Geoidal curvature radii from satellite data for different degrees of smoothing

Summary Radii of curvature and their anomalies of a smoothed geoidal surface are computed using Stokes's constants J _n ^(k) , S _n ^(k) of the Earth's body, obtained from satellite orbit dynamics[2]. Different degrees n of smoothing are used (n = 8, 12, 21). The notations are the same as in[4, 5].     

Global geoid sections determined by satellite orbit dynamics

Summary This paper ties up with [5, 6] the fundamental notations of which have been adopted. The sets of Stokes' constants (harmonic coefficients) J _n ^(k) , S _n ^(k) were adopted from [4], and the scale factor for lengths, R₀=GM/W₀, from [5]. The equations for global meridional and parallel sections of the geoid surface W=W₀ are formulated. The geoid sections are represented by best fitting ellipses, as regards the meridians always for the arcs between the equator and the pole. Address: Politickych vězňů 12, Praha 1-Nové Město.     

Fundamental geodetic parameters of the earth's figure and the structure of the earth's gravity field derived from satellite data

Summary Using the geocentric constant GM=398 601.3 × 10 ⁹ m ³s ^–2 , the known value of the angular velocity of the Earth's rotation , Stokes' constants J _n ^(k) and S _n ^(k) upto n=21 (zonal), n=16 (tesseral and sectorial) [2], the geocentric co-ordinates and heights above sea-level of SAO satellite stations [2], the following will be derived: the potential on the geoid W_o, the scale factor for lengths R_o=GM/W_o, the radius-vector of the surface W=W_o, the parameters of the best-fitting Earth tri-axial ellipsoid, and the components of the deflections of the vertical with respect to the geocentric rotational IAG ellipsoid (Lucerne 1967), as well as to the best-fitting geocentric tri-axial ellipsoid. Some of the differences in the structure of the gravity field over the Northern and Southern Hemispheres will be given, and the mean values of gravity over the equatorial zone, determined from the dynamics of satellite orbits, on the one hand, and from terrestrial gravity data, on the other, will be compared.Presented at the Fifteenth IUGG General Assembly, Moscow, July 30 — August 14, 1971.     

The effect of the number of charges carried by the argon ion on the darkening of ilford Q2 emulsion as ion detectors in mass-spectrometer

Summary The darkening (S) of Illford Q₂ photographic plates as ion detectors in mass spectrometer has been investigated. The dependence of the darkening (S) on the ion density (n=ions/mm²) i.e.S=S(n)E for constant energy (E)=z U ranging from 4U20 Kv of the impinging⁴⁰A⁺¹-,⁴⁰A⁺²- and⁴⁰A⁺³-ions whenS does not exceed the value 0.15 and the second relationn=n(z U) _S for darkening 0.05S0.15 constructed from the above relationS=S(n) _E has been determined. The darkening was found to increase with increasing ion-density which inturn decreases with the ionenergy. For⁴⁰A⁺¹-,⁴⁰A⁺²-, and⁴⁰A⁺³-ion of equal energy and ion-density the darkening effect was independent of the number of the charges carried by the argon ion.     

Comparison of satellite and terrestrial gravity data

Summary The integral mean values of gravity on the surface W=W ₀ , obtained from satellite observations with the use of harmonic coefficients[3, 7] and from terrestrial gravity measurements[12], are compared. The squares and products of the harmonic coefficients were neglected, with the exception of [J ₂ ⁽⁰⁾ ] ² , which was taken into account. The Potsdam correction and the geocentric constant are being discussed. The paper ties up with[13–15] and the symbols used are the same. The given problem was treated, e.g., in[2, 4, 6, 8–10]; in the present paper the values of gravity are compared directly.     

