Simulation of risk-consistent earthquake motion

A method to combine probabilistic seismic hazard analysis and stochastic earthquake motion models is presented. A set of parameters characterizing stochastic earthquake motion models is determined on a consistent probabilistic basis. The method proposed herein consists of two steps. First, the ground motion intensity is determined in the context of the conventional hazard curve technique. Next, other ground motion parameters such as duration, predominant frequency and spectral shape parameters are determined as conditional means corresponding to the annual probability of exceedance for the ground motion intensity. Some example applications are presented.     

Rectangular rotation of spherical harmonic expansion of arbitrary high degree and order

In order to move the polar singularity of arbitrary spherical harmonic expansion to a point on the equator, we rotate the expansion around the y-axis by \(90^{\circ }\) such that the x-axis becomes a new pole. The expansion coefficients are transformed by multiplying a special value of Wigner D-matrix and a normalization factor. The transformation matrix is unchanged whether the coefficients are \(4 \pi \) fully normalized or Schmidt quasi-normalized. The matrix is recursively computed by the so-called X-number formulation (Fukushima in J Geodesy 86: 271–285, 2012a). As an example, we obtained \(2190\times 2190\) coefficients of the rectangular rotated spherical harmonic expansion of EGM2008. A proper combination of the original and the rotated expansions will be useful in (i) integrating the polar orbits of artificial satellites precisely and (ii) synthesizing/analyzing the gravitational/geomagnetic potentials and their derivatives accurately in the high latitude regions including the arctic and antarctic area.     

New type of pycnostad in the western subtropical-subarctic transition region of the North Pacific: Transition Region Mode Water

A new type of pycnostad has been identified in the western subtropical-subarctic transition region of the North Pacific, based on the intensive hydrographic survey carried out in July, 2002. The potential density, temperature and salinity of the pycnostad were found to be 26.5–26.7 σ _θ , 5°–7°C and 33.5–33.9 psu respectively. The pycnostad is denser, colder and fresher than those of the North Pacific Central Mode Water and different from those of other known mode waters in the North Pacific. The thickness of the pycnostad is comparable to that of other mode waters, spreading over an area of at least 650 × 500 km around 43°N and 160°E in the western transition region. Hence, we refer to the pycnostad as Transition Region Mode Water (TRMW). Oxygen data, geostrophic current speed and climatology of mixed layer depth in the winter suggest that the TRMW is formed regularly in the deep winter mixed layer near the region where it was observed. Analysis of surface heat flux also supports the idea and suggests that there is significant interannual variability in the property of the TRMW. The TRMW is consistently distributed between the Subarctic Boundary and the Subarctic Front. It is also characterized by a wide T-S range with similar density, which is the characteristic of such a transition region between subtropical and subarctic water masses, which forms a density-compensating temperature and salinity front. The frontal nature also tends to cause isopycnal intrusions within the pycnostad of the TRMW.     

On the long-term stability of terrestrial reference frame solutions based on Kalman filtering

The Global Geodetic Observing System requirement for the long-term stability of the International Terrestrial Reference Frame is 0.1 mm/year, motivated by rigorous sea level studies. Furthermore, high-quality station velocities are of great importance for the prediction of future station coordinates, which are fundamental for several geodetic applications. In this study, we investigate the performance of predictions from very long baseline interferometry (VLBI) terrestrial reference frames (TRFs) based on Kalman filtering. The predictions are computed by extrapolating the deterministic part of the coordinate model. As observational data, we used over 4000 VLBI sessions between 1980 and the middle of 2016. In order to study the predictions, we computed VLBI TRF solutions only from the data until the end of 2013. The period of 2014 until 2016.5 was used to validate the predictions of the TRF solutions against the measured VLBI station coordinates. To assess the quality, we computed average WRMS values from the coordinate differences as well as from estimated Helmert transformation parameters, in particular, the scale. We found that the results significantly depend on the level of process noise used in the filter. While larger values of process noise allow the TRF station coordinates to more closely follow the input data (decrease in WRMS of about 45%), the TRF predictions exhibit larger deviations from the VLBI station coordinates after 2014 (WRMS increase of about 15%). On the other hand, lower levels of process noise improve the predictions, making them more similar to those of solutions without process noise. Furthermore, our investigations show that additionally estimating annual signals in the coordinates does not significantly impact the results. Finally, we computed TRF solutions mimicking a potential real-time TRF and found significant improvements over the other investigated solutions, all of which rely on extrapolating the coordinate model for their predictions, with WRMS reductions of almost 50%.     

