Trace-element zoning patterns in porphyroblastic garnets in low-T eclogites: Parameter optimization of the diffusion-limited REE-uptake model

Compositional zoning patterns of the major elements and REEs in prograde-zoned garnets whose Mg/(Mg + Fe) atomic ratios increase rimward have been widely used to understand the metamorphic P–T–t trajectories, and the diffusion-limited REE-uptake model is a promising way to interpret their growth rates and the REE diffusion kinetics in the low-temperature eclogite. In order to elucidate their growth kinetics with Skora et al.'s (2006) diffusion-limited REE uptake model for prograde-zoned garnets, we examine the trace-element zoning patterns of two prograde-zoned porphyroblastic garnets (~6 mm in size) in low-temperature eclogites from two different localities. Core-to-rim trace-element profiles in a garnet (prp_5–9alm_61–67sps_1–3grs_24–30) of a glaucophane-bearing epidote eclogite of Syros (Cyclades, Greece) are characterized by the presence of Y + HREE peaks in the mantle, which might be attributed to a continuous breakdown of the titanite to form rutile during the garnet growth. In contrast, those in a garnet (prp_4–7alm_61–68sps_3–10grs_23–24) extracted from a lawsonite-eclogite of the South Motagua Mélange (SMM) (Guatemala) have prominent central peaks of Y + HREEs. Although the REE profiles of both the garnets can be explained by the diffusion-limited uptake, their Mn profiles suggest that their growth-rate laws are different: i.e., diffusion-controlled (Syros) and interface-controlled (SMM). Prior to the model application, we optimize the number of the parameters as the garnet grows with the interface-controlled processes based on the growth Péclet number. In particular, we propose the ratio of the REE diffusivity in the eclogitic matrix to the garnet growth rate as the new parameter. Visualizing the values of the new parameters allows to readily understand the relationship between the REE profiles and the REE-diffusion/garnet-growth kinetics in low-T eclogite. Our model refinement leads to the simple quantitative characterization of core-to-rim REE profiles in garnet in low-temperature eclogites.     

Evaluation of the structural damage of high‐rise reinforced concrete buildings using ambient vibrations recorded before and after damage

Evaluation of the degrees of structural damage suffered by high‐rise residential buildings after being subjected to strong ground motions is extremely important to the development of life continuity planning for building residents. However, these evaluations cannot be based on strong‐motion records alone, because earthquake observation equipment is not installed in most such buildings in Japan. In this study, we propose simple equations for estimating the stiffness degradation rate and the peak inter‐story drift ratio (PIDR) by using ambient vibration records instead of strong‐motion records when high‐rise RC buildings are subjected to a severe earthquake. More specifically, we propose one equation that relates the square root of the stiffness degradation rate, which is the ratio of natural frequencies at the maximum response to the preliminary tremor response (elastic state), in strong‐motion records with the ratio of natural frequencies identified from ambient vibrations before and after damage was suffered. We also propose an equation that relates the PIDR with the stiffness degradation rate on the basis of the stiffness‐degrading bilinear restoring force characteristic derived from the strong‐motion records of 13 high‐rise buildings for the 1995 Hyogoken‐Nanbu Earthquake (Mw 6.9) and the 2011 Tohoku‐Oki Earthquake (Mw 9.0). Copyright © 2015 John Wiley & Sons, Ltd.     

Cyclic magma storages and transfers at Piton de La Fournaise volcano (La Réunion hotspot) inferred from deformation and geochemical data

Piton de La Fournaise is in a period of intense volcanic activity since 1998. To constrain the magma dynamics responsible for this activity, we combined GPS ground deformation monitoring interpreted through numerical modelling and geochemistry. Two cycles of continuous volcano inflation are evidenced for the May 2004–December 2005 period, with a rest from March to October 2005. These inflations are consistent with two cycles of compatible major element enrichment in the emitted lavas. Numerical models indicate that the pressurization of a single magma reservoir may be responsible for the observed pre-eruptive inflations of the volcano. The reservoir, located at 2300 m depth, has a radius of  500 m. At the beginning of each cycle, dykes propagate from the roof of the reservoir and yield eruptions of differentiated basalt near the summit. At the end of the cycle, dykes propagate from the eastern sidewall of the reservoir and yield distal eruptions of primitive magmas away from the summit. The volumes of magma emitted during the primitive eruptions seem too large to explain the surface deformations and therefore suggest some refill of the reservoir by deeper magmas. Our results may be used to predict the location and lava volume of future eruptions at Piton de La Fournaise volcano, depending on the timing of these eruptions within a cycle of volcanic activity.     

