On the co-orbital motion of two planets in quasi-circular orbits

We develop an analytical Hamiltonian formalism adapted to the study of the motion of two planets in co-orbital resonance. The Hamiltonian, averaged over one of the planetary mean longitudes, is expanded in power series of eccentricities and inclinations. The model, which is valid in the entire co-orbital region, possesses an integrable approximation modeling the planar and quasi-circular motions. First, focusing on the fixed points of this approximation, we highlight relations linking the eigenvectors of the associated linearized differential system and the existence of certain remarkable orbits like the elliptic Eulerian Lagrangian configurations, the anti-Lagrange (Giuppone et al. in MNRAS 407:390–398, 2010) orbits and some second sort orbits discovered by Poincaré. Then, the variational equation is studied in the vicinity of any quasi-circular periodic solution. The fundamental frequencies of the trajectory are deduced and possible occurrence of low order resonances are discussed. Finally, with the help of the construction of a Birkhoff normal form, we prove that the elliptic Lagrangian equilateral configurations and the anti-Lagrange orbits bifurcate from the same fixed point $L_4$ L 4 .     

Distribution and transfer of trace elements in the Western Mediterranean

Results concerning the concentration of cadmium and lead in Mediterranean waters collected during the 2nd PHYCEMED cruise (Oct. 1983) are discussed. Sampling has been performed at seven stations in the Western Mediterranean Basin, two in the Strait of Gibraltar and the near Atlantic, two in the Sicily Strait and the Eastern Basin.In the Western Basin the observations are in fair agreement with those of PHYCEMED 1. Cadmium has a fairly homogeneous distribution vertically as well as from one station to another, with an average concentration of 8 ng l⁻¹; while lead shows a slight but continuous decrease in concentrations with depth (from at least 50 ng l⁻¹ in surface waters to 20 or 25 ng l⁻¹ at depth). On the other hand, at the basin boundaries, where waters from different origins are present, vertical distributions appear very different. On the basis of calculated water budgets it can be estimated that the Mediterranean Sea discharges about 200 t y⁻¹ of cadmium and about 250 t y⁻¹ of lead into the Atlantic Ocean while 1000 t y⁻¹ of lead are transferred from the Western to the Eastern Basin.     

Propagation of the Southwest Indian Ridge at the Rodrigues Triple Junction

The analysis of multibeam bathymetric data of the Southwest Indian Ridge(SWIR) domain between the triple junction traces from 68° E to theRodrigues Triple Junction (RTJ; 70° E) reveals the evolution of thisridge since magnetic anomaly 4 (8 Ma). Image processing has been used toshow that the horizontal component of strain due to a network of normal stepfaults increases dramatically between 69°30 E and the RTJ. Thisarea close to the RTJ is characterized by a deep graben at the foot of thetriple junction trace on the African plate and by a narrow fault-boundedridge that joins an offset of the trace on the Antarctic plate. In thatarea, spreading is primarily amagmatic and dominated by tectonic extensionprocesses. To the west of 69°30 E, some lobate bathymetricfeatures atop of a large topographic high suggest volcanic constructions.Between 68°10 E and 69°25 E the southern flank of theSWIR domain is wider than the northern one and is characterized by a series of 7 en echelon bathymetric highs similar in size,shape and orientation to the one centred at 69°30E near the present-day triple junction. Their en echelon organization along the triple junction trace on the Antarctic plate and the typical lack of conjugated parts on the northern flank show that these bathymetric highs have been shifted to the south by successive northward relocalisations of the SWIR rifting zone. This evolution results in the asymmetric spreading of the SWIR in the survey area. The off-axis bathymetric highs connect to the offsets of the triple junction trace on the Antarctic plate when the Southeast Indian Ridges lightly lengthenstoward the northwest and the triple junction is relocated to the north. We propose that the SWIR lengthens toward the northeast with two propagation modes: 1) a continuous and progressive propagation with distributed deformation in preexisting crust of the Central Indian Ridge, 2) a discontinuous propagation with focusing of the deformation in a rift zone when the triple junction migrates rapidly to the north. The modes of propagation of the SWIR are related to different localisation and distribution of strain which are in turn controlled by changes of the triple junction configurations due to propagation, recession or a symmetric spreading on the Central and Southeast Indian Ridges.     

