Solution to the rotation of the elastic earth by method of rigid dynamics

Hamiltonian mechanics is applied to the problem of the rotation of the elastic Earth. We first show the process for the formulation of the Hamiltonian for rotation of a deformable body and the derivation of the equations of motion from it. Then, based on a simple model of deformation, the solution is given for the period of Euler motion, UT1 and the nutation of the elastic Earth. In particular it is shown that the elasticity of the Earth acts on the nutation so as to decrease the Oppolzer terms of the nutation of the rigid Earth by about 30 per cent. The solution is in good agreement with results which have been obtained by other, different approaches.     

Equation of state of MgGeO3 perovskite to 65 GPa: comparison with the post-perovskite phase

The equation of state of MgGeO₃ perovskite was determined between 25 and 66 GPa using synchrotron X-ray diffraction with the laser-heated diamond anvil cell. The data were fit to a third-order Birch–Murnaghan equation of state and yielded a zero-pressure volume (V ₀) of 182.2 ± 0.3 Å³ and bulk modulus (K ₀) of 229 ± 3 GPa, with the pressure derivative (K′₀ = (?K ₀/?P) _T ) fixed at 3.7. Differential stresses were evaluated using lattice strain theory and found to be typically less than about 1.5 GPa. Theoretical calculations were also carried out using density functional theory from 0 to 205 GPa. The equation of state parameters from theory (V ₀ = 180.2 Å³, K ₀ = 221.3 GPa, and K′₀ = 3.90) are in agreement with experiment, although theoretically calculated volumes are systematically lower than experiment. The properties of the perovskite phase were compared to MgGeO₃ post-perovskite phase near the observed phase transition pressure (～65 GPa). Across the transition, the density increased by 2.0(0.7)%. This is in excellent agreement with the theoretically determined density change of 1.9%; however both values are larger than those for the (Mg,Fe)SiO₃ phase transition. The bulk sound velocity change across the transition is small and is likely to be negative [?0.5(1.6)% from experiment and ?1.2% from theory]. These results are similar to previous findings for the (Mg,Fe)SiO₃ system. A linearized Birch–Murnaghan equation of state fit to each axis yielded zero-pressure compressibilities of 0.0022, 0.0009, and 0.0016 GPa^?1 for the a, b, and c axis, respectively. Magnesium germanate appears to be a good analog system for studying the properties of the perovskite and post-perovskite phases in silicates.     

Evaluation of predictors of non‐linear seismic demands using ‘fishbone’ models of SMRF buildings

Predictors (or estimates) of seismic structural demands that are less computationally time‐consuming than non‐linear dynamic analysis can be useful for structural performance assessment and for design. In this paper, we evaluate the bias and precision of predictors that make use of, at most, (i) elastic modal vibration properties of the given structure, (ii) the results of a non‐linear static pushover analysis of the structure, and (iii) elastic and inelastic single‐degree‐of‐freedom time‐history analyses for the specified ground motion record. The main predictor of interest is an extension of first‐mode elastic spectral acceleration that additionally takes into account both the second‐mode contribution to (elastic) structural response and the effects of inelasticity. This predictor is evaluated with respect to non‐linear dynamic analysis results for ‘fishbone’ models of steel moment‐resisting frame (SMRF) buildings. The relatively small number of degrees of freedom for each fishbone model allows us to consider several short‐to‐long period buildings and numerous near‐ and far‐field earthquake ground motions of interest in both Japan and the U.S. Before doing so, though, we verify that estimates of the bias and precision of the predictor obtained using fishbone models are effectively equivalent to those based on typical ‘full‐frame’ models of the same buildings. Copyright © 2003 John Wiley & Sons, Ltd.     

Effects of inertial and kinematic interaction on seismic behavior of pile with embedded foundation

Effects of inertial and kinematic forces on pile stresses are studied based on large shaking table tests on pile-structure models with a foundation embedded in dry and liquefiable sand deposits. The test results show that, if the natural period of the superstructure, T_b, is less than that of the ground, T_g, the ground displacement tends to be in phase with the inertial force from the superstructure, increasing the shear force transmitted to the pile. In contrast, if T_b is greater than T_g, the ground displacement tends to be out of phase with the inertial force, restraining the pile stress from increasing. With the effects of earth pressures on the embedded foundation and pile incorporated in, pseudo-static analysis is conducted to estimate maximum moment distribution in pile. It is assumed that the maximum moment is equal to the sum of the two stresses caused by the inertial and kinematic effects if T_b<T_g or the square root of the sum of the squares of the two if T_b>T_g. The estimated pile stresses are in good agreement with the observed ones regardless of the occurrence of soil liquefaction.     

