3d curvature attributes - a new approach for seismic interpretation

7/27/2019 3D Curvature Attributes - A New Approach for Seismic Interpretation

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special topicfirst break volume 26, April 2008

We present a different approach to computing volu-

metric curvature and the application of volume cur-

vature attributes to seismic interpretation. Volume

curvature attributes are geometric attributes com-

puted at each sample of a 3D seismic volume from local sur-

faces fitted to the volume data in the region of the sample. The

curvature attributes respond to bends and breaks in seismicreflectors. Because volume curvature focuses on changes of

shape rather than changes of amplitude, it is less affected by

changes in the seismic amplitude field caused by variations in

fluid and lithology and focuses more on variations caused by

faults and folding. Tight folds at seismic scale may indicate

sub-seismic faults. Interpretation of the tight folds can also

provide qualitative estimates of basic fracture parameters

such as fracture density, spacing, and orientation. This

knowledge of both faults and fractures is valuable for the

estimation of structural frameworks including closure and

also for the estimation of reservoir flow characteristics.

Seismic interpreters have used attribute volumes for faultinterpretation of 3D seismic data since they became avail-

able. Coherency (Bahorich and Farmer, 1995) is without

doubt the most popular attribute for this purpose. More

recently, curvature attributes have been found to be useful

in delineating faults and predicting fracture distribution and

orientation. Because curvature is sensitive to noise and is a

relatively intensive computational task, calculations of cur-

vature were initially performed geometrically for seismic

horizon data. Very recently, algorithms of volumetric cur-

vature were formulated that make the assumption that the

structure is locally defined by an iso-intensity surface. These

approaches suppose, moreover, that the orientation volumes

(dip and azimuth) are available.Donias (Donias et al., 1998) propose an estimate of the

curvature based on the divergence formulation of the dip-azi-

muth vector field calculated in normal planes. Chopra and

Marfurt (2007) use the fractional derivatives of apparent dip

on each time slice to extract measurements of the curvature at

each sample of the 3D volume. West et al. (2003) give a meth-

od where individual curvatures are computed as horizontal

gradients of apparent dip for a given number of directions, and

are then combined to generate a combined curvature volume.

This paper proposes a method to compute volumetric

curvatures and their application to structural closure and

qualitative estimation of basic fracture parameters. The illus-

tration and discussion use a data set from offshore Indone-

sia. The original seismic data is zero-phase and comprises

300 in-lines and 1300 cross lines with in-line spacing of 25

m, cross line spacing of 12.5 m, and a sample rate of 4 ms.The regional basin geometry is made of pull-apart basins

due to tectonic extrusion of Southeast Asia in response to

the collision of India since the early Tertiary. The structural

framework of the basin consists of a number of extension-

al grabens, half-grabens, normal faults, horsts, and en-ech-

elon faults (Figure 1). Part of sedimentation was syntecton-

ic implying important thickness variation in the sedimenta-

ry series. Literature describes four tectonic periods occurring

in the study area: extension, quiescence, compression, and

another period of quiescence.

Surface curvatureSurface curvature is well described by Roberts (Roberts,

2001) In brief, surfaces of anticlines will yield positive

curvature, synclinal surfaces will yield negative curvature,

and saddles will yield both positive and negative curvature.

Ridges will yield positive curvature in the direction across the

ridge and zero curvature in the direction along the ridge line.

Troughs will yield negative curvature in the direction across

the trough and zero curvature along the trough line.

At any point of a surface, the curvature can be measured

as a bending number (positive or negative) at any azimuth.

One of these azimuths will yield the largest curvature. This

curvature is named the maximum curvature and the curva-

ture in the orthogonal azimuth is named the minimum cur-vature. This set of curvatures can be used for defining other

curvature attributes. For example, the average of the mini-

mum and maximum curvature or any other pair of curva-

tures measured on orthogonal azimuths is called the mean

curvature. The product of minimum and maximum curva-

ture is called Gaussian curvature.

Surfaces that are initially flat will have a minimum and

maximum curvature of zero and consequently a Gaussian

curvature of zero. Folding such surfaces may increase the

3D curvature attributes: a new approachfor seismic interpretation

Pascal Klein, Loic Richard, and Huw James* (Paradigm) present a new method to computevolumetric curvatures and their application to structural closure and qualitative estimationof basic fracture parameters.