Prediction of the calcium carbonate budget in a sedimentary basin: A “source-to-sink” approach applied to Great Salt Lake,Utah, USA

Most source-to-sink studies typically focus on the dynamics of clastic sediments and consider erosion, transport and deposition of sediment particles as the sole contributors. Although often neglected, dissolved solids produced by weathering processes contribute significantly in the sedimentary dynamics of basins, supporting chemical and/or biological precipitation. Calcium ions are usually a major dissolved constituent of water drained through the watershed and may facilitate the precipitation of calcium carbonate when supersaturating conditions are reached. The high mobility of Ca²⁺ ions may cause outflow from an open system and consequently loss. In contrast, in closed basins, all dissolved (i.e. non-volatile) inputs converge at the lowest point of the basin. The endoreic Great Salt Lake basin constitutes an excellent natural laboratory to study the dynamics of calcium on a basin scale, from the erosion and transport through the watershed to the sink, including sedimentation in lake's waterbody. The current investigation focused on the Holocene epoch. Despite successive lake level fluctuations (amplitude around 10 m), the average water level seems to have not been affected by any significant long-term change (i.e. no increasing or decreasing trend, but fairly stable across the Holocene). Weathering of calcium-rich minerals in the watershed mobilizes Ca²⁺ ions that are transported by surface streams and subsurface flow to the Great Salt Lake (GSL). Monitoring data of these flows was corrected for recent anthropogenic activity (river management) and combined with direct precipitation (i.e. rain and snow) and atmospheric dust income into the lake, allowing estimating the amount of calcium delivered to the GSL. These values were then extrapolated through the Holocene period and compared to the estimated amount of calcium stored in GSL water column, porewater and sediments (using hydrochemical, mapping, coring and petrophysical estimates). The similar estimate of calcium delivered (4.88 Gt) and calcium stored (3.94 Gt) is consistent with the premise of the source-to-sink approach: a mass balance between eroded and transported compounds and the sinks. The amount of calcium deposited in the basin can therefore be predicted indirectly from the different inputs, which can be assessed with more confidence. When monitoring is unavailable (e.g. in the fossil record), the geodynamic context, the average lithology of the watershed and the bioclimatic classification of an endoreic basin are alternative properties that may be used to estimate the inputs. We show that this approach is sufficiently accurate to predict the amount of calcium captured in a basin and can be extended to the whole fossil record and inform on the storage of calcium.     

Present limitations of accurate satellite Doppler positioning for tectonics. An example: Djibouti

One of the possibilities of the Doppler positioning from satellite is to provide geodetic measurements continuous in time without the need for reference stations. If measurements of sufficient accuracy can be achieved they may be used to study local surface displacements in relation to tectonic activity. A Doppler receiver of the MEDOC network is located near Djibouti in the Ghoubhat-Asal rift region which corresponds to the accreting plate boundary between the Arabian and African plates. In November 1978, a seismic and volcanic crisis occured in this area. Surface geodetic measurements and levellings performed in 1973 and 1978–79, just after the crisis, reveal a 60–80 cm sinking of the graben floor and a lateral extension of about 2 meters. Here we analyse Doppler measurements for the period January 1977 to November 1980. Point positions are computed for 7 to 10 day intervals using a precise ephemeris, and a moving window analysis is applied to the data. An apparent 2 meter uplift preceding the November 1978 seismic crisis is detected at Djibouti, whereas no similar phenomenon is observed at the two closest stations, Pretoria and Uccle-Brussels. However, field observations rule out a tectonic origin for this uplift. In Djibouti, the correlation between the apparent vertical station position and the electron density in the ionospheric F-layer reveals that a bias may be induced by the third order term of the ionospheric refractive index not previously taken into account, or more probably by the ray curvature through the ionosphere. This bias is particularly strong for our data set, from a station located close to the magnetic equator, and related to a period of rapid increase in the solar activity. Although our analysis fails to detect any tectonic displacement related to the rift seismic activity, it shows that similar tectonic studies by the Doppler method will be possible once the residual ionospheric errors are removed, for example by use of higher radio frequencies.     