The role of sodium bicarbonate in the nucleation of noctilucent clouds

It is proposed that a component of meteoric smoke, sodium bicarbonate (NaHCO₃), provides particularly effective condensation nuclei for noctilucent clouds. This assertion is based on three conditions being met. The first is that NaHCO₃ is present at sufficient concentration (10⁴ cm^–3) in the upper mesosphere between 80 and 90 km. It is demonstrated that there is strong evidence for this based on recent laboratory measurements coupled with atmospheric modelling. The second condition is that the thermodynamics of NaHCO₃(H₂O)_n cluster formation allow spontaneous nucleation to occur under mesospheric conditions at temperatures below 140 K. The Gibbs free energy changes for forming clusters with n = 1 and 2 were computed from quantum calculations using hybrid density functional/Hartree-Fock (B3LYP) theory and a large basis set with added polarization and diffuse functions. The results were then extrapolated to higher n using an established dependence of the free energy on cluster size and the free energy for the sublimation of H₂O to bulk ice. A 1-dimensional model of sodium chemistry was then employed to show that spontaneous nucleation to form ice particles (n > 100) should occur between 84 and 89 km in the high-latitude summer mesosphere. The third condition is that other metallic components of meteoric smoke are less effective condensation nuclei, so that the total number of potential nuclei is small relative to the amount of available H₂O. Quantum calculations indicate that this is probably the case for major constituents such as Fe(OH)₂, FeO₃ and MgCO₃.     

The derivatives of the lunar disturbing potential harmonics with respect to euler's angles

Summary The derivatives of the harmonicsP _n ^(k) (sin _O)cos kT_O andP _n ^(k) (sin _O)sin kT_O, occurring in the development of the lunar disturbing potential, are derived upto n=4 and for k== 0, 1, ..., n. The equatorial co-ordinates _OT_O are referred to the Moon's mass centre; the procedure for the solar disturbing potential is formally identical.     

Influence of Atmospheric Solar Radiation Absorption on Photodestruction of Ions at D-Region Altitudes of the Ionosphere

The influence of atmospheric solar radiation absorption on the photodetachment, dissociative photodetachment, and photodissociation rate coefficients (photodestruction rate coefficients) of O^?, Cl^?, O₂ ^?, O₃ ^?, OH^?, NO₂ ^?, NO₃ ^?, O₄ ^?, OH^?(H₂O), CO₃ ^?, CO₄ ^?, ONOO^?, HCO₃ ^?, CO₃ ^?(H₂O), NO₃ ^?(H₂O), O₂ ⁺(H₂O), O₄ ⁺, N₄ ⁺, NO⁺(H₂O), NO⁺(H₂O)₂, H⁺(H₂O) _n for n = 2–4, NO⁺(N₂), and NO⁺(CO₂) at D-region altitudes of the ionosphere is studied. A numerical one-dimensional time-dependent neutral atmospheric composition model has been developed to estimate this influence. The model simulations are carried out for the geomagnetically quiet time period of 15 October 1998 at moderate solar activity over the Boulder ozonesonde. If the solar zenith angle is not more than 90° then the strongest influence of atmospheric solar radiation absorption on photodestruction of ions is found for photodissociation of CO₄ ^? ions when CO₃ ^? ions are formed. It follows from the calculations that decreases in the photodestruction rate coefficients of ions under consideration caused by this influence are less than 2 % at 70 km altitude and above this altitude if the solar zenith angle does not exceed 90°.     

Inversion of normal moveout for monoclinic media1

Multiple vertical fracture sets, possibly combined with horizontal fine layering, produce an equivalent medium of monoclinic symmetry with a horizontal symmetry plane. Although monoclinic models may be rather common for fractured formations, they have hardly been used in seismic methods of fracture detection due to the large number of independent elements in the stiffness tensor. Here, we show that multicomponent wide-azimuth reflection data (combined with known vertical velocity or reflector depth) or multi-azimuth walkaway VSP surveys provide enough information to invert for all but one anisotropic parameters of monoclinic media. In order to facilitate the inversion procedure, we introduce a Thomsen-style parametrization for monoclinic media that includes the vertical velocities of the P-wave and one of the split S-waves and a set of dimensionless anisotropic coefficients. Our notation, defined for the coordinate frame associated with the polarization directions of the vertically propagating shear waves, captures the combinations of the stiffnesses responsible for the normal-moveout (NMO) ellipses of all three pure modes. The first group of the anisotropic parameters contains seven coefficients (ε^(1,2), δ^(1,2,3) and γ^(1,2)) analogous to those defined by Tsvankin for the higher-symmetry orthorhombic model. The parameters ε^(1,2), δ^(1,2) and γ^(1,2) are primarily responsible for the pure-mode NMO velocities along the coordinate axes x₁ and x₂ (i.e. in the shear-wave polarization directions). The remaining coefficient δ⁽³⁾ is not constrained by conventional-spread reflection traveltimes in a horizontal monoclinic layer. The second parameter group consists of the newly introduced coefficients ζ^(1,2,3) which control the rotation of the P-, S₁- and S₂-wave NMO ellipses with respect to the horizontal coordinate axes. Misalignment of the P-wave NMO ellipse and shear-wave polarization directions was recently observed on field data by Pérez et al. Our parameter-estimation algorithm, based on NMO equations valid for any strength of the anisotropy, is designed to obtain anisotropic parameters of monoclinic media by inverting the vertical velocities and NMO ellipses of the P-, S₁- and S₂-waves. A Dix-type representation of the NMO velocity of mode-converted waves makes it possible to replace the pure shear modes in reflection surveys with the PS₁- and PS₂-waves. Numerical tests show that our method yields stable estimates of all relevant parameters for both a single layer and a horizontally stratified monoclinic medium.     

