A normal approximation to the Fisher distribution

Summary. A simple normal approximation is given for the joint probability density function of the polar coordinates (θ, φ) of a random vector following the Fisher distribution with arbitrary mean direction (θ₀, φ₀). Two important applications of this approximation are discussed, and conditions for the validity of the approximation are investigated and summarized.     

Guidelines for international data collection and resource assessments and analyses

The ever-increasing world interdependency required to provide the basic energy and mineral commodities needed by society, has created a need to assess, on a common basis, the location, number, and quality of deposits of natural resources. In order to evaluate and compare the resource potential of any area, two major factors must be considered: (1) the type of commodity being evaluated and (2) the specific parameter (reserves or resources) which is being defined. Each commodity or parameter being studied requires a separate methodology for analysis and different basic data. Porphyry copper deposits must be treated differently from stratabound copper deposits or massive sulfide deposits of copper. Similarly, oil and gas deposits associated with stratigraphic traps must be treated differently from those associated with salt domes. Resource assessments attempt to estimate the aggregate resource potential of an area whereas resource analyses attempt to define the specific characteristics of the individual occurrences which comprise the aggregate resource potential. Assessment programs may range from a national inventory of known deposits and occurrences to detailed studies which require an extensive integration of geological, geochemical, and geophysical data. Examples of national inventories are the small mine inventory of Bolivia and presently operating resource programs in Turkey and Argentina. Detailed programs of assessment include the AMRAP (Alaska Mineral Resource Appraisal Program) program and studies in the Coeur d'Alene district and Ely, Nevada. Worldwide resource analysis is a rapidly expanding field of endeavor necessitated by the need to more clearly define the characteristics of known deposits and to provide quantitative estimates of hypothetical and speculative resources. Studies presently underway deal with the development of search and occurrence models, field size distributions of energy resources, tonnage and grade relationships of mineral deposits, the zone of influence of exploratory drill holes, and models of the exploration process.This paper was presented at the International Geological Correlation Program (IGCP) Project 98 entitled Standards for Computer Applications in Resource Studies held at Loen, Norway, September 27–October 1, 1976.     

A high-sensitivity search for extraterrestrial intelligence at γ18 cm

We have conducted a targeted high-sensitivity search for narrow-band signals near γ18 cm using the 91-m radiotelescope of the National Radio Astronomy Observatory. The search included 201 nearby solar-type stars and achieved a frequency resolution of 5.5 Hz over a 1.4-MHz bandwidth. This high spectral Mark I VLBI recording terminal in conjunction with the CDC 7600 computational facility at the NASA-Ames Research Center. This is the first high-resolution search for narrow-band signals in this wavelength regime. To date it is the most sensitive search per unit observing time of any search strategy which does not postulate a unique magic frequency. Our data show no evidence for narrow-band signals due to extraterrestrial intelligence at a 12-σ upper limit on signal strength of 1.1 × 10^?23 W m^?2.     

Asteroids and meteorites: Origin of stony-iron meteorites at mantle-core boundaries

Stony-iron meteorites formed at the core/mantle interfaces of small asteroidal parents. The mesosiderites formed when the thick crust of a largely molten parent body (100–200 km in diameter) foundered and sank through the mantle to the core. Pallasites formed in smaller parent bodies (50–100 km) in which olivine crystals from the partially molten mantle sank to the core/mantle interface and rafted there. Subsequent collisions stripped away the rocky mantles of both kinds of parent bodies, exposing the stony-iron surfaces of their cores to direct impacts, which continue to knock off meteorite fragments.     

Characterization of potential zones of dust generation at eleven stations in the southern Sahara

Summary Synoptic wind data for multi-decadal periods at eleven stations located in the southern Sahara region (Agadez, Atar, Bilma, Dori, Gao, Kayes, Nema, Niamey, Nouadhibou, Ouagadougou and Tessalit) are used to study the monthly dust deflation power over the region. We found that, regardless of the conditions of the soil, the deflation power (or wind efficiency) is not sufficient to generate significant amounts of aerosols south of 15°N. North of this latitude, the deflation power is much larger, with potential zones of either very strong deflation (Nouadhibou and Bilma) or severe deflation (Gao, Tessalit, Nema, Atar, Agadez). Stations in the Sahel region such as Gao, Agadez and Tessalit are characterized by a gradual reinforcement of the deflation power between 1970 and 1984 in correspondence of increasing desertification over the region. During this same period, Bilma, a well know region of dust source, experienced a major reduction in deflation power due to shifts in large scale wind patterns.     

