Comparison of structural and least-squares lines for estimating geologic relations

Two different goals in fitting straight lines to data are to estimate a true linear relation (physical law) and to predict values of the dependent variable with the smallest possible error. Regarding the first goal, a Monte Carlo study indicated that the structural-analysis (SA) method of fitting straight lines to data is superior to the ordinary least-squares (OLS) method for estimating true straight-line relations. Number of data points, slope and intercept of the true relation, and variances of the errors associated with the independent (X) and dependent (Y) variables influence the degree of agreement. For example, differences between the two line-fitting methods decrease as error in X becomes small relative to error in Y. Regarding the second goal—predicting the dependent variable—OLS is better than SA. Again, the difference diminishes as X takes on less error relative to Y. With respect to estimation of slope and intercept and prediction of Y, agreement between Monte Carlo results and large-sample theory was very good for sample sizes of 100, and fair to good for sample sizes of 20. The procedures and error measures are illustrated with two geologic examples.     

The charge distribution on interstellar grains—The effect of induced charge

A calculation of the equilibrium charge acquired by interstellar grains is given, which takes account of polarization charges that are induced in a grain by incident ions and electrons.Both metal and dielectric grains are considered and photoionization of the latter grains by UV radiation is taken into account where necessary. It is found that the inclusion of the polarization charges in the calculation is only important in gas clouds where the mean charge on a grain is low (<1e); that is, for HI regions and dense molecular clouds. In such clouds, the effect of the polarization charges is to increase the amount of negative charge acquired by a grain. A discussion is given concerning the validity of the classical electrostatic theory employed in the paper for small grains of radius 10^–6 cm, and some astrophysical consequences of the modification of the grain charge by polarization effects are considered.     

Observations of cosmic gamma-ray bursts

The occasional occurrence of brief but intense bursts of cosmic gamma-rays was disclosed through a systematic search of data acquired from the Vela satellites. Confirmation of the nature of the events and additional detail of their characteristics has subsequently been provided by 15 other groups of experimenters with instruments on 13 spacecraft. Thirty-nine such events have been identified from data spanning a period of four and a half years. The record of intensity as a function of time varies considerably for different events, with total durations ranging from 0.1 to 60s. Time-integrated flux density ranges from 10^–6 to 10^–3 erg cm^–2. Spectral measurements have been accomplished by several groups of experimenters, showing a broad maximum in the energy distribution at about 150 keV. The distribution of source directions implies either near galactic or extragalactic locations. The existing data are not sufficient to distinguish between the various models proposed to explain the phenomenon; no model is completely consistent with all observed characteristics.Work performed under the auspices of the United States Energy Research and Development Administration.Paper presented at the COSPAR Symposium on Fast Transients in X-and Gamma-Rays, held at Varna, Bulgaria, 29–31 May, 1975.     

Estimation of runoff distribution within river systems: Application to the Lena Basin (Siberia)

A channel account approach is proposed to estimate longitudinal changes in runoff along large river systems. This new method provides a quantitative basis for describing the fluvial transport of suspended particulate material and dissolved substances. This method includes an evaluation of basic elements of water balance in separate sections of the river network and subsequent correction of channel accounting equations for the entire system using a maximum likelihood principle. To calculate water discharges of tributaries that have no hydrological information, structural analysis of river network is performed. This approach provides less error in comparison with traditional methods of estimating lateral inflow. The method is used to trace water discharge with increasing distance along the Lena river basin and to evaluate the contribution of geologically and lithologically uneven sub-basins in water discharge formation during a summer low water period.     

U–Pb and Hf isotopic analysis of zircon in lower crustal xenoliths from the Navajo volcanic field: 1.4 Ga mafic magmatism and metamorphism beneath the Colorado Plateau

Zircon from lower crustal xenoliths erupted in the Navajo volcanic field was analyzed for U–Pb and Lu–Hf isotopic compositions to characterize the lower crust beneath the Colorado Plateau and to determine whether it was affected by ∼1.4 Ga granitic magmatism and metamorphism that profoundly affected the exposed middle crust of southwestern Laurentia. Igneous zircon in felsic xenoliths crystallized at 1.73 and 1.65 Ga, and igneous zircon in mafic xenoliths crystallized at 1.43 Ga. Most igneous zircon has unradiogenic initial Hf isotopic compositions (ɛ_Hf=+4.1–+7.8) and 1.7–1.6 Ga depleted mantle model ages, consistent with 1.7–1.6 Ga felsic protoliths being derived from “juvenile” Proterozoic crust and 1.4 Ga mafic protoliths having interacted with older crust. Metamorphic zircon grew in four pulses between 1.42 and 1.36 Ga, at least one of which was at granulite facies. Significant variability within and between xenoliths in metamorphic zircon initial Hf isotopic compositions (ɛ_Hf=−0.7 to +13.6) indicates growth from different aged sources with diverse time-integrated Lu/Hf ratios. These results show a strong link between 1.4 Ga mafic magmatism and granulite facies metamorphism in the lower crust and granitic magmatism and metamorphism in the exposed middle crust.