Tidal currents and residual currents at Norderney,Elbe 1, and Aussen-Eider lightships and their variation under the influence of prevailing winds

Summary Four hourly current-and wind observations during the years 1924–1927 at the German lightvessels Norderney, Elbe 1, and Aussen-Eider were subjected to harmonic analysis with emphasis on the influence of the wind on the residual as well as on the tidal current. The tidal current is strongest at Elbe 1 and weakest at Aussen-Eider. The half-monthly inequality of the current is strongly influenced by a ₂ tidal component. Wind influences the velocity, phase and duration of ebb-and flow current in a systematic way at Norderney and Elbe 1. Deviations from the mean tidal current are caused mainly by the change in wind direction rather than by wind velocity. The mean residual current is weak at the three stations. But wind driven currents have a velocity up to 5 times as great as the mean residual current and reverse their direction with the wind. The annual variation of the mean residual current, however, is caused only to a small part by the annual wind variation.Abbreviations used in this paper Gr. M. Tr. Greenwich moon transit, i.e. Greenwich civil time of the upper or lower transit of the moon through the meridian of Greenwich - C _n computed tidal current at M1/2Hn - C _n ^m computed mean tidal current at M1/2Hn - M _n Moon-half hour mean, i.e. mean of all current velocities observed during M1/2Hn - M.A. Moon age of an observation, true Greenwich time of Gr.M.Tr. directly preceeding the time of observation, expressed in 12 integral numbers, each representing M.A. falling in 12 different hourly intervals - M1/2H Moon-half hour, 1/2 of the interval between one moon transit and the next, i.e. 1/24 of 12h25m - R _n ^o ,R _n ^' ,R _n ^" residual current computed by harmonic analysis ofn M1/2H means of the mean current, the current at weak winds, and the current at strong winds respectively - d.o.f. degrees of freedom - standard deviation ofC _n fromM _n - ^* mean standard deviation ofC _n fromM _n for analysis with weighted means - A _o Standard error of the residual currentA _o - AB standard error of the harmonic coefficientsA ₁,B ₁,A ₂,B ₂,... - S ₂ Phase of the current componentS ₂     

太湖冬季有色可溶性有机物吸收荧光特性及遥感算法

基于2006年和2007年1月两次太湖采样,对50个点位的有色可溶性有机物(CDOM)光谱吸收、荧光、溶解性有机碳(DOE)浓度及遥感反射率进行测定与分析,探讨冬季太湖CDOM的吸收荧光特性及空间分布,建立CDOM吸收系数的遥感反演算法.结果表明,太湖冬季CDOM在355nm处吸收系数a(355)变化范围和均值分别为1...     

The role of vibrationally excited oxygen and nitrogen in the ionosphere during the undisturbed and geomagnetic storm period of 6–12 April 1990

