The Bayesian detection of discontinuities in a polynomial regression and its application to the cycle-slip problem

This paper deals with the problem of detecting and correcting cycle-slips in Global Navigation Satellite System (GNSS) phase data by exploiting the Bayesian theory. The method is here applied to undifferenced observations, because repairing cycle-slips already at this stage could be a useful pre-processing tool, especially for a network of permanent GNSS stations. If a dual frequency receiver is available, the cycle-slips can be easily detected by combining two phase observations or phase and range observations from a single satellite to a single receiver. These combinations, expressed in a distance unit form, are completely free from the geometry and depend only on the ionospheric effect, on the electronic biases and on the initial integer ambiguities; since these terms are expected to be smooth in time, at least in a short period, a cycle-slip in one or both the two carriers can be modelled as a discontinuity in a polynomial regression. The proposed method consists in applying the Bayesian theory to compute the marginal posterior distribution of the discontinuity epoch and to detect it as a maximum a posteriori (MAP) in a very accurate way. Concerning the cycle-slip correction, a couple of simultaneous integer slips in the two carriers is chosen by maximazing the conditional posterior distribution of the discontinuity amplitude given the detected epoch. Numerical experiments on simulated and real data show that the discontinuities with an amplitude 2 or 3 times larger than the noise standard deviation are successfully identified. This means that the Bayesian approach is able to detect and correct cycle-slips using undifferenced GNSS observations even if the slip occurs by one cycle. A comparison with the scientific software BERNESE 5.0 confirms the good performance of the proposed method, especially when data sampled at high frequency (e.g. every 1 s or every 5 s) are available.     

Modelling Positional Uncertainty of Line Features by Accounting for Stochastic Deviations from Straight Line Segments

The assessment of positional uncertainty in line and area features is often based on uncertainty in the coordinates of their elementary vertices which are assumed to be connected by straight lines. Such an approach disregards uncertainty caused by sampling and approximation of a curvilinear feature by a sequence of straight line segments. In this article, a method is proposed that also allows for the latter type of uncertainty by modelling random rectangular deviations from the conventional straight line segments. Using the model on a dense network of sub‐vertices, the contribution of uncertainty due to approximation is emphasised; the sampling effect can be assessed by applying it on a small set of randomly inserted sub‐vertices. A case study demonstrates a feasible way of parameterisation based on assumptions of joint normal distributions for positional errors of the vertices and the rectangular deviations and a uniform distribution of missed sub‐vertices along line segments. Depending on the magnitudes of the different sources of uncertainty, not accounting for potential deviations from straight line segments may drastically underestimate the positional uncertainty of line features.     

Possible consequences of absence of “jupiters” in planetary systems

The formation of the gas giant planets Jupiter and Saturn probably required the growth of massive 15 Earth-mass cores on a time scale shorter than the 10⁷ time scale for removal of nebular gas. Relatively minor variations in nebular parameters could preclude the growth of full-size gas giants even in systems in which the terrestrial planet region is similar to our own. Systems containing failed Jupiters, resembling Uranus and Neptune in their failure to capture much nebular gas, would be expected to contain more densely populated cometary source regions. They will also eject a smaller number of comets into interstellar space. If systems of this kind were the norm, observation of hyperbolic comets would be unexpected. Monte Carlo calculations of the orbital evolution of region of such systems (the Kuiper belt) indicate that throughout Earth history the cometary impact flux in their terrestrial planet regions would be 1000 times greater than in our Solar System. It may be speculated that this could frustrate the evolution of organisms that observe and seek to understand their planetary system. For this reason our observation of these planets in our Solar System may tell us nothing about the probability of similar gas giants occurring in other planetary systems. This situation can be corrected by observation of an unbiased sample of planetary systems.Paper presented at the Conference onPlanetary Systems: Formation, Evolution, and Detection held 7–10 December, 1992 at CalTech, Pasadena, California, U.S.A.     

A preliminary study of the carbon-isotopic content of ambient formic acid and two selected sources: Automobile exhaust and formicine ants

Relatively large quantities (1 mg) of formic acid have been collected from the atmosphere and subjected to carbon-isotopic analysis, as a means of source discrimination. Ambient formic acid was captured on Ca(OH)₂-treated filters using a high-volume sampler. The collection method was not only efficient (>96%), but also appears to have low artifact production.Most of the samples (36 out of 52) were collected over a two-year period at the summit of Mount Lemmon, Arizona, where a strong seasonality in HCOOH mixing ratio was observed (0.2 ppb during winter months to 1.5 ppb in the summer). Other collection sites included the Oregon coast, Colorado Rockies, urban Tucson, and the North Dakota prairie. The carbon-13 content of atmospheric HCOOH was found to be have little variation (–18 to –25), regardless of location or season. This is consistent with a single dominant source of formic acid. The carbon-14 measurements of 6 Mount Lemmon samples showed high levels of modern carbon (93–113% modern).The emissions from formicine ants and automobile combustion were selected as two other potential sources for isotopic analysis. The HCOOH collected from auto exhaust was much more depleted in¹³C than the atmospheric samples, with a ¹³C of –28.0 and –48.6 from a leaded and unleaded automobile, respectively. Formicine ants, on the other hand, ranged from –17.2 to –20.6.     

