Linear Unmixing in the Geologic Sciences: More Than A Half-Century of Progress

Abstract

For more than a half-century, scientists have been developing a tool for linear unmixing utilizing collections of algorithms and computer programs that is appropriate for many types of data commonly encountered in the geologic and other science disciplines. Applications include the analysis of particle size data, Fourier shape coefficients and related spectrum, biologic morphology and fossil assemblage information, environmental data, petrographic image analysis, unmixing igneous and metamorphic petrographic variable and the unmixing and determination of oil sources, to name a few. Each of these studies used algorithms that were designed to use data whose row sums are constant. Non-constant sum data comprise what is a larger set of data that permeates many of our sciences. Many times, these data can be modeled as mixtures even though the row sums do not sum to the same value for all samples in the data. This occurs when different quantities of one or more end-member are present in the data. Use of the constant sum approach for these data can produce confusing and inaccurate results especially when the end-members need to be defined away from the data cloud. The approach to deal with these non-constant sum data is defined and called Hyperplanar Vector Analysis (HVA). Without abandoning over 50 years of experience, HVA merges the concepts developed over this time and extends the linear unmixing approach to more types of data. The basis for this development involves a translation and rotation of the raw data that conserves information (variability). It will also be shown that HVA is a more appropriate name for both the previous constant sum algorithms and future programs algorithms as well.

Simulating our ability to accurately detect abrupt changes in assemblage-based paleoenvironmental proxies

“…Time-averaged sedimentary samples that represent mixtures of non-contemporaneous environmental conditions are often difficult to differentiate from true intermediate environmental conditions. Previous studies have recognized this temporal averaging and have attempted to "unmix" fossil assemblages or geochemical records to deconvolve the paleoenvironmental signal, however these methods require knowledge of the end member assemblage compositions, underlying linear relationships among the variables (Schiffelbein, 1985;Zellers and Gary, 2007;Full, 2018;Liu et al, 2021), or information that assigns constituent specimens to different ages (Wit et al, 2013;Tomašových et al, 2017). Instead of this inverse approach where an observed assemblage is "unmixed," others have designed forward models in which they impose simulated sedimentary processes on a simplified, modeled, time-series of chemical or faunal variables and measure the resulting impact on the proxy record (Hutson, 1980;Trauth, 1998;Lowermark et al, 2008;Evans et al, 2013;Trauth, 2013;Dolman and Laepple, 2018;Hülse et al, 2022).…”