Fast computation of Jacobian elliptic functions and incomplete elliptic integrals for constant values of elliptic parameter and elliptic characteristic

In order to accelerate the numerical evaluation of torque-free rotation of triaxial rigid bodies, we present a fast method to compute various kinds of elliptic functions for a series of the elliptic argument when the elliptic parameter and the elliptic characteristic are fixed. The functions we evaluate are the Jacobian elliptic functions and the incomplete elliptic integral of the second and third kinds regarded as a function of that of the first kind. The key technique is the utilization of the Maclaurin series expansion and the addition theorems with respect to the elliptic argument. The new method is around 25 times faster than the method using the incomplete elliptic integral of general kind and around 70 times faster than the method using mathematical libraries given in the latest version of Numerical Recipes.     

An earthquake swarm in the northern part of the Aso caldera and migration of their foci

A seismicity gap was observed in the early stage of the activity of the earthquake swarm which has been taken place in the northern part of the Aso caldera during January 1975. In the following stage, small earthquakes began to occur, until at last the largest earthquake occured within the seismicity gap. The b-value appreciably increased after the largest earthquake. The above-mentioned characteristics of this earthquake swarm may be a typical example of the fracturing phenomena in relatively heterogeneous rocks. From the estimation of the ultimate strain energy that can be stored up in the seismicity gap, it may be concluded that the above-mentioned largest earthquake took place by the release of ultimate strain energy stored within the seismicity gap.     

Transformation from Cartesian to Geodetic Coordinates Accelerated by Halley’s Method

By using Halley’s third-order formula to find the root of a non-linear equation, we develop a new iterative procedure to solve an irrational form of the “latitude equation”, the equation to determine the geodetic latitude for given Cartesian coordinates. With a limit to one iteration, starting from zero height, and minimizing the number of divisions by means of the rational form representation of Halley’s formula, we obtain a new non-iterative method to transform Cartesian coordinates to geodetic ones. The new method is sufficiently precise in the sense that the maximum error of the latitude and the relative height is less than 6 micro-arcseconds for the range of height, −10 km ≤ h ≤ 30,000 km. The new method is around 50% faster than our previous method, roughly twice as fast as the well-known Bowring’s method, and much faster than the recently developed methods of Borkowski, Laskowski, Lin and Wang, Jones, Pollard, and Vermeille.     

Origin of 30 ∼ 100 kev protons observed in the upstream region of the Earth's bow shock

a Fermi-type acceleration model is constructed to explain the origin of energetic protons (30 ～ 100 keV) which have been observed upstream of the bow shock. It is shown that the suprathermal protons (with energy of several keV) can be accelerated up to several tens of keV through the Fermi-type process in which the reflection at the shock front and the scattering in the upstream region are coupled. The efficiency of the scattering process is estimated by using the result of Barnes' quasilinear treatment of the wave excitation. The resultant energy spectrum and flux intensity ($\text{10}{}^3\text{～ 10}{}^4\text{protons}\text{(}\text{cm}{}^2\text{s ster keV}$) in 32 ～ 45.3keV) are consistent with the observation, and the softening of the energy spectrum observed in the dawn region can be explained by the decrease in the efficiency of the acceleration process in the dawn region due to the curvature of the bow shock and the reduction of shock strength. The spatial distribution of the flux predicted by the model is also consistent with the observation. In view of these consistencies the Fermi-type acceleration process is suggested as a possible candidate mechanism to explain the upstream protons although we do not intend to exclude other possibilities.     

Blueschist blocks at Mochimaru in the Tari-Misaka ultramafic complex: Their petrologic characteristics and significance

Blueschist tectonic blocks occur in serpentinites at Mochimaru, Hiroshima Prefecture, Southwest Japan. They contain alkali amphibole coexisting with pumpellyite and chlorite, with or without calcic amphibole. Textural and chemical analyses reveal that the blueschists, together with other mafic schists, have similar metamorphic history. After their capture by serpentinites and before the emplacement of the serpentinites into the present geological position, the tectonic blocks were subjected to high P/T metamorphism around the boundary between the blueschist and pumpellyite–actinolite facies. The amphiboles formed by this metamorphism change from tremolite through glaucophane to ferroglaucophane with increasing FeO/MgO of whole rock compositions. The P–T conditions are estimated to be within 200–350°C and 5–7 kbar. These are higher P/T conditions than those of the regional metamorphism of Southwest Japan. The difference in the P–T conditions implies differences in tectonic situation and timing of metamorphism between the blocks and regional metamorphic rocks. In addition, the high P/T metamorphism of the tectonic blocks probably occurred in more reducing environments than the regional metamorphism. Because the ferric/ferrous iron ratios of the tectonic blocks are within a narrow range, it is stressed that oxygen fugacity was externally buffered during the high P/T metamorphism by the serpentinization process of the host ultramafic rocks. The reducing effect of serpentinization is common throughout the high P/T metamorphic terranes of Southwest Japan.     

