QGrain: An open-source and easy-to-use software for the comprehensive analysis of grain size distributions

In the last hundred years, analyses of grain size have been widely performed, and numerous powerful tools have been published. The unmixing of grain size distributions is a popular topic in recent research. As one kind of decomposition method, single-sample unmixing (SSU) is usually regarded as not genetically meaningful with another unmixing method, end-member modeling analysis (EMMA), although it is still widely used. Some recent studies have noted that EMMA also has limits, and different EMMA algorithms may yield various results. However, no research has discussed the similarities and differences between EMMA and SSU and provided objective conclusions regarding their ranges of application. In this study, a detailed discussion is given regarding the similarities and differences of these methods based on the corresponding mathematical models, and detailed explanations of their features are presented based on numerical optimization and information theory. In addition, the ranges of application are objectively constrained, and we suggest that SSU may have greater potential, although the corresponding fitting process is more complex and difficult. We also highlight the importance of a comprehensive analysis. Traditional methods and geological settings are also important for the interpretation of grain size distributions. An easy-to-use software for the comprehensive analysis of grain size distributions called QGrain is introduced; it not only integrates many traditional analysis tools but also provides new high-performance EMMA and SSU algorithms. Compared to other EMMA algorithms, our EMMA algorithm exhibits outstanding performance. Furthermore, our SSU algorithm can overcome the shortcomings of the traditional method and can compete and collaborate with EMMA algorithms.