Why q-Expectation Values Must Be Used In Nonextensive Statistical Mechanics

There is a controversy in the area of nonextensive statistical mechanics regarding the form of the expectation value of a physical quantity. Two definitions have been discussed in the literature: one is the ordinary definition and the other is the normalized q-expectation value associated with the escort distribution. Here, it is proved that the normalized q-expectation value is the correct one to be employed. The Shore-Johnson theorem is used to show that the formalism with the normalized q-expectation value is theoretically consistent with minimum cross entropy principle, whereas the ordinary expectation value has to be excluded.     

Synthesis of a Tsunami Spectrum in a Semi-Enclosed Basin Using Its Background Spectrum

We explained spectra of distant tsunamis observed in enclosed basins by applying the synthesis method based on joint analysis of tsunami and background spectra from a number of stations. This method is the generalization of the method proposed by Rabinovich (J. Geopys. Res. 102, 12663-12676, 1997) to separate source and topography effects in recorded tsunami waves. The source function is extracted by inversion of the tsunami/background spectra averaged from many observational sites. The method is applied to the 2009 Papua tsunami observed at the Owase tide station in southwest Japan, a region with complicated topography and numerous bays and inlets. The synthesized spectrum explains the observed spectral amplitudes for each frequency component. It is shown that averaging of tsunami and background from various tide gauge stations in semi-enclosed basins is an efficient approach to extract the source function.     

Magnitudes of large shallow earthquakes from 1904 to 1980

In order to obtain a uniform magnitude catalogue, surface-wave magnitudes M_s and broad-band body-wave magnitudes m_B have been determined for large shallow earthquakes from 1904 to 1980. In making the catalogue homogeneous, the author consistently adheres to the original definitions of M_s and m_B given by Gutenberg (1945) and Gutenberg and Richter (1956). The determinations of M_s and m_B are all based on the amplitude and period data listed in Gutenberg and Richter's unpublished notes, bulletins from stations worldwide, and other basic information. m_B is measured on broad-band instruments in periods of ～8 s. Consistency of the magnitude determinations from these different sources is carefully checked in detail. More than 900 shallow shocks of magnitude 7 and over are catalogued. The meaning of the magnitude scales in various catalogues is examined in terms of M_s and m_B. Most of the magnitudes listed by Gutenberg and Richter (1954) in their “Seismicity of the Earth” are basically M_s for large shocks shallower than 40 km, but are basically m_B for large shocks at depths of 40–60 km. The surface-wave magnitudes given by “Earthquake Data Reports” are higher than M_s by 0.2 unit whether the combined horizontal amplitude or the vertical amplitude is used. m_B and the currently used 1 s body-wave magnitude are measured at different periods and should not be directly compared.     

Improving flood forecasting using an input correction method in urban models in poorly gauged areas

ABSTRACT

Poorly monitored catchments could pose a challenge in the provision of accurate flood predictions by hydrological models, especially in urbanized areas subject to heavy rainfall events. Data assimilation techniques have been widely used in hydraulic and hydrological models for model updating (typically updating model states) to provide a more reliable prediction. However, in the case of nonlinear systems, such procedures are quite complex and time-consuming, making them unsuitable for real-time forecasting. In this study, we present a data assimilation procedure, which corrects the uncertain inputs (rainfall), rather than states, of an urban catchment model by assimilating water-level data. Five rainfall correction methods are proposed and their effectiveness is explored under different scenarios for assimilating data from one or multiple sensors. The methodology is adopted in the city of São Carlos, Brazil. The results show a significant improvement in the simulation accuracy.     

Parallel 3-D Simulation of a Fault Gouge Using the Lattice Solid Model

Despite the insight gained from 2-D particle models, and given that the dynamics of crustal faults occur in 3-D space, the question remains, how do the 3-D fault gouge dynamics differ from those in 2-D? Traditionally, 2-D modeling has been preferred over 3-D simulations because of the computational cost of solving 3-D problems. However, modern high performance computing architectures, combined with a parallel implementation of the Lattice Solid Model (LSM), provide the opportunity to explore 3-D fault micro-mechanics and to advance understanding of effective constitutive relations of fault gouge layers. In this paper, macroscopic friction values from 2-D and 3-D LSM simulations, performed on an SGI Altix 3700 super-cluster, are compared. Two rectangular elastic blocks of bonded particles, with a rough fault plane and separated by a region of randomly sized non-bonded gouge particles, are sheared in opposite directions by normally-loaded driving plates. The results demonstrate that the gouge particles in the 3-D models undergo significant out-of-plane motion during shear. The 3-D models also exhibit a higher mean macroscopic friction than the 2-D models for varying values of interparticle friction. 2-D LSM gouge models have previously been shown to exhibit accelerating energy release in simulated earthquake cycles, supporting the Critical Point hypothesis. The 3-D models are shown to also display accelerating energy release, and good fits of power law time-to-failure functions to the cumulative energy release are obtained.     

