real trace Coherence of analytic trace

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

Eigenstructure coherence:Eigenstructure coherence:Time slice through seismicTime slice through seismic

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

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

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

Canyon

Seismic Crosscorrelation

EigenstructureSemblance(Gersztenkorn and Marfurt, 1999)

Channels

Coherence Coherence

algorithm algorithm

evolutionevolution

seismicGST

coherencedip scan

coherence

Comparison of Comparison of

Gradient Gradient

Structure Tensor Structure Tensor

and dip scan and dip scan

eigenstructureeigenstructure

coherencecoherence

(Bakker, 2003)

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

Seismic section

A A′′′′

SeismicSeismic

Coherence section

A A′′′′

Coherence Coherence

without dip without dip

searchsearch

Coherence section

A A′′′′

Coherence Coherence

with dip with dip

searchsearch

radius = 12.5 m radius = 25 m

radius = 37.5 m radius = 50 m

Impact of Impact of

lateral analysis lateral analysis

windowwindow

Temporal aperture = 8 ms

Impact of vertical analysis windowImpact of vertical analysis window

On a stratigraphic

target

On a structural

target

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

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

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

00+8+8

+24+24+16+16

+32+32

--88--1616--2424--3232

analysis windowanalysis window

Figure 3.46

Impact of Impact of

height of height of

analysis analysis

windowwindow

00+8+8

+24+24+16+16

+32+32

--88--1616--2424--3232

analysis window

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.

Volumetric curvature and reflector shapeVolumetric curvature and reflector shape

• 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.

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

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

(Roberts, 2001)

3D Curvature and Topographic Mapping3D Curvature and Topographic Mapping

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

3D Curvature and Molecular Docking3D Curvature and Molecular Docking

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

3D Curvature 3D Curvature

and Biometric and Biometric

Identification Identification

of Suspiciousof Suspicious

TravelersTravelerskpos> 0

kneg > 0kneg < 0

kpos < 0

kpos > 0

kneg = 0

kpos < 0 kpos = 0 kpos > 0

kneg = 0

kneg > 0

kneg < 0bowl

synform

saddle

antiform

(Bergbauer et al., 2003)

Geometries of folded surfacesGeometries of folded surfaces

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

Curvature of picked horizonsCurvature of picked horizons

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)

kx-ky spectrum

kx (cycles/m)

+0.02+0.00 +0.02-0.02

Footprint!

kxkx--ky transform of time picksky transform of time picks

Long wavelength

Short wavelength

5-77 (Bergbauer et al, 2003)kx (cycles/m)

+0.00 +0.02-0.02

kxkx--ky transform of time picks after bandpass filterky transform of time picks after bandpass filter

Long wavelength

Short wavelength Short wavelength

Maximum curvature after kMaximum curvature after kxx--kkyy bandpass filterbandpass filter

(Bergbauer et al, 2003)

0 100005000

Contours

Faults

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

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

Radius of Curvature Radius of Curvature 3 km

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

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)

““FractionalFractional”” derivativesderivatives

distance in grid points

-20 +200

αααα=1.00

αααα=0.75

αααα=0.50

αααα=0.25

αααα=0.01

αααα=1.25

kx wavenumber (cycles/grid point) a

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

Interpretation of Interpretation of ‘‘fractional derivativefractional derivative’’ as a filteras a filter

Wavelength, λ

applie

stderivative

Idealiz

ed firs

t deriv

Wavenumber, k

π/∆

(Chopra and Marfurt, 2007b)

Attributes extracted along a geological horizonAttributes extracted along a geological horizon

Ellenburger

B B′′′′t

Vertical Slice Vertical Slice –– Fort Worth Basin, USAFort Worth Basin, USA

kkmeanmean=1/2(d=1/2(d22T/dxT/dx22++dd22T/dyT/dy2)2) –– CaddoCaddo

(Horizon pick calculation)(Horizon pick calculation)

B′′′′

kkmeanmean horizon slice horizon slice –– CaddoCaddo

(volumetric calculation)(volumetric calculation)

B′′′′

Coherence horizon slice Coherence horizon slice –– CaddoCaddo

B′′′′5 km

Attributes extracted along time slicesAttributes extracted along time slices

Ellenberger

B B′′′′t

Vertical slice through seismicVertical slice through seismic

Time slice through coherenceTime slice through coherence

t=0.8 st=0.8 s

(al-Dossary and Marfurt, 2006)B

B′′′′5 km

Most negative curvature (Most negative curvature (αααααααα=1.00)=1.00)

t=0.800 st=0.800 s

αααα=1.00

B′′′′

Spectral estimates of most negative Spectral estimates of most negative

curvature t=0.8 scurvature t=0.8 s

αααα=2.00αααα=1.75αααα=1.50αααα=1.25αααα=1.00αααα=0.75αααα=0.50αααα=0.25

B′′′′

Principal component coherencePrincipal component coherence

t=0.8 st=0.8 s

B′′′′

Principal component coherencePrincipal component coherence

t=1.2 st=1.2 s

B′′′′

Most negative curvature (Most negative curvature (αααααααα=0.25)=0.25)

t=1.2 st=1.2 s

B′′′′

Most positive curvature (Most positive curvature (αααααααα=0.25)=0.25)

t=1.2 st=1.2 s

B′′′′

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

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’’

