Statistics of seismic cluster durations

Using the standard ETAS model of triggered seismicity, we present a rigorous theoretical analysis of the main statistical properties of temporal clusters, defined as the group of events triggered by a given main shock of fixed magnitude m that occurred at the origin of time, at times larger than some present time t. Using the technology of generating probability function (GPF), we derive the explicit expressions for the GPF of the number of future offsprings in a given temporal seismic cluster, defining, in particular, the statistics of the cluster's duration and the cluster's offsprings maximal magnitudes. We find the remarkable result that the magnitude difference between the largest and second largest event in the future temporal cluster is distributed according to the regular Gutenberg-Richer law that controls the unconditional distribution of earthquake magnitudes. For earthquakes obeying the Omori-Utsu law for the distribution of waiting times between triggering and triggered events, we show that the distribution of the durations of temporal clusters of events of magnitudes above some detection threshold \nu has a power law tail that is fatter in the non-critical regime $n<1$ than in the critical case n=1. This paradoxical behavior can be rationalised from the fact that generations of all orders cascade very fast in the critical regime and accelerate the temporal decay of the cluster dynamics.Comment: 45 pages, 15 figure

Contact metamorphism in the Malashan dome, North Himalayan gneiss domes, southern Tibet: An example of shallow extensional tectonics in the Tethys Himalaya

Combined petrographic, structural and geochronological study of the Malashan dome, one of the North Himalayan gneiss domes, reveals that it is cored by a Miocene granite, the Malashan granite, that intruded into the Jurassic sedimentary rocks of Tethys Himalaya. Two other granites in the area are referred to as the Paiku and Cuobu granites. New zircon SHRIMP U-Pb and muscovite and biotite 40Ar-39Ar dating show that the Paiku granite was emplaced during 22.2–16.2 Ma (average 19.3 ± 3.9 Ma) and cooled rapidly to 350–400 °C at around 15.9 Ma. Whole-rock granite chemistry suggests the original granitic magma may have formed by muscovite dehydration melting of a protolith chemically similar to the High Himalayan Crystalline Sequence. Abundant calcareous metasedimentary rocks and minor garnet-staurolite-biotite-muscovite ± andalusite schists record contact metamorphism by three granites that intruded intermittently into the Jurassic sediments between 18.5 and 15.3 Ma. Two stages of widespread penetrative ductile deformation, D1 and D2, can be defined. Microstructural studies of metapelites combined with geothermobarometry and pseudosection analyses yield P–T conditions of 4.8 ± 0.8 kbar at 550 ± 50 °C during a non-deformational stage between D1 and D2, and 3.1–4.1 kbar at 530–575 °C during syn- to post-D2. The pressure estimates for the syn- to post-D2 growth of andalusite suggest relatively shallow (depth of ∼15.2 km) extensional ductile deformation that took place within a shear zone of the South Tibetan Detachment System. Close temporal association between intrusion of the Malashan granite and onset of D2 suggests extension may have been triggered by the intrusion of the Malashan granite

Middle to Late Miocene Extremely Rapid Exhumation and Thermal Reequilibration in the Kung Co Rift, Southern Tibet

The Kung Co rift is an approximately NNW striking, WSW dipping normal fault exposed in southern Tibet and is part of an extensive network of active approximately NS striking normal faults exposed across the Tibetan Plateau. Detailed new and published (U-Th)/He zircon and apatite thermochronometric data from the footwall of the early Miocene Kung Co granite provide constraints on the middle Miocene to present-day exhumation history of the footwall to the Kung Co fault. Inverse modeling of thermochronometric data yield age patterns that are interpreted as indicating (1) initiation of normal fault slip at ∼12–13 Ma and rapid exhumation of the footwall between ∼13 and 10 Ma, (2) acceleration of normal fault slip at rates of 21.9–6.9 mm/yr at ∼10 Ma, (3) rapid thermal reequilibration between 10 and 9 Ma, and (4) slow exhumation and/or quiescence from ∼9 Ma to the present day. Hanging glacial valleys in the footwall and fault scarps that cut late Quaternary till and moraine deposits indicate that fault slip continues today. Middle to late Miocene initiation of extension across the Kung Co rift is broadly the same as the documented initiation of EW extension across the south central Tibetan Plateau. Eastward flow of middle or lower crust from beneath Tibet accommodated by northward underthrusting of Indian crust beneath Tibet provides a plausible explanation for the onset of EW extension across the Tibetan Plateau

