Effects of non-conserved denominators on pearce element ratio diagrams

Abstract

Pearce element ratios (PER's) have “conserved” denominators which have not participated in the material transfer processes that cause chemical variations in rocks. Theoretically, there is no truly conserved element (constituent) which can be used as a PER denominator because in every material transfer process all constituents have non-zero concentrations in the phases that are being transferred. Thus, constituents used as denominators of PERs may have undergone at least a small amount of material transfer. This communication investigates the degree to which a non-conserved PER denominator changes the trend of data produced by a material transfer process from that produced by the same process but plotted on a PER diagram with a truly conserved denominator. An equation is developed that utilizes the partition coefficient as the measure of the degree of involvement of the denominator constituent in the phase undergoing transfer. This equation is examined to determine how the magnitude and direction of a PER diagram data trend change with increasing involvement of the denominator constituent in the transferring phase. A set of plagioclase fractionation examples are presented which use different elements as PER denominators and consider the effects that small amounts of these elements in the plagioclase structure will have on the data trend, as a function of the element partition coefficient between crystal and melt. Results demonstrate that the direction of change in slope of a material transfer data trend is a function of the initial relative magnitudes of the numerator constituents on the PER diagram. Additionally, if the amount of involvement of a PER denominator in a separating phase is very small relative to the amount of the numerator constituents in the separating phase, there is no significant change in the data trend caused by material transfer on a PER diagram. Moreover, if the denominator constituent substitutes for a numerator constituent in the phase undergoing transfer, the intercept of the trend of the data may not converge to zero when there is a large partition coefficient, as would be expected from theory. Thus, statistical tests to determine if a PER denominator is conserved, which evaluate whether the intercept is significantly different from zero, may not be very powerful because a large amount of denominator variation is necessary before the intercept of a data trend is forced through the origin, if at all.