Derek York

Least squares fitting of a straight line with correlated errors

Earlier least squares treatments of the fitting of a straight line when both variables are subject to crrors are generalized to allow for correlation of the z and y errors. The method is illustrated by reference to lead isochron fitting.

Unified equations for the slope, intercept, and standard errors of the best straight line

It has long been recognized that the least-squares estimation method of fitting the best straight line to data points having normally distributed errors yields identical results for the slope and intercept of the line as does the method of maximum likelihood estimation. We show that, contrary to previous understanding, these two methods also give identical results for the standard errors in slope and intercept, provided that the least-squares estimation expressions are evaluated at the least-squares-adjusted points rather than at the observed points as has been done traditionally. This unification of standard errors holds when both x and y observations are subject to correlated errors that vary from point to point. All known correct regression solutions in the literature, including various special cases, can be derived from the original York equations. We present a compact set of equations for the slope, intercept, and newly unified standard errors.

Geothermometry from 40Ar39Ar dating experiments

Abstract We have selected a variety of minerals from three basic intrusions within the high-grade metamorphic terrane near Haliburton, Ontario, for K-Ar dating. By application of 40 Ar 39 Ar incremental heating experiments, we conclude that the discordant K-Ar mineral dates can best be explained by a slow-cooling history. From the stepwise heating experiments we calculated isotopic closure temperatures using Dodsons theory for slow-cooling and from these constructed a cooling curve. This curve was then compared to independent constraints to test the overall validity of our procedures and assumptions. The results are geologically reasonable insofar as: 1. (a) the maximum calculated temperatures (from hornblendes) of ∼-700°C are consistent with independent, approximate metamorphic grid arguments: 2. (b) the Ar closure temperatures for biotites (350–400°C) are consistent with independent evidence, and 3. (c) minerals with older K-Ar dates have higher calculated closure temperatures. The resultant geological cooling curve implies that a maximum temperature of >700 C was reached before 1000 Ma ago and thereafter the temperature decreased via changes in uplift and cooling rates to below 200°C by 700 Ma ago. We have discovered that plutonic plagioclases are very sensitive indicators (comparable to K-felds-pars) of Ar loss and, therefore, can usefully extend the range of application of the 40 Ar 39 Ar stepwise heating method. We also describe experiments in which we have tested the effects on the Ar systematics of acid leaching of plagioclases.

The best isochron

Abstract A pictorial presentation is made of the least squares cubic method of constructing straight lines such as Rb-Sr isochrons. It is shown that the somewhat complicated analytical expressions have simple pictorial representations.

Single grain argon laser probe dating of phengites from the blueschist to greenschist transition on Sifnos (Cyclades, Greece)

Measurements of 40Ar/39Ar age spectra on single white mica crystals of Tertiary age is a new means of obtaining detailed geochronological information of Alpine blueschists. Internal consistency of the data set, as well as excellent agreement with previous conventional K−Ar results, demonstrates that this new technique can be used with confidence to obtain information on the thermal evolution of young metamorphic belts.As mineral grains can be dated individually with this technique, problems related to multiple generations of mica occurring side in the rock can be addressed, potentially yielding much information which cannot be obtained easily by other dating techniques. Ages decrease from 41.7±0.3 Ma in the fresh blueschists and eclogites in northern Sifnos to ca 30 Ma in the more severely overprinted greenschists of central Sifnos. It is argued that this decreasing trend appears gradual, rather than stepwise. This gradual character of the age trend is taken to indicate that it may be caused by differential uplift and cooling, rather than by tectonic juxtaposition of different rock units. In addition, the rocks of central Sifnos contain mica with a plateau age of 18.9±0.3 Ma. This latter age is younger than previous estimates for the age of greenschist overprinting, and more in line with the age of high temperature metamorphism and granite emplacement elsewhere in the Cyclades.

The age of the Popigai impact event and its relation to events at the Eocene/Oligocene boundary

Ages ranging from the Late Cretaceous (∼65 Myr) to the Oligocene (∼29 Myr) have been reported for the 100-km-diameter Popigai impact structure on the Anabar shield, central Siberia. These ages overlap the timing of several possible impact-related features, including the Cretaceous/Tertiary and Eocene/Oligocene stratigraphic boundaries, the North American tektites, and the recently reported occurrences of an iridium anomaly and shocked quartz in Late Eocene deposits in northern Italy. Here we report age determinations of several Popigai impact melt rocks using the 40Ar–39Ar step heating technique to constrain the age of the impact event. Our results are consistent with a Late Eocene impact age of 35.7± 0.2 Myr (2σ)—coincident in time with the impact deposits found in Italy. As this age is also similar to that of the North American tektites, which have been associated with the Chesapeake Bay impact structure in the eastern United States, there seem to have been at least two large and essentially contemporaneous impacts during the Late Eocene.