* Corresponding author, E-mail: [email protected].




www.firstbreak.org © 2008 EAGE106

special topic first break volume 26, April 2008

maximum curvature but so long as the minimum curva-

ture stays at zero the Gaussian curvature will also remain

at zero. This is an indication that the surface has not

been deformed. Naturally, if the unit bounded by the sur-

face has thickness and the unit is not completely plastic,

there will be some fracturing as the unit is folded. Gaus-

sian curvature may have some role to play as an indicator

of deformation.

Instead of choosing the azimuth of maximum curvature

the choice of azimuth can be made to select the most pos-

Figure 2 Elliptical paraboloid.

Figure 1 General overview of data set from Indonesia. a) Time structure of a shallow horizon H1; b) Amplitude map for horizon H1; c) Maximum curvature

extracted along H1; d) Amplitude section.






itive or the most negative curvatures. These measures will

yield similar measures to that of maximum curvature but

will preserve the sign of curvature so that curvature images

will consistently represent ridges or troughs. The disadvan-

tage is that the interpreter needs to view two separate imag-

es of positive and negative curvature and fuse them into one

interpretation. Patterns that include both minimum and

maximum curvature are separated and may become less

apparent. Alternatively, if the initial choice of azimuths is

the azimuth of maximum surface dip, then the curvature is

called the dip curvature and the curvature in the orthogo-

nal azimuth is called the strike curvature.

Three very simple shapes illustrate the previous discus-

sions about curvatures attributes. All the simple surfac-

es have been made as anti-form, but the conclusions are

the same for the syn-form, only the sign of the curvature

attribute will be changed.The first one considered here is the elliptic paraboloid

surface (Figure 2) which has geologic analogues of dia-

pir, basin, and karst dissolution. The distributions of max-

imum, minimum and dip curvature are radial. We notice

also that the azimuth of the dip curvature is equal to the

azimuth of the maximum curvature.

The second shape is the cylindrical surface (Figure 3)

with geological analogues of diapir, syncline, and anticline.

The minimum curvature is equal to zero. We also remark

that the azimuth of the dip curvature is equal to the azi-

muth of the maximum curvature. Lineaments of the maxi-

mum curvature and dip curvature are parallel and show the

apex of the antiform or the axis of the synform.

The last shape is the hyperbolic paraboloid surface (Fig-

ure 4) with geologic analogues of diaper and spill point.

Lineaments from maximum curvature and lineaments for

minimum curvature are orthogonal. The intersection of the

both lineaments corresponds to a possible spill point.

Volume curvature will be computed directly from the

volume data but the same measures as surface curvature

are available.

Volume curvatureIn the examples above, curvature is computed directly from

surfaces and these same computations may be applied tointerpreted horizon and fault surfaces. Instead of comput-

ing curvature for surfaces, it is possible to compute curva-

tures at every point of the volume. These curvatures may

then be extracted along interpreted surfaces, time and depth

slices, or any kind of seismic section. Volume curvatures

may also be displayed directly in volume or voxel visu-

alization displays. We have found that volume curvature

extracted along an interpreted horizon is less noisy than

Figure 3 Cylinder.






surface curvature for the same horizon. This is because the

volume curvature is directly measuring the curvature of

the amplitude field while the surface curvature is usually

following a ‘snapped horizon’ which will be influenced

by the shape of a single trace or the shape of a manually

interpreted fault which we can expect to contain noise due

to manual picking.

MethodologyThe proposed estimation of curvatures is performed in

three stages. First, for each volume sample, a small sur-

face is propagated around the sample within the defined

horizontal range of analysis. The surface depths are foundby finding the maximum cross-correlation value over a

vertical analysis window between the central trace and

each surrounding trace within the defined range for analy-

sis. The cross-correlations are back interpolated, using a

parabolic fit to determine the precise vertical shift of the

maximal cross-correlation. Then a least squares quadratic

surface z(x,y) of the form is fitted to the vertical shifts

within the analysis range. Finally, the set of curvature

attributes are computed from the coefficients of quadratic

surface using classic differential geometry (Roberts, 2001).

The curvature attributes most frequently used are the

maximum and minimum curvatures which we designate κ1

and κ2 respectively.

