A canonical theory for short GPS baselines. Part II: the ambiguity precision and correlation

The present contribution is the second of four parts. It considers the precision and correlation of the least-squares estimators of the carrier phase ambiguities. It is shown how the precision and correlation of the double-differenced ambiguities as well as of the widelane ambiguities are effected by the observation weights, by the number of satellites tracked, by the number of observation epochs used, and by the change over time of the relative receiver-satellite geometry. Also the ability of the widelane transformation to decorrelate and to improve the precision is investigated. Received: 16 July 1996 / Accepted: 14 November 1996     

Transient electromagnetic responses in seafloor with triaxial anisotropy

Electrical anisotropy of young oceanic crust at mid-ocean ridges is detectable by observation of the rate and geometry of the diffusion of electromagnetic fields. The anisotropy in electrical properties arises from the presence of conductive seawater in an interconnected network of mostly ridge-parallel cracks. In this paper, we first justify the choice of a triaxial model to represent young oceanic crust, with three distinct electrical conductivities in the vertical, strike and spreading directions. We then present an algorithm to calculate the transient electromagnetic responses generated by an electric dipole source over such a triaxially anisotropic seafloor. We show that if the transient passages are measured with three distinct electric dipole-dipole configurations, it is possible to discern all three unknown conductivities independently of each other.     

Monitoring of rapid salt weathering in the central Namib Desert using limestone blocks

Pre-weighed blocks of a Jurassic Limestone were exposed on the ground surface in the coastal Namib Desert for a period of 2 years. The environment is both salty and foggy. Some of the blocks suffered extensive disintegration, and laboratory analyses (including geochemistry, XRD and SEM) indicate that the weathered samples have a high halite (sodium chloride) content. Cycles of wetting and drying associated with the frequent fog events of the area cause cycles of halite crystallization. Rocks exposed at the surface absorb salts from the surrounding desert surface and then disintegrate, contributing to planation of the landscape.     

Mineral inclusions in diamonds from the Sputnik kimberlite pipe, Yakutia

The Sputnik kimberlite pipe is a small “satellite” of the larger Mir pipe in central Yakutia (Sakha), Russia. Study of 38 large diamonds (0.7-4.9 carats) showed that nine contain inclusions of the eclogitic paragenesis, while the remainder contain inclusions of the peridotitic paragenesis, or of uncertain paragenesis. The peridotitic inclusion suite comprises olivine, enstatite, Cr-diopside, chromite, Cr-pyrope garnet (both lherzolitic and harzburgitic), ilmenite, Ni-rich sulfide and a Ti-Cr-Fe-Mg-Sr-K phase of the lindsleyite-mathiasite (LIMA) series. The eclogitic inclusion suite comprises omphacite, garnet, Ni-poor sulfide, phlogopite and rutile. Peridotitic ilmenite inclusions have high Mg, Cr and Ni contents and high Nb/Zr ratios; they may be related to metasomatic ilmenites known from peridotite xenoliths in kimberlite. Eclogitic phlogopite is intergrown with omphacite, coexists with garnet, and has an unusually high TiO₂ content. Comparison with inclusions in diamonds from Mir shows general similarities, but differences in details of trace-element patterns. Large compositional variations among inclusions of one phase (olivine, garnet, chromite) within single diamonds indicate that the chemical environment of diamond crystallisation changed rapidly relative to diamond growth rates in many cases. P-T conditions of formation were calculated from multiphase inclusions and from trace element geothermobarometry of single inclusions. The geotherm at the time of diamond formation was near a 35 mW/m² conductive model; that is indistinguishable from the Paleozoic geotherm derived by studies of xenoliths and concentrate minerals from Mir. A range of Ni temperatures between garnet inclusions in single diamonds from both Mir and Sputnik suggests that many of the diamonds grew during thermal events affecting a relatively narrow depth range of the lithosphere, within the diamond stability field. The minor differences between inclusions in Mir and Sputnik may reflect lateral heterogeneity in the upper mantle.     