The middle Pleistocene transition: characteristics, mechanisms, and implications for long-term changes in atmospheric pCO2

The emergence of low-frequency, high-amplitude, quasi-periodic (100-kyr) glacial variability during the middle Pleistocene in the absence of any significant change in orbital forcing indicates a fundamental change internal to the climate system. This middle Pleistocene transition (MPT) began 1250 ka and was complete by 700 ka. Its onset was accompanied by decreases in sea surface temperatures (SSTs) in the North Atlantic and tropical-ocean upwelling regions and by an increase in African and Asian aridity and monsoonal intensity. During the MPT, long-term average ice volume gradually increased by 50 m sea-level equivalent, whereas low-frequency ice-volume variability experienced a 100-kyr lull centered on 1000 ka followed by its reappearance 900 ka, although as a broad band of power rather than a narrow, persistent 100-kyr cycle. Additional changes at 900 ka indicate this to be an important time during the MPT, beginning with an 80-kyr event of extreme SST cooling followed by the partial recovery and subsequent stabilization of long-term North Atlantic and tropical ocean SSTs, increasing Southern Ocean SST variability primarily associated with warmer interglacials, the loss of permanent subpolar sea-ice cover, and the emergence of low-frequency variability in Pacific SSTs and global deep-ocean circulation. Since 900 ka, ice sheets have been the only component of the climate system to exhibit consistent low-frequency variability. With the exception of a near-universal organization of low-frequency power associated with marine isotope stages 11 and 12, all other components show an inconsistent distribution of power in frequency-time space, suggesting a highly nonlinear system response to orbital and ice-sheet forcing.Most hypotheses for the origin of the MPT invoke a response to a long-term cooling, possibly induced by decreasing atmospheric pCO₂. None of these hypotheses, however, accounts for the geological constraint that the earliest Northern Hemisphere ice sheets covered a similar or larger area than those that followed the MPT. Given that the MPT was associated with an increase in ice volume, this constraint requires that post-MPT ice sheets were substantially thicker than pre-MPT ice sheets, indicating a change in subglacial conditions that influence ice dynamics. We review evidence in support of the hypothesis that such an increase in ice thickness occurred as crystalline Precambrian Shield bedrock became exposed by glacial erosion of a thick mantle of regolith. This exposure of a high-friction substrate caused thicker ice sheets, with an attendant change in their response to the orbital forcing. Marine carbon isotope data indicate a rapid transfer of organic carbon to inorganic carbon in the ocean system during the MPT. If this carbon came from terrigenous sources, an increase in atmospheric pCO₂ would be likely, which is inconsistent with evidence for widespread cooling, Apparently rapid carbon transfer from terrestrial sources is difficult to reconcile with gradual erosion of regolith. A more likely source of organic carbon and nutrients (which would mitigate pCO₂ rise) is from shelf and upper slope marine sediments, which were fully exposed for the first time in millions of years in response to thickening ice sheets and falling sealevels during the MPT. Modeling indicates that regolith erosion and resulting exposure of crystalline bedrock would cause an increase in long-term silicate weathering rates, in good agreement with marine Sr and Os isotopic records. We use a carbon cycle model to show that a post-MPT increase in silicate weathering rates would lower atmospheric pCO₂ by 7–12 ppm, suggesting that the attendant cooling may have been an important feedback in causing the MPT.     

X-ray absorption contrast images of binary chemical reactions

Low-divergence synchrotron-sourced X-rays enable a radiographic imaging scheme for full characterization of binary chemical reactions and characterization by type of more complex reactions, in situ, in diamond anvil cells (DAC). Spatially resolved reactants are induced to react by laser heating of their interface. The spatially intermediate products are observed through X-ray absorption contrast. Limits to the technique include the ability to maintain controlled experiment geometry during compression and the ability to resolve chemical differences between reactants and products by X-ray absorption. The ability to make in situ observations at experimental pressure and temperature obviates the problem with quenching techniques for capturing liquid compositions in experiments with dimensions smaller than the diffusion length during quenching time. Partially molten Fe-alloy systems, of poor quenchability, are examined at DAC pressures and temperatures for relevance to Earth's core constitution and evolution. Determinations of eutectic melting in Fe–FeS match known results. Of the probable light elements that may alloy with Fe in the Earth's liquid outer core, Fe–FeS experiments show only modest quenching problems, but C and Si alloy experiments are highly vulnerable to quenching artifacts. The observed reactivity of FeS, Fe₃C, FeSi, and FeO(OH) with Fe in DAC makes the observed non-reactivity between Fe and FeO more significant, reducing the probability that oxygen alone is the major alloy in Earth's molten outer core.