Process of the Tsushima Current formation revealed by ADCP measurements in summer

In order to clarify detailed current structures over the continental shelf margin in the East China Sea, ADCP measurements were carried out in summers in 1991 and 1994 by the quadrireciprocal method (Katoh, 1988) for removing diurnal and semidiurnal tidal flows from observed flows, together with CTD measurements. We discussed the process of the Tsushima Current formation in the East China Sea. The Tsushima Current with a volume transport of 2 Sv (1 Sv=10⁶ m³s^–1) was found north of 31°N. A current with a volume transport of 0.4 Sv was clearly found along the 100 m isobath. Between the Kuroshio and the current along the 100 m isobath, southeastward component of velocity was dominant compared to northwestward one. Four eastward to southeastward currents were found over the sea bed shallower than 90 m depth. Total volume transport of these four currents was 1 Sv, and they seemed to be originated from the Taiwan Strait. Intrusion of offshore water into the inner shelf northwest of Amami Oshima was estimated to have a volume transport of 0.6 Sv. It is concluded that the Tsushima Current is the confluence of these currents over the continental shelf margin with the offshore water intruding northwest of Amami Oshima.     

Small-scale topography of 25143 Itokawa from the Hayabusa laser altimeter

The surface topography of Asteroid 25143 Itokawa is explored using the LIght Detection And Ranging instrument (LIDAR). The data confirm the presence of a rough highland and a smooth lowland. The highland is dominated by boulders, but also possesses topography associated with surface lineaments and broad surface facets. The boulders ensure that the roughness of the highlands over short distances is typically greater relative to most surfaces on 433 Eros. Over larger distances, Itokawa is always smoother than Eros possibly because of its smaller size and weak rubble-pile structure. The lowlands of Itokawa are very smooth, and are typically devoid of boulders. Some transitional regions midway between the highlands and lowlands also exist. In these areas, craters that retain their regolith fill possess flat floors and resemble “ponds” seen on 433 Eros. Analyses of surface elevation, imagery and a quantitative measure of surface roughness are consistent with regolith flowing downhill from the highlands to fill in the low areas of Itokawa, probably covering up any pre-existing rough terrain. Using this interpretation, we find a minimum 2.3±0.4 m thick layer of regolith in the lowlands, which, if spread evenly across the entire asteroid, corresponds to a 42±1 cm thick layer. It is very difficult to generate this amount of regolith with the population of craters seen on Itokawa. However, an Itokawa composed of several large masses may have retained this regolith during its formation. The presence of such large masses could account for the observed lineaments and what appear to be exposures of bedrock on the largest steep slope observed.     

Topography and landslides in weathered granitic rock areas—Hai Van landslide in central Vietnam

Many landslides occur every year during heavy rains at the Hai Van Pass and surrounding area in central Vietnam, where granitic rocks are distributed. As is common in granite areas, these landslides often occur as small-scale flow-type and slump-type landslides. However, several horseshoe-shaped loose slopes of widths and lengths of 500 to 800 m, which incorporate these landslides, are observed on slopes across the area. These topographies resemble those formed by past and present large-scale landslides. The presence of such a topography and the repeated occurrences of landslides within this topography are rare in granite areas, where shallow flow-type landslides are generally frequent. To understand the mechanism causing the landslides in the Hai Van region, and as a support for future risk assessment, the factors and processes leading to the formation of such a topography and their relationship with these landslides must be identified and assessed. This study investigated the history of past landslide movement in the Hai Van Pass and surrounding area through observations of drill cores and outcrops, and analysis of the direction of remanent magnetism in the granitic rocks. Mineral compositions, cracks, degrees of weathering, and topographic shapes of the granitic rocks and their relationship to the landslides occurring today were also investigated. The results of the study reveal no variation in the direction of remanent magnetism in the granitic rocks in the region that would indicate disturbance of the ground due to a past large-scale landslide. No evidence of such an event could also be found both in the drill cores and the rock outcrops. Further, results of the analysis of cracks and weathering pattern confirm that the topography of the region is affected by the weathering of the granitic rocks that progresses in concentric circles of various sizes. Thus, it can be concluded that these topographies were not formed by a singular large-scale landslide of the past, but rather by a composite of relatively shallow landslides occurring on the slope of dome structures unique to granite areas, which are formed by differential weathering and denudation regulated by cracks.     

Oceanic Rossby waves induced by the meridional shift of the ITCZ in association with ENSO events

This study investigated the eastern Pacific Intertropical Convergence Zone (ITCZ) as an atmospheric forcing to the ocean by using various observed and reanalysis data sets over 29 years. Climatologically, a zonal band of positive wind stress curl (WSC) with a 10° meridional width was exhibited along the ITCZ. A southward shift of the positive WSC band during the El Niño phase induced a negative (positive) WSC anomaly along the northern (southern) portion of the ITCZ, and vice versa during the La Niña phase. This meridional dipole accounted for more than 25 % of interannual variances of the WSC anomalies (WSCAs), based on analysis of the period 1993–2008. The negative (positive) WSCA in the northern portion of the ITCZ during the El Niño (La Niña) phase was collocated with a positive (negative) sea surface height anomaly (SSHA) that propagated westward as a Rossby wave all the way to the western North Pacific. This finding indicates that this off-equatorial Rossby wave is induced by the WSCA around the ITCZ. Our analysis of a 1.5-layer reduced gravity model revealed that the Rossby waves are mostly explained by wind stress forcing, rather than by reflection of an equatorial Kelvin wave on the eastern coastal boundary. The off-equatorial Rossby wave had the same SSHA polarity as the equatorial Kelvin wave, and generation of a phase-preserving Rossby wave without the Kelvin wave reflection was explained by meridional movement of the ITCZ. Thus, the ITCZ acts as an atmospheric bridge that connects the equatorial and off-equatorial oceanic waves.