Characteristics of isolated hybrid tremor (HBT) during a calm activity period at Aso Volcano

Isolated-type tremors having two events with different dominant frequencies are characteristic seismological phenomena observed during the fumarolic activity stage at Aso Volcano. These isolated tremors are called hybrid tremors (HBT) and comprise two parts: an initial part named the “HF-part” with a dominant frequency in the high-frequency region (approximately 10 Hz) and the following part named the “LF-part” with a dominant frequency in the low-frequency region (approximately 2 Hz). The LF-part is observed after the HF-part, and the HBT is accompanied by a long-period tremor (LPT). Hypocenters and source parameters are estimated using seismograms recorded at 64 stations around Nakadake crater. The amplitude distributions of all HF-parts have almost similar trends. Similarly, the amplitude distributions of all LF-parts have almost similar trends. However, the amplitude distributions of HF- and LF-parts are not similar. From these results, we proposed that the hypocenters and source parameters of HF- and LF-parts are not common, but each of them have common hypocenters and source parameters. The hypocenter region of HF-parts was estimated to be just beneath the fumarole region south of the 1st crater: the volume fluctuation is the major source factor. The hypocenter region of LF-parts is estimated to be at a depth of approximately 300 m beneath the first crater: the strike–slip component is the major source parameter. The hypocentral depth of LF-parts is located at the upper end of the crack estimated to be the source of the LPTs. The LPTs and HBTs are observed almost simultaneously. We consider that volcanic fluid is involved in the source mechanisms of both HBT and LPT.     

Fast transform from geocentric to geodetic coordinates

 A new iterative procedure to transform geocentric rectangular coordinates to geodetic coordinates is derived. The procedure solves a modification of Borkowski's quartic equation by the Newton method from a set of stable starters. The new method runs a little faster than the single application of Bowring's formula, which has been known as the most efficient procedure. The new method is sufficiently precise because the resulting relative error is less than 10⁻¹⁵, and this method is stable in the sense that the iteration converges for all coordinates including the near-geocenter region where Bowring's iterative method diverges and the near-polar axis region where Borkowski's non-iterative method suffers a loss of precision. Received: 13 November 1998 / Accepted: 27 August 1999     

A model of river flow forecasting for a small forested mountain catchment

A model for quantitatively expressing the hydrological cycle in a forested mountain catchment is proposed as a HYCYMODEL. HYCYMODEL is able to predict both short- and long-term hydrographs because the model parameters remain independent of time. It shows a good applicability for ten years of continuous data at both hourly and daily intervals for the Kiryu catchment—a forested mountain basin. Since HYCYMODEL does not need hydrograph separation between storm flow and base flow, it is a particularly attractive model.     

The Fermi coordinate system in the post-Newtonian framework

The Fermi coordinate system (or the non-rotating proper reference frame) is studied within the framework of the post-Newtonian approximation of general relativity. First its general functional form is found to consist of three parts; (1) the motion of the space origin of the Fermi coordinate system relative to the background one, (2) the Fermi-Walker tetrad transported along the world line of the space origin, and (3) the spacelike geodesic starting from the space origin. Next, the post-Newtonian expressions of the latter two are obtained under the condition that the first is given. Then the full coordinate transformation formula connecting the Fermi coordinate system to the background one is derived explicitly. The effectiveness of the Fermi coordinate system is discussed and the effective region is found to be a cylinder with the radius of about 0.5 kpc for the Fermi coordinate system comoving with the Earth. The mathematical way to derive the generalized Fermi coordinate system which Ashby and Bertotti defined is also shown.     

Seasonal dependences of geomagnetic variations in the polar region in connection with large-amplitude annual Z-variation at the geomagnetic pole

A noticeable depression of the vertical component Z of the geomagnetic field is observed in the polar cap in summer. From the statistical analysis of the equivalent overhead current patterns for daily geomagnetic variations in the summer and winter polar regions for three different conditions of IMF (interplanetary magnetic field), it was concluded that the annual variation of geomagnetic Z in the vicinity of the geomagnetic pole is attributed to the relative spatial shift of the twin-vortex current patterns over the polar cap from summer to winter. In winterthe clockwise current vortex in the dawn sector extends almost over the entire polar cap (except for the periods when the B_z component of IMF has a large positive value), and this will result in the positive variation of the Z-value at the geomagnetic pole. In summer the counter-clockwise current vortex in the dusk sector always extends over the whole polar cap even when B_z of IMF is positiveso that the variation of Z becomes negative. The persistent existence of current vortex in the dawn sector is important for the further study of magnetospheric convection when B_z is positive.     

A system of astronomical constants in the relativistic framework

The relation between the units and readings of time and space coordinates of terrestrial and barycentric reference frames is discussed from the viewpoint of general relativity. Attention is paid to the unit of space coordinates since the International Astronomical Union (IAU) regulates only the unit of time in the above two frames. Two definitions of unit of length are examined and their effects on the numerical expression of coordinate transformation, equations of planetary motions, and those for light propagation time are discussed. A clear conflict is found between the IAU (1976) recommendation on the definition of the time-scales in different frames of reference and the statement that all constants in the IAU (1976) new system of astronomical constants are defined in terms of the Internationsl System of units (SI units). One of the above two definitions is proposed to resolve this conflict by the least alteration to current procedures for analysing the recent astrometric observations such as the radar/laser rangings, the range and range-rate, and the very long baseline interferometric observations. Also, an interpretation of numerical values in the IAU (1976) new system of astronomical constants is presented. It is stressed that the definition proposed in this paper requires that a formula slightly different from that in current use be employed in the numerical transformation of readings of coordinates between the terrestrial and barycentric reference frames.