Integrating Indoor and Outdoor Spaces for Pedestrian Navigation Guidance: A Review

In light of the many improvements within 3D urban modeling and Location‐Based Services, this article provides a timely review of the state‐of‐the‐art on integrating indoor and outdoor spaces in pedestrian navigation guidance aids. With people moving seamlessly between buildings and surrounding areas, navigation guidance tools should extend from merely outdoor or indoor guidance, to provide support in the combined indoor‐outdoor context. This article first examines the challenges and complexities of integrating indoor and outdoor spaces into a single navigation system. Next, by using objective selection criteria, 36 relevant studies were withheld and further reviewed on their specific developments in data model requirements, and algorithmic and context support for integrated IO navigation systems. This review shows that the challenges of dealing with both indoor and outdoor space structures, while taking into account pedestrian's freer use of space, currently complicate the proposition of a unified IO space concept for navigation. However, there are some ongoing developments (e.g. context definitions, algorithmic extensions, increased data availability, growing awareness of pedestrians’ perception during wayfinding) that will help to bring outdoor and indoor spaces closer together in the realm of combined geospatial analysis.     

Estimating Long-Term Solar Irradiance Variability: A New Approach

The detection of solar irradiance variations (both bolometric and at various wavelengths) by satellite-based experiments during the last one-and-a-half decades stimulated modeling efforts to help identify their causes and to provide estimates of irradiance data for those time intervals when no satellite observations exist. In this paper we present estimates of the long-term irradiance changes developed with Fourier and wavelet transforms. The month-to-month irradiance variations, after removing the solar cycle related long-term changes, are studied with the cross-correlation technique. Results of the analysis reveal a significant phase shift at 3 months between the full-disk magnetic field strength and total solar and UV irradiance, with irradiance leading the magnetic field variability. In addition to this time delay between the changes in solar irradiance and the magnetic field, a 10-month phase shift has been found between the UV flux at 280 nm and total solar irradiance corrected for sunspot darkening. The existence of these phase shifts suggests the possibility of a coupling between the physical processes taking place below, in, and above the photosphere.     

Three-dimensional model and late stage warping of the Plattengneis Shear Zone in the Eastern Alps

The Plattengneis shear zone is a 250–600 m thick, flat lying, Cretaceous, eclogite facies, mylonitic shear zone, with north-over-south transport direction, that is exposed over almost 1000 km² in the Koralpe region along the eastern margin of the Alps. Although the shear zone is one of the largest in the Alps, its role in the Eoalpine metamorphic evolution and the subsequent exhumation of the region, remain enigmatic and its large-scale geometry is not well understood. The outcrop pattern suggests that the shear zone is made up of a single sheet that is folded into a series of open syn- and antiforms with wavelengths of about 10 km. Eclogite bodies occur above, within and below the shear zone and there is no metamorphic grade change across the shear zone. In the south, the fold axes strike east–west and plunge shallowly to the east. In the north, the fold axes are oriented in north–south direction and form a dome shaped structure of the shear zone. Total shortening during this late stage warping event was of the order of 5%. Indirect evidence constrains this folding event to have occurred between 80 and 50 Ma and the fold geometry implies that the final exhumation in the Koralpe occurred somewhat later than further north. Interestingly, the shear zone appears to strike out of the topography in the south and dip into the topography in the north, so that north of the shear zone only hanging-wall rocks are exposed and south of it only foot-wall rocks. Possibilities for the geometric relationship of the Plattengneis shear zone with the surrounding south dipping detachments are discussed.