ANALYTICAL AERIAL TRIANGULATION WITH ANGULAR MEASUREMENTS

In recent years interest has been increasing in the use of measurements from single photographs for analytical work. A monocular instrument based on the theodolite is described, together with preliminary test results.     

Observations of eclipsing dwarf novae

High Speed Photometry of four eclipsing dwarf novae, z Cha, OY Car, HT Cas and IP Peg, is used to determine the orbital parameters and the masses of the two stars in each system. The mass ratio, q, and inclination, i, are found by constraining theoretical stream trajectories (Lubow and Shu 1975) to pass through the observed light centre of the bright spot eclipse. The light centre is defined as the point corresponding to the half flux points in the ingress and egress of the eclipse of the compact part of the bright spot. The theoretical stream width indicates that the centre of the stream must intersect the bright spot close to this point.The length of ingress and egress in the primary eclipse, constrains the radius of the central object relative to the orbital separation. The shape of this eclipse and the temperature of the central objects in z Cha, OY Car and HT Cas imply that the measuredPaper presented at the IAU Colloquium No. 93 on Cataclysmic Variables. Recent Multi-Frequency Observations and Theoretical Developments, held at Dr. Remeis-Sternwarte Bamberg, F.R.G., 16–19 June, 1986.     

Close triple star systems

Triple star systems, especially those in which one star has very small mass may be more common than has been generally considered. Here is summarized some of the recent evidence supporting this possibility.Communication presented at the International Conference on Astrometric Binaries, held on 13–15 June, 1984, at the Remeis-Sternwarte Bamberg, Germany, to commemorate the 200th anniversary of the birth of Friedrich Wilhelm Bessel (1784–1846)     

Trace element partitioning and substitution mechanisms in calcium perovskites

We have determined the partition coefficients of a large number of trace elements between CaTiO₃ perovskite and anhydrous silicate melts at atmospheric pressure and 3 GPa. Determination of the concentration limits of Henrys law behaviour in the CaO-Al₂O₃–SiO₂–TiO₂ system reveals that the incorporation of rare earth elements (REE) and tetravalent large ion lithophile elements (LILE⁴⁺ such as U and Th) at the Ca-site of CaTiO₃ perovskite occurs with charge compensation through Ca-vacancy formation rather than by coupled substitution of Al for Ti. When melt composition is varied, we find that partition coefficients for REE and Th are strong functions of the CaO content of the melt. The observed trends are in excellent agreement with those predicted from the Ca-vacancy model. Given that they adopt the same crystal structure and have similar trace element partitioning behaviour, CaTiO₃ perovskite and the deep mantle phase CaSiO₃ perovskite can be considered analogous to one another. When the analogy is pursued in detail, we find that partitioning into both phases follows the composition-dependence predicted by the Ca-vacancy model. Thus, substitution of REE, U⁴⁺ and Th into CaSiO₃ in the lower mantle also occurs with Ca-vacancy formation to balance charge. Furthermore when 2+, 3+ and 4+ partition coefficients for both phases are plotted as functions of CaO melt content, the trends for CaSiO₃ and CaTiO₃ appear to be continuous. This surprising result means that partitioning into Ca-perovskite is independent of pressure and temperature and also of whether or not the host is CaSiO₃ or CaTiO₃. One implication is that CaSiO₃ crystallising from a peridotitic magma ocean may have partition coefficients for Th and U up to about 400. Crystallisation and sequestration of as little as 0.25 volume% of this phase in the lower mantle early in earth history would make a significant contribution to current mantle heat production.Electronic Supplementary Material Supplementary material is available for this article at     

Small-scale electrical resistivity tomography of wet fractured rocks

This paper describes a series of experiments that tested the ability of the electrical resistivity tomography (ERT) method to locate correctly wet and dry fractures in a meso-scale model. The goal was to develop a method of monitoring the flow of water through a fractured rock matrix. The model was a four by six array of limestone blocks equipped with 28 stainless steel electrodes. Dry fractures were created by placing pieces of vinyl between one or more blocks. Wet fractures were created by injecting tap water into a joint between blocks. In electrical terms, the dry fractures are resistive and the wet fractures are conductive. The quantities measured by the ERT system are current and voltage around the outside edge of the model. The raw ERT data were translated to resistivity values inside the model using a three-dimensional Occam's inversion routine. This routine was one of the key components of ERT being tested. The model presented several challenges. First, the resistivity of both the blocks and the joints was highly variable. Second, the resistive targets introduced extreme changes the software could not precisely quantify. Third, the abrupt changes inherent in a fracture system were contrary to the smoothly varying changes expected by the Occam's inversion routine. Fourth, the response of the conductive fractures was small compared to the background variability. In general, ERT was able to locate correctly resistive fractures. Problems occurred, however, when the resistive fracture was near the edges of the model or when multiple fractures were close together. In particular, ERT tended to position the fracture closer to the model center than its true location. Conductive fractures yielded much smaller responses than the resistive case. A difference-inversion method was able to correctly locate these targets.     