Molecular and bulk isotopic analyses of organic matter in marls of the Mulhouse Basin (Tertiary, Alsace, France)

Contents of 13C in kerogens and carbonates in 21 samples from a core of the MAX borehole, Mulhouse Evaporite Basin, range from -27.3 to -23.5 and -3.7 to -1.8% vs PDB, respectively. Organic nitrogen in the same samples is enriched in 15N relative to atmospheric N2 by 12.2-15.7%. Hydrogen indices and delta values for kerogens vary systematically with facies, averaging 493 mg HC/g Corg and -25.7% in the most saline facies (dominated by inputs from aquatic sources) and 267 mg HC/g Corg and -23.7% in the least saline facies (50/50 aquatic/terrigenous). Values of delta were measured for individual aliphatic hydrocarbons from three samples representing three different organic facies. For all samples, terrigenous inputs were unusually rich in 13C, the estimated delta value for bulk terrigenous debris, apparently derived partly from CAM plants, being -22.5%. In the most saline facies, isotopic evidence indicates the mixing of 13C-depleted products of photosynthetic bacteria with 13C-enriched products of halotolerant eukaryotic algae. At lower salinities, a change in the producer community is marked by a decrease in the 13C content of algal lipids. The content of 13C in algal lipids increases in the least saline facies, due either to succession of different organisms or to decreased concentrations of dissolved CO2.     

Corona textures in Proterozoic olivine melanorites of the Equeefa Suite,Natal Metamorphic Province,South Africa

Summary Olivine-plagioclase and phlogopite-plagioclase coronas have been identified from olivine melanorites of the Mid- to Late Proterozoic Equeefa Suite in southern Natal, South Africa. Olivine, in contact with plagioclase, is mantled by a shell of clear orthopyroxene, in turn rimmed by pale green (pargasitic) clinoamphibole. Locally a third rim, composed of a fine pargasite-spinel symplectite is developed adjacent to the plagioclase. The second corona reaction has produced greenish-brown pargasite at phlogopite-plagioclase interfaces. A third, less obvious reaction, between olivine and phlogopite is also noted. Analytical data of all the mineral phases present, along with the coronas, are given. Two-pyroxene thermometry yields magmatic core temperatures ( 1120°C), with rim compositions indicating equilibration at 850°C. Consistent with this, the modelled olivine-plagioclase reaction occurs between 830–1050°C with a_waterbetween 0.1 and 1.0 at 7 kbar. The three reactions took place during a prolonged history of cooling and partial hydration of the magmatic olivine melanorites from over 1000°C down to 600°C. The P-T conditions indicated by the reactions suggest this cooling process was essentially isobaric, indicating that the area was not subjected to rapid uplift or burial throughout this entire period.

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Korona-Texturen in proterozoischen Olivin-Melanoriten der Equeefa Suite, Natal Metamorphic Province, Südafrika

Zusammenfassung Aus Olivin-Melanoriten der mittel- bis spätproterozoischen Equeefa Suite im südlichen Natal, Südafrika, wurden Olivin-Plagioklas und Phlogopit-Plagioklas-Koronartexturen beobachtet. Olivin, der mit Plagioklas im Kontakt steht, wird von einem klaren Saum vom Orthopyroxen ummantelt, der seinerseits von blaßgrünem (pargasitischem) Klinoamphibol umsäumt wird. Stellenweise ist ein dritter Saum, bestehend aus feinkörnigem symplektitischem Pargasit-Spinell im Kontakt mit Plagioklas ausgebildet. Die zweite koronabildende Reaktion resultiert in Bildung eines grünbraunen Pargasites an Phlogopit-Plagioklas Kornkontakten. Eine dritte, weniger auffällige Reaktion zwischen Olivin und Phlogopit wurde ebenfalls beobachtet. Zwei-Pyroxen-Thermometrie ergab magmatische Temperaturen der Kernbereiche ( 1120°C) und belegt eine Gleichgewichtseinstellung in den Randzonen bei ca. 850°C. Olivin-Plagioklas-Modellreaktionen liegen ebenfalls in einem Temperaturbereich von 830–1050°C bei Wasseraktivitäten von 0.1 bis 1.0 und einem Druck von 7 kbar. Die drei Reaktionen liefen im Zuge einer länger andauernden Abkühlung unter teilweiser Hydratisierung der magmatischen Melanorite in einem Temperaturbereich von 1000°C bis ca. 600°C ab. Die aus den Reaktionen ableitbaren P-T-Bedingungen sprechen für eine im wesentlichen isobare Abkhlungsgeschichte und zeigen, daß dieses Gebiet wáhrend dieser gesamten Periode keiner raschen Hebung bzw. keiner Versenkung unterworfen worden ist.

