Seismic interpreters have used attribute volumes for fault interpretation of 3D seismic data since they became available. Coherency (Bahorich) 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

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. Three-dimensional seismic data and well logs were available for the study. The original seismic data is zero-phase and made of 300 inlines and 1300 crosslines with inline spacing of 25 m, crossline spacing of 12.5 m, and a sample rate of 4ms. 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 INTRODUCTION

IMPROVING STRUCTURAL SEISMIC INTERPRETATION USING 3D CURVATURE ATTRIBUTES

Pascal Klein, Loic Richard, Huw JamesParadigm Geophysical{pklein,lrichard,hjames}@paradigmgeo.com

SUMMARYThis paper presents 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.Our examples will use a data set from Offshore Indonesia.1 of 5

azimuth) are available. Donias et al. (Donias) propose an estimate of the curvature based on the divergence formulation of the dip-azimuth vector field calculated in normal planes. Marfurt (Marfurt) 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 (West) gives a method where individual curvatures are computed as horizontal gradients of apparent dip for a given

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 variations in the sedimentary series. Literature describes four tectonic periods which took place in the study area: extension, quiescence, compression and another period of quiescence.

METHODOLOGY orthogonal to the direction of maximum curvature is called minimal curvature . The maximum and

Figure 1: General overview of the data set from Offshore Indonesia. (a) time structure of the shallow event; (b) amplitude map extracted along H1; (c) maximum curvature extracted along H1; (d) Time migrated amplitude section.2 of 5

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 z-positions 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 data within the analysis range.Finally, the set of curvature attributes are computed from the coefficients of quadratic surface using classic differential geometry (Roberts).

The curvature attributes most frequently used are the normal curvatures, they are defined by orthogonal planes to the surface (Roberts). The greatest normal curvature is called maximum curvature 1. The curvature taken in the direction which is horizontally

2minimal curvatures constitute the principal curvatures.

Figure 2: Principal curvatures and the dip curvature of a regular surface at a given point.

The dip curvature d is the curvature extracted along the dip direction and measures the rate of dip variation within the direction of the maximum dip (Figure 2).

eydxcxybyaxyxz ++++= 22),(

extracted from the three-dimensional curvature cube

ovcuenable 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 3.c)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

Figure 3: Dip curvature and max curvature: image imprslice on dip curvature; (c) Structural slice on maximum STRUCTURAL CLOSUREThe structural hydrocarbon traps are frequently composed of 3 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 horizontal average throw equal to 150 meters (Figure 4.a). Separation between strong negative and strong positive values of the dip curvature attribute (red and blue colours on Figure 4) measures the vertical displacement. In the present case study, the vertical displacement was varying from 35 to 110 milliseconds (Figure 4.b). 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 major curvature and dip curvature attributes suggest that the regime of constraint is a trans-tensional stress with northeast-southwest sinistral shear.

ement. (a) Structural slice on coherency; (b) Structural rvature.shows en-echelon patterns with an average length of the fault equal to 400 meters (Figure 4.c).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 3 of 5

RESERVOIR CHARACTERIZATION. 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

Figure 4: Dip curvature quantitative analysis, length, lateral throw and vertical displacement measurement. (a) Lateral throw from dip curvature; (b) vertical displacement from dip curvature; (c) Length from dip curvature. 4 of 5

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 5).

Figure 5: Fracture area illuminated by the minimum principal curvature; Structural slice on minimum curvature.

The area of the zone affected by fracturing is approximately equal to 0.8 km2 for the channel and 1 km2 for the western part from the main fault (Figure 6.b). Fractures are parallel to the main fault, and the estimated density of fracturing is 50 to 60 meters in the area of the channel and 90 to 100 meters in the western part of the survey(Figure 6.b).

Figure 6: Basic parameters fracture estimation: density and orientation (a) time migrated amplitude section; (b) time slice on minimum curvature; (c) time migrated amplitude section; (d) time slice on coherency; (e) time slice on maximum curvature.

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.

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.

ReferencesBahorich, Farmer, 3D seismic coherency for faults and stratigraphic features, The Leading Edge 14,1995,1053-1058.Donias M., Baylou P., Keskes N., Curvature of oriented patterns: 2-D and 3-D Estimation from Differential Geometry: ICIP98, 246-250.Al-Dossary , Marfurt K., 3D volumetric multispectral estimates of reflector curvature and rotation. Geophysics 71,2006,P41.Chopra S., Marfurt K., Curvature attribute applications to 3D surface seismic data; The Leading Edge, April 2007, 404-414.Roberts, A., 2001, Curvature attributes and their application to 3D interpreted horizons: first break, 19.2, 85-100.West B. P., May S. R., Gillard D., Eastwood J. E., Gross M. D., Frantes T. J. Method for analyzing reflection curvature in seismic data volumes : US Patent No 6,745,394.

AcknowledgementsWe thank Paradigm for permission to publish this work.5 of 5

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