Roles of mode waters in the formation and maintenance of central water in the North Pacific

This study describes the three-dimensional distributions of the Turner angle (Tu) and the potential vorticity (PV) of the main pycnocline water in the subtropical North Pacific (10–50°N, 120°E–120°W) using a large in situ CTD data set taken by the Argo profiling floats during June to October of 2001–2009 to clarify the detailed distribution of the central water and the mode waters as well as the relationship between these water masses. The ventilated part of the main pycnocline water (σ _θ < 26.7 kg m⁻³) in the subtropical gyre generally displays a sharp peak in Tu value of 59° in the histogram. The Tu histograms for 10° × 10° geographical boxes mostly show that the mode for the Tu value is 59° too, but they also show some regional differences, suggesting some types of relations with the North Pacific mode waters. To further investigate this relationship, the appearance probability density function of the central water (defined as the main pycnocline water with Tu = 56°–63°) and those of the mode waters with PVs lower than the critical value on each isopycnal surface were analyzed. The distribution area of the central mode water (CMW) corresponds so well with that of the central water that a direct contribution of the CMW to the formation and maintenance of the central water is suggested. On the other hand, the distribution areas of subtropical mode water (STMW), Eastern STMW, and transition region mode water do not correspond to that of the central water. Nevertheless, indirect contributions of these mode waters to the formation and maintenance of the central water through salt finger type convection or diapycnal mixing are suggested.     

Long-term variations of surface and intermediate waters in the southern Indian Ocean along 32°S

Variations of water properties in surface and intermediate layers along 32°S in the southern Indian Ocean were examined using a 50-year (1960–2010) time series reproduced from historical hydrographic and Argo data by using optimum interpolation. Salinity in the 26.7–27.3σ_θ density layer decreased significantly over the whole section, at a maximum rate of 0.02 decade⁻¹ at 26.8–26.9σ_θ, for the 50-year average. Three deoxygenating cores were identified east of 75°E, and the increasing rate of apparent oxygen utilization in the most prominent core (26.9–27.0σ_θ) exceeded 0.05 ml l⁻¹ decade⁻¹. The pycnostad core of Subantarctic Mode Water (SAMW) and the salinity minimum of Antarctic Intermediate Water shifted slightly toward the lighter layers. Comparisons with trans-Indian Ocean survey data from 1936 suggest that the tendencies found in the time series began before 1960. Interestingly, cores of many prominent trends were located just offshore of Australia at 26.7–27.0σ_θ, which is in the SAMW density range. Spectrum analysis revealed that two oscillation components with time scales of about 40 and 10 years were dominant in the subsurface layers. Our results are fairly consistent with, and thus support, the oceanic responses in the southern Indian Ocean to anthropogenic climate change predicted by model studies.     

Parallel/Vector Integration Methods for Dynamical Astronomy

This paper reviews three recent works on the numerical methods to integrate ordinary differential equations (ODE), which are specially designed for parallel, vector, and/or multi-processor-unit(PU) computers. The first is the Picard-Chebyshev method (Fukushima, 1997a). It obtains a global solution of ODE in the form of Chebyshev polynomial of large (> 1000) degree by applying the Picard iteration repeatedly. The iteration converges for smooth problems and/or perturbed dynamics. The method runs around 100-1000 times faster in the vector mode than in the scalar mode of a certain computer with vector processors (Fukushima, 1997b). The second is a parallelization of a symplectic integrator (Saha et al., 1997). It regards the implicit midpoint rules covering thousands of timesteps as large-scale nonlinear equations and solves them by the fixed-point iteration. The method is applicable to Hamiltonian systems and is expected to lead an acceleration factor of around 50 in parallel computers with more than 1000 PUs. The last is a parallelization of the extrapolation method (Ito and Fukushima, 1997). It performs trial integrations in parallel. Also the trial integrations are further accelerated by balancing computational load among PUs by the technique of folding. The method is all-purpose and achieves an acceleration factor of around 3.5 by using several PUs. Finally, we give a perspective on the parallelization of some implicit integrators which require multiple corrections in solving implicit formulas like the implicit Hermitian integrators (Makino and Aarseth, 1992), (Hut et al., 1995) or the implicit symmetric multistep methods (Fukushima, 1998), (Fukushima, 1999). This revised version was published online in July 2006 with corrections to the Cover Date.     

