Explicit, approximate expressions for the resolution and a posteriori covariance of massive tomographic systems

We present an approximate method to estimate the resolution, covariance and correlation matrix for linear tomographic systems Ax = b that are too large to be solved by singular value decomposition. An explicit expression for the approximate inverse matrix A ⁻ is found using one-step backprojections on the Penrose condition AA ⁻≈ I , from which we calculate the statistical properties of the solution. The computation of A ⁻ can easily be parallelized, each column being constructed independently.
The method is validated on small systems for which the exact covariance can still be computed with singular value decomposition. Though A ⁻ is not accurate enough to actually compute the solution x , the qualitative agreement obtained for resolution and covariance is sufficient for many purposes, such as rough assessment of model precision or the reparametrization of the model by the grouping of correlating parameters. We present an example for the computation of the complete covariance matrix of a very large (69 043 × 9610) system with 5.9 × 10⁶ non-zero elements in A . Computation time is proportional to the number of non-zero elements in A . If the correlation matrix is computed for the purpose of reparametrization by combining highly correlating unknowns x _i , a further gain in efficiency can be obtained by neglecting the small elements in A , but a more accurate estimation of the correlation requires a full treatment of even the smaller A _ij . We finally develop a formalism to compute a damped version of A ⁻.     

Short contribution: Nile flow failure at the end of the Old Kingdom,Egypt: Strontium isotopic and petrologic evidence

Strontium isotopic and petrologic information, obtained from sediment cores collected in the Nile delta of Egypt, indicate that paleoclimatic and Nile baseflow conditions changed considerably from about 4200 to 4000 cal yr B.P. in the Nile basin. Our study records a higher proportion of White Nile sediment transported during the annual floods at ca. 6100 cal yr B.P. than towards 4200 cal yr B.P., at which time suspended sediment from the Blue Nile formed a significantly larger fraction of the total load. This resulted from a decrease in vegetative cover and an increase in erosion rate accompanying the marked decline in rainfall. These new geoscience data indicate major changes in annual flooding and baseflow of the river Nile, marked short‐term paleoclimatic‐related events that may in part have led to the collapse of the Old Kingdom. © 2003 Wiley Periodicals, Inc.     

Andoyer construction for Hill and Delaunay variables

Andoyer variables are well known for the study of rotational dynamics. These variables were derived by Andoyer through a procedure that can be also used to obtain the Hill variables of the Kepler problem. Andoyer construction can also forecast the Delaunay variables which canonicity is then obtained without the use of a generating function.     

Regolith breccia Northwest Africa 7533: Mineralogy and petrology with implications for early Mars

Northwest Africa 7533, a polymict Martian breccia, consists of fine‐grained clast‐laden melt particles and microcrystalline matrix. While both melt and matrix contain medium‐grained noritic‐monzonitic material and crystal clasts, the matrix also contains lithic clasts with zoned pigeonite and augite plus two feldspars, microbasaltic clasts, vitrophyric and microcrystalline spherules, and shards. The clast‐laden melt rocks contain clump‐like aggregates of orthopyroxene surrounded by aureoles of plagioclase. Some shards of vesicular melt rocks resemble the pyroxene‐plagioclase clump‐aureole structures. Submicron size matrix grains show some triple junctions, but most are irregular with high intergranular porosity. The noritic‐monzonitic rocks contain exsolved pyroxenes and perthitic intergrowths, and cooled more slowly than rocks with zoned‐pyroxene or fine grain size. Noritic material contains orthopyroxene or inverted pigeonite, augite, calcic to intermediate plagioclase, and chromite to Cr‐bearing magnetite; monzonitic clasts contain augite, sodic plagioclase, K feldspar, Ti‐bearing magnetite, ilmenite, chlorapatite, and zircon. These feldspathic rocks show similarities to some rocks at Gale Crater like Black Trout, Mara, and Jake M. The most magnesian orthopyroxene clasts are close to ALH 84001 orthopyroxene in composition. All these materials are enriched in siderophile elements, indicating impact melting and incorporation of a projectile component, except for Ni‐poor pyroxene clasts which are from pristine rocks. Clast‐laden melt rocks, spherules, shards, and siderophile element contents indicate formation of NWA 7533 as a regolith breccia. The zircons, mainly derived from monzonitic (melt) rocks, crystallized at 4.43 ± 0.03 Ga (Humayun et al. 2013 ) and a ¹⁴⁷Sm‐¹⁴³Nd isochron for NWA 7034 yielding 4.42 ± 0.07 Ga (Nyquist et al. 2016 ) defines the crystallization age of all its igneous portions. The zircon from the monzonitic rocks has a higher Δ¹⁷O than other Martian meteorites explained in part by assimilation of regolith materials enriched during surface alteration (Nemchin et al. 2014 ). This record of protolith interaction with atmosphere‐hydrosphere during regolith formation before melting demonstrates a thin atmosphere, a wet early surface environment on Mars, and an evolved crust likely to have contaminated younger extrusive rocks. The latest events recorded when the breccia was on Mars are resetting of apatite, much feldspar and some zircons at 1.35–1.4 Ga (Bellucci et al. 2015 ), and formation of Ni‐bearing pyrite veins during or shortly after this disturbance (Lorand et al. 2015 ).     

