Propagation of surface waves on a nonhomogenous spherically aeolotropic shell

Summary This paper studies the propagation of Surface Waves on a spherically aeolotropic shell surrounded by vacuum. The elastic constantsc _ij and density of the material of the shell are assumed to be of the form _ij r ^l and _o r ^m respectively, where _{ij o} are constants andl, m are any integers.     

Amplitude Response of a LCR Gravimeter with Feedback at Periods of Microseisms and Earthquake Waves

The amplitude response of a LCR gravimeter with the SRW-E feedback was determined on a vertical vibrating platform. The ink-pen recorder was connected parallel with the digital voltmeter input to obtain an analog response of the gravimeter to the harmonic motion of the base with a peak-to-peak amplitude of 10 m and periods excited in an interval of 4 - 10 s as by the ground motion of meteorological microseisms, and in the interval 10 -100 s as by surface waves of distant strong earthquakes. In the first interval, an unexpected maximum of the amplitude response was observed with the double amplitude of apparent 6,5 Gal (6.5 × 10 _–8 m/s ² ) at a period of 4.8 s, and a baseline shift with the amplitude of–64Gal was observed at the same period. The value of this direct component cannot be separated from the effect of the Earth's gravity field. In the second interval, the amplitude response of the gravimeter displayed one expected maximum at a period of 40 s with the double amplitude of 8.1Gal. At the usual level of microseisms with a peak-to-peak amplitude of up to 2 m the fluctuation of the gravimeter on the direct baseline shifted by –4.9 Gal was estimated at 1 Gal. With typical Rayleigh surface waves with periods of 20 s and double amplitudes of up to 100 m, the fluctuation reached 67 Gal.     

Cs137 gamma-ray absorption in eclogites

Summary The coefficient of the gamma-ray absorption _Cs ¹³⁷ investigated in eclogites of the Bohemian Massif varies with fresh samples from0.2477 cm ^–1 to 0.2804 cm ^–1 . Symplectite is the main factor decreasing the value of down to0.242 cm ^–1 . On the contrary, the coefficient increases with the increasing content of clinopyroxene and especially of garnet. The linear dependence of the coefficient on the density may be expressed by the equation =0.0682+0.028.     

On the propagation of wave from a cylindrical cavity

Summary This paper discusses the disturbance produced in an infinite layer of non-homogeneous elastic material characterised by =0 ⁿ and =0ⁿ(n>0) where and are the density and shear modulus respectively of the material, due to periodic torsional force applied on the wall of a cylindrical hole in the layer. The variation of the displacement component with the radius vector is shown graphically and compared with the corresponding homogeneous case.     

Rayleigh waves in an inhomogeneous medium

Summary Dispersion in Rayleigh waves is discussed for semi-infinite media with = ₁(1 ± cos s z) and = ₁(1 ± cosh s z), being the rigidity of the medium. A few workers tried with the above Fourier type of model but failed to find the dispersive nature. Because they neglected s due to the complexity of the calculation they arrived at a non dispersive frequency equation. This difficulty is removed in this paper and a dispersive frequency equation is obtained which shows both direct and inverse dispersion. The second model leads to non-convergent solution forz but shows many interesting results which are also discussed.     

Torsional vibration of non-homogeneous isotropic hollow thick cylinder

Summary Free vibration of a thick hollow cylinder of non-homogeneous elastic material having rigidity and density varying according to the laws: (i) =₀(₀+₀ z) and Q=Q₀(Q₀+₀ z) for finite and infinite length of the cylinder and (ii) ₁/r = and Q = ₁/r for finite length only are considered in this paper. Frequency equations are deduced and respective numerical solutions are obtained.     

The secular variation of the geomagnetic field in Egypt in the last 5000 years

The palaeo-intensities (F _a) of the geomagnetic field in Egypt at some ages are determined by archaeomagnetic measurements and found to be:F _a=36.2 T at 3100 B.C., F_a=46.8 T at 3000 B.C.,F _a=36.5 T at 2780 B.C., 49.0 T at 2500 B.C., 36.4 T at 2200 B.C., 57.5 T at 1990 B.C., 62.1 T atca 1400 B.C., 61.5 T at 1400 B.C., 69.9 T at 600 B.C., 59.3 T at 550 B.C., 79.9 T at 460 B.C., 73.7 T at 450 B.C., 69.7 T at 320 B.C., 56.2 T at A.D. 50, 64.9 T, at A.D. 400, 54.4 T at A.D. 300, 57.5 T at A.D. 700 and 43.0 T at A.D. 1975.The palaeo-inclinations (I _a) at some ages are found to be:I _a=24.2° at 420 B.C., 44° at A.D. 50, 60.7° at A.D. 703 and 42° at A.D. 1795.The measured values ofF _a are affected by the anisotropy of magnetic susceptibility of the samples by 13% to 20% of the expected correct value. The suitable correction of this effect is by multiplyingF by 1/((1+0.2(/90)) andF by 1/((1–0.13 (/90)), whereF andF are the resultant values ofF _a if the laboratory field is perpendicular or parallel to the wall of the sample during the Thelliers' experiments, respectively, and is the angle between the direction of natural remnant magnetization of the sample and the direction of the laboratory field.The results of this paper, together with the previous results for Egypt and the neighbourhoods, lead to the production of the secular variation curve of the geomagnetic field in Egypt for the last 5000 years. The intensity of the field shows a periodicity of about 400 years with multiples.     

