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     

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.     

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.     

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.