Combining double probability distribution functions to unmix bimodal grain-size distributions of sediments

Grain-size distribution (GSD) is the superposition of multiple subpopulations from different sedimentary processes, conveying the indispensable message of original sediments, and the frequency curve may show a bimodal character. Traditional methods of sedimentological grain-size analysis use a single probability density function (PDF) to fit their frequency profile. In practice, however, the sandstone and small grain compositions do not necessarily come from the same distribution family. The mixture distribution model is based on mixing PDFs from two different distribution families and provides a novel technique for decomposing GSD data from bimodal sediments. Taking 131 bimodal sediment GSD data from an offshore oil field in China as an example, 262 subpopulations are separated and extracted by using the mixture distribution model. Calculating the mean, sorting, skewness, and kurtosis of all samples by Folk-Ward formula, while these of subpopulations are calculated by moment method. The average coefficient of determination and fitting residual between 131 fitted GSD data and original samples are 0.9783 and 0.25, which indicates that the fitting quality is excellent. The variance of coefficient of determination and fitting residual for these 131 samples are 0.0001 and 0.1326 respectively, illustrating that the fit results fluctuated little and the fit was stable. The results demonstrate that the mixture distribution model is effective in fitting and unmixing the sediment GSD frequency data.