NegNeg PosPos00

2.5 km2.5 km

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’’

NegNeg PosPos00

2.5 km2.5 km

AA’’

Curvature computed from volumetric dip/azimuthCurvature computed from volumetric dip/azimuth

Most-positive Most-negative

s=-1.0

s=-0.5

synform

saddle

antiform

(Bergbauer et al., 2003)

The shape index, s:The shape index, s:

+−= ATAN

21 kk ≥

s=+0.5

s=+1.0

Principal curvatures

Shape index and biometric identificationShape index and biometric identification

photographic image distance scan

Shape indices

(Woodward and Flynn, 2004)

Shape index

-1.0 -0.5 0.0 +0.5 +1.00.0

2D color table2D color table

Shape index modulated by curvedness Shape index modulated by curvedness

((αααααααα=0.25)=0.25)5 km

(Guo et al., 2007)

1.4Tim

Shape index

Shape index modulated by curvedness Shape index modulated by curvedness

((αααααααα=0.25)=0.25)5 km

(Guo et al., 2007)

1.4Tim

Shape index

Transparent

-1.0 -0.5 0.0 0.5 1.0

valley

saddle

Shape index

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)

Shape components (Shape components (αααααααα=0.25)=0.25)

t=1.2 st=1.2 s

Bowl Valley Saddle

RidgeDome

‘‘LineamentLineament’’ attribute attribute –– an attempt to use shapes to an attempt to use shapes to

accentuate linear featuresaccentuate linear features

Shape index

-1.00 -0.50 0.00 0.50 1.00

(Guo et al., 2007)

2D color bar for lineament attribute2D color bar for lineament attribute

(strike=azimuth of minimum curvature)(strike=azimuth of minimum curvature)

Strike

0 +90-90strong

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

Strike

lley c

5-115 (Guo et al., 2007)

Volumetric view of lineament attribute (Volumetric view of lineament attribute (αααααααα=0.25)=0.25)

Strike

0 +90-90

transparent

Example: Attribute time slices through Example: Attribute time slices through

Vinton Dome, Louisiana, USAVinton Dome, Louisiana, USA

Coherence time slice at t=1.0 sCoherence time slice at t=1.0 s

Most negative curvature time slice at t=1.0 sMost negative curvature time slice at t=1.0 s

Most positive curvature time slice at t=1.0 sMost positive curvature time slice at t=1.0 s

Reflector rotation time slice at t=1.0 sReflector rotation time slice at t=1.0 s

A A’

Vertical seismic sliceVertical seismic slice

Computational vs. Interpretational curvatureComputational vs. Interpretational curvature

Normal fault seen by curvature

Strike slip fault not seen by curvature

Channels seen by curvature

Channel not seen by curvature

Computational vs. Interpretational curvatureComputational vs. Interpretational curvature

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.

Lateral Changes in Amplitude and Pattern Lateral Changes in Amplitude and Pattern

RecognitionRecognition

• 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 50thickness (ms)

impedance

envelope

reflectivity

seismic

Thin bed tuning and the wedge modelThin bed tuning and the wedge model

temporal thickness (ms)

0 10 20 30 40 50

-0.005

-0.000

-0.010

-0.015

-0.020

-0.025

Tuning thickness

Temporal thickness (ms)

0 10 20 30 40 50

Tuning thickness

Thin bed tuning and the wedge modelThin bed tuning and the wedge model

Sobel edge detectorSobel edge detector

(numerical approximation to first derivative)(numerical approximation to first derivative)

∆−−∆+=

>−∆ x

xxuxxu

)()(lim

ERROR: stackunderflow

OFFENDING COMMAND: ~

STACK:

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$PNQBSJTPO PG %SZ7FSTVT (FM'JMMFE0QUJDBM$BCMFT · Curl is one of the geometrical attributes of optical fiber. This paper describes measurement and importance of Fiber Curl. Keywords

forums.autodesk.com · 2014-06-03 · Elastic foundation Non4inear hinges Geometrical impafe-CüOñS Calculation elements Display attributes only for selected objects Apply Roof Level

Geometrical Optics 95