Transformation between surface spherical harmonic expansion of arbitrary high degree and order and double Fourier series on sphere     

Toshio Fukushima 《Journal of Geodesy》2018,92(2):123-130

In order to accelerate the spherical harmonic synthesis and/or analysis of arbitrary function on the unit sphere, we developed a pair of procedures to transform between a truncated spherical harmonic expansion and the corresponding two-dimensional Fourier series. First, we obtained an analytic expression of the sine/cosine series coefficient of the \(4 \pi \) fully normalized associated Legendre function in terms of the rectangle values of the Wigner d function. Then, we elaborated the existing method to transform the coefficients of the surface spherical harmonic expansion to those of the double Fourier series so as to be capable with arbitrary high degree and order. Next, we created a new method to transform inversely a given double Fourier series to the corresponding surface spherical harmonic expansion. The key of the new method is a couple of new recurrence formulas to compute the inverse transformation coefficients: a decreasing-order, fixed-degree, and fixed-wavenumber three-term formula for general terms, and an increasing-degree-and-order and fixed-wavenumber two-term formula for diagonal terms. Meanwhile, the two seed values are analytically prepared. Both of the forward and inverse transformation procedures are confirmed to be sufficiently accurate and applicable to an extremely high degree/order/wavenumber as \(2^{30}\,{\approx }\,10^9\). The developed procedures will be useful not only in the synthesis and analysis of the spherical harmonic expansion of arbitrary high degree and order, but also in the evaluation of the derivatives and integrals of the spherical harmonic expansion.  相似文献   

Liquid bridge contribution to shear behavior of unsaturated soil: modeling and application to a micromechanics model     

Fukushima  Yo  Higo  Yosuke  Matsushima  Takashi  Otake  Yu 《Acta Geotechnica》2021,16(9):2693-2711

Acta Geotechnica - Liquid bridges in unsaturated soils attach to grain contacts and contribute to strengthening microscopic bonding forces, which leads to macroscopic high strength and stiffness...  相似文献   

Strong motion uncertainty determined from observed records by dense network in Japan   总被引：2，自引：1，他引：1  

Nobuyuki Morikawa  Tatsuo Kanno  Akira Narita  Hiroyuki Fujiwara  Toshihiko Okumura  Yoshimitsu Fukushima  Aybars Guerpinar 《Journal of Seismology》2008,12(4):529-546

The variation of ground motions at specific stations from events in six narrow areas was inspected by using K-NET and KiK-net records. A source-area factor for individual observation stations was calculated by averaging ratios between observed values for horizontal peak acceleration and velocity, as well as acceleration response spectra for 5% damping, and predicted values using a ground-motion model (usually known as an attenuation relation) by Kanno et al. (Bull Seismol Soc Am, 96:879–897, 2006). Standard deviations between observed and predicted amplitudes after the correction factor are less than 0.2 on the logarithmic scale and decrease down to around 0.15 in the short-period range. Intra-event standard deviation clearly increases with decreasing distance due to differing paths around near source area. Standard deviations may increase with amplitude or decrease with magnitude; however, both amplitude and magnitude of the data are strongly correlated with distance. The standard deviation calculated in this study is obviously much smaller than that of the original ground-motion model, as epistemic uncertainties are minimized by grouping ground motions at specific stations. This result indicates that the accuracy of strong ground motion prediction could be improved if ground-motion models for specified region are determined individually. For this to be possible, it is necessary to have dense strong-motion networks in high-seismicity regions, such as K-NET and KiK-net.  相似文献   

Report of the International Astronomical Union Division I Working Group on Precession and the Ecliptic   总被引：1，自引：0，他引：1  

J. L. Hilton  N. Capitaine  J. Chapront  J. M. Ferrandiz  A. Fienga  T. Fukushima  J. Getino  P. Mathews  J.-L. Simon  M. Soffel  J. Vondrak  P. Wallace  J. Williams 《Celestial Mechanics and Dynamical Astronomy》2006,94(3):351-367

The IAU Working Group on Precession and the Equinox looked at several solutions for replacing the precession part of the IAU 2000A precession–nutation model, which is not consistent with dynamical theory. These comparisons show that the (Capitaine et al., Astron. Astrophys., 412, 2003a) precession theory, P03, is both consistent with dynamical theory and the solution most compatible with the IAU 2000A nutation model. Thus, the working group recommends the adoption of the P03 precession theory for use with the IAU 2000A nutation. The two greatest sources of uncertainty in the precession theory are the rate of change of the Earth’s dynamical flattening, ΔJ₂, and the precession rates (i.e. the constants of integration used in deriving the precession). The combined uncertainties limit the accuracy in the precession theory to approximately 2 mas cent⁻². Given that there are difficulties with the traditional angles used to parameterize the precession, z_A, ζ_A, and θ_A, the working group has decided that the choice of parameters should be left to the user. We provide a consistent set of parameters that may be used with either the traditional rotation matrix, or those rotation matrices described in (Capitaine et al., Astron. Astrophys., 412, 2003a) and (Fukushima Astron. J., 126, 2003). We recommend that the ecliptic pole be explicitly defined by the mean orbital angular momentum vector of the Earth–Moon barycenter in the Barycentric Celestial Reference System (BCRS), and explicitly state that this definition is being used to avoid confusion with previous definitions of the ecliptic. Finally, we recommend that the terms precession of the equator and precession of the ecliptic replace the terms lunisolar precession and planetary precession, respectively.  相似文献   

