Norman M. Evensen

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.

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.

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.

The Edge of Time: Dating Young Volcanic Ash Layers with the 40Ar-39Ar Laser Probe

Argon-40-argon-39 single-crystal dating of young (5000 to 30,000 years ago) volcanic ash layers erupted from the Mono Craters, California, shows that the method can yield meaningful ages in Holocene tephra. Because of ubiquitous xenocrystic contamination, the data do not form isochrons but plot in wedge-shaped regions on an argon isotopic diagram. The upper boundary of the region is an isochron matching the 14C-derived age of the eruption. Such contamination-related patterns may be common in dating young materials by the single-crystal method. Argon dating by this method can help refine the time scale of physical and biological evolution over the past 100,000 years.

Single-crystal 40Ar-39Ar dating of pyrite: No fool's clock

Single crystals of dispersed trace pyrite from two igneous rocks were dated by using the 40 Ar- 39 Ar laser probe method, and the resulting ages were compared to step-heating ages of associated amphibole and phlogopite. The isochron ages for 0.1–0.3 mm cubes of pyrite agree well with the respective amphibole ages of these igneous samples. Preliminary step-heating analyses of single pyrite crystals yield internal isochrons with indistinguishable, although less precise, ages. Both pyrite and amphibole are significantly older than associated phlogopite in one sample, which has undergone postcrystallization alteration. These results suggest that pyrite can give reliable and precise 40 Ar- 39 Ar ages even in the presence of subsequent alteration. Given the ubiquity of pyrite in many geologic environments, this technique has great promise for application to the dating of ores, sediments, and hydrocarbon migration, all of which have been very difficult to date directly.

Lasing in the Holocene: extending the 40Ar39Ar laser probe method into the 14C age range

Abstract Dating methods applicable to the last 50,000 yr, such as 14 C, require absolute calibrations, which are difficult to obtain over much of this interval. Extension of the 40 Ar 39 Ar isochron technique to ages 14 C dating. We have dated the Mono craters, California, at 12,560 ± 470 yr, using laser fusion to generate an isochron from 63 sanidine crystals from 5 sites. The near-atmospheric initial isotopic ratios and the agreement in ages from all sites suggest that no significant excess argon is present. It thus appears that, particularly with improved instrumentation and techniques currently under development, most of the 14 C age range is accessible to 40 Ar 39 Ar laser dating.

Under the volcano: A new dimension in Ar‐Ar dating of volcanic ash

A significant part of the history of the Greek island of Kos has been decoded from a handful of volcanic ash by argon-argon laser probe dating of single crystals of the minerals sanidine, plagioclase and quartz. On a 3-D argon isotope plot, the data define six straight lines, corresponding to four distinct volcanic events from 161 to 1728 ka. All four events produced plagioclase crystals, whose ages and Ca/K ratios are consistent with the known evolution of the rest of the Aegean arc. Sanidine appeared only in the final eruption at 161 ka. The joint occurrence of quartz and plagioclase at a 925 ka event implies that quartz did not reside for millennia in the magma, as has been suggested for quartz from the Bishop Tuff, California. The step-heated cooling age of a schist fragment from the ash provides the first radiometric evidence for ∼250 Ma crust under the volcano.