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Curvature is aseismic attributes which is a measure of similarity between waveforms or traces in 2D or 3D seismic volumes. This attribute is designed to emphasize discontinuous events, like faults in structural interpretation . In map view  or time slices  it can also be used to aid in stratigraphic interpretation.
Contents
What is curvature?
Geometrically, curvature (k) is defined as the radius of a circle that is tangent to a curve. Mathematically it can be represented as k= 1/r, where k is the curvature, and r is the radius of the circle that is tangent to a curve. The smaller the radius of curvature is, the more bent the curve is. And, if the radius of curvature is infinite, then the curvature (k) would be very small having essentially zero curvature and approximating a straight line.
Curvature can be calculated in both 2D and 3D, where in 3D it attempts to fit circles, and not just a curve to the surface. A circle with a minimal radius where the curvature is very small and tight would be defined as the maximum curvature (kmax), while a second circle, perpendicular to the first, would have a greater radius than the maximum curvature, and would be defined as the minimum curvature (kmin) for that quadratic, curved surface.
What does curvature reveal about the subsurface?
Curvature is an extremely useful seismic attribute, as it can help us image the shape of features in the subsurface. For instance, anticlinal features would have a positive curvature, while synclinal features would have a negative curvature. Flat features, or those with a constant dipping place would exhibit a curvature close to zero.
Types of curvature
Add and discuss Fig 6 from Chopra and Marfurt
Subsurface features identified with the curvature attribute
Many subsurface features can be imaged in 3D seismic with curvature attributes. As with all attributes, the ability to identify features in the subsurface is dependent on the quality of the seismic data. Some of the more common features for which curvature is commonly used are discussed below.
Fractures
Compaction features
Channel edges
Fault edges
Grabens
References
See also
 Seismic attributes
 Semblance, coherence, and other discontinuity attributes
 Stratigraphic interpretation
 Structural interpretation
 Time slices
External references
ADD IHS reference