Temporal variations of the net Kuroshio transport and its relation to atmospheric variations

Temporal variations of the net Kuroshio transport are investigated using long-term hydrographic data from repeat section of the 137°E meridian from the south of Japan (34°N) to New Guinea (1°S) conducted by the Japan Meteorological Agency. In this study, boundaries of the Kuroshio and the Kuroshio Counter Current (KCC) are defined based on the sea surface dynamic height distribution. Westward flows associated with the KCC and cold-core eddy north of the Kuroshio are removed from the eastward flow associated with the Kuroshio in order to estimate the net Kuroshio transport strictly. The net Kuroshio transport reveals low-frequency variations: significant signals on a decadal (about 10-year) timescale. The variations of net Kuroshio transport are predominantly caused by changes in the magnitude of oceanic current speed fields associated with a vertical movement of the main pycnocline depth around the southern boundary of the Kuroshio: deepening of the main pycnocline around the southern boundary of the Kuroshio forms a sharp northern upward-tilting slope of the isopycnal surfaces at the Kuroshio region, and eventually the net Kuroshio transport increases together with the Kuroshio eastward transport. By using a wind-driven hindcast model, it is found that the main pycnocline depth variation results from the first-mode baroclinic Rossby waves attributable to two types of Aleutian Low (AL) changes: a change in the magnitude of AL and meridional movement of AL.     

Characteristics of coastal trapped waves along the southern and eastern coasts of Australia

The spatial structures and propagation characteristics of coastal trapped waves (CTWs) along the southern and eastern coasts of Australia are investigated using observed daily mean sea level data and results from a high-resolution ocean general circulation model (OGCM), and by conducting sensitivity studies with idealized numerical models. The results obtained from the sea level observations show that shortterm variations, with a typical period of 1 to 2 weeks, dominate the sea level variability in the southern half of Australia. The signal propagates anticlockwise around Australia with a propagation speed of 4.5 m/s or faster in the western and southern coasts and 2.1 to 3.6 m/s in the eastern coast. Strong seasonality of the wave activity, with large amplitude during austral winter, is also observed. It turns out that the waves are mainly generated by synoptic weather disturbances in the southwestern and southeastern regions. The numerical experiment with idealized wind forcing and realistic topography confirms that the propagating signals have characteristics of the CTW both in the southern and eastern coasts. Sensitivity experiments demonstrate that the difference in the phase speed between the coasts and reduction of the amplitude of the waves in the eastern coast are attributed to the different shape of the continental shelf in each region. The structures and the propagation characteristics of the CTWs around Australia are well reproduced in OFES (OGCM for the Earth Simulator) with dominant contribution from the first mode, although meso-scale eddies may modify the structure of the CTWs in the eastern coast. It is also found that generation or reinforcement of the waves by the wind forcing in the southern part of the eastern coast is necessary to obtain realistically large amplitude of the CTWs in the eastern coast.     

Sedimentary Steryl Chlorin Esters (SCEs) and Other Photosynthetic Pigments as Indicators of Paleolimnological Change Over the Last 28,000 Years from the Buguldeika Saddle of Lake Baikal

Detailed depth profiles of photosynthetic pigments in a sediment core (G-12) collected at the BDP93 site, the Buguldeika saddle, of south Lake Baikal, along with depth profiles of total organic carbon (TOC) and biogenic silica, were studied to elucidate the temporal changes of phytoplankton assemblages in the lake during the past 28 kyr. In addition to the quantification of carotenoids by high-performance liquid chromatography with photodiode-array detection (HPLC-PDA), steryl chlorin esters (SCEs) were analyzed by HPLC-PDA, HPLC-mass spectrometry (LC-MS) and sterols in SCEs by gas chromatography–mass spectrometry (GC–MS) to enrich the taxonomical information on the phytoplankton composition. Allochthonous input of organic matter from the Selenga River resulted in the higher TOC contents in core G-12 than in a previously reported core (G-6) collected at another site from the southern basin. The poorer correlation in core G-12 than in G-6 between TOC and chlorophyll-a-originating pigments, which are indicative of autochthonous production, also indicated a significant allochthonous input at the site. The abundance of lutein among the carotenoids detected, and the good correlation of total chlorophyll a and b shows that green algae represented a significant portion of the phytoplankton, accompanying the diatoms at the G-12 site, after the last glacial period. The presence of cryptomonads and cyanobacteria were confirmed from marker carotenoids in the sediment core. GC–MS analysis of sterols in SCEs detected marker sterols of diatoms, green algae, chrysophytes and dinoflagellates. The depth profiles of the measured indicators gave consistent features for temporal changes in phytoplankton assemblage at the G-12 site of Lake Baikal after the last glacial maximum. Notably, the profile of a chrysophyte-specific sterol in SCEs was consistent with the reported distribution of chrysophyte cysts during the Holocene. The presence of phytoplankton, such as green algae, diatoms and chrysophytes, in Lake Baikal during the late last glacial period was indicated by the analysis of sterols in SCEs. Sedimentary carotenoids and sterols in SCEs were found to give complementary information about phytoplankton composition. These molecular indicators allow us to reconstruct past lake phytoplankton assemblages responding to environmental changes with a time resolution as high as age–depth relationship in sediments attainable at present.