Late Cretaceous rift-related upwelling and melting of the Trindade starting mantle plume head beneath western Brazil

High mantle potential temperatures and local extension, associated with the Late-Cretaceous impact of the Trindade mantle plume, produced substantial widespread and voluminous magmatism around the northern half of the Paraná sedimentary basin. Our previous studies have shown that, above the central and eastern portions of the postulated impact zone where lithosphere extension is minimal, heat conducted by the plume caused large-scale melting of the more fusible parts of the subcontinental lithospheric mantle beneath the margin of the São Francisco craton and the surrounding Brasilía mobile belt. Here we combine geochemical data and field evidence from the Poxoreu Igneous Province, western Brazil to show how more intense lithospheric extension above the western margin of the postulated impact zone permitted greater upwelling and melting of the Trindade plume than further east. Laser ⁴⁰Ar/³⁹Ar age determinations indicate that rift-related basaltic magmas of the Poxoreu Igneous Province were emplaced at ? 84 Ma. Our detailed geochemical study of the mafic magmas shows that the parental melts underwent polybaric crystal fractionation within the crust prior to final emplacement. Furthermore, some magmas (quartz-normative) appear to have assimilated upper crust whereas others (nepheline- and hypersthene-normative) appear to have been unaffected by open-system crustal magma chamber processes. Incompatible trace element ratios (e.g. chondrite-normalised La/Nb?=?1) and isotopic ratios (⁸⁷Sr/⁸⁶Sr?=?0.704 and ¹⁴³Nd/¹⁴⁴Nd?=?0.51274) of the Hy-normative basalts resemble those of oceanic islands (OIB). We therefore propose that these “OIB-like” magmas were predominantly derived from convecting-mantle-source melts (i.e. Trindade mantle plume). Inverse modelling of rare-earth element (REE) abundances suggests that the initial melts were predominantly generated within the depth range of ?80–100 km, in mantle with a potential temperature of ?1500 °C.     

Detection of Local Inhomogeneities by Means of Cross-borehole Seismic Tomography

—This numerical study is devoted to distortions of local anomalies which are revealed by 2-D and 3-D cross-borehole seismic tomography based on first arrival travel times. The fact that prolonged subvertical anomalies may disappear in the final velocity model is well known. But distortions are also inherent to images of local inhomogeneities. These distortions are accompanied with false anomalies of the opposite sign located just above and below true ones. I offer a semi-empirical explanation of their existence, proving that they are an inherent consequence of observation geometry incompleteness. To improve the quality of the model obtained with cross-borehole tomography, a 3-D acquisition geometry may be used when additional boreholes are positioned around the target object. Results of 3-D tomographic experiments however may be considerably distorted for another reason nonaccounted bending of seismic rays.¶To generate the travel times, a ray-tracing procedure making use of the graph theory was applied. Tomographic inversion was performed by an algorithm based on the assumption of the unknown function smoothness.     

The little-known earthquakes of 1866 and 1916 in Anatolia (Turkey)

In this paper we assess the size and effects of the earthquakes of 12 May 1866, and 24 January 1916 in Anatolia (Turkey). We show that these events had a magnitude M_s 7.2 and that the former was associated with a 45-km long surface fault break along the north-east part of the East Anatolian Fault Zone. These two earthquakes are chosen among others in order to demonstrate how easy it is to miss out large earthquakes of the historical, even of the early instrumental period, and to draw the incompleteness of many existing catalogues to the attention of those who use them for the estimation of slip rates and the assessment of seismic hazard. Of the two earthquakes studied here, the former was only vaguely known and the latter is not included in Gutenberg and Richter's catalogue.     

Doppler radar spectral width broadening due to beamwidth and wind shear

The spectral width observed by Doppler radars can be due to several effects including the atmospheric turbulence within the radar sample volume plus effects associated with the background flow and the radar geometry and configuration. This study re-examines simple models for the effects due to finite beam-width and vertical shear of the horizontal wind. Analytic solutions of 1- and 2-dimensional models are presented. Comparisons of the simple 2-dimensional model with numerical integrations of a 3-dimensional model with a symmetrical Gaussian beam show that the 2-dimensional model is usually adequate. The solution of the 2-dimensional model gives a formula that can be applied easily to large data sets. Analysis of the analytic solutions of the 2-dimensional model for off-vertical beams reveals a term that has not been included in mathematical formulas for spectral broadening in the past. This term arises from the simultaneous effects of the changing geometry due to curvature within a finite beamwidth and the vertical wind shear. The magnitude of this effect can be comparable to that of the well-known effects of beam-broadening and wind shear, and since it can have either algebraic sign, it can significantly reduce (or increase) the expected spectral broadening, although under typical conditions it is smaller than the beam-broadening effect. The predictions of this simple model are found to be consistent with observations from the VHP radar at White Sands Missile Range, NM.     

On the Problem of Differential Payment for the Use of Different-Quality Surface Waters in Ukraine

The evolution of views and practical decisions regarding the problem of collecting payment for the use of surface waters with regard to their quality in the former USSR and present-day Ukraine is discussed. A simple and feasible method is proposed for differentitation of regional (basin) rates of payment for the use of surface water in Ukraine with allowance made for its quality assessed based on a system of environmental classifications.