We present a comparison of the observed behavior of the F-region ionosphere over Millstone Hill during the geomagnetically quiet and storm periods of 6–12 April 1990 with numerical model calculations from the IZMIRAN time-dependent mathematical model of the Earths ionosphere and plasmasphere. The major enhancement to the IZMIRAN model developed in this study is the use of a new loss rate of O⁺(⁴S) ions as a result of new high-temperature flowing afterglow measurements of the rate coefficients K₁ and K₂ for the reactions of O⁺(⁴S) with N₂ and O₂. The deviations from the Boltzmann distribution for the first five vibrational levels of O₂(v) were calculated, and the present study suggests that these deviations are not significant. It was found that the difference between the non-Boltzmann and Boltzmann distribution assumptions of O₂(v) and the difference between ion and neutral temperature can lead to an increase of up to about 3% or a decrease of up to about 4% of the calculated NmF2 as a result of a respective increase or a decrease in K₂. The IZMIRAN model reproduces major features of the data. We found that the inclusion of vibrationally excited N₂(v > 0) and O₂(v > 0) in the calculations improves the agreement between the calculated NmF2 and the data on 6, 9, and 10 April. However, both the daytime and nighttime densities are reproduced by the IZMIRAN model without the vibrationally excited nitrogen and oxygen on 8 and 11 April better than the IZMIRAN model with N₂(v > 0) and O₂(v > 0). This could be due to possible uncertainties in model neutral temperature and densities, EUV fluxes, rate coefficients, and the flow of ionization between the ionosphere and plasmasphere, and possible horizontal divergence of the flux of ionization above the station. Our calculations show that the increase in the O⁺ + N₂ rate factor due to N₂(v > 0) produces a 5–36% decrease in the calculated daytime peak density. The increase in the O⁺ + O₂ loss rate due to vibrationally excited O₂ produces 8–46% reductions in NmF2. The effects of vibrationally excited O₂ and N₂ on N_e and T_e are most pronounced during the daytime.     

大型浅水湖泊与大气之间的动量和水热交换系数——以太湖为例

湖泊水面与大气之间垂直方向的动量、水汽和热量通量与风速、湿度和温度梯度之间存在比例关系,因此在湖泊水-气相互作用研究中,这比例系数(交换系数)是关键因子.在以往的研究中,交换系数通常直接采用水面梯度观测法或海洋大气近地层的参数化方案进行计算.本文采用涡度相关系统和小气候系统仪器在太湖平台上直接观测的通量和气象要素,对上述交换系数(最小均方差原则)进行优化,结果为:动量交换系数C_D10N=1.52×10^-3、水汽交换系数C_E10N=0.82×10^-3、热量交换系数CH10N=1.02×10^-3,与其他内陆湖泊涡度相关观测数据的推导结果一致.本文的研究结果表明:与海洋参数化方案相比,在相同的风速条件下,湖面的空气动力学粗糙度比海洋高,这可能是由于受到水深的影响;如果采用海洋参数化方案,会导致湖泊年蒸发量的估算值偏大40%.太湖的动量、水汽和热量交换系数可以视为常数,可以不考虑稳定度和风速的影响.这是因为本文中83%的数据为近中性条件.敏感性分析表明:如果考虑稳定度的影响,LE模拟值的平均误差降低了0.5 W/m²,H的平均误差降低了0.4 W/m²,u*的计算值没有变化;如果考虑风速的影响,u*模拟值的平均误差降低了0.004 m/s,LE的平均误差升高了1.3 W/m²,H的模拟结果几乎不受影响.这一结果能为湖气相互作用研究提供参考.     

淮河流域周村水库夏季CDOM吸收光谱特征、空间分布及其来源分析

基于2015年8月采集的24个淮河流域以周村水源水库为代表的表层水样的有色溶解性有机物(CDOM)吸收系数数据,研究了CDOM吸收光谱的空间分布特征,考察了CDOM的吸收系数与水质参数的相关关系,同时探讨了周村水库夏季CDOM的潜在来源.结果显示:依据CDOM的吸收光谱空间分布特性及采样点分布特征,周村水库分为入库口、过渡区和主库区3个特征水域;CDOM的吸收系数沿入库口到主库区依次递减,S值呈现相反的趋势;分析发现S240~500与a(355)和a*(355)呈极显著负相关(R~2=0.98、0.88);CDOM吸收系数a(355)与溶解性有机碳(DOC)浓度具有良好的线性相关,有利于建立DOC遥感反演模型;同时,CDOM吸收系数a(355)与a_(ph)(440)存在极显著正线性相关,表明浮游植物的新陈代谢及其降解产物是夏季周村水库CDOM的潜在来源.综上,通过对夏季周村水库水体CDOM的研究,丰富了关于水源水体CDOM的调查资料,可为日后水库的管理提供技术支撑.     

