Integer estimation in the presence of biases

 Carrier phase ambiguity resolution is the key to fast and high-precision GNSS (Global Navigation Satellite System) kinematic positioning. Critical in the application of ambiguity resolution is the quality of the computed integer ambiguities. Unsuccessful ambiguity resolution, when passed unnoticed, will too often lead to unacceptable errors in the positioning results. Very high success rates are therefore required for ambiguity resolution to be reliable. Biases which are unaccounted for will lower the success rate and thus increase the chance of unsuccessful ambiguity resolution. The performance of integer ambiguity estimation in the presence of such biases is studied. Particular attention is given to integer rounding, integer bootstrapping and integer least squares. Lower and upper bounds, as well as an exact and easy-to-compute formula for the bias-affected success rate, are presented. These results will enable the evaluation of the bias robustness of ambiguity resolution. Received: 28 September 2000 / Accepted: 29 March 2001     

Application of Hilbert‐like transforms for enhanced processing of full tensor magnetic gradient data

Commonly, geomagnetic prospection is performed via scalar magnetometers that measure values of the total magnetic intensity. Recent developments of superconducting quantum interference devices have led to their integration in full tensor magnetic gradiometry systems consisting of planar‐type first‐order gradiometers and magnetometers fabricated in thin‐film technology. With these systems measuring directly the magnetic gradient tensor and field vector, a significantly higher magnetic and spatial resolution of the magnetic maps is yield than those produced via conventional magnetometers. In order to preserve the high data quality in this work, we develop a workflow containing all the necessary steps for generating the gradient tensor and field vector quantities from the raw measurement data up to their integration into high­resolution, low­noise, and artefactless two‐dimensional maps of the magnetic field vector. The gradient tensor components are processed by superposition of the balanced gradiometer signals and rotation into an Earth‐centred Earth‐fixed coordinate frame. As the magnetometers have sensitivity lower than that of gradiometers and the total magnetic intensity is not directly recorded, we employ Hilbert‐like transforms, e.g., integration of the gradient tensor components or the conversion of the total magnetic intensity derived by calibrated magnetometer readings to obtain these values. This can lead to a better interpretation of the measured magnetic anomalies of the Earth's magnetic field that is possible from scalar total magnetic intensity measurements. Our conclusions are drawn from the application of these algorithms on a survey acquired in South Africa containing full tensor magnetic gradiometry data.     

Comparison of the LEW88516 and ALHA77005 martian meteorites: Similar but distinct

Abstract By mineral and bulk compositions, the Lewis Cliff (LEW) 88516 meteorite is quite similar to the ALHA77005 martian meteorite. These two meteorites are not paired because their mineral compositions are distinct, they were found 500 km apart in ice fields with different sources for meteorites, and their terrestrial residence ages are different. Minerals in LEW88516 include: olivine, pyroxenes (low- and high-Ca), and maskelynite (after plagioclase); and the minor minerals chromite, whitlockite, ilmenite, and pyrrhotite. Mineral grains in LEW88516 range up to a few mm. Texturally, the meteorite is complex, with regions of olivine and chromite poikilitically enclosed in pyroxene, regions of interstitial basaltic texture, and glass-rich (shock) veinlets. Olivine compositions range from Fo₆₄ to Fo₇₀, (avg. Fo₆₇), more ferroan and with more variation than in ALHA77005 (Fo₆₉ to Fo₇₃). Pyroxene compositions fall between En₇₇Wo₄ and En₆₅Wo₁₅ and in clusters near En₆₃Wo₉ and En₅₃Wo₃₃, on average more magnesian and with more variation than in ALHA77005. Shock features in LEW88516 range from weak deformation through complete melting. Bulk chemical analyses by modal recombination of electron microprobe analyses, instrumental neutron activation, and radiochemical neutron activation confirm that LEW88516 is more closely related to ALHA77005 than to other known martian meteorites. Key element abundance ratios are typical of martian meteorites, as is its non-chondritic rare earth pattern. Differences between the chemical compositions of LEW88516 and ALHA77005 are consistent with slight differences in the proportions of their constituent minerals and not from fundamental petrogenetic differences. Noble gas abundances in LEW88516, like those in ALHA77005, show modest excesses of ⁴⁰Ar and ¹²⁹Xe from trapped (shock-implanted) gas. As with other ALHA77005 and the shergottite martian meteorites (except EETA79001), noble gas isotope abundances in LEW88516 are consistent with exposure to cosmic rays for 2.5–3 Ma. The absence of substantial effects of shielding from cosmic rays suggest LEW88516 spent this time as an object no larger than a few cm in diameter.     