A method solving kepler's equation without transcendental function evaluations     

Toshio Fukushima 《Celestial Mechanics and Dynamical Astronomy》1996,66(3):309-319

We developed two approximations of the Newton-Raphson method. The one is a sort of discretization, namely to search an approximate solution on pre-specified grid points. The other is a Taylor series expansion. A combination of these was applied to solving Kepler's equation for the elliptic case. The resulting method requires no evaluation of transcendental functions. Numerical measurements showed that, in the case of Intel Pentium processor, the new method is three times as fast as the original Newton-Raphson method. Also it is more than 2.5 times as fast as Halley's method, Nijenhuis's method, and others.  相似文献   

Polar magnetic substorms     

Naoshi Fukushima 《Planetary and Space Science》1972

From the world distribution of geomagnetic disturbance, the connection between the electric current in the ionosphere, the field-aligned current and asymmetric equatorial ringcurrent in the magnetosphere is discussed. The partial ring-current in the afternoon-evening region, whose intensity is closely correlated with the AE-index, usually develops and decays earlier than the symmetric ring-current in the course of magnetic storms. The partial ringcurrent seems to have a direct connection with the positive geomagnetic bay in high latitudes in the evening hours through the ionizing effect of the particles leaking from the partial ringcurrent. The dawn-to-dusk electric field in the magnetospheric tail is transferred to the polar ionosphere, producing there the twin vortex Hall current responsible for polar cap geomagnetic variation. The magnetic effect of the associated Pedersen current in the ionosphere is shown to be small but still worth considering. The electrojet near midnight along the auroral oval is thought to appear when the electric conductivity of the ionosphere is locally increased under the presence of large scale dawn-to-dusk electric field. The occasional appearance of a localized abnormal geomagnetic disturbance with reversed direction near the geomagnetic pole seems to suggest the occasional reversal of electric field near the outer surface of the magnetospheric tail, especially when the interplanetary magnetic field is northward.  相似文献   

Erratum to: Reports of the IAU Working Group on Cartographic Coordinates and Rotational Elements: 2006 & 2009     

B. A. Archinal  M. F. A��Hearn  A. Conrad  G. J. Consolmagno  R. Courtin  T. Fukushima  D. Hestroffer  J. L. Hilton  G. A. Krasinsky  G. Neumann  J. Oberst  P. K. Seidelmann  P. Stooke  D. J. Tholen  P. C. Thomas  I. P. Williams 《Celestial Mechanics and Dynamical Astronomy》2011,110(4):401-403

The primary poles for (243) Ida and (134340) Pluto and its satellite (134340) Pluto : I Charon were redefined in the IAU Working Group on Cartographic Coordinates and Rotational Elements (WGCCRE) 2006 report (Seidelmann et al. in Celest Mech Dyn Astr 98:155, 2007), and 2009 report (Archinal et al. in Celest Mech Dyn Astr 109:101, 2011), respectively, to be consistent with the primary poles of similar Solar System bodies. However, the WGCCRE failed to take into account the effect of the redefinition of the poles on the values of the rotation angle W at J2000.0. The revised relationships in Table 3 of Archinal et al. 2011) are $$\begin{array}{llll} W & = & 274^{\circ}.05 +1864^{\circ}.6280070\, d\;{\rm for\; (243)\,Ida} \\ W & = & 302^{\circ} .695 + 56^{\circ} .3625225\, d\;{\rm for\; (134340)\,Pluto,\; and}\\ W & = & 122^{\circ} .695 + 56^{\circ} .3625225\, d\;{\rm for\; (134340)\,Pluto : I \,Charon}\end{array}$$ where d is the time in TDB days from J2000.0 (JD2451545.0).  相似文献   

Report of the IAU Working Group on Cartographic Coordinates and Rotational Elements: 2009   总被引：5，自引：0，他引：5  

B. A. Archinal  M. F. A��Hearn  E. Bowell  A. Conrad  G. J. Consolmagno  R. Courtin  T. Fukushima  D. Hestroffer  J. L. Hilton  G. A. Krasinsky  G. Neumann  J. Oberst  P. K. Seidelmann  P. Stooke  D. J. Tholen  P. C. Thomas  I. P. Williams 《Celestial Mechanics and Dynamical Astronomy》2011,109(2):101-135

