3D curvature attributes: a new approach for seismic interpretation

first break volume 26, April 2008 special topic 3D curvature attributes: a new approach for seismic interpretation Pascal Klein, Loic Richard, and Huw James* (Paradigm) present a new method to compute volumetric curvatures and their application to structural closure and qualitative estimation of basic fracture parameters. W e present a different approach to computing volumetric curvature and the application of volume curvature attributes to seismic interpretation. Volume curvature attributes are geometric attributes computed at each sample of a 3D seismic volume from local surfaces fitted to the volume data in the region of the sample. The curvature attributes respond to bends and breaks in seismic reflectors. 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 fault interpretation of 3D seismic data since they became available. 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 curvature were initially performed geometrically for seismic horizon data. Very recently, algorithms of volumetric curvature 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-azimuth 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 method 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 illustration and discussion use a data set from offshore Indonesia. 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 extensional grabens, half-grabens, normal faults, horsts, and en-echelon faults (Figure 1). Part of sedimentation was syntectonic implying important thickness variation in the sedimentary series. Literature describes four tectonic periods occurring in the study area: extension, quiescence, compression, and another period of quiescence. Surface curvature Surface 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 curvature in the orthogonal azimuth is named the minimum curvature. This set of curvatures can be used for defining other curvature attributes. For example, the average of the minimum and maximum curvature or any other pair of curvatures measured on orthogonal azimuths is called the mean curvature. The product of minimum and maximum curvature 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 * Corresponding author, E-mail: Huw.James@PDGM.com. 2008 EAGE www.firstbreak.org 105

special topic first break volume 26, April 2008 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. maximum curvature but so long as the minimum curvature 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 surface has thickness and the unit is not completely plastic, there will be some fracturing as the unit is folded. Gaussian 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. 106 www.firstbreak.org 2008 EAGE

first break volume 26, April 2008 special topic 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 disadvantage is that the interpreter needs to view two separate images 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 orthogonal azimuth is called the strike curvature. Three very simple shapes illustrate the previous discussions about curvatures attributes. All the simple surfaces 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 diapir, basin, and karst dissolution. The distributions of maximum, 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 azimuth of the maximum curvature. Lineaments of the maximum 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 (Figure 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 curvature In the examples above, curvature is computed directly from surfaces and these same computations may be applied to interpreted horizon and fault surfaces. Instead of computing curvature for surfaces, it is possible to compute curvatures 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 visualization displays. We have found that volume curvature extracted along an interpreted horizon is less noisy than Figure 3 Cylinder. 2008 EAGE www.firstbreak.org 107

special topic first break volume 26, April 2008 Figure 4 Hyperbolic paraboloid or saddle. 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. Methodology The proposed estimation of curvatures is performed in three stages. First, for each volume sample, a small surface is propagated around the sample within the defined horizontal range of analysis. The surface depths are found by finding the maximum cross-correlation value over a vertical analysis window between the central trace and each surrounding trace within the defined range for analysis. 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 curvature Both coherency (Bahorich and Farmer, 1995) and curvature 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 channel boundaries interrupt horizons and these too are well imaged by coherency. Volume curvature will show high values where horizons are bent rather than broken. Volume curvature at discontinuities need not yield predictable results, but typically 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 positive and negative curvatures can be used to interpret low throw faults. At channel boundaries volume curvature may 108 www.firstbreak.org 2008 EAGE

first break volume 26, April 2008 special topic 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 qualitative 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 single wavelet. The value of volume curvature may more reliably be used in further numerical calculations and volume curvature is more likely to usefully indicate regions of folding 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 lineament Curvature attributes are mainly analyzed using the lineament concept, introduced by Hobbs (Hobbs, 1904). A lineament 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 necessarily 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 shallow 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 stack amplitude volume. Rose diagrams for azimuth and dip may be plotted for lineaments interpreted from maximum curvature. These Rose diagrams can in turn be interpreted to identify lineaments due to geology versus lineaments due to surface noise or acquisition footprint. Structural closure The 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 juxtaposition on the up thrown block against the downthrown 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 qualifying most of these aspects and illuminate the analysis of each structural trap. Vertical throw in sub-vertical faulting is generally best seen on vertical seismic sections, while strike-slip faults (lateral displacement) are better seen in horizontal sections (slices). Horizontal sections extracted from the three-dimensional curvature cube enable the interpreter to qualify vertical and strike-slip faulting displacement. 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 values of minimum curvature and maximum curvature will be spatially arranged in such a way that they will define geological lineaments corresponding to faults.(figure 5c) Lateral continuity, length, orientation, spacing between faults are defined from the analysis of lineaments on horizontal sections (slices) extracted from the minimum and maximum curvature 3D attribute cubes. The result of this analysis 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 the areas 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, relatively low values indicate ductile deformation or no deformation at all. Limits between ductile and brittle deformation may be highlighted on maps by colour coding. Lateral misalignment of these limits between the foot wall and the hanging wall will reflect strike-slip movement. Qualification and quantification of the strike-slip displacement is then possible. In the current case study, sinistral movement was evidenced with a horizontal average throw equal to 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. 2008 EAGE www.firstbreak.org 109

special topic first break volume 26, April 2008 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. Reservoir characterisation and fracture analysis Naturally-fractured reservoirs are an important component 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 content which limits seismic resolution. In our example data set, despite the fact that the fractures are poorly illuminated, the curvature attribute detected the fractured areas. Fracture signatures derived from curvature attributes are indicated by a relatively medium to high value of the minimum 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). Conclusions The 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. 110 www.firstbreak.org 2008 EAGE

first break volume 26, April 2008 special topic Figure 7 Structural slice with minimum curvature. Fractured areas indicated close to faults. Curvature attributes allow quantifying and qualifying lateral continuity of the fault and its vertical displacement. They support 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 curvature attributes may be implemented in order to sort out singular geological lineament orientations. This approach could also be used to remove non-geological lineaments such as acquisition footprints The curvature attributes can augment the coherency attribute in the analysis of the geological scheme. Acknowledgements We thank Paradigm for permission to publish this work and Clyde Petroleum for the use of its seismic data. References Al-Dossary, S. and Marfurt, K. [2006] 3D Volumetric multispectral estimates 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 patterns: 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. Geological 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. 2008 EAGE www.firstbreak.org 111

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