# Geometric attributes for structural interpretation

Geometric seismic attributes are derived calculations of 3D seismic reflection data. They are used to extract geological features such as faults, stratigraphy, channels, and rock properties from seismic data. For structural interpretation, faults, folds, and fractures are important for identifying possible hydrocarbon leads and developing plays. This leads to the importance of geometric attributes for the ease of fault, fold, and fracture identification. The main geometric attributes used for structural interpretation include: dip magnitude & azimuth, coherence, and curvature.

## Geometric attributes

### Dip magnitude & azimuth

Dip magnitude and azimuth attributes are analogous to strike and dip of sedimentary layers. These attributes show the deviation of a seismic reflector from a horizontal plane. Dip magnitude is defined as the angle between the steepest direction of a plane and a horizontal plane, where values range from 0 to 90. Dip azimuth is the direction (relative to north) that plane is dipping, where values range from 0 to 360. Specifically, dip magnitude and azimuth are calculated from the apparent dips of inlines and crosslines. Dip magnitude and azimuth are good attributes, not only for showing overall structural folds, but can be used to identify faults with very small displacements.

Figure 1.[1] Nomenclature of dip magnitude and azimuth. Vectors n and a are unit vectors normal to the plane and dip along the reflector, respectively. θx and θy are apparent dips along the inline and crossline, respectively. θ is the dip magnitude and θ is the dip azimuth.

### Coherence

Coherence is a class of attributes that show the differences or similarities between neighboring waveforms or traces. Since, seismic data is a result of a seismic wavelet that is responding to subsurface geology, differences in neighboring wavelet corresponds to differences in the subsurface.[1] Therefore, coherence is useful for showing faults that have reflector displacement. Common algorithms for coherence include: variance, semblance, and cross-correlation.

### Curvature

Curvature is a seismic attribute that shows how a reflector is changing shape. Curvature(k) is defined in 2D as a circle that is tangent to reflector, where k = 1/radius.[1] Values of curvature range from negative to zero to positive, where negative and positive curvature are concave up and concave down, respectively. Extreme values of curvature (ie. highly negative or highly positive) show areas of the reflector with sharp bends. 3D curvature is defined as having two perpendicular circles tangent to the reflector; the circle with the maximum curvature is kmax and the circle with minimum curvature is kmin.

Figure 2. Defining 2D curvature of a line.

## Case Studies

### Subtle fault identification: dip magnitude and azimuth

Figures 3 and 4 show a time map, in Nun River field in the Niger delta, extracted through dip magnitude and dip azimuth volumes, respectively.[2] Large faults can be easily interpreted in amplitude volumes, because of their large reflector displacement. Rijks and Jauffred, 1991, used both dip magnitude and azimuth to highlight subtle faults (i.e. faults with small reflector displacement). These faults were found by seeing slight variations in dip magnitude and/or dip azimuth.

Figure 3.[2] Dip magnitude along same time map as in figure 4. Green colors represent areas of greater dip, while red colors represent areas of shallower dip. Black arrows show lineations where there are slight dip changes.
figure 4.[2] Dip azimuth and shaded relief along same time map as in figure 3. Blue and orange colors represent opposite dip directions. Black arrows show the same lineations as in figure 3 that have been interpreted as faults with little reflector displacement.

### Fracture identification: coherence and curvature

Chopra and Marfurt, 2007, used both coherence and curvature attributes to highlight faults and fractures.[3] Figure 5a is a time slice structure map representing the top of a formation in central-north British Colombia, Canada. Figure 5b is the time slice through coherence, which reveals many more faults than was shown in the structure map.[3] Figures 5c and d are most-positive curvature and most negative curvature extracted on the structure map; these two attributes show the overall fault trend.[3] Additionally, areas of high positive or negative curvature have been correlated with highly fractured areas.[4]

figure 5. a) time structure map. b) structure map through coherence. c) structure map through most-positive curvature. d) structure map through most-negative curvature. [3]

## References

1. Chopra, S., & Marfurt, K. J., 2007, Seismic attributes for prospect identification and reservoir characterization (Geophysical development series ; v. 11). Tulsa, OK: Society of Exploration Geophysicists : European Association of Geoscientists & Engineers.
2. Rijks, E., and Jauffred, J, 1991, Attribute extraction: An important application in any detailed 3-D interpretation study: The Leading Edge, 10(9), 11-19.
3. Chopra, S., and Marfurt, K., 2007, Curvature attribute applications to 3D surface seismic data. The Leading Edge, 26(4), 404-414.
4. Hart, B., 2002, Validating seismic attribute studies: Beyond statistics. The Leading Edge, 21(10), 1016-1021.