| Sediments are solid particles that are moved by fluids and eventually settle to the bottom of the liquid,its grain size is the diameter or "size" of the sediment grains,and the grain size distribution frequency data of sediment contains plenty of valuable information.Grain size distribution and the dynamic conditions of sediment formation can form a good corresponding relation,and the grain size distribution can be used as an important basis for revealing the provenance,transportation,and depositional environment of the sediment.The grain size distribution frequency data is expressed as the percentage of each grain size in the grain size population.Grain size parameters such as mean,sorting,skewness and kurtosis can well characterize the grain size distribution frequency data of sediments,these parameters can be calculated by graphic method and moment method generally.Grain size distribution of sediment is generally superimposed by several secondary distributions,mostly presenting in the form of bimodal or multi-modal.In purpose of exploring the rich implicit information in the grain size distribution,researchers have introduced many statistical methods into the grain size analysis work and proposed numerous methods such as grain size distribution subpopulation separation method,probability density function fitting method and endmember model algorithm and applied these methods to the decomposition of the grain size distribution.Several subpopulations can be obtained by unmixing the grain size distribution,and the superposition of the individual subpopulation is the fitting population of sediment grain size distribution.The conventional probability density function fitting method mechanically considers each subpopulation of multi-modal grain size distribution sample as obeying the same family of distributions.In pure sandstones,however,due to dust and sediment fill in the grains,the grain size distributions of rock sand and fine grains do not necessarily come from the same distribution family.Therefore,using probability density function from a single distribution family to separate and extract the subpopulations from the multiple populations has some limitations.In view of this,the present thesis combines probability density functions of different distribution families,including the normal,skew normal and Weibull distributions,and applies them to the decomposition of grain size distribution.The nonlinear least square method is used to solve the combined model to minimize the error between the fitting data and the original data.The grain size parameters were calculated by Folk-Ward formula and moment value method respectively.In this paper,a software named SS-GSD is compiled on the MATLAB platform based on the above methods,and compared with the existing software GRADISTAT and CFLab,which were designed for unmixing the grain size distribution.GRADISTAT,CFLab and SS-GSD were used to decompose and fit 131 bimodal grain size distribution sample data from an offshore oil field in China,respectively.Only a small part of the grain size parameters obtained by GRADISTAT are consistent with the original granularity parameters.The mean and kurtosis obtained by CFLab are basically consistent with those of the original data,while the sorting and skewness deviate from those of the original data.The grain size parameters obtained by SS-GSD are basically consistent with the grain size parameters of the original data,which indicates that the subpopulations and fitted populations decomposed and fitted by SSGSD basically restore the information of the original data.The coefficients of determination between the fitted 131 populations and the original samples fluctuated from 0.851 to 0.998,with the mean value of 0.9783 and the variance of 0.0001;the MSE fluctuated from 0.0258 to 2.1226,with the mean value of 0.25 and the variance of 0.1326,indicating that the method was effective in the separation and extraction of the subpopulations of the grain size distribution and the fitting of the populations. |
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