Bootstrap techniques and the location of the source of siliciclastic detritus in the lower Paleozoic Shoo Fly Complex, northern Sierra terrane, California

Abstract

Published data unambiguously indicate that the source of clastic materials in the lower southwestern miogeocline is located in the adjacent interior of North America. In contrast, the source of siliciclastic materials in the Shoo Fly Complex has been difficult to locate due to its location outboard of clear-cut aboriginal North American materials. Because the Shoo Fly Complex is west of the southern segment of the North American craton that is dominated by Proterozoic components, we explore in this chapter whether the source of detritus in the Shoo Fly Complex was restricted to this southern segment. Our approach in addressing this question was to collect and chemically analyze a number of mudstone samples from the southwest Cordilleran miogeocline and from the Shoo Fly Complex. As a measure of central tendency we utilized the Aitchison Measure of Location (AML). If mudstones from both areas were derived from the same source, then they should have similar compositions. Hence, under this condition the ratios of c 1 m i o /c 1 S F C , c 2 m i o /c 2 S F C , ..., c n m i o /c n S F C should equal 1, where mio refers to a constituent of the miogeoclinal sampling group, subscript SFC refers to a constituent of the Shoo Fly Complex group, and c 1 ,c 2 ,... ,c m are AML-based average concentrations of chemical constituents 1 through m. In order to address the inherent statistical uncertainties in these ratios we developed a Visual Basic 6 bootstrap program. The results of 5000 bootstrap replications indicate that 60% of the constituent ratios (i.e., c 1 m i O /c 1 S F C , c 2 m i o /c 2 S F C , ..., C n m i o /c n S F C ) are statistically different from 1 at the 95% confidence level. We therefore conclude that samples analyzed from the southwest Cordilleran miogeocline and from the Shoo Fly Complex did not share the same source. Where was the source of detritus in the Shoo Fly Complex? Published single-crystal U-Pb detrital zircon data show that the detrital zircon population in a number of samples analyzed from the Shoo Fly Complex contains an Archean component. In addition, the cumulative probability diagram of single-crystal U-Pb detrital zircon ages from the Shoo Fly Complex is similar to that produced by detrital zircon ages derived from miogeoclinal strata, the source of which was located in northwestern North America. Hence, these and other data discussed in this chapter are consistent with the idea that the source of the voluminous siliciclastic detritus in the Shoo Fly Complex was probably located in northwestern rather than southwestern North America.