     

Effects of ageing and overconsolidation on the elastic stiffness of a remoulded clay

Summary Results of resonant column tests were used to determine values of low amplitude shear modulus (G ₀) of a remoulded kaolinite clay for different durations of ageing and for different values of consolidation stress (₀) and overconsolidation ratio (OCR). It was found that after completion of primary consolidation the values of G ₀ increased linearly with the logarithm of time and after a week of confinement the value of normalized rate of secondary increase of shear modulus (N _G ) could be reliably estimated. Values of N _G were found to derease linearly with the logarithm of OCR and with the logarithm of ageing duration. This similarity of behaviour provided a basis for establishing an equivalency between age and equivalent overconsolidation ratio (OCR)_eq. The effects of ₀ and OCR on the value of G ₀ were also established in a functional form that indicated a stronger influence compared to that predicted by the Hardin Equation.     

The role of bathymetry and directional wave conditions on observed crescentic bar dynamics

Nearshore sandbars are important features in the surf zone of many beaches because they strongly influence the mean circulation and evolving morphology. Due to variations in wave conditions, sandbars can experience cross-shore migration and vary in shape from alongshore uniform (shore-parallel) to alongshore rhythmic (crescentic). Sandbar dynamics have been studied extensively, but existing observational studies usually do not quantify the processes leading to crescentic bar formation and straightening. This study analyses the dynamics of crescentic bar events at the fetch-limited beach of Castelldefels (northwestern Mediterranean Sea, Spain) using 7.5 years of hourly time-exposure video images and detailed wave conditions. The results show that, despite the generally calm wave conditions, the sandbars were very dynamic in the cross-shore and longshore directions. They often migrated rapidly offshore during storms (up to 70 m in one day) and more slowly onshore during post-storm conditions. Crescentic bars were often present at the study site (48% of the time), but only when the sandbar was at least 10 m from the shoreline. They displayed a large variability in wavelengths (100–700 m), alongshore migration speeds (0–50 m/day) and cross-shore amplitudes (5–20 m). Wavelengths increased for larger bar–shoreline distances and the alongshore migration speeds were strongly correlated with the alongshore component of the radiation stresses. Crescentic patterns typically developed during low–medium energetic waves with limited obliquity ( $\theta \lesssim 20$° at 10 m depth), while bar straightening occurred during medium–high energetic waves with strong oblique angles of incidence ( $\theta \gtrsim 15$°). Overall, this study provides further proof for the important role of wave direction in crescentic bar dynamics and highlights the strong dependence of crescentic bar development on the initial bathymetric configuration.     

Carbonatites from Eastern Paraguay and genetic relationships with potassic magmatism: C, O, Sr and Nd Isotopes

Summary Geochemical characteristics were systematically determined for Early Cretaceous samples of carbonatitic rocks from Eastern Paraguay (Rio Apa, Amambay and Central Provinces). The data show that all the occurrences have an enriched isotopic signature and that the carbonatites have negligible or absent crustal signature. A petrogenetic model (parent liquids, fractional crystallization, hydrothermal interactions and weathering) is proposed as a function of incompatible trace element, stable (O-C) and radiogenic (Sr-Nd) isotope variations with the aim to test the significance of carbonatitic complexes as a marker of the metasomatized subcontinental lithospheric mantle. The results indicate that the carbonatites and primary carbonates from eastern Paraguay, and those from the north eastern Paraná Basin (SE Brazil), were affected by metasomatic events distinct in time and composition.

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Karbonatite aus Ost-Paraguay und ihre genetische Beziehung zu Kalium-Magmatismus: C O, Sr und Nd isotope

Zusammenfassung Die geochemischen Charakteristika von frühkretazischen Karbonatitproben aus Ostparaguay (Rio Alpa, Amambay und Zentrale Provinzen) wurden untersucht. Die Daten belegen, daß alle Vorkommen eine isotopische Anreicherungssignatur zeigen und daß ihnen eine entsprechende Krustensignatur fehlt. Ein Petrologisches Modell (Ausgangsschmelze, fraktionierte Kristallisation, hydrothermale Interaktion und Verwitterung) wird auf Grund der Verteilung der inkompatiblen Spurenelemente, der stabilen (C-O) und radiogenen (Sr-Nd) Isotope vorgeschlagen. Es versucht die Bedeutung der Karbonatitkomplexe als Markerhorizonte des metasomatischen subkontinentalen Mantels zu überprüfen. Die Ergebnisse zeigen, daß die Karbonatite und die primären Karbonate in Ostparaguay, und jene aus dem Paraná Becken SüdostBrasiliens durch zeitlich und zusammensetzungsmäßig unterschiedliche metasomatische Prozesse erfaßt wurden.