Additional 40Ar-39Ar dating of the basement and the alkaline volcanism of Gorringe Bank (Atlantic Ocean)

Abstract 40 Ar/ 39 Ar step heating analyses are reported for a variety of samples from Gorringe Bank (Atlantic Ocean). Flat age spectra for two primary, igneous hornblendes of Gorringe (corresponding to an age of 143 Ma) show that the K-Ar ages obtained on these samples by Prichard and Mitchell [4] are evidently crystallization and not hybrid ages. This sustains the concept of an initiation age of 140 Ma [4] for Gorringe Bank. No support is found for Carpenas suggestion [7] that the formation of Gorringe Bank began 200 Ma ago. Secondary hornblendes from Ormonde seamount rocks appear to have formed shortly after the initiation of the Bank. Precise plateau ages on samples of two alkaline volcanics from Ormonde correspond to the older limit of the alkaline volcanism suggested by Feraud et al. [3,5].

Single crystal 40Ar‐39Ar dating of a Late Quaternary paroxysm on Kos, Greece: Concordance of terrestrial and marine ages

The late Quaternary plinian eruption forming the Kos Plateau Tuff on the island of Kos, Greece, was one of the largest in the Mediterranean. A precise date for this eruption would significantly improve the chronology of the deep-sea tephra layer W-3, because reliable correlation of W-3 with the KOS Plateau Tuff has been previously established. We have dated sanidine from the eruption at 161.3±1.1 ka using the laser-fusion single crystal 40Ar-39Ar technique. This age represents a significant refinement over both conventional and highly precise (Cassignol method) K-Ar ages, and the 40Ar-39Ar age is shown to be in remarkably good agreement with the age of W-3 inferred from recent astronomically calibrated oxygen isotope chronologies.

40Ar39Ar step-heating and laser fusion dating of a quaternary pumice from Neschers, Massif Central, France: The defeat of xenocrystic contamination

K-feldspars from a Quaternary pumice flow near Neschers, France, yield 40Ar39Ar age spectra which display a marked “saddle shape” whose minima are well in excess of the age of an underlying basalt unit. The K-feldspars form two populations: (1) a group of euhedral and clear crystals; and (2) a group of rounded cloudy grains. By 40Ar39Ar dating of individual grains by laser fusion it was possible to demonstrate that the clear grains are 0.58 Ma old, while the cloudy grains are contaminating ancient feldspars with ages as old as 330 Ma. Subsequently, hand-picked mineral separates were analysed by step-heating in a radio-frequency fusion system and the results show: (1) the ancient cloudy grains are probably Hercynian-age feldspars which were included in the young pumice during eruption and have only lost modest amounts of 40Ar during the eruptive re-heating; and (2) the saddle shape of the original 40Ar39Ar age spectra was due solely to the different Ar-release patterns of the two populations of feldspars and not due to excess 40Ar incorporated within all of the grains. This study shows that the ability to measure single grains is critical in unravelling the ages of young volcanic materials when country-rock contamination is likely. Conventional KAr ages of bulk samples of hand-picked feldspars may be seriously in error, even when contaminations are at a level of less than one grain in a thousand.

First successful 40Ar-39Ar dating of glauconies: Argon recoil in single grains of cryptocrystalline material

Potassium-argon dating of glaucony, one of the few widely occurring authigenic materials in the sedimentary record, has provided a large percentage of the dates used for the calibration of the geologic time scale. This material has been considered unsuitable for 40 Ar- 39 Ar dating because of the large losses of neutron-induced 39 Ar during or subsequent to irradiation of samples. We have measured recoiled 39 Ar and 37 Ar from single grains of glaucony (100-350 μm in diameter). Irradiations were done both in air and in vacuo by using a microampoule technique of encapsulation. The observed in vacuo behavior of recoiled atoms can be readily understood by a simple model of their interaction with the network of very fine laminae composing the grains. When the microampoule technique is used, the integrated 40 Ar- 39 Ar ages and their associated precision compare very favorably with conventional K-Ar results. Because glauconies are inherently heterogeneous populations, owing to their complex evolution, it is anticipated that single-grain 40 Ar- 39 Ar dating may lead to significant refinements in the geologic time scale, especially for the Cenozoic.