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The Leading Edge; November 2003; v. 22; no. 11; p. 1122-1126; DOI: 10.1190/1.1634916
© 2003 Society of Exploration Geophysicists
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Curvature attributes and seismic interpretation

Case studies from Argentina basins

Mario E. Sigismondi

Petrobras Energía SA, Neuquén, Argentina

Juan C. Soldo

Heriot Watt University, Scotland

Corresponding author: msigismo@petrobrasenergia.com

Corresponding author: juan.soldo@pet.hw.ac.uk

The first 20% of the full text of this article appears below.

The concept of surface curvature dates from work by Gauss in the 1820s but practical applications have only been possible with the advent of powerful workstations in recent years.

In order to explain the concept of curvature, let's first focus on a two-dimensional curve on a x-y coordinate (Figure 1). This curved line can be thought of being made up of many arcs of a circle, with differing centers and radii. The curvature at any given point on this curve is the reciprocal of the radius of the particular arc at that point. It can also be defined as the derivative of the curve's tangent angle with respect to position on the curve at that point. In other words, if {theta}(s) denotes the angle which the curve makes with some fixed reference axis as a function of the path length s along the curve, then k = d{theta}/ds. In terms of Cartesian coordinates x-y, tan({theta}) = dY/dX.


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  		Figure 1. Definition of curvature k and its relationship to radii.

 
A plane curve can be represented as a function Y = f(X) where X and Y are Cartesian coordinates. Pythagoras gives us (ds)2 = (dX)2 + (dY)2, which can be rearranged as ds/dX = [1 + (dY/dX)2]1/2. The curvature k can then be determined by directly evaluating the derivative d{theta}/ds as follows:

(1)

If the X axis is tangent to the curve at the point in question, then tan ({theta}) approaches d{theta} and dX approaches ds (i.e., the zero dip situation) and from equation 1 the curvature can be defined as simply the second derivative, {kappa} = d2Y/dX2. We can get a sense for both the sign and magnitude of curvature of a curve if we replace these radii by normal vectors (Figure 2. . . [Full Text of this Article]






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