Solutions homoclinic to regular precessions of a symmetric satellite

The aim of this paper is to study numerically asymptotic manifolds and homoclinic solutions to the regular precessions of a rigid symmetric satellite in a circular orbit.     

Problems concerning the Directivity of Tsunami

If knowledge of our theories on the directivity of tsunamis had received worldwide attention, the following operations could have been carried out internationally just after the large earthquake of 19 September 1985 which occurred near Acapulco, Mexico. Having found the great circle, “line S” which is perpendicular to the coast around Acapulco, we could have calculated the angles between line S and line A and between line S and line D, where line A and line D are the great circle connecting Acapulco and Auckland, New Zealand and that connecting Acapulco and Duke of York Island (Chile), respectively. The resultant angles are 30?43′ and 41?49′(>68?48′/2), we could thereafter neglect the eastern half of the offshore energy flux. When we assume that the speed of trans-Pacific tsunami is 400 knots, the probability that the actual tsunami will come earlier than the calculated arrival time proves to be $$\frac{1}{{\sqrt {2\pi } }}\int_{ - {\text{ }}\infty }^{ - {\text{ }}0.689} {e^{ - t^{{2 \mathord{\left/ {\vphantom {2 2}} \right. \kern-\nulldelimiterspace} 2}} } dt = 0.2454} $$ Contact with New Zealand prior to the forecasted arrival time was essential, but the tsunami attention for the Japanese coast was unnecessary. Without such application of our directivity theories, frequent fruitless warnings will be issued for future trans-Pacific tsunamis. Quick improvements in warning procedures are required.     

Patterns of Cenozoic sediment flux from western Scandinavia

The significance of variations in the sediment flux from western Scandinavia during the Cenozoic has been a matter of debate for decades. Here we compile the sediment flux using seismic data, boreholes and results from other publications and discuss the relative importance of causal agents such as tectonism, climate and climate change. Western Scandinavia, the northern British Isles and the Faeroe‐Shetland Platform were significant sediment sources during the Paleocene, which is well founded in tectonic causes related to the opening of the North Atlantic. From the Eocene and onward, variations in the sediment flux from western Scandinavia correlate better with climate and climate change. During the Eocene, sediment production was low. From the late Eocene onward, increased seasonality may have contributed to stimulating the sediment flux. Significant climatic cooling episodes correlate with Oligocene deposits in the North Sea, the post‐mid‐Miocene Molo and Kai Formations of the Norwegian Shelf, the southern North Sea delta system and large volumes of the Late Pliocene‐Holocene Naust Formation. The sediment flux from Scandinavia during the Cenozoic is in general agreement with the detrital flux to the world's oceans. Furthermore, the large variations in the size of sediment catchment areas as well as the possibility of submarine and glacial erosion must be incorporated to understand regional variations in climate driven sediment flux.     

S-wave velocity structures of sediments estimated from array microtremor records and site responses in the near-fault region of the 1999 Chi-Chi,Taiwan earthquake

The 1999 Chi-Chi, Taiwan earthquake, M_W = 7.6, caused severe damage in the near-fault region of the earthquake. In order to evaluate site effects in the near-field strong motions we estimate S-wave velocity structures of sediments at four sites using array records of microtremors. We also recalculated S-wave velocity structures at other four sites previously reported. To show the validity of the estimated S-wave velocity structures we separate empirical site responses from aftershock records using the generalized inversion method and show the agreement between empirical and theoretical site responses. We also show an observed fact that suggests soil nonlinearity during the Chi-Chi earthquake by comparing horizontal-to-vertical spectral ratios (HVRs) for main shock records with HVRs for aftershock records. Then we calculate one-dimensional equivalent-linear site responses using the estimated S-wave velocity structures and the main shock records observed on the surface. It is found that site amplification due to thick (about 6 km) sediments is one of the important factors for explaining the long-period velocity pulses of about 5 to 10 sec observed at sites in the footwall during the Chi-Chi earthquake. It is also found that the theoretical site responses of shallow soft sediments at sites that sustained severe damage in the hanging wall shows significant amplification around 1 sec. As the amplitude of velocity pulses with period around 1 sec is most critical in causing damage to ordinary buildings of moderate heights, our results suggest that the 1-sec period velocity pulses, amplified by the site response of shallow sediments should contribute to the severe damage during the Chi-Chi earthquake.     