North Pacific Tropical Water: its climatology and temporal changes associated with the climate regime shift in the 1970s

North Pacific Tropical Water (NPTW) is characterized as a subsurface salinity maximum flowing in the North Equatorial Current and is the main source of salt for the North Pacific. We briefly describe the climatological features of its formation and circulation, and then examine temporal changes in its properties associated with the climate regime shift in the 1970s. We use a variety of data, which include the repeat hydrographic sections along 130°E, 137°E, 144°E and 155°E meridians, the hydrographic data from the Hawaii Ocean Time-series, the World Ocean Atlas 1994, and available gridded data of wind stress and evaporation. The classical idea that NPTW originates from the zone of the highest sea surface salinity at 20°–30°N centered around the international date line and spreads along the isopycnal geostrophic flow patterns is confirmed. Further, it is shown that the meridional extent of NPTW along 137°E is from 10°N to 23°N on average and the highest salinity core lies at about 15°N and 24.0σ_θ, and that the portion of NPTW north (south) of about 15°N originates from the formation region west (east) of the date line. NPTW in the 137°E section changed remarkably associated with the mid-1970s regime shift. North of 15°N NPTW increased both in its salinity and thickness while to the south of 15°N only its salinity increased and its thickness remained unchanged. The westward geostrophic velocity is increased significantly in both the southern and northern parts of NPTW. The northern thickening and speedup and the southern speedup increased NPTW transport across 137°E. The changes in the thermohaline forcing such as evaporation and Ekman salt convergence in the NPTW formation region possibly contributed to the increases in salinity in the southern part of NPTW, but not to that of the northern part. On the other hand, the increased Ekman pumping accounts for the increase of the NPTW inventory and transport at 137°E. The increased salinity of NPTW at 137°E, especially its northern portion, was presumably caused by an increase in its formation rate rather than changes in the sea surface salinity in its formation region; the thicker the NPTW layer is, the saltier is the core that tends to survive the mixing processes.     

Forty-five years of oceanographic and meteorological observations at a coastal station in the NW Mediterranean: a ground truth for satellite observations

Ocean Dynamics - Marine and atmospheric parameters, including temperature observations from surface to 80&nbsp;m (at 6 depths) are measured since September 1973 on a higher-than-weekly...     

A multi‐geochronological study of the Hakusan volcano,central Japan

The Hakusan volcano, central Japan, is located in a region where two subducting plates (the Pacific Plate and the Philippine Sea Plate) overlap near the junction of four plates adjacent to the Japanese Islands (the Pacific Plate, the Philippine Sea Plate, the Eurasia Plate, and the North American Plate). The Hakusan volcano consists of products from four major volcanic episodes: Kagamuro, Ko‐hakusan, and Shin‐Hakusan I and II. To date the eruption events of the Hakusan volcano we applied thermoluminescence and fission track methods. ²³⁸U(²³⁴U)–²³⁰Th disequilibrium and ²⁰⁶Pb/²³⁸U methods were applied to date the zircon crystallization ages for estimating the magma residence time before the eruptions. The eruption ages we obtained are ca 250 ka for Kagamuro, ca 100 ka and ca 60 ka for Ko‐Hakusan, ca 50 ka for Shin‐Hakusan I, and <10 ka for Shin‐Hakusan II. They are concordant with previous reports based on K–Ar dating. Some of the pyroclastic rocks, possibly originating from Shin‐Hakusan II activities, are dated to be ca 36 ka or 50 ka, and belong to the Shin‐Hakusan I activity. The zircon crystallization ages show several clusters prior to eruption. The magma residence time was estimated for each volcanic activity by comparing the major crystallization events and eruption ages, and we found a gradual decrease from ca. 500 ky for the Kagamuro activity to ca. 5 ky for the Shin‐Hakusan II activity. This decrease in residence time may be responsible for the decrease in volume of erupted material estimated from the current topography of the region. The scale of volcanic activity, which was deduced from the number of crystallized zircons, is more or less constant throughout the Hakusan volcanic activity. Therefore, the decrease in magma residence time is most likely the result of stress field change.