A gamma‐ray spectroscopy survey of Omani meteorites

The gamma‐ray activities of 33 meteorite samples (30 ordinary chondrites, 1 Mars meteorite, 1 iron, 1 howardite) collected during Omani‐Swiss meteorite search campaigns 2001–2008 were nondestructively measured using an ultralow background gamma‐ray detector. The results provide several types of information: Potassium and thorium concentrations were found to range within typical values for the meteorite types. Similar mean ²⁶Al activities in groups of ordinary chondrites with (1) weathering degrees W0‐1 and low ¹⁴C terrestrial age and (2) weathering degree W3‐4 and high ¹⁴C terrestrial age are mostly consistent with activities observed in recent falls. The older group shows no significant depletion in ²⁶Al. Among the least weathered samples, one meteorite (SaU 424) was found to contain detectable ²²Na identifying it as a recent fall close to the year 2000. Based on an estimate of the surface area searched, the corresponding fall rate is ~120 events/10⁶ km²*a, consistent with other estimations. Twelve samples from the large JaH 091 strewn field (total mass ~4.5 t) show significant variations of ²⁶Al activities, including the highest values measured, consistent with a meteoroid radius of ~115 cm. Activities of ²³⁸U daughter elements demonstrate terrestrial contamination with ²²⁶Ra and possible loss of ²²²Rn. Recent contamination with small amounts of ¹³⁷Cs is ubiquitous. We conclude that gamma‐ray spectroscopy of a selection of meteorites with low degrees of weathering is particularly useful to detect recent falls among meteorites collected in hot deserts.     

Mass-transport deposits on the Rosetta province (NW Nile deep-sea turbidite system, Egyptian margin): Characteristics, distribution, and potential causal processes

In the Nile deep-sea turbidite system (NDSTS), the province fed by the Rosetta branch of the Nile delta is characterised by the recurrent activity of gravity processes. Seven mass-transport deposits (MTDs) were recognised from the upper to the mid slope, downstream from imbricated scars (~ 30 km-long, ~ 200 m high) running along the shelf edge nearby the Rosetta canyon. Extending on surfaces between 200 and 5000 km², with estimated volumes from 3 to 500 km³, these MTDs represent about 40% (up to 90% locally) of the total Pleistocene–Holocene sedimentary thickness. Three types of MTDs can be distinguished on the basis of their scale. Each has also a distinctive internal configuration and distribution within the Rosetta depositional setting. Age estimates of two MTDs point towards relationships between climate and submarine mass failures through sea-level changes, sediment supply, or a combination of both. Additionally, the presence of gas in the sediment and earthquake shaking may have concurred to trigger large-scale failures on the low slope angles (1°–2°) of the Rosetta area.     

Suspended-sediment concentration and mineralogy in the central and western Mediterranean and mineralogic comparison with bottom sediment

Concentrations and mineralogy of suspensates in the central and western Mediterranean are vertically and laterally variable. This variability is related to input by resuspension of bottom sediments and from local terrigenous sources. Bottom currents flowing through constrictions at the straits of Sicily and Gibraltar and the eastern entrance of the Alboran Sea resuspend bottom sediments, giving rise to increased concentrations of suspensates in near-bottom waters and limited inputs to higher levels. There is no evidence of a suspensate-rich bottom water in the Balearic Sea.Terrigenous sources are believed to be the cause of increasing relative amounts of montmorillonite in surface waters as they flow eastward within the Mediterranean. Montmorillomite is relatively more important in suspended sediments than in bottom sediments where kaolinite—chlorite is dominant.     