Nonlinear Stability of the Lagrangian Libration Points in the Chermnykh Problem

In this paper we consider the problem of motion of an infinitesimal point mass in the gravity field of an uniformly rotating dumb-bell. The aim of our study is to investigate Liapunov stability of Lagrangian libration points of this problem. We analyze the stability of libration points in the whole range of parameters ω, μ of the problem. In particular, we consider all resonance cases when the order of resonance is not greater than five. This revised version was published online in August 2006 with corrections to the Cover Date.     

Bio-Optical Relationship of Case I Waters: The Difference between the Low- and Mid-Latitude Waters and the Southern Ocean

Both historic and currently operational chlorophyll algorithms of the satellite-borne ocean color sensors, such as SeaWiFS, were evaluated for in situ spectral radiation and chlorophyll data in some Case I waters, including the waters in the Indian Ocean sector of the Southern Ocean. Chlorophyll a concentration of the data set (n = 73) ranged from 0.04 to 1.01 mg m^–3. The algorithms had higher accuracy for the low- and mid-latitude waters (RMSE: 0.163–0.253), specifically the most recently developed algorithms of OCTS and Sea WiFS showed 0.163 and 0.170 of Root Mean Square Errors, respectively. However, these algorithms had large errors (0.422–0.621) for the Southern Ocean data set and underestimated the surface chlorophyll by more than a factor of 2.6. The absorption coefficients in the blue spectral region retrieved from remote sensing reflectance varied in a nonlinear manner with chlorophyll a concentration, and the value in the Southern Ocean was significantly lower than that in the low- and mid-latitude waters for each chlorophyll a concentration. The underestimation of chlorophyll a concentration in the Southern Ocean with these algorithms was caused by the lower specific absorption coefficient in the region compared with the low- and mid-latitude waters under the same chlorophyll a concentration.     

Analysing the contribution of snow water equivalent to the terrestrial water storage over Canada

In this study, the spatial and temporal variabilities of terrestrial water storage anomaly (TWSA) and snow water equivalent anomaly (SWEA) information obtained from the Gravity Recovery and Climate Experiment (GRACE) twin satellites data were analysed in conjunction with multisource snow products over several basins in the Canadian landmass. Snow water equivalent (SWE) data were extracted from three different sources: Global Snow Monitoring for Climate Research version 2 (GlobSnow2), Advanced Microwave Scanning Radiometer-Earth Observing System (AMSR-E), and Canadian Meteorological Centre (CMC). The objective of the study was to understand whether SWE variations have a significant contribution to terrestrial water storage anomalies in the Canadian landmass. The period was considered from December 2002 to March 2011. Significant relationships were observed between TWSA and SWEA for most of the 15 basins considered (53% to 80% of the basins, depending on the SWE products considered). The best results were obtained with the CMC SWE products compared with satellite-based SWE data. Stronger relationships were found in snow-dominated basins (R_s > = 0.7), such as the Liard [root mean square error (RMSE) = 21.4 mm] and Peace Basins (RMSE = 26.76 mm). However, despite high snow accumulation in the north of Quebec, GRACE showed weak or insignificant correlations with SWEA, regardless of the data sources. The same behaviour was observed in the Western Hudson Bay basin. In both regions, it was found that the contribution of non-SWE compartments including wetland, surface water, as well as soil water storages has a significant impact on the variations of total storage. These components were estimated using the Water-Global Assessment and Prognosis Global Hydrology Model (WGHM) simulations and then subtracted from GRACE observations. The GRACE-derived SWEA correlation results showed improved relationships with three SWEA products. The improvement is particularly important in the sub-basins of the Hudson Bay, where very weak and insignificant results were previously found with GRACE TWSA data. GRACE-derived SWEA showed a significant relationship with CMC data in 93% of the basins (13% more than GRACE TWSA). Overall, the results indicated the important role of SWE on terrestrial water storage variations.