Reevaluation of historical ocean heat content variations with time-varying XBT and MBT depth bias corrections

As reported in former studies, temperature observations obtained by expendable bathythermographs (XBTs) and mechanical bathythermographs (MBTs) appear to have positive biases as much as they affect major climate signals. These biases have not been fully taken into account in previous ocean temperature analyses, which have been widely used to detect global warming signals in the oceans. This report proposes a methodology for directly eliminating the biases from the XBT and MBT observations. In the case of XBT observation, assuming that the positive temperature biases mainly originate from greater depths given by conventional XBT fall-rate equations than the truth, a depth bias equation is constructed by fitting depth differences between XBT data and more accurate oceanographic observations to a linear equation of elapsed time. Such depth bias equations are introduced separately for each year and for each probe type. Uncertainty in the gradient of the linear equation is evaluated using a non-parametric test. The typical depth bias is +10 m at 700 m depth on average, which is probably caused by various indeterminable sources of error in the XBT observations as well as a lack of representativeness in the fall-rate equations adopted so far. Depth biases in MBT are fitted to quadratic equations of depth in a similar manner to the XBT method. Correcting the historical XBT and MBT depth biases by these equations allows a historical ocean temperature analysis to be conducted. In comparison with the previous temperature analysis, large differences are found in the present analysis as follows: the duration of large ocean heat content in the 1970s shortens dramatically, and recent ocean cooling becomes insignificant. The result is also in better agreement with tide gauge observations. On leave from the Meteorological Research Institute of the Japan Meteorological Agency.     

The δ18O in the Guliya shallow ice core during the prevailing summer monsoons and sea-air interactions

The correlations of the δ¹⁸O_max in the shallow ice core from the Guliya ice cap on the Tibetan Plateau with the global sea surface temperatures (SST) and height at the 500 hPa over the Northern Hemisphere were analyzed. The correlated regions on oceans that have a significant influence on the δ¹⁸O_max in the Guliya ice core are all located in ocean currents, or convergent regions of currents. They are the eastern Equatorial Pacific, the Northern Pacific Current, the Hot Pool in the eastern Indian Ocean, the Mozambique Current, the Northern Atlantic Current, the Canary Current and the Atlantic Equatorial Current. The δ¹⁸O_max in the Guliya ice core has negative correlations with the SST located in the lower latitudes, and positive correlations with the SST in the middle latitudes. The correlated areas at the 500 hPa that have a great impact on the δ¹⁸O_max are located in the subtropical highs over the mid-low-latitude oceans and the long-wave trough area over Balkhash Lake, where there are marked negative correlations between the heights in those areas and the δ¹⁸O_max. The influencing mechanism is displayed by the diversity of the vapor origins transported to the Guliya region. The strengths of the European ridge and the ridge over Baikal Lake have notable positive correlations with the δ¹⁸O_max. The two systems indirectly influence the vapor transportation towards the Guliya region by the adjustment of long-wave trough and ridge.     

Variation of precipitation in Langtang Valley,Himalayas

The variation of the δ 18O in precipitation and the relationship with precipitation amountat Kyangjin Base House and Yala Glacier Camp in Langtang Valley, Nepal Himalayas were ana-lyzed. The variations of the δ 18O with precipitation had great scatter, and the correlations betweenthe δ18O and precipitation changed with time on the synoptic scale. On the seasonal scale, therewas marked amount effect at Kyangjin Base House. However, the δ18O-precipitation gradient wassmaller than that on the synoptic scale. Because of the maintenance of the basic equilibrium be-tween stable isotopic compositions in atmospheric vapor and precipitation, the evaporation en-richment was light during the rainy season. Therefore, the variation of stable isotopic compositionsin precipitation was independent on the sampling intervals. Simulations show that the rainfall inLangtang Valley was not the outcome of the initial condensation of ocean vapor that originatedfrom low latitudes. The stable isotopic compositions in precipitation were greatly depleted due tothe strong rainout of the vapor from oceans as the vapor was raised over the Himalayas     