Northwestern Hellenic Arc: Concurrent sedimentation and deformation in a compressive setting

Seismic (air-gun) and 3.5-kHz systems and coring in the northwestern sector of the Hellenic Arc, Ionian Sea, serve to define the regional configuration, attitude and geometry of the unconsolidated sedimentary cover in a compressive tectonic setting. The Pliocene and Quaternary deposits are deformed to varying degrees throughout the region southwest of the island of Zakinthos. Depositional trends, overall structural configuration of the cover, and assemblages of deformation structures, including tilted, folded and faulted strata associated with a very complex topography, clearly reflect syndepositional modification in a tectonically mobile area. The structural attitude of the unconsolidated strata can be distinguished from that in tectonically active regions of the Mediterranean where extension prevails. The youthful physiography, sediment dispersal patterns and depositional distribution reveal prevailing NW—SE and NE—SW trends. Sediment deformation structures, whose axes strike primarily NW—SE, reveal a general NE—SW compressive stress trend. The geologically recent nature and orientation of the deformation are compatible with present theories concerning the evolution of the Hellenic Arc.     

The Erbisberg drilling 2011: Implications for the structure and postimpact evolution of the inner ring of the Ries impact crater

The 26 km diameter Nördlinger Ries is a complex impact structure with a ring structure that resembles a peak ring. A first research drilling through this “inner crystalline ring” of the Ries was performed at the Erbisberg hill (SW Ries) to better understand the internal structure and lithology of this feature, and possibly reveal impact‐induced hydrothermal alteration. The drill core intersected the slope of a 22 m thick postimpact travertine mound, before entering 42 m of blocks and breccias of crystalline rocks excavated from the Variscan basement at >500 m depth. Weakly shocked gneiss blocks that show that shock pressure did not exceed 5 GPa occur above polymict lithic breccias of shock stage Ia (10–20 GPa), with planar fractures and planar deformation features (PDFs) in quartz. Only a narrow zone at 49.20–50.00 m core depth exhibits strong mosaicism in feldspar and {102} PDFs in quartz, which are indicative of shock stage Ib (20–35 GPa). Finally, 2 m of brecciated Keuper sediments at the base of the section point to an inverse layering of strata. While reverse grading of clast sizes in lithic breccias and gneiss blocks is consistent with lateral transport, the absence of diaplectic glass and melt products argues against dynamic overthrusting of material from a collapsing central peak, as seen in the much larger Chicxulub structure. Indeed, weakly shocked gneiss blocks are rather of local provenance (i.e., the transient crater wall), whereas moderately shocked polymict lithic breccias with geochemical composition and ⁸⁷Sr/⁸⁶Sr signature similar to Ries suevite were derived from a position closer to the impact center. Thus, the inner ring of the Ries is formed by moderately shocked polymict lithic breccias likely injected into the transient crater wall during the excavation stage and weakly shocked gneiss blocks of the collapsing transient crater wall that were emplaced during the modification stage. While the presence of an overturned flap is not evident from the Erbisberg drilling, a survey of all drillings at or near the inner ring point to inverted strata throughout its outer limb. Whether the central ring of the Ries represents remains of a collapsed central peak remains to be shown. Postimpact hydrothermal alteration along the Erbisberg section comprises chloritization, sulfide veinlets, and strong carbonatization. In addition, a narrow zone in the lower parts of the polymict lithic breccia sequence shows a positive Eu anomaly in its carbonate phase. The surface expression of this hydrothermal activity, i.e., the travertine mound, comprises subaerial as well as subaquatic growth phases. Intercalated lake sediments equivalent to the early parts of the evolution of the central crater basin succession confirm a persistent impact‐generated hydrothermal activity, although for less time than previously suggested.     

Links Between Weather Phenomena and Characteristics of Refractivity Measured by Precipitation Radar

Refractivity depends on meteorological parameters such as temperature and water vapour pressure and can be measured using a weather radar. A realistic atmospheric simulation from the Meso-NH numerical model is used in order to describe and establish the relation between refractivity and the dynamic and thermodynamic phenomena responsible for the development and propagation of convection. These investigations lead to discussion of the complementarity between the refractivity and the convective available potential energy. The relation observed between the refractivity signal and the meteorological parameters calls the refractivity measurement into question, since it is based on phase differentiation with time and space and can be degraded by phase aliasing problems. These aliasing problems increase with the radar frequency (perceptible in the S-band, serious in the C-band, and more serious in the X-band) and also with the integration range and sampling time. Thus, a statistical approach permits us to simulate the possibility of measuring the refractivity with operational radar during convective events. A typical case in the south-east region of France is selected to simulate measurements by radar (S-band, C-band, X-band) in convective systems, in order to evaluate the measurement feasibility, particularly in terms of phase ambiguity, related to temporal and spatial sampling, of a future implementation of the refractivity measurement over the French operational radar network. This numerical statistical approach is completed with a similar study using in-situ measurements performed at the Trappes station. The seasonal and diurnal dependencies of aliasing are investigated, leading to clarification of the impact of the turbulent fluxes on the refractivity measurement.