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K. Hron, M. Engle, P. Filzmoser, E. Fiserová:
"Weighted symmetric pivot coordinates for compositional data with geochemical applications";
Mathematical Geosciences, 4 (2020).

Negative correlations between elements, molecules, or minerals can indicate a variety of geochemical processes, such as ion exchange, incongruent mineral precipitation/dissolution, and redox reactions. However, compositional data (those composed of relative parts) can also exhibit negative correlations simply due to displacement of one part by another, such as the addition of sodium chloride lowering the concentration of all ions other than sodium and chloride in a solution. Apart from this practical problem, the question is more general: how to address the relationships between components in data carrying relative information. For this purpose, the symmetric pivot coordinates were developed which allow for the identification of both positive and negative correlations between two parts in compositional data in terms of their relative dominance to the other parts. Accordingly, the symmetric pivot coordinate approach aggregates all of the logratios with those two parts of interest. This may not be desirable if data quality problems occur, because such parts would contribute the same weight to the coordinate as parts with good data quality. As a way out, the new method of weighted symmetric coordinates focusing on pairwise associations is proposed. In this approach, variables with large logratio variances are down-weighted to suppress their effect on the remaining variables, which is also demonstrated in a small simulation study. Finally, the weighted symmetric pivot coordinates are applied to chemistry data from a series of waste water samples from oil and gas wells produced from the lower Eagle Ford Group in the U.S. Gulf Coast Basin. In particular, strong negative correlations between ions are examined using this method to reveal processes which occur as a function of depth, including clay diagenesis, de-dolomitization, kerogen maturation, and sulfate and carbonate mineral saturation.

http://dx.doi.org/10.1007/s11004-020-09862-5

https://link.springer.com/article/10.1007%2Fs11004-020-09862-5