Computing the area of a spherical polygon of arbitrary shape

An algorithm for determining the area of a spherical polygon of arbitrary shape is presented. The kernel of the problem is to compute the interior angle at each vertex of the spherical polygon; a well-known relationship between the area of a spherical polygon and the sum of its interior angles then may be exploited. The algorithm has been implemented as a FORTRAN subroutine and a listing is provided. Both algorithm and subroutine are general in their capabilities and can be used, for example, to determine the area of a spherical polygon containing one or more holes.     

Polar Compounds from the Dissolution of Weathered Diesel

Hydrocarbon and nonhydrocarbon components dissolving in water from fresh diesel and field samples of highly weathered diesel (spilled up to 50 years ago) from two sites were investigated. The fresh and weathered diesels were equilibrated with water using a slow-stirring method, and the product and equilibrated aqueous water samples analyzed by a range of analytical procedures. The water phase equilibrated with weathered diesels had higher total dissolved organics concentrations (96 and 8.6 mg/L at the two sites) compared to the water phase equilibrated with fresh diesel (average of 3.4 mg/L). Compound class characterization of dissolved organics in water from the weathered diesel showed that polar components were a significant compound class (98% and 42% at the two sites) and appeared largely as an unresolved complex mixture (UCM) in the total ion chromatograms (TICs). Identification of 1-adamantanol in the polar fraction of both weathered diesel samples (3.6 and 0.3 μg/L at the two sites) suggested that at least some of the associated polar components are from a petroleum source. The analysis of total petroleum hydrocarbons (TPH) is aimed at measuring only dissolved carbon and hydrogen-containing compounds, and dissolved polar compounds present as a UCM are often assumed to be from natural organic matter (NOM) and removed. This may result in a gross underestimation of the total soluble organic material in water associated with weathered diesels. In addition, the risk posed by these fuel-derived polar compounds is unknown.     

Regional beryllium-10 production rate calibration for late-glacial northeastern North America

The major uncertainty in relating cosmogenic-nuclide exposure ages to ages measured by other dating methods comes from extrapolating nuclide production rates measured at globally scattered calibration sites to the sites of unknown age that are to be dated. This uncertainty can be reduced by locating production rate calibration sites that are similar in location and age to the sites to be dated. We use this strategy to reconcile exposure age and radiocarbon deglaciation chronologies for northeastern North America by compiling ¹⁰Be production rate calibration measurements from independently dated late-glacial and early Holocene ice-marginal landforms in this region. ¹⁰Be production rates measured at these sites are 6–12% lower than predicted by the commonly accepted global ¹⁰Be calibration data set used with any published production rate scaling scheme. In addition, the regional calibration data set shows significantly less internal scatter than the global calibration data set. Thus, this calibration data set can be used to improve both the precision and accuracy of exposure dating of regional late-glacial events. For example, if the global calibration data set is used to calculate exposure ages, the exposure-age deglaciation chronology for central New England is inconsistent with the deglaciation chronology inferred from radiocarbon dating and varve stratigraphy. We show that using the regional data set instead makes the exposure age and radiocarbon chronologies consistent. This increases confidence in correlating exposure ages of ice-marginal landforms in northeastern North America with glacial and climate events dated by other means.     

Comment on Fofonoff's mode

Abstract

Recently Merkine, Mo and Kalnay (1985) have re-examined the possible existence of Fofonoff's (1954) steady free inertial solution and the role of Fofonoff's mode in numerical circulation models after Veronis (1966). Merkine et al. conclude that the Fofonoff mode does not occur, that such a mode would be barotropically unstable and that resemblances between numerical circulations and Fofonoff's mode are more dependent upon the natures of forcing and dissipation. On the contrary, I suggest that Fofonoff's mode very naturally does emerge and that forcing and dissipation only impede the full realization of Fofonoff's mode. Moreover, statistical mechanical arguments from Salmon, Holloway and Hendershott (1976) show that the Fofonoff mode is expected to co-exist with a transient eddy field whose statistics are in equilibrium with the mode; thus bartotropic instability does not argue for non-realization of Fofonoff's mode.     