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Textures exhibited by feldspars in the Giant Mottled Anorthosite (GMA) of the bastard unit in the Upper Critical Zone,Western Bushveld Complex

Summary The Bastard Unit, overlying the Merensky Unit, is the uppermost and most complete of the cyclic units in the Upper Critical Zone and its upper contact is taken as the boundary between the Critical and Main Zones (as recommended by SACS, 1980). The Unit is different from underlying units for three reasons: it does not have a well-defined top contact (with an overlying unit); it is much thicker than the Merensky and Footwall Units; and it has an unusually thick sequence of mottled anorthosite at its top. This distinctive composite anorthositic sequence is termed the Giant Mottled Anorthosite (GMA) which is predominantly made up of poikilitic anorthosite. The GMA can broadly be subdivided into three distinct parts; the Lower Giant Mottled Anorthosite (LGMA), Giant Mottled Middling (GMM) and the Upper Giant Mottled Anorthosite (UGMA).Petrographic examination of 82 samples taken in the GMA from 11 borehole profiles around the western limb of the Complex revealed that the LGMA and GMM are essentially adcumulates while the UGMA is orthocumulate in character. By its very nature the dominant phase throughout the GMA is cumulus plagioclase feldspar ( 85%) with the balance being made up of intercumulus orthopyroxene and clinopyroxene and minor biofite — all of which constitute the darker mottles. Intercumulus inverted pigeonite occurs in the upper part of the GMM, throughout the UGMA and for c. 30 m into the Main Zone. K-feldspar also joins the paragenesis within the UGMA and occurs both as intercumulus orthoclase and antiperthite. Cumulus plagioclase grains, showing varying degrees of complex oscillatory-zonal growth are common in the upper part of the GMA. These grains are interpreted as records of growth episodes during earlier influxes of magma which were responsible for the development of the underlying cyclic units, but escaped incorporation into the cumulate pile.

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Feldspat-Texturen im Giant Mottled Anorthosite der Bastard-Einheit in der oberen kritischen Zone des westlichen Bushveld-Komplexes

Zusammenfassung Die Bastard-Einheit, die die Merensky-Einheit überlagert, ist die oberste und am besten entwickelte der zyklischen Einheiten in der oberen kritischen Zone; ihr oberer Kontakt gilt als die Grenze zwischen der Kritischen und der Main-Zone (entsprechend den Empfehlungen von SACS, 1980). Die Einheit unterscheidet sich aus drei Gründen von den Einheiten im liegenden: sie hat keinen gut definierten oberen Kontakt (mit einer darüberliegenden Einheit), sie ist wesentlich mächtiger als die Merensky und die Footwall-Einheiten, und sie hat eine ungewöhnliche mächtige Abfolge von Mottled Anorthosite als obersten Teil der Abfolge. Diese wohldefinierte anorthositische Abfolge wird als Giant Mottled Anorthosite (GMA) bezeichnet, und besteht hauptsächlich aus poikilitischem Anorthosit. Die GMA kann in 3 Teile, den unteren (LGMA), den mittleren (GMM) un den oberen (UGMA) unterteilt werden.Die petrographische Untersuchung von 82 Proben in der GMA aus 11 Bohrlöchern im Westteil des Bushveld-Komplexes zeigt, daß LGMA und GMM im wesentlichen Adkumulate sind, während die UGMA ein Orthokumulat darstellt. Die Hauptphase in der gesamten GMA ist Kumulus-Plagioklas ( 85 %); der Rest besteht aus Intercumulus-Orthopyroxen, Klinopyroxen, und geringen Mengen von Biotit. Diese sind die Komponenten der dunkleren mottles. Intercumulus invertierter Pigeonit kommt im oberen Teil der GMM, in der gesamten UGMA und in den unteren 30 Metern der Main-Zone vor. Innerhalb der UGMA tritt K-Feldspat hinzu, dieser kommt als Intercumulus Orthoklas und Antiperthit vor. Körner von Cumulusplagioklas mit verschiedenen Intensitäten komplexer Zonierung sind im oberen Teil der GMA verbreitet. Diese Körner werden als Hinweise auf Wachstumsepisoden während früherer Magmenzufuhr-Phasen interpretiert, die für die Entwicklung der zyklischen Einheiten im Liegenden verantwortlich waren, aber selbst nicht Teil der Cumulatabfolge wurden.

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