Coherency and curvatureBoth coherency (Bahorich and Farmer, 1995) and curva-

ture are used to delineate faults and stratigraphic features

such as channels. Coherency accentuates parts of the

amplitude volume where there are discontinuities in the

amplitude field. These occur where there are faults and

the horizon amplitudes are discontinuous because the

rocks are broken. Discontinuities also occur where chan-

nel boundaries interrupt horizons and these too are well

imaged by coherency.Volume curvature will show high values where hori-

zons are bent rather than broken. Volume curvature at dis-

continuities need not yield predictable results, but typical-

ly horizons are bent prior to breaking at faults so volume

curvature may well pick out a fault. For example, volume

curvature calculated in the region of a low throw normal

fault will show high positive curvature at the edge of the

footwall coupled with high negative curvature at the edge

of the hanging wall. This characteristic pair of high posi-

tive and negative curvatures can be used to interpret low

throw faults. At channel boundaries volume curvature may

Figure 4 Hyperbolic paraboloid or saddle.






juxtaposition on the up thrown block against the down-

thrown block. For this reason, lateral continuity of the

fault and vertical displacement of the hanging wall from

the foot wall need to be carefully analyzed.

Curvature attributes allow quantifying and qualify-

ing most of these aspects and illuminate the analysis of

each structural trap. Vertical throw in sub-vertical fault-

ing is generally best seen on vertical seismic sections, while

strike-slip faults (lateral displacement) are better seen in

horizontal sections (slices). Horizontal sections extract-

ed from the three-dimensional curvature cube enable the

interpreter to qualify vertical and strike-slip faulting dis-

placement.

Minimum curvature and maximum curvature attributes

are highly sensitive to brittle deformation especially in the

fault nose areas. High values of major curvature correlate

directly with high values of brittle deformation. High val-ues of minimum curvature and maximum curvature will be

spatially arranged in such a way that they will define geo-

logical lineaments corresponding to faults.(Figure 5c) Lat-

eral continuity, length, orientation, spacing between faults

are defined from the analysis of lineaments on horizontal

sections (slices) extracted from the minimum and maxi-

mum curvature 3D attribute cubes. The result of this anal-

ysis will help to appraise the possible connectivity between

both blocks. In the present case study, lineament analysis

shows en-echelon patterns with an average length of the

fault equal to 400 m (Figure 6c).

Dip curvature is an attribute which often highlights theareas where the layer is broken. In an extensive regime,

positive values of this attribute correspond to ‘bottom-up’

shapes such as fault noses; negative values correspond to

synform shapes such as erosional scours. High values of

this attribute indicate the deformation is brittle, relative-

ly low values indicate ductile deformation or no defor-

mation at all. Limits between ductile and brittle deforma-

tion may be highlighted on maps by colour coding. Later-

al misalignment of these limits between the foot wall and

the hanging wall will reflect strike-slip movement. Quali-

fication and quantification of the strike-slip displacement

is then possible. In the current case study, sinistral move-

ment was evidenced with a horizontal average throw equalto 150 m (Figure 6a).

Separation between strong negative and strong positive

values of the dip curvature attribute (red and blue colours on

Figure 6) measures the vertical displacement. In the present

case study, the vertical displacement was varying from 35

to 110 milliseconds (Figure 6b). Using the above-mentioned

attributes, it has been inferred that hydrocarbon trapping in

the study area is controlled by a series of normal north to south

trending en-echelon faults The maximum curvature and dip

curvature attributes suggest that the regime of constraint is a

trans-tensional stress with northeast-southwest sinistral shear.

have high positive values at the levees and negative values

in the thalweg.

So both attributes can detect faults and channels.

Coherency can be calculated over relatively long time gates

to create very precise images of faults in plan view. When

used in this fashion, coherency becomes a detailed qual-

itative indicator of faults and their position. This allows

interpreters to quickly pick them without anguishing over

the precise position as they may do when using amplitude

data alone.

Volume curvature produces quantitative measures of

folds and is typically calculated over the interval of a sin-

gle wavelet. The value of volume curvature may more reli-

ably be used in further numerical calculations and volume

curvature is more likely to usefully indicate regions of fold-

ing or sub-seismic faulting.

These two attributes illuminate different features of faults, folding, and stratigraphic features. So it is wise to

use both of them for detailed interpretation.