Shrinking pupal cocoons of Rhyacophila lezeyi (Trichoptera, Rhyacophilidae) in a highly acidic stream during the summer season

Shrinking pupal cocoons of Rhyacophila lezeyi were often found during summer in Shibukuro Stream, a highly acidic mountain stream in northern Japan (pH = 2.82 on average). We performed both field surveys and laboratory rearing experiments to clarify the mechanisms of R. lezeyi cocoon shrinkage. The R. lezeyi cocoon shrinkage proportion increased in years with high stream water temperatures and was related to water temperatures before and after pupation at the study site. Approximately 90% of the prepupae and pupae inside the shrinking cocoons died during the rearing experiment, implying that cocoon shrinkage caused by high water temperature strongly influenced R. lezeyi pupal survival. Laboratory experiments showed that R. lezeyi’s pupal cocoon membranes were semi-permeable and that the cocoon fluids were always hyperosmotic, indicating that water molecules can continuously enter the cocoon fluids from the stream water until the turgor of the cocoon wall is reached. However, the shrinking cocoons showed lower fluid volume and higher osmolarity than the normal turgescent cocoons. The reduction of osmotic gradient across the membrane during decreased stream flow due to less precipitation and/or the damage to the cocoon membrane and pupal body from high and fluctuating water temperatures and low pH are possible mechanisms for R. lezeyi pupal cocoon shrinkage

Raman spectroscopy as a tool to determine the thermal maturity of organic matter : application to sedimentary, metamorphic and structural geology

Raman spectrometry is a rapid, non-destructive alternative to conventional tools employed to assess the thermal alteration of organic matter (OM). Raman may be used to determine vitrinite reflectance equivalent OM maturity values for petroleum exploration, to provide temperature data for metamorphic studies, and to determine the maximum temperatures reached in fault zones. To achieve the wider utilisation of Raman, the spectrum processing method, and the positions and nomenclature of Raman bands and parameters, all need to be standardized. We assess the most widely used Raman parameters as well as the best analytical practices that have been proposed. Raman band separation and G-band full-width at half-maximum are the best parameters to estimate the maturity for rocks following diagenesis–metagenesis. For metamorphic studies, the ratios of band areas after performing deconvolution are generally used. Further work is needed on the second-order region, as well as assessing the potential of using integrated areas on the whole spectrum, to increase the calibrated temperature range of Raman parameters. Applying Raman spectroscopy on faults has potential to be able to infer both temperature and deformation processes. We propose a unified terminology for OM Raman bands and parameters that should be adopted in the future. The popular method of fitting several functions to a spectrum is generally unnecessary, as Raman parameters determined from an un-deconvoluted spectrum can track the maturity of OM. To progress the Raman application as a geothermometer a standardized approach must be developed and tested by means of an interlaboratory calibration exercise using reference materials

Overprint of secondary Du folding in the Sambagawa metamorphic belt, SW Japan : implications for strain ellipsoids and Paleogene tectonics of the east-Eurasian margin

Two contrasting results of strain analyses, constriction and flattening, are recognized in the Sambagawa high-pressure/temperature metamorphic belt, SW Japan. An unverified proposal to account for this situation is that the constrictional strain ellipsoids develop only in areas where there is strong overprinting by a secondary Du-phase folding after a penetrative Ds-phase deformation. Field studies in the Hibihara district, central Shikoku, which is located between a southern constructional region and a northern flattening region, reveal there is a map-scale contrast in the effect of Du: outcrop-scale Du upright folds are common in the southern region while they are rare in the northern region. Field measurements show that overall orientation of Ds strain is characterized by E–W stretching and vertical shortening, while that of Du strain is characterized by N–S shortening and vertical extension. The shortening caused by Du in the southern high-Du-strain regions estimated by the fold-curve tracing method are down to about 70-56 % and by removing this Du shortening most of the constrictional strain ellipsoids are restored back to the flattening field with only a few exceptions, suggesting that pre-Du strain states of the Sambagawa metamorphic rocks were dominantly of the flattening type. These results support the previous ideas that invoke differences in the strength of Du overprinting for the two different types of strain ellipsoids observed in the Sambagawa belt. From a tectonic point of view, the semi-penetrative occurrence of Du folds throughout the Sambagawa belt, which stretches about 800 km in SW Japan, suggests that the Du phase can be related to some ancient plate movement. The significant shortening subnormal to the orogen that characterizes Du may reflect a shift to orogen-subnormal subduction of the Pacific plate beneath the Eurasian plate at around 60 Ma