Fractal Dimensions of Particle Size Distribution in Littoral Sandstones of Carboniferous Donghetang Formation in Hade Oilfield, Tarim Basin, NW China

Fractal theory of particle size distribution (PSD) is a widely used approach in soil science. However, fractal studies on sandstone PSDs are scarce in sedimentology and geology. Taking littoral sandstones in the Carboniferous Donghetang Formation of the Hade Oilfield as an example, fractal dimensions of 115 fine sandstone and 150 silty sandstone PSDs are calculated and compared with particle size compositions and traditional statistical parameters in this paper. The results show that fractal dimension values in fine sandstones, 1.69–2.17 averaged at 1.99, are usually lower than that in silty sandstones, 2.12–2.73 averaged at 2.37. Fractal dimension and sandy content of littoral sandstones show a strong negative linear relationship. Significant logarithmic correlations are implied between fractal dimension and silty and clayey contents of littoral sandstones, which is different from linear relations in soil PSDs. The relationships between fractal dimension and mean, sorting, and skewness of silty sandstone PSDs are better than those of fine sandstones. Fractal dimension and kurtosis of silty sandstones and fine sandstones exhibit weak negative and positive linear relationships, respectively. Fractal dimension values in lower-shoreface facies, 2.05–2.47 averaged at 2.33, are generally higher than that in upper-shoreface facies, 1.79–2.30 averaged at 2.11. Fractal dimension values in bar and beach microfacies are commonly lower than those in trough microfacies. Combined with additional sedimentary information from various clastic deposits, the fractal dimension can serve as a new depositional environment indicator.