On the propagation of wave from a cylindrical cavity,II

Summary We have discussed in the paper the disturbance produced in an infinite layer of nonhomogeneous elastic material characterised by = ₀ Z and = ₀ Z where and are the density and shear modulus respectively of the material due to periodic torsional force applied on the wall of a cylindrical hole in the layer. The variation of the displacement component with the depth of the layer is shown graphically and compared with the corresponding homogeneous case.     

On the efficiency with which aerosol particles of radius less than 1 μm are collected by columnar ice crystals

A theoretical model is presented which allows computing the efficiency with which aerosol particles of 0.001 r1 m are collected by columnar ice crystals in air of various relative humidities, temperatures, and pressures. Particle capture due to Brownian diffusion, thermo- and diffusiophoresis is considered. It is shown that phoretic effects importantly determine the particle capture process of 0.01r1 m. The various pressure-temperature levels studied are found to affect the collection efficiency only ifr>0.1 m. Comparison shows that water drops generally are better aerosol particle scavengers than columnar ice crystals.     

A numerical study of the heat transfer through a fluid layer with recirculating flow between concentric and eccentric spheres

A numerical study has been made of the heat transfer through a fluid layer with recirculating flow. The outer fluid surface was assumed to be spherical, while the inner surface consisted of a sphere concentrically or eccentrically located with respect to the outer spherical surface. The recirculating flow was assumed to be driven by a gas flow creating stress on the fluid's outer surface so that creeping (low Reynolds number) flow developed in its interior. The present study solves the Stokes equation of motion and the convective diffusion equation in bispherical coordinates and presents the streamline and isotherm patterns.Nomenclature a _i inner sphere radius - a _d outer sphere radius - A ₁ defined by equation (5) - A ₂ defined by equation (6) - B ₁ defined by equation (7) - B ₂ defined by equation (8) - c dimensional factor for bispherical coordinates - C constant in equation (4) - d narrowest distance between the two eccentric spheres - E ² operator defined by equation (1) in spherical coordinates and by equation (21) in bispherical coordinates - G modified vorticity, defined in equation (22) - G ^* non-dimensional modified vorticity, defined in equation (28) - h metric coefficient of bispherical coordinate system, defined in equation (18) - k _w thermal conductivity of water - K ₁ defined by equation (9) - K ₂ defined by equation (10) - N _Re Reynolds number=2a _dU/gn - N _Pe,h Peclet number=2a _dU/ - n integer counter - q heat flux - r radius - r ^* non-dimensional radius=r/a _d - S surface area - t time - t ^* non-dimensional time=t/a _d ² - T temperature - T _o temperature at inner sphere surface - T _a temperature at outer sphere surface - T ^* non-dimensional temperature;=(T–T _o)/(T_a–T_o) - u velocity - u _r radial velocity in spherical coordinates - u angular velocity in spherical coordinates - u radial velocity in bispherical coordinates - u angular velocity in bispherical coordinates - U free stream velocity - u _r ^* =u _r/U - u ^* =u /U - u ^* =u /U - u ^* =u /U Greek symbols a ₁ small displacement - vorticity, defined in equation (17) - ^* non-dimensional vorticity, defined in equation (27) - radial bispherical coordinates - _o bispherical coordinate of inner sphere - _a bispherical coordinate of outer sphere - angular coordinate in spherical coordinates - thermal diffusivity - _w thermal diffusivity of water - kinematic viscosity - angular bispherical coordinate - spherical coordinate - streamfunction - non-dimensional streamfunction for spherical coordinates, = /(U a _d ² ) - ^* non-dimensional streamfunction for bispherical coordinates, defined in equation (26)     

Note on the torsional vibration of a thin beam of varying cross-section

Summary In the present note the problem of torsional vibration of a bar in which the moment of inertia and the torsional rigidity are proportional to 0 + 1s, wheres is the spanwise co-ordinate and ₀ and ₁ are real numbers, has been considered.     

