1. Series of diagrams illustrating the application of lacunarity and Ripley’s K function in this study.
Series of diagrams illustrating the application of lacunarity and Ripley’s K function in this study. (a) Binary image of ‘window’ A1 (Fig. 4a) in which ‘foreground’ channelized sandbodies (black) are distinguished from ‘background’ floodplain and lagoonal deposits (white) in order to measure lacunarity. The centroid of each sandbody is shown as a white dot, and the distribution of centroids is used for our application of Ripley’s K function. (b) Plot of variance-stabilized K function (i.e. Besag’s L function) for ‘window’ A1 (a) (after Flood & Hampson 2015). The horizontal and vertical axes show distances expressed as multiples of mean apparent sandbody dimensions in order to minimize the effects of anisotropy in sandbody dimensions (i.e. width >> thickness) and to facilitate comparison between data sets of different length scales. For the studied exposure ‘windows’ (Fig. 4a–c), ×1 is equal to 400 m horizontally (mean apparent sandbody width) and 6.8 m vertically (mean maximum sandbody thickness). Clustering and regular spacing are shown, respectively, by negative and positive values of the L function that lie outside of the envelope of complete spatial randomness defined by 99 Monte Carlo simulations (after the convention of Rosenberg & Anderson 2011). ‘Window’ A1 exhibits clustering of sandbody centroids over distances of ×0.4–×3.9 mean apparent sandbody dimensions. (c) Plot of lacunarity v. inhomogeneity in spatial positioning of sandbody centroids, as identified using Ripley’s K function. Data are shown for three cartoons that illustrate type examples of spatial patterns (right of plot) and for ‘window A’ (a) (after Flood & Hampson 2015). Grey bars represent the spatial extent of data for each cartoon or ‘window’, and superimposed black bars show the length scales of sandbody-centroid clustering or regular spacing. Length scales not represented by the black portions of the grey–black bars correspond to the random spacing of sandbody centroids. Length scales are expressed as multiples of mean apparent sandbody dimensions. Lacunarity is dimensionless.
Carlos A. Villamizar et al. Petroleum Geoscience 2015;21:
© 2015 The Author(s)‏