BLU Estimators and Compositional Data

One of the principal objections to the logratio approach for the statistical analysis of compositional data has been the absence of unbiasedness and minimum variance properties of some estimators: they seem not to be BLU estimator. Using a geometric approach, we introduce the concept of metric variance and of a compositional unbiased estimator, and we show that the closed geometric mean is a c-BLU estimator (compositional best linear unbiased estimator with respect to the geometry of the simplex) of the center of the distribution of a random composition. Thus, it satisfies analogous properties to the arithmetic mean as a BLU estimator of the expected value in real space. The geometric approach used gives real meaning to the concepts of measure of central tendency and measure of dispersion and opens up a new way of understanding the statistical analysis of compositional data.     

On the periodic solutions of a rigid dumbbell satellite in a circular orbit

The aim of the present paper is to provide sufficient conditions for the existence of periodic solutions of the perturbed attitude dynamics of a rigid dumbbell satellite in a circular orbit.     

Holocene evolution of mud depocentres on a high-energy, low-accumulation shelf (NW Iberia)

The high-energy, low-accumulation NW Iberian shelf features three confined Holocene mud depocentres. Here, we show that the evolution of such depocentres follows successive steps. The flooding of inner shelf zones and river catchment areas by the late deglacial sea-level rise provided the precondition for shelf mud deposition. Following this, the Holocene deceleration of the sea-level rise caused a rapid refill of the accommodation space within river valleys. Subsequently, the export of major amounts of fines was initiated. The initial onset and loci of shelf mud deposition were related to deposition-favouring conditions in mid-shelf position or to the presence of morphological highs, which act as sediment traps by providing protection against stronger hydrodynamic energy. The detailed reconstruction of the Holocene depocentre evolution shows for the first time that the expansion of such shelf mud deposits cannot only occur by linear growth off the associated sediment source. Rather, they might develop around centres that are fully disconnected from the source of original sediment supply, and expand later into specific directions. Based on these differences and on the connection of the individual mud depocentres to the material source we propose a conceptual subdivision of the group “mid-shelf mud depocentres”.     

Imaging Faults and Shear Zones Using Receiver Functions

The geometry of faults at seismogenic depths and their continuation into the ductile zone is of interest for a number of applications ranging from earthquake hazard to modes of lithospheric deformation. Teleseismic passive source imaging of faults and shear zones can be useful particularly where faults are not outlined by local seismicity. Passive seismic signatures of faults may arise from abrupt changes in lithology or foliation orientation in the upper crust, and from mylonitic shear zones at greater depths. Faults and shear zones with less than near-vertical dip lend themselves to detection with teleseismic mode-converted waves (receiver functions) provided that they have either a contrast in isotropic shear velocity (V _s), or a contrast in orientation or strength of anisotropic compressional velocity (V _p). We introduce a detection method for faults and shear zones based on receiver functions. We use synthetic seismograms to demonstrate common features of dipping isotropic interfaces and contrasts in dipping foliation that allows determination of their strike and depth without making further assumptions about the model. We proceed with two applications. We first image a Laramide thrust fault in the western U.S. (the Wind River thrust fault) as a steeply dipping isotropic velocity contrast in the middle crust near the surface trace of the fault; further downdip and across the range, where basin geometry suggests the fault may sole into a subhorizontal shear zone, we identify a candidate shear zone signal from midcrustal depths. The second application is the use of microstructural data from exhumed ductile shear zones in Scotland and in the western Canadian Shield to predict the character of seismic signatures of present-day deep crustal shear zones. Realistic anisotropy in observed shear fabrics generates a signal in receiver functions that is comparable in amplitude to first-order features like the Moho. Observables that can be robustly constrained without significant tradeoffs are foliation strike and the depth of the foliation contrast. We find that an anisotropy of only a few percent in the shear zone is sufficient to generate a strong signal, but that the shear zone width is required to be >2 km for typical frequencies used in receiver function analysis to avoid destructive interference due to the signals from the boundaries of the shear zone.     

Storm influence on SPM concentrations in a coastal turbidity maximum area with high anthropogenic impact (southern North Sea)

Multi-sensor tripod measurements in the high-turbidity area of the Belgian nearshore zone (southern North Sea) allowed investigating storm effects on near bed suspended particulate matter (SPM) concentrations. The data have shown that during or after a storm the SPM concentration increases significantly and that high concentrated mud suspensions (HCMS) are formed. Under these conditions, about 3 times more mass of SPM was observed in the water column, as compared to calm weather conditions. The following different sources of fine-grained sediments, influencing the SPM concentration signal, have been investigated: wind direction and the advection of water masses; the previous history and occurrence of fluffy layers; freshly deposited mud near the disposal grounds of dredged material, navigation channels and adjacent areas; and the erosion of medium-consolidated mud of Holocene age.     

Elliptical boundary of an intraplate volcanic field, Auckland, New Zealand

The outer vents in the Auckland Volcanic Field lie within 19 to 559 m (mean 224.75 m) of a ‘best-fit' ellipse with a 28.9-km-long major axis trending almost north–south, and a minor axis 16.5 km long. The ellipse has formed the outer boundary of the field since the inception of volcanism 140,000 years ago. We present the following testable hypotheses as an explanation of this pattern: The boundary is the expression of a corresponding elliptical source area at depth in the lithospheric mantle (possibly asthenosphere material trapped at this level). The ellipse may represent a depth contour on a very small upper mantle dome or of a lens intruding into a neck of an extensional structure. Alternatively it could be the boundary of a flat elliptical area where tensional stresses allow decompressional melting. The elliptical tensional region may either have developed in a releasing bend during strike-slip faulting along a fundamental lithosphere structure inherited from Mesozoic tectonics, associated with the NNW-trending Dun Mountain ophiolite belt, or may represent the tip of a fracture along which the Auckland Volcanic Province is propagating northward.