Space-Time scales of internal waves

Abstract

We have contrived a model E(αω) α μ^?1ω^?p+1(ω ²?ω _i ²)^?+ for the distribution of internal wave energy in horizontal wavenumber, frequency-space, with wavenumber α extending to some upper limit μ(ω) α ω ^r-1 (ω ²?ω _i ²)^½, and frequency ω extending from the inertial frequency ω _i to the local Väisälä frequency n(y). The spectrum is portrayed as an equivalent continuum to which the modal structure (if it exists) is not vital. We assume horizontal isotropy, E(α, ω) = 2παE(α₁, α₂, ω), with α₁, α₂ designating components of α. Certain moments of E(α₁, α₂, ω) can be derived from observations. (i) Moored (or freely floating) devices measuring horizontal current u(t), vertical displacement η(t),…, yield the frequency spectra F _(u,η,…)(ω) = ∫∫ (U ², Z ²,…)E(α₁, ∞₂, ω) dα₁ dα₂, where U, Z,… are the appropriate wave functions. (ii) Similarly towed measurements give the wavenumber spectrum F _(…)(α1) = ∫∫… dα₂ dω. (iii) Moored measurements horizontally separated by X yield the coherence spectrum R(X, ω) which is related to the horizontal cosine transform ∫∫ E(α1, α2 ω) cos α₁ Xdα₁ dα₁. (iv) Moored measurements vertically separated by Y yield R(Y, ω) and (v) towed measurements vertically separated yield R(Y, α₁), and these are related to similar vertical Fourier transforms. Away from inertial frequencies, our model E(α, ω) α ω ^?p-r for α ≦ μ ω ω ^r, yields F(ω) ∞ ω ^?p, F(α₁) ∞ α₁ ^?q, with q = (p + r ? 1)/r. The observed moored and towed spectra suggest p and q between 5/3 and 2, yielding r between 2/3 and 3/2, inconsistent with a value of r = 2 derived from Webster's measurements of moored vertical coherence. We ascribe Webster's result to the oceanic fine-structure. Our choice (p, q, r) = (2, 2, 1) is then not inconsistent with existing evidence. The spectrum is E(∞, ω) ∞ ω ^?1(ω ²?ω _i ^{2 ?1}, and the α-bandwith μ ∞ (ω ²?ω _i ²)⁺ is equivalent to about 20 modes. Finally, we consider the frequency-of-encounter spectra F([sgrave]) at any towing speed S, approaching F(ω) as S ≦ S _o, and F(α₁) for α₁ = [sgrave]/S as S ≧ S _o, where S _o = 0(1 km/h) is the relevant Doppler velocity scale.     

Planar charged-particle trajectories in multipole magnetic fields

This paper provides a complete generalization of the classic result that the radius of curvature () of a charged-particle trajectory confined to the equatorial plane of a magnetic dipole is directly proportional to the cube of the particles equatorial distance () from the dipole (i.e. ³). Comparable results are derived for the radii of curvature of all possible planar chargedparticle trajectories in an individual static magnetic multipole of arbitrary order m and degree n. Such trajectories arise wherever there exists a plane (or planes) such that the multipole magnetic field is locally perpendicular to this plane (or planes), everywhere apart from possibly at a set of magnetic neutral lines. Therefore planar trajectories exist in the equatorial plane of an axisymmetric (m = 0), or zonal, magnetic multipole, provided n is odd: the radius of curvature varies directly as ⁿ⁼². This result reduces to the classic one in the case of a zonal magnetic dipole (n = 1). Planar trajectories exist in 2m meridional planes in the case of the general tesseral (0 < m < n) magnetic multipole. These meridional planes are defined by the 2m roots of the equation cos[m()–_n^m)] = 0, where _n^m = (1/m) arctan (h_n^m/g_n^m); g_n^m and h_n^m denote the spherical harmonic coefficients. Equatorial planar trajectories also exist if (n – m) is odd. The polar axis ( = O,) of a tesseral magnetic multipole is a magnetic neutral line if m > I. A further 2_m(n – m) neutral lines exist at the intersections of the 2_m meridional planes with the (n – m) cones defined by the (n – m) roots of the equation P_n^m(cos ) = 0 in the range 0 < 9 < , where P_n^m(cos ) denotes the associated Legendre function. If (n – m) is odd, one of these cones coincides with the equator and the magnetic field is then perpendicular to the equator everywhere apart from the 2m equatorial neutral lines. The radius of curvature of an equatorial trajectory is directly proportional to ⁿ⁼² and inversely proportional to cos[m(–)]. Since this last expression vanishes at the 2m equatorial neutral ines, the radius of curvature becomes infinitely large as the particle approaches any one of these neutral lines. The radius of curvature of a meridional trajectory is directly proportional to rⁿ⁺², where r denotes radial distance from the multiple, and inversely proportional to P_n^m(cos )/sin . Hence the radius of curvature becomes infinitely large if the particle approaches the polar magnetic neutral ine (m > 1) or any one of the 2m(n – m) neutral ines located at the intersections of the 2m meridional planes with the (n – m) cones. Illustrative particle trajectories, derived by stepwise numerical integration of the exact equations of particle motion, are pressented for low-degree (n 3) magnetic multipoles. These computed particle trajectories clearly demonstrate the non-adiabatic scattering of charged particles at magnetic neutral lines. Brief comments are made on the different regions of phase space defined by regular and irregular trajectories.Also Visiting Reader in Physics, University of Sussex, Falmer, Brighton, BN1 9QH, UK     