Filtering curvature lineamentCurvature attributes are mainly analyzed using the linea-

ment concept, introduced by Hobbs (Hobbs, 1904). A line-

ament is a mappable, simple, or composite linear feature of

a surface, whose parts are aligned in a rectilinear or slightly

curvilinear relationship and which differs distinctly from

the patterns of adjacent features and presumably reflects

a subsurface phenomenon. Two dimensional analysis of

curvature attribute shows that lineaments do not necessar-ily indicate a geological structure, such as a deformation

zone or a sedimentary pattern. The general question is

how to identify features that are only related to geological

feature. The best answer is to reverse the question and try

to exclude non-geological pattern.

Filtering noise lineaments from anthropogenic sources,

such as surface installations, when interpreting for shal-

low hazards, can be easily managed. On the other hand,

acquisition footprint reduction is not an easy task. It is

recommended to perform this process within the seismic

data processing sequence. Regardless, volume curvature

allows us to significantly reduce the noise that results from

the acquisition footprint still remaining in the post stackamplitude volume. Rose diagrams for azimuth and dip may

be plotted for lineaments interpreted from maximum cur-

vature. These Rose diagrams can in turn be interpreted to

identify lineaments due to geology versus lineaments due to

surface noise or acquisition footprint.

Structural closureThe structural hydrocarbon traps are frequently composed

of three way dip closures occurring against faults. The

trapping efficiency of this kind in the tectonic regime of the

study area depends, among other factors, on the reservoir






indicated by a relatively medium to high value of theminimum curvature. Most of the lineaments defined by the

spatial arrangement of the minimum curvature attribute

correspond to fractures.

In the present case study, zones of fracturing are mainly

detected close to the major brittle fault events (Figure 7).

ConclusionsThe new technique proposed here to compute volumetric

curvature attributes performs calculations in a single step,

without requiring any pre-computation of intermediate

volumes such as dip and azimuth.

Reservoir characterisation and fracture analysisNaturally-fractured reservoirs are an important compo-

nent of global hydrocarbon reserves. It is important for the

prediction of future reservoir performance to detect zones

of fracturing and, at least qualitatively, estimate their basic

parameters, for example, the density and orientation of

the fractures. Fractures are usually difficult to resolve from

seismic amplitude data due to the seismic frequency con-

tent which limits seismic resolution. In our example data

set, despite the fact that the fractures are poorly illumi-

nated, the curvature attribute detected the fractured areas.

Fracture signatures derived from curvature attributes are

Figure 5 a) Structural slice with coherency; b) Structural slice with dip curvature; c) Structural slice with maximum curvature.

Figure 6 a) Lateral throw from dip curvature; b) Vertical displacement from dip curvature; c) Length from dip curvature.






ReferencesAl-Dossary, S. and Marfurt, K. [2006] 3D Volumetric multispectral esti-

mates of reflector curvature and rotation. Geophysics, 71(5).

Bahorich, M. and Farmer, S [1995] 3D seismic coherency for faults and

stratigraphic features. The Leading Edge, 14(10).

Chopra, S. and Marfurt, K. [2007] Curvature attribute applications to

3D surface seismic data. The Leading Edge, 26(4).

Donias, M., Baylou P., and Keskes, N. [1998] Curvature of oriented pat-

terns: 2-D and 3-D Estimation from Differential Geometry. IEEE

International Conference on Image Processing, 1, 236-40.

Hobbs, W. H. [1904] Lineaments of the Atlantic border region. Geolog-

ical Society of America Bulletin, 15.

Roberts, A. (2001) Curvature attributes and their application to 3D

interpreted horizons. First Break, 19(2)

West, B. P., May, S. R., Gillard, D., Eastwood, J. E., Gross, M. D., and

Frantes T. J. [2003] Method for analyzing reflection curvature in

seismic data volumes. US Patent No 6662111.

Curvature attributes allow quantifying and qualifying later-

al continuity of the fault and its vertical displacement. They sup-

port the analysis of structural traps occurring against faults.

Geological model properties benefit from the qualitative

and quantitative information extracted from the curvature

attributes, such as fracture density and orientation.As a future perspective, a post processing of the curva-

ture attributes may be implemented in order to sort out singu-

lar geological lineament orientations. This approach could also

be used to remove non-geological lineaments such as acquisi-

tion footprints

The curvature attributes can augment the coherency

attribute in the analysis of the geological scheme.

AcknowledgementsWe thank Paradigm for permission to publish this work

and Clyde Petroleum for the use of its seismic data.

Figure 7 Structural slice with minimum curvature. Fractured areas indicated close to faults.




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3d curvature attributes - a new approach for seismic interpretation

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