A rooftop tuned mass damper frame

This article documents the analytical study and feasibility of placing a tuned mass damper in the form of a limber rooftop moment frame atop relatively stiff structures to reduce seismic acceleration response. Six existing structures were analytically studied using a suite of time history and response spectra records. The analyses indicate that adding mass in conjunction with a limber frame results in an increase in the fundamental period of each structure. The fundamental period increase generally results in a decrease in seismic acceleration response for the same time history and response spectra records. Owing to the limber nature of the rooftop frames, non‐linear analysis methods were required to evaluate the stability of the rooftop tuned mass damper frame. The results indicate the addition of a rooftop tuned mass damper frame reduces the seismic acceleration response for most cases although acceleration response can increase if the rooftop frame is not tuned to accommodate the specific structure's dynamic behaviour and localized soil conditions. Appropriate design of the rooftop tuned mass damper frame can result in decreased seismic acceleration response. This translates to safer structures if used as a retrofit measure or a more economical design if used for new construction. Copyright © 2003 John Wiley & Sons, Ltd.     

Occurrence and characteristics of sporadic sodium layer observed by lidar at a mid-latitude location

Na lidar observations of SSL during the past 5 years at a mid-latitude location (Wuhan, China, 31°N, 114°E) are reported in this paper. From 26 SSL events detected in about 230 h of observation, an SSL occurrence rate of 1 event/9 h at our location was obtained. This result, combined with that reported by Nagasawa and Abo (Geophys. Res. Lett. 22 (1995) 263) at Tokyo, Japan, reveals that the SSL occurrence can be relatively frequent at some mid-latitude locations. The statistical analyses of main parameters for the 26 SSL events were made, and the results were compared with those previously reported. By examining the corresponding data from a nearby ionosonde, it was found that there was a fairly good correlation between SSL and Es. Of the 18 pairs of SSL and Es events checked, 15 of SSL were accompanied by Es, and 8 pairs of them were correlated within 1 h in time and within 5 km in altitude. From the analyses of observed perturbations during SSL development, the role of dynamic processes of atmosphere in the SSL formations were emphasized.     

Quantification of the environmental structural risk with spoiling ties: is randomization worthwhile?

Many recent works show that copulas turn out to be useful in a variety of different applications, especially in environmental sciences. Here the variables of interest are usually continuous, being times, lengths, weights, and so on. Unfortunately, the corresponding observations may suffer from (instrumental) adjustments and truncations, and eventually may show several repeated values (i.e., ties). In turn, on the one hand, a tricky issue of identifiability of the model arises, and, on the other hand, the assessment of the risk may be adversely affected. A possible remedy is to adopt suitable randomization procedures: here three different strategies are outlined. The goal of the work is to carry out a simulation study in order to evaluate the effects of the randomization of multivariate observations when ties are present. In particular, it is investigated whether, how, and to what extent, the randomization may change the estimation of the structural risk: for this purpose, a coastal engineering example will be used, as archetypical of a broad class of models and problems in engineering applications. Practical advices and warnings about the use of randomization techniques are hence given.     

Stability and phase relations of nonstoichiometric clinopyroxenes in the join diopside-Ca-Eskola component at high pressures

The stability of nonstoichiometric clinopyroxenes in the Di-CaEsk join was experimentally studied, and phase diagrams were constructed for this join at pressures of 2.0 and 3.0 GPa. It was found that melting in the diopside part of the join occurs at anomalously low temperatures, and nonstoichiometric clinopyroxene coexists with a phase approaching diopside in composition. Phase relations along the Di-CaEsk join can be described and consistently interpreted only assuming that the diopside phase (α-diopside) is thermodynamically stable. The following phase volumes were observed along the solidus of the join at a pressure of 3.0 GPa: Cpx, αDi+Cpx, αDi+Cpx+Qtz, αDi+Cpx+Grt+Qtz, Cpx+Grt+Qtz, Cpx+Grt+Ky+Qtz, Grt+Ky+Qtz. Melting occurs via the eutectic reaction αDi+Cpx+Grt+Qtz=L at a temperature of about 1200°C in the diopside part of the system and via the eutectic reaction Cpx+Grt+Ky+Qtz=L at a temperature of 1400°C in the calcium-rich part of the system. At a pressure of 2.0 GPa, melting occurs at temperatures of 1200–1300°C via the eutectic reaction αDi+Cpx+ An + Qtz=L. The invariant equilibrium (L, An, Cpx, Grt, αDi, Qtz) lies within the pressure range 2.0–3.0 GPa. Nonstoichiometric clinopyroxenes form complex solid solutions, the compositions of which are not strictly confined to the Di-CaEsk join and depend on temperature, pressure, and phase association. Grossular garnets coexist with nonstoichiometric clinopyroxenes and α-diopside.     

FORWARD MODELING IN THE FREQUENCY-SPACE DOMAIN*

Forward modeling of zero-offset data is performed in the frequency-space domain using a one-way extrapolation equation. The use of the frequency domain offers several advantages over conventional time domain methods. The greatest advantage of the frequency domain is that all time derivatives are evaluated exactly by a simple multiplication. Synthetic zero-offset sections are computed with a high degree of accuracy for arbitrary velocity and reflectivity structures. Examples are shown for realistic complicated models and compared with results from physical modeling.