Estimating the duration of geologic intervals from a small number of age determinations: A challenge common to petrology and paleobiology

Abstract

The duration of a geologic interval, such as the time over which a given volume of magma accumulated to form a pluton, or the lifespan of a large igneous province, is commonly determined from a relatively small number of geochronologic determinations (e.g., 4–10) within that interval. Such sample sets can underestimate the true length of the interval by a significant amount. For example, the average interval determined from a sample of size n = 5, drawn from a uniform random distribution, will underestimate the true interval by 50%. Even for n = 10, the average sample only captures ∼80% of the interval. If the underlying distribution is known then a correction factor can be determined from theory or Monte Carlo analysis; for a uniform random distribution, this factor is n+1n−1. Systematic undersampling of interval lengths can have a large effect on calculated magma fluxes in plutonic systems. The problem is analogous to determining the duration of an extinct species from its fossil occurrences. Confidence interval statistics developed for species origination and extinction times are applicable to the onset and cessation of magmatic events.

Pulsed magmatic fluid release for the formation of porphyry deposits: Tracing fluid evolution in absolute time from the Tibetan Qulong Cu-Mo deposit

“…The pulsed magmatic fluid flux inferred from δ 18 O fluid is in agreement with the cyclic mineralization process defined by Re-Os dating, and therefore suggests that the three intermittent pulses defined by Re-Os dating (Li et al, 2017a) are robust, rather than an artifact caused by undersampling (Glazner and Sadler, 2016). For example, if the duration of the first mineralization pulse is underestimated, then the decreasing trend of δ 18 O fluid would extend beyond the interval determined by Re-Os dating.…”

“…In contrast, a pulsed hydrothermal process is obvious for active magmatic systems, and also has been proposed for the formation of porphyry deposits, as shown by high-precision U-Pb zircon and Re-Os molybdenite dating (Stein, 2014;Spencer et al, 2015;Buret et al, 2016;Tapster et al, 2016;Li et al, 2017a). However, the duration of a geological event could be significantly underestimated from a relatively small number (e.g., <10) of chronologic determinations (Glazner and Sadler, 2016); hence, the intermittent pulses inferred from radiometric dating could be biased from dating a protracted event.…”

Timing and evolution of Middle Triassic magmatism in the Southern Alps (northern Italy)

“…As these ash beds are also stratigraphically constrained to be the oldest and youngest products within the stratigraphic interval investigated in this study, we are confident that this duration is not significantly underestimated due to under-sampling (e.g. Glazner & Sadler 2016).…”

Constraints on the timescales and processes that led to high-SiO2 rhyolite production in the Searchlight pluton, Nevada, USA

“…5B). These durations should be considered minimum estimates for the duration of magma emplacement and crystallization, because (1) it is impossible for zircon to record the interval of time that the magma spent at temperatures above zircon saturation; (2) there is difficulty in sampling small domains that grew at low melt fractions; and (3) there is a tendency for low-n geochronologic data sets to underestimate duration when the analytical precision is small relative to the duration of interest (e.g., Glazner and Sadler, 2016).…”