Photochemistry of Ions at D-region Altitudes of the Ionosphere: A Review

The current state of knowledge of the D-region ion photochemistry is reviewed. Equations determining production rates of electrons and positive ions by photoionization of atmospheric neutral species are presented and briefly discussed. Considerable attention is given to the progress in the chemistry of O⁺(⁴S), O⁺(²D), O⁺(²P), N⁺, N₂ ⁺, O₂ ⁺, NO⁺, N₄ ⁺, O₄ ⁺, NO⁺(N₂), NO⁺(CO₂), NO⁺(CO₂)₂, NO⁺(H₂O) _n for n = 1–3, NO⁺(H₂O)(N₂), NO⁺(H₂O)₂(N₂), NO⁺(H₂O)(CO₂), NO⁺(H₂O)₂(CO₂), O₂ ⁺(H₂O), H₃O⁺(OH), H⁺(H₂O) _n for n = 1–8, O^?, O₂ ^?, O₃ ^?, O₄ ^?, OH^?, CO₃ ^?, CO₄ ^?, NO₂ ^?, NO₃ ^?, ONOO^?, Cl^?, Cl^?(H₂O), Cl^?(CO₂), HCO₃ ^?, CO₃ ^?(H₂O), CO₃ ^?(H₂O)₂, NO₃ ^?(H₂O), NO₃ ^?(H₂O)₂, OH^?(H₂O), and OH^?(H₂O)₂ ions. The analysis of the D-region rocket ion mass spectrometer measurements shows that, among these ions, O₂ ⁺, NO⁺, NO⁺(H₂O), and H⁺(H₂O) _n for n = 1–7 can make the main contribution to the total positive ion number density, and O^?, O₂ ^?, Cl^?, OH^?(H₂O), CO₃ ^?, HCO₃ ^?, NO₃ ^?, ONOO^?, CO₄ ^?, NO₃ ^?(H₂O), NO₃ ^?(H₂O)₂, and ³⁵Cl^?(CO₂) ions can be responsible for the main contribution to the total negative ion number density. Photodetachment of electrons from O^?, Cl^?, O₂ ^?, O₃ ^?, OH^?, NO₂ ^?, and NO₃ ^?, dissociative electron photodetachment of O₄ ^? and OH^?(H₂O), and photodissociation of O₃ ^?, O₄ ^?, CO₃ ^?, CO₄ ^?, ONOO^?, HCO₃ ^?, CO₃ ^?(H₂O), NO₃ ^?(H₂O), O₂ ⁺(H₂O), O₄ ⁺, N₄ ⁺, NO⁺(H₂O), NO⁺(H₂O)₂, H⁺(H₂O) _n for n = 2–4, NO⁺(N₂), and NO⁺(CO₂) are studied, and the photodetachment and photodissociation rate coefficients are calculated using the current state of knowledge on the cross sections of these processes and fluxes of solar radiation.     