The extreme ultraviolet emissions of solar flares: A comparison between OSO-6 spectroheliograph observations and SFDs

The time structure and intensity of OSO-6 observations of EUV bursts were studied in relation to the corresponding 10–1030 Å enhancements deduced from SFD data. Impulsive EUV emissions from lines normally emitted from either the chromosphere or from the chromosphere-corona transition region rise simultaneously with the 10–1030 Å flash, to within the time resolution of the OSO-6 observations. Mg × 625 Å also showed concurrent impulsive emissions and a close intensity relation to the 10–1030 Å enhancement. The observational results are consistent with the hypothesis that most of the EUV radiation is being produced thermally in a region of chromospheric density, which is being heated by collisional losses of nonthermal electrons.     

The solubility of Pt and Pd sulfides and Au in bisulfide solutions

Two sets of measurements of the solubility of Pt and Pd in bisulfide solutions have been carried out at low temperatures. The first involved the equilibration of Pt metal with bisulfide solutions at 25 °C and pH = 6–12 for periods up to five years. These experiments yielded Pt concentrations on the order of tens of g/L at sulfide concentrations as low as 0.001 molal under conditions too reducing to permit significant contributions from hydroxide complexes. The second set of experiments consisted of reacting PtS, PdS and Au with H₂S-saturated solutions having pH values of 3–4 at 25°, 50° and 90 °C. These experiments showed that the solubilities of all three metals increased with temperature. The observed order of solubility was Au > Pt Pd. Solubilities ranged from 10 to 75 g/L Au, 4 to 20 g/L Pt and 0.5 to 10 g/L Pd. The data do not permit definitive identification of the Pt and Pd species present in either set of experiments, but do strongly suggest that the species present under acidic and basic conditions are different. The measured solubility of gold at 25° and 50 °C is consistent with that measured in previous studies.Although the measured Pt and Pd solubilities are not as high as those estimated by theoretical methods, it is nevertheless evident that bisulfide complexation can lead to the remobilization of Pt and Pd over a wide range of pH under reducing conditions at geologically reasonable sulfide concentrations, at low as well as high temperatures. Such conditions are characteristic of a wide variety of geological environments where Pt and Pd have been inferred to have been affected by hydrothermal transport. In these cases, bisulfide complexation is far more effective than chloride or hydroxide complexes in transporting the PGE. On leave from: Shenyang Laboratory of Rock and Mineral Resources, Ministry of Geology and Mineral Resources, People's Republic of China     

On the condition number of covariance matrices in kriging, estimation, and simulation of random fields

The numerical stability of linear systems arising in kriging, estimation, and simulation of random fields, is studied analytically and numerically. In the state-space formulation of kriging, as developed here, the stability of the kriging system depends on the condition number of the prior, stationary covariance matrix. The same is true for conditional random field generation by the superposition method, which is based on kriging, and the multivariate Gaussian method, which requires factoring a covariance matrix. A large condition number corresponds to an ill-conditioned, numerically unstable system. In the case of stationary covariance matrices and uniform grids, as occurs in kriging of uniformly sampled data, the degree of ill-conditioning generally increases indefinitely with sampling density and, to a limit, with domain size. The precise behavior is, however, highly sensitive to the underlying covariance model. Detailed analytical and numerical results are given for five one-dimensional covariance models: (1) hole-exponential, (2) exponential, (3) linear-exponential, (4) hole-Gaussian, and (5) Gaussian. This list reflects an approximate ranking of the models, from best to worst conditioned. The methods developed in this work can be used to analyze other covariance models. Examples of such representative analyses, conducted in this work, include the spherical and periodic hole-effect (hole-sinusoidal) covariance models. The effect of small-scale variability (nugget) is addressed and extensions to irregular sampling schemes and higher dimensional spaces are discussed.