Every three years the IAU Working Group on Cartographic Coordinates and Rotational Elements revises tables giving the directions of the poles of rotation and the prime meridians of the planets, satellites, minor planets, and comets. This report takes into account the IAU Working Group for Planetary System Nomenclature (WGPSN) and the IAU Committee on Small Body Nomenclature (CSBN) definition of dwarf planets, introduces improved values for the pole and rotation rate of Mercury, returns the rotation rate of Jupiter to a previous value, introduces improved values for the rotation of five satellites of Saturn, and adds the equatorial radius of the Sun for comparison. It also adds or updates size and shape information for the Earth, Mars?? satellites Deimos and Phobos, the four Galilean satellites of Jupiter, and 22 satellites of Saturn. Pole, rotation, and size information has been added for the asteroids (21) Lutetia, (511) Davida, and (2867) ?teins. Pole and rotation information has been added for (2) Pallas and (21) Lutetia. Pole and rotation and mean radius information has been added for (1) Ceres. Pole information has been updated for (4) Vesta. The high precision realization for the pole and rotation rate of the Moon is updated. Alternative orientation models for Mars, Jupiter, and Saturn are noted. The Working Group also reaffirms that once an observable feature at a defined longitude is chosen, a longitude definition origin should not change except under unusual circumstances. It is also noted that alternative coordinate systems may exist for various (e.g. dynamical) purposes, but specific cartographic coordinate system information continues to be recommended for each body. The Working Group elaborates on its purpose, and also announces its plans to occasionally provide limited updates to its recommendations via its website, in order to address community needs for some updates more often than every 3 years. Brief recommendations are also made to the general planetary community regarding the need for controlled products, and improved or consensus rotation models for Mars, Jupiter, and Saturn.  相似文献   

Geochemical study of arsenic and other trace elements in groundwater and sediments of the Old Brahmaputra River Plain,Bangladesh   总被引：1，自引：1，他引：0  

Faruque Ahmed  M. Hawa Bibi  Hiroaki Ishiga  Takehiko Fukushima  Teruyuki Maruoka 《Environmental Earth Sciences》2010,60(6):1303-1316

The geochemical study of groundwaters and core sediments from the Old Brahmaputra plain of Bangladesh was conducted to investigate the distribution of arsenic and related trace elements. Groundwaters from tube wells are characterized by pH of 6.4–7.4, dissolved oxygen (DO) of 0.8–1.8 mg/l, Ca contents of 5–50 mg/l, and Fe contents of 0.2–12.9 mg/l. Arsenic concentrations ranged from 8 to 251 μg/l, with an average value of 63 μg/l. A strong positive correlation exists between As and Fe (r ² = 0.802; p = 0.001) concentrations in groundwater. The stratigraphic sequences in the cores consist of yellowish silty clays at top, passing downward into grayish to yellowish clays and sands. The uppermost 3 m and lower parts (from 13 to 31 m) of the core sediments are oxidized (average oxidation reduction potential (ORP) +170 and +220 mV, respectively), and the ORP values gradually become negative from 3 to 13 m depths (−35 to −180 mV), indicating that anoxic conditions prevail in the shallow aquifers of the Brahmaputra plain. Age determinations suggest that clay horizons at ~10 m depth were deposited at around 2,000 and 5,000 years BP (¹⁴C ages) during the transgressive phase of sea-level change. Elevated concentrations of As, Pb, Zn, Cu, Ni, Cr, and V are present in the silts and clays, probably due to adsorption onto clay particles. Significant concentrations of As occur in black peat and peaty sediments at depths between 9 and 13 m. A strong positive correlation between As and Fe was found in the sediments, indicating As may be adsorbed onto Fe oxides in aquifer sediments.  相似文献   

Calibration and validation of the ocean color version-3 product from ADEOS OCTS     

Masanobu Shimada  Hiromi Oaku  Yasushi Mitomi  Hiroshi Murakami  Akira Mukaida  Yasuhisa Nakamura  Joji Ishizaka  Hiroshi Kawamura  Tasuku Tanaka  Motoaki Kishino  Hajime Fukushima 《Journal of Oceanography》1998,54(5):401-416

We present calibration and validation results of the OCTS’s ocean color version-3 product, which mainly consists of the chlorophyll-a concentration (Chl-a) and the normalized water-leaving radiance (_nL_w). First, OCTS was calibrated for the inter-detector sensitivity difference, offset, and absolute sensitivity using external calibration source. It was also vicariously calibrated using in-situ measurements for water (Chl-a and_nL_w) and atmosphere (optical thickness), which were acquired synchronously with OCTS under cloud-free conditions. Second, the product was validated using selected 17 in-situ Chl-a and 11 in-situ_nL_w measurements. We confirmed that Chl-a was estimated with an accuracy of 68% for Chl-a less than 2 mg/m³, and_nL_w from 94% (band 2) to 128% (band 4). Geometric accuracy was improved to 1.3 km. Stripes were significantly reduced by modifying the detector normalization factor as a function of input radiance.  相似文献