Closed-form solution of P4P or the three-dimensional resection problem in terms of Möbius barycentric coordinates

 The perspective 4 point (P4P) problem - also called the three-dimensional resection problem - is solved by means of a new algorithm: At first the unknown Cartesian coordinates of the perspective center are computed by means of M?bius barycentric coordinates. Secondly these coordinates are represented in terms of observables, namely space angles in the five-dimensional simplex generated by the unknown point and the four known points. Substitution of M?bius barycentric coordinates leads to the unknown Cartesian coordinates (2.8)–(2.10) of Box 2.2. The unknown distances within the five-dimensional simplex are determined by solving the Grunert equations, namely by forward reduction to one algebraic equation (3.8) of order four and backward linear substitution. Tables 1.–4. contain a numerical example. Finally we give a reference to the solution of the 3 point (P3P) problem, the two-dimensional resection problem, namely to the Ansermet barycentric coordinates initiated by C.F. Gau? (1842), A. Schreiber (1908) and A.␣Ansermet (1910). Received: 05 March 1996; Accepted: 15 October 1996     

Depositional history of the Main Tuff Interval of the Wittenoom Formation, late Archean—early Proterozoic Hamersley Group, Western Australia

The Main Tuff Interval (MTI) is a 3.5 to 16.4 m thick sequence of pyroclastic turbidites in the Wittenoom Formation of the late Archean to early Proterozoic Hamersley Group, Western Australia. The Hamersley Group accumulated in a basin located on the Archean Pilbara Craton, Western Australia. MTI pyroclasts formed via hydrovolcanic eruption processes from a magma that was likely intermediate in composition. Eruption took place in a shallow subaqueous setting. The MTI was deposited by high- and low- concentration turbidity currents in four overlapping regional depositional packages. Paleocurrent and stratigraphic data indicate the MTI source lay to the north of the present exposure limits of the Hamersley Group on the Pilbara Craton, and was likely to have been a single volcano. Reflection of turbidity currents in the southeastern part of the study area and westward travel of the reflected flows indicate that the Hamersley Group depositional basin shallowed to the east and south at the time of MTI deposition. The presence of the MTI source volcano on the northern Pilbara Craton indicates that the subsidence and marine deposition recorded by the Hamersley Group may be limited to the southern portion of the craton, and that volcanism may have continued on the northern Pilbara Craton.     

Reservoir construction from the Newberry Volcano EGS Demonstration

The Newberry Volcano EGS Demonstration in central Oregon tests recent technological advances designed to reduce the cost of power generated by EGS in a hot, dry well (NWG 55-29) drilled in 2008. An EGS reservoir was created by injecting large volumes of cold water, causing existing fractures to slip in shear (known as hydroshearing) generating the seismic waves that can be used to map fracture location and size. At the Newberry Demonstration the final injectivity ranged between 1.4 and 1.7 L/s/MPa a ~6x improvement over the initial injectivity of the well. The injectivity improvement and seismic analysis indicate that previously impermeable fractures were enhanced during the NWG 55-29 stimulation.     

Is there a link between deep‐sea biodiversity and ecosystem function?

Studying the diversity‐ecosystem function relationship in the deep sea is of primary importance in the face of biodiversity loss and for our understanding of how the deep sea functions. Results from the first study of diversity‐ecosystem function relationships in the deep sea (Danovaro et al. 2008; Current Biology, 18, 1–8) are unexpected and show an exponential relationship between deep‐sea nematode diversity and ecosystem function and efficiency, although this relationship appears largely restricted to relatively low diversities [ES(51) <25]. Here, we investigate the relationship between nematode diversity and several independent measures/proxies of ecosystem function (sediment community oxygen consumption, bacterial biomass, bacterial extracellular enzyme activity) and efficiency (ratio of bacterial/nematode carbon to organic C content of the sediment) on the New Zealand continental slope. Nematode diversity at our study sites was relatively high [ES(51) = 30–42], and there was no relationship between species/functional diversity and ecosystem function/efficiency after accounting for the effects of water depth and food availability. Our results are consistent with a breakdown of the exponential diversity‐function relationship at high levels of diversity, which may be due to increased competition or greater functional redundancy. Future studies need to take into account as many environmental factors and as wide a range of diversities as possible to provide further insights into the diversity‐ecosystem function relationship in the largest ecosystem on Earth.     

Approximate evaluation of the distortion to the peak ocean wavelength and direction derived from SAR image spectra

A calculation procedure using the modulation transfer function approach is presented to estimate the distortions to the values of the peak ocean wavelength and direction derived from SAR images of these waves. The distortions are calculated for ranges of SAR parameters which are typical for aircraft and satellites, and ocean wave parameters which reflect sea states which can be imaged by these SARs. The calculated distortions are discussed in terms of overall trends, effect of particular SAR and wave parameters, and qualitatively compared with observed differences between SAR and in situ measurements.     