Mechanisms for incompatible-element enrichment on the Moon deduced from the lunar basaltic meteorite Northwest Africa 032

The lunar meteorite Northwest Africa (NWA) 032 is a low-Ti basalt that has incompatible-element abundances and Th/Sm ratios characteristic of the involvement of late stage magma ocean crystallization products (urKREEP) in its petrogenesis. This sample is very fine-grained and contains terrestrial weather products. A progressive leaching procedure was therefore developed and applied to magnetic separates and whole rock fractions to obtain Rb-Sr and Sm-Nd ages. Although many of the leachates, as well as the unleached mineral and whole rock fractions contain terrestrial alteration products, selected residue fractions yield concordant Rb-Sr and Sm-Nd ages. Rubidium-Sr isotopic analyses yield an age of 2947 ± 16 Ma with an initial ⁸⁷Sr/⁸⁶Sr of 0.700057 ± 17. These characteristics indicate NWA 032 is derived from a source region with an ⁸⁷Rb/⁸⁶Sr ratio of 0.044 ± 0.001. This value is higher than all but those determined for KREEP basalts, and suggests that NWA 032 is derived from a source region that has higher incompatible-element abundances than other low-Ti basalts. Samarium-neodymium isotopic analysis yield a concordant age of 2931 ± 92 Ma and an initial ε_Nd of +9.71 ± 0.74 corresponding to a source region with ¹⁴⁷Sm/¹⁴⁴Nd ratio of 0.246 ± 0.004. The initial Nd isotopic composition stands in contrast to the initial Sr isotopic composition by requiring NWA 032 to be derived from a source with lower incompatible-element abundances than most low-Ti basalts. The source of NWA 032 is therefore unlike those of other lunar basalts.Modeling of magma ocean cumulate formation demonstrates that unlike other low-Ti basalt source regions the NWA 032 source is a mixture of olivine, pigeonite, and clinopyroxene bearing cumulates and only a small amount of urKREEP. Furthermore, unlike other mare basalt sources, the NWA 032 source does not contain appreciable quantities of plagioclase. Partial melting models demonstrate that the incompatible-element characteristics of the NWA 032 result from formation by smaller degrees of partial melting than other mare basalts. Thus, the incompatible-element geochemical signature that is observed in NWA 032 appears to reflect the combined effects of generation from an unusual plagioclase-free incompatible-element-depleted source region by very small degrees of partial melting. This study demonstrates that both the presence of urKREEP in the source region and small degrees of partial melting generate magmas with similar, but not identical, incompatible-element characteristics. In addition, it underscores the fact that there is significantly more geochemical diversity on the Moon than is represented by samples collected by the American and Soviet lunar missions.     

Inner Solar System dynamical analogs of plutinos

By studying orbits of asteroids potentially in 3:2 exterior mean motion resonance with Earth, Venus, and Mars, we have found plutino analogs. We identify at least 27 objects in the inner Solar System dynamically protected from encounter through this resonance. These are four objects associated with Venus, six with Earth, and seventeen with Mars. Bodies in the 3:2 exterior resonance (including those in the plutino resonance associated with Neptune) orbit the Sun twice for every three orbits of the associated planet, in such a way that with sufficiently low libration amplitude close approaches to the planet are impossible. As many as 15% of Kuiper Belt objects share the 3:2 resonance, but are poorly observed. One of several resonance sweeping mechanisms during planetary migration is likely needed to explain the origin and properties of 3:2 resonant Kuiper Belt objects. Such a mechanism likely did not operate in the inner Solar System. We suggest that scattering by the next planet out allows entry to, and exit from, 3:2 resonance for objects associated with Venus or Earth. 3:2 resonators of Mars, on the other hand, do not cross the paths of other planets, and have a long lifetime. There may exist some objects trapped in the 3:2 Mars resonance which are primordial, with our tests on the most promising objects known to date indicating lifetimes of at least tens of millions of years. Identifying 3:2 resonant systems in the inner Solar System permits this resonance to be studied on shorter timescales and with better determined orbits than has been possible to date, and introduces new mechanisms for entry into the resonant configuration.