The area of a spherical region can be easily measured by considering which sampling points of a lattice are located inside or outside the region. This point-counting technique is frequently used for measuring the Earth coverage of satellite constellations, employing a latitude-longitude lattice. This paper analyzes the numerical errors of such measurements, and shows that they could be greatly reduced if the Fibonacci lattice were used instead. The latter is a mathematical idealization of natural patterns with optimal packing, where the area represented by each point is almost identical. Using the Fibonacci lattice would reduce the root mean squared error by at least 40%. If, as is commonly the case, around a million lattice points are used, the maximum error would be an order of magnitude smaller.

A spatially localized seismic sequence originated few tens of kilometres offshore the Mediterranean coast of Spain, close to the Ebro river delta, starting on 2013 September 5, and lasting at least until 2013 October. The sequence culminated in a maximal moment magnitude M w 4.3 earthquake, on 2013 October 1. The most relevant seismogenic feature in the area is the Fosa de Amposta fault system, which includes different strands mapped at different distances to the coast, with a general NE-SW orientation, roughly parallel to the coastline. However, no significant known historical seismicity has involved this fault system in the past. The epicentral region is also located near the offshore platform of the Castor project, where gas is conducted through a pipeline from mainland and where it was recently injected in a depleted oil reservoir, at about 2 km depth. We analyse the temporal evolution of the seismic sequence and use full waveform techniques to derive absolute and relative locations, estimate depths and focal mechanisms for the largest events in the sequence (with magnitude mbLg larger than 3), and compare them to a previous event (2012 April 8, mbLg 3.3) taking place in the same region prior to the gas injection. Moment tensor inversion results show that the overall seismicity in this sequence is characterized by oblique mechanisms with a normal fault component, with a 30 • low-dip angle plane oriented NNE-SSW and a subvertical plane oriented NW-SE. The combined analysis of hypocentral location and focal mechanisms could indicate that the seismic sequence corresponds to rupture processes along shallow low-dip surfaces, which could have been triggered by the gas injection in the reservoir, and excludes the activation of the Amposta fault, as its known orientation is inconsistent with focal mechanism results. An alternative scenario includes the iterated triggering of a system of steep faults oriented NW-SE, which were identified by prior marine seismics investigations.

The size or energy of diverse structures or phenomena in geoscience appears to follow power law distributions. A rigorous statistical analysis of such observations is tricky, though. Observables can span several orders of magnitude, but the range for which the power law may be valid is typically truncated, usually because the smallest events are too tiny to be detected and the largest ones are limited by the system size. We revisit several examples of proposed power law distributions dealing with potentially damaging natural phenomena. Adequate fits of the distributions of sizes are especially important in these cases, given that they may be used to assess long‐term hazard. After reviewing the theoretical background for power law distributions, we improve an objective statistical fitting method and apply it to diverse data sets. The method is described in full detail, and it is easy to implement. Our analysis elucidates the range of validity of the power law fit and the corresponding exponent and whether a power law tail is improved by a truncated lognormal. We confirm that impact fireballs and Californian earthquakes show untruncated power law behavior, whereas global earthquakes follow a double power law. Rain precipitation over space and time and tropical cyclones show a truncated power law regime. Karst sinkholes and wildfires, in contrast, are better described by truncated lognormals, although wildfires also may show power law regimes. Our conclusions only apply to the analyzed data sets but show the potential of applying this robust statistical technique in the future.

Adult renal transplant recipients at risk for SCs can be identified by age, DGF, graft vessel and recipient atheromatosis, difficult bench surgery, obesity, rejection and the use of antiplatelet drugs and rapamycin.

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