The structure of the mid- and high-latitude ionosphere during the November 2004 storm event obtained from GPS observations

GPS data from the International GNSS Service (IGS) network were used to study the development of the severe geomagnetic storm of November 7–12, 2004, in the total electron content (TEC) on a global scale. The TEC maps were produced for analyzing the storm. For producing the maps over European and North American sectors, GPS measurements from more than 100 stations were used. The dense network of GPS stations provided TEC measurements with a high temporal and spatial resolution. To present the temporal and spatial variation of TEC during the storm, differential TEC maps relative to a quiet day (November 6, 2004) were created. The features of geomagnetic storm attributed to the complex development of ionospheric storm depend on latitude, longitude and local time. The positive, as well as negative effects were detected in TEC variations as a consequence of the evolution of the geomagnetic storm. The maximal effect was registered in the subauroral/auroral ionosphere during substorm activity in the evening and night period. The latitudinal profiles obtained from TEC maps for Europe gave rise to the storm-time dynamic of the ionospheric trough, which was detected on November 7 and 9 at latitudes below 50°N. In the report, features of the response of TEC to the storm for European and North American sectors are analyzed.     

Time-dependent convection at high latitudes

A fully time-dependent ionospheric convection model, in which electric potentials are derived by an analytic solution of Laplaces equation, is described. This model has been developed to replace the empirically derived average convection patterns currently used routinely in the Sheffield/SEL/UCL coupled thermosphere/ionosphere/plasmasphere model (CTIP) for modelling disturbed periods. Illustrative studies of such periods indicate that, for the electric field pulsation periods imposed, long-term averages of parameters such as Joule heating and plasma density have significantly different values in a time-dependent model compared to those derived under the same mean conditions in a steady-state model. These differences are indicative of the highly non-linear nature of the processes involved.     

Glacial advances constrained by Be exposure dating of bedrock landslides, Kyrgyz Tien Shan

Numerous large landslide deposits occur in the Tien Shan, a tectonically active intraplate orogen in Central Asia. Yet their significance in Quaternary landscape evolution and natural hazard assessment remains unresolved due to the lack of "absolute" age constraints. Here we present the first ¹⁰Be exposure ages for three prominent (> 10⁷ m³) bedrock landslides that blocked major rivers and formed lakes, two of which subsequently breached, in the northern Kyrgyz Tien Shan. Three ¹⁰Be ages reveal that one landslide in the Alamyedin River occurred at 11–15 ka, which is consistent with two ¹⁴C ages of gastropod shells from reworked loess capping the landslide. One large landslide in Aksu River is among the oldest documented in semi-arid continental interiors, with a ¹⁰Be age of 63–67 ka. The Ukok River landslide deposit(s) yielded variable ¹⁰Be ages, which may result from multiple landslides, and inheritance of ¹⁰Be. Two ¹⁰Be ages of 8.2 and 5.9 ka suggest that one major landslide occurred in the early to mid-Holocene, followed by at least one other event between 1.5 and 0.4 ka. Judging from the regional glacial chronology, all three landslides have occurred between major regional glacial advances. Whereas Alamyedin and Ukok can be considered as postglacial in this context, Aksu is of interglacial age. None of the landslide deposits show traces of glacial erosion, hence their locations and ¹⁰Be ages mark maximum extents and minimum ages of glacial advances, respectively. Using toe-to-headwall altitude ratios of 0.4–0.5, we reconstruct minimum equilibrium-line altitudes that exceed previous estimates by as much as 400 m along the moister northern fringe of the Tien Shan. Our data show that deposits from large landslides can provide valuable spatio-temporal constraints for glacial advances in landscapes where moraines and glacial deposits have low preservation potential.     

IGU Commission on the Organisation of Industrial Space

The International Geographical Union Reports

IGU Commission on the Organisation of Industrial Space     

Correction of the ionospheric distortion on the MARSIS surface sounding echoes

Mars Advanced Radar for Subsurface and Ionospheric Sounding (MARSIS) on the Mars Express (MEX) spacecraft has made numerous measurements of the Martian surface and subsurface. However, all of these measurements are distorted by the ionosphere and must be compensated before any analysis. We have developed a technique to compensate for the ionospheric distortions. This technique provides a powerful tool to derive the total electron content (TEC) and other higher-order terms of the limited expansion of the plasma dispersion function that are related to overall shape of the electron column profile. The derived parameters are fitted by using a Chapman model to derive ionospheric parameters like n₀, electron density primary peak (maximum for solar zenith angle (SZA) equal 0), and the neutral height scale H.

Our estimated ionospheric parameters are in good agreement with Mars Global Surveyor (MGS) radio-occultation data. However, since MARSIS does not have the observation geometry limitations of the radio occultation measurements, our derived parameters extend over a large range of SZA for each MEX orbit.

The first results from our technique have been discussed by Safaeinili et al. [2007, Estimation of the total electron content of the Martian ionosphere using radar sounder surface echoes. Geophys. Res. Lett. 34, L23204, doi:10.1029/2007GL032154].