Solar Wind Speed and Expansion Rate of the Coronal Magnetic Field in Solar Maximum and Minimum Phases

Relationships between solar wind speed and expansion rate of the coronal magnetic field have been studied mainly by in-ecliptic observations of artificial satellites and some off-ecliptic data by Ulysses. In this paper, we use the solar wind speed estimated by interplanetary scintillation (IPS) observations in the whole heliosphere. Two synoptic maps of SWS estimated by IPS observations are constructed for two Carrington rotations CR 1830 and 1901; CR 1830 starting on the 11th of June, 1990 is in the maximum phase of solar activity cycle and CR 1901 starting on the 29th of September, 1995 is in the minimum phase. Each of the maps consist of 64800 (360×180) data points. Similar synoptic maps of expansion rate of the coronal magnetic field (RBR) calculated by the so-called potential model are also constructed under a radial field assumption for CR 1830 and CR1901. Highly significant correlation (r=–0.66) is found between the SWS and the RBR during CR1901 in the solar minimum phase; that is, high-speed winds emanate from photospheric areas corresponding to low expansion rate of the coronal magnetic field and low speed winds emanate from photospheric areas of high expansion rate. A similar result is found during CR 1830 in solar maximum phase, though the correlation is relatively low (r=–0.29). The correlation is improved when both the data during CR 1830 and CR 1901 are used together; the correlation coefficient becomes –0.67 in this case. These results suggest that the correlation analysis between the SWS and the RBR can be applied to estimate the solar wind speed from the expansion rate of the coronal magnetic field, though the correlation between them may depend on the solar activity cycle. We need further study of correlation analysis for the entire solar cycle to get an accurate empirical equation for the estimation of solar wind speed. If the solar wind speed is estimated successfully by an empirical equation, it can be used as an initial condition of a solar wind model for space weather forecasts.     

Formation of collimated beams

A mechanism is proposed for the formation of collinated beams in radio galaxies. Collimated flows are considered to be non-thermally driven by high energy particles and magneto-hydrodynamic (MHD) waves. The galactic nucleus is regarded as being surrounded by a cool gas. The cool gas accretes onto the nucleus, and then the high energy particles are completely locked to the MHD waves. When a quasi-radial magnetic field is embedded in the accretion flow, the resulting MHD wave packets are collimated into the direction of the symmetry axis of the galactic nuclear disc. The fluid around the nucleus is considered to be accelerated and heated by these MHD waves. The fluid beam is ejected along the symmetry axis.Paper presented at the IAU Third Asian-Pacific Regional Meeting, held in Kyoto, Japan, between 30 September–6 October, 1984.     

Kinematical modeling of the Earth rotation,focusing on the Oppolzer terms in a rigid Earth and the Oppolzer-like terms in an elastic Earth

Under perturbations from outer bodies, the Earth experiences changes of its angular momentum axis, figure axis and rotational axis. In the theory of the rigid Earth, in addition to the precession and nutation of the angular momentum axis given by the Poisson terms, both the figure axis and the rotational axis suffer forced deviation from the angular momentum axis. This deviation is expressed by the so-called Oppolzer terms describing separation of the averaged figure axis, called CIP (Celestial Intermediate Pole) or CEP (Celestial Ephemeris Pole), and the mathematically defined rotational axis, from the angular momentum axis. The CIP is the rotational axis in a frame subject to both precession and nutation, while the mathematical rotational axis is that in the inertial (non-rotating) frame. We investigate, kinematically, the origin of the separation between these two axes—both for the rigid Earth and an elastic Earth. In the case of an elastic Earth perturbed by the same outer bodies, there appear further deviations of the figure and rotational axes from the angular momentum axis. These deviations, though similar to the Oppolzer terms in the rigid Earth, are produced by quite a different physical mechanism. Analysing this mechanism, we derive an expression for the Oppolzer-like terms in an elastic Earth. From this expression we demonstrate that, under a certain approximation (in neglect of the motion of the perturbing outer bodies), the sum of the direct and convective perturbations of the spin axis coincides with the direct perturbation of the figure axis. This equality, which is approximate, gets violated when the motion of the outer bodies is taken into account.