On the efficiency with which aerosol particles of radius larger than 0.1 μm are collected by simple ice crystal plates

A theoretical model is presented which allows computing the efficiency with which aerosol particles of radius 0.1r10 m are collected by simple ice crystal plates of radius 50a _c 640 m in air of various relative humidities, temperatures and pressures. Particle capture due to thermophoresis, diffusiophoresis and inertial impaction are considered. It is shown that the capture efficiency of an ice crystal in considerably affected by phoretic effects in the range 0.1r1 m. For aerosol particles ofr>1 m the efficiency is strongly controlled by the flow field around the crystal and the density of the aerosol material. Trajectory analysis also predicts that aerosol particles are preferentially captured by the ice crystal rim. Our theoretica results are found to agree satisfactorily with the laboratory studies presently available. Comparison shows that for the same pressure, temperature and relative humidity of the ambient air ice crystal plates are better aerosol particle scavengers than water drops.     

Q measurements for PhaseX overtones

Linear stacking procedures are used to retrieve the attenuation of 91 modes belonging to the 3rd, 4th and 5th Rayleigh overtones branches in the 80–160 s period range, and contributing to the so-called PhaseX wave group. Our data show in general slightly less attenuation than expected from available models. Data space inversion shows that, when combined with previously measured fundamental modeQ's, this new dataset improves resolution significantly in the 1000–2000 km depth range. Based on this remark, we carry out a number of parameter space inversions. Our results suggest a narrow (80–200 km) zone of high attenuation (Q =75–90), low attenuation in the intermediate mantle (670–1500 km); (Q 350), and lower values in the deeper mantle (Q 200).     

Atmosphärische aerosolstreuung im sichtbaren und nahen infrarot

Zusammenfassung Die atmosphärische Aerosolstreuung wird im Bereich 0.52.1 m und 4°40° experimentell untersucht. Sie scheint im Infraroten weitgehend durch die Verhältnisse im Sichtbaren charakterisierbar zu sein, wenn auch die Streudispersion ein unerwartet gegensätzliches Verhalten zeigt. BeiA-ähnlichen, visuellen Streutypen (oder Typen nahe 1) verschwindet diese ab etwa 1.1 m fast vollständig. DieB-ähnlichen, visuellen Streutypen (oder Typen nahe 2) tritt in einem Zwischenbereich (etwa 0.8 bis 1.3 m) starke Streudispersion auf. Für den Gesamtstreutyp wird eine Klassifizierung in Anlehnung an die im Sichtbaren gebräuchliche [11–14]²) vorgeschlagen.

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Summary The scattering by the atmospheric aerosol of radiation in the region 0.52.1 m and 4°40° is investigated experimentally. The features in the infrared can be characterized by that in the visible, but the scattering dispersion is found to be different to that expected. At scattering types nearA (or 1) in the visible there is almost no scattering dispersion for 1.1 m. At types nearB (or 2) in the visible a high scattering dispersion in the region between 0.8 m and 1.3 m was observed. For the whole region of wavelength including the infrared a classification similar to that used in the visible [11–14]²) is suggested.

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Mitteilungen des Astronomischen Instituts der Universität Tübingen Nr. 77     

Détermination des paramètres d'Ångström par des observations actionmétriques courantes

Summary By comparing the equalities expressing the solar flux within a wide spectral region on the assumption of an extintion within the atmospheric aerosol given by ^– and that of an extintion represented by ₁^–1, a relationship is established by means of which: 1) The error is discussed which is done when the air opacity is expressed by ₁, in the case when 1; 2) A simple and quick method is worked out for determining the parameters and from actinometric observations, carried out within the spectral regions <525 m and 525 m<<625 m.     

Rayleigh wave dispersion equation for a layered spherical earth with exponential function solutions in each shell

We consider the second-order differential equations ofP-SV motion in an isotropic elastic medium with spherical coordinates. We assume that in the medium Lamé's parameters , r ^p and compressional and shear-wave velocities , r, wherer is radial distance. With this regular heterogeneity both the radial functions appearing in displacement components satisfy a fourth-order differential equation which provides solutions in terms of exponential functions. We then consider a layered spherical earth in which each layer has heterogeneity as specified above. The dispersion equation of the Rayleigh wave is obtained using the Thomson-Haskel method. Due to exponential function solutions in each layer, the dispersion equation has similar simplicity, as in a flat-layered earth. The dispersion equation is further simplified, whenp=–2. