A basic end-member model algorithm for grain-size data of marine sediments

Abstract End-member (EM) unmixing algorithms are widely used in the earth sciences for unmixing compositional data such as grain-size data of sediments. However, many unmixing algorithms only use goodness-of-fit measures that justify the EMs in the absence of geological feasibility, and others tend to find EMs that enclose the sample points as tightly as possible, resulting in the calculated EMs are still mixed products, especially when unmixing highly mixed dataset. This paper proposes that EM unmixing algorithms should search for the Basic-EMs, i.e., the outermost points in the EM space. The EMs that can be unmixed by mathematics can also be purified by physical processes, i.e., the actual EMs are most likely the Basic-EMs. This paper also introduces a basic end-member model algorithm (BasEMMA) that uses genetic algorithms which mimic natural evolution processes, to seek the Basic-EMs. The evaluations by BasEMMA using both artificial and actual grain-size data show that BasEMMA can accurately find the Basic-EMs. This paper also introduces a procedure for determining the appropriate EM number, which has plagued previous researchers. In summary, this paper introduces a new way to determine geologically feasible EMs, a new EM unmixing algorithm and a new method to determine the appropriate EM number.