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Amerada Hess Ltd, 33 Grosvenor Place, London SW1X 7HY, UK
Surface curvature is related to strain and hence fracture density in most lithologies relevant to hydrocarbon exploration, and can be calculated at negligible expense as a surface attribute of horizons mapped on three-dimensional (3D) seismic data. Surfaces mapped using 3D seismic exist as data grids. Direct application of strict mathematical approaches to curvature measurement of gridded data is hindered by several problems inherent to discretized data. The grid node spacing in a horizontal plane is initially equal to the 3D seismic bin spacing and is some arbitrary value greater than the infinitely small mathematical limit, so the measured curvature is also arbitrary. Poor resolution of reflectors gives noise which can be removed by smoothing, but this subjective step impacts subsequent curvature extraction.
Fracture distributions also reflect the effect of large- and small-scale fold structures so there is merit in measuring curvature at a range of scales in addition to that defined by the grid node spacing. As curvature varies with direction of measurement, observations in the grid x and y directions alone are unlikely to coincide with the key maximum and minimum curvature values. Resampling a data grid using a large sliding window permits curvature measurement at a range of different wavelengths, and several orientations can be searched in addition to those parallel to the grid axes. Problems which are present regardless of the sample interval include inherent curvature of geological structures, signal aliasing and regional surface tilt relative to the horizontal grid reference plane.
Total, or Gaussian, curvature which is the product of the maximum and minimum curvatures may not be the best format for presenting curvature data, as strata characterized by zero total curvature may be significantly strained within cylindrical fold structures. Instead, the sum of the absolute values of the principal curvatures gives a representation of spatial variance in strain due to maximum and double curvature.
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