Attenuation characteristics of peak horizontal acceleration in Northeast and Southwest China

Regional seismic characteristics in northeastern and southwestern China are quite different. Earthquakes are more frequent in SW China than in NE China and intensity attenuates faster in SW China than in NE China. Through regression analyses of data from these two regions we have found the attenuation of peak horizontal accelerations also to be noticeably different. For northeastern China the regression is log₁₀(a) = ?0.474 + 0.613M ? 0.873 log₁₀ (R) ?0.00206R and for southwestern China, the regression is log₁₀ (a) = 0.437 + 0.454M ? 0.739 log₁₀ (R) ?0.00279R where a is acceleration in cm/sec², M is the Chinese surface wave magnitude (Institute of Geophysics, State Seismological Bureau), and R is the distance in kilometres. The formula for northeastern China has distance coefficients similar to those for Central United States as derived by Nuttli and Herrmann¹⁴.     

A new dissipation model based on memory mechanism

Summary The model of dissipation based on memory introduced by Caputo is generalized and checked with experimental dissipation curves of various materials.List of symbols unidimensional stress - unidimensional strain - Q ^–1 specific dissipation function - c(t) creep compliance - m(t) relaxation modulus - c ₀ instantaneous compliance - m equilibrium modulus - (t) creep function - relaxation function - () spectral distribution of retardation times - spectral distribution of relaxation times - c ^*() complex compliance - m ^*() complex modulus - tang loss-tangent     

Introductory notes on shock remanent magnetization and shock demagnetization of igneous rocks

Summary Effects of mechanical shocks of about 0.5 msec in duration on the remanent magnetization of igneous rocks are experimentally studied. The remanent magnetization acquired by applying a shock (S) in the presence of a magnetic field (H), which is symbolically expressed asJ _R (H₊S H_o), is very large compared with the ordinary isothermal remanent magnetization (IRM) acquired in the same magnetic field.J _R (H₊S H_o) is proportional to the piezo-remanent magnetization,J _R (H₊P₊P_o H_o).The effect of applyingS in advance of an acquisition of IRM is represented symbolically byJ _R (S H₊ H_o).J _R (S H₊ H_o) can become much larger than the ordinary IRM, and is proportional to the advance effect of pressure on IRM,J _R(P₊ P₀ H₊ H₀).The effect of shockS applied on IRM in non-magnetic space is represented by the shock-demagnetization effect,J _R(H₊ H₀ S), which also is proportional toJ _R(H₊ H₀ P₊ P₀).Because, the duration of a shock is very short, a single shock effect cannot achieve the final steady state. The effect ofn-time repeated shocks, is represented byJ ₀+J ^*(n), whereJ ₀ means the immediate effect and J ^*(n) represent the resultant effect of repeating, which is of mathematical expression proportional to [1–exp {–(n–1)}].

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Zusammenfassung Die Effekte des mechanischen Stosses mit der Dauer von etwa 0.5 ms auf der remanenten Magnetisierung wurden experimentell nachgesucht. Das erworbene Remanenz der Magnetisierung nach dem Stoss (S) unter dem magnetischen Feld (H), das hier symbolisch alsJ _R(H₊ SH₀) bezechnet wird, ist sehr stark im Vergleich mit der normalen isothermischen remanenten Magnetisierung (IRM) unter demselben magnetischen Feld.J _R(H₊ S H₀) ist im Verhältnis zur piezoremanenten Magnetisierung,J _R(H₊ P₊ P₀ H₀).Der Effekt vom Stoss vor der Erwerbung von IRM wird symbolisch alsJ _R(S H₊ H₀) bezeichnet.J _R(S H₊ H₀) kann viel stärker als die normale IRM werden, im verhältnis zum Effekt des vorausgegebenen Drucks auf IRMJ _R(P₊ P₀ H₊ H₀).Der Effekt des Stosses auf IRM im Raum ohne magnetisches Feld wird mit dem Stossentmagnetisierungseffekt dargestellt,J _R(H₊ H₀ S), der auch proportional zuJ _R(H₊ H₀ P₊ P₀) ist.Da die Dauer einzelnen Stosses sehr kurz ist, kann der Effekt des einmaligen Stosses den endgültigen stabilen Zustand nicht erreichen. Der Effekt nachn-maligen wiederholten Stossen wird alsJ ₀+J ^*(n) bezeichnet, wobeiJ ₀ den unverzüglichen Effekt bedeutet, und J ^*(n) beschreibt den resultanten Effekt der Stosswiederholung, dessen mathematische Darstellung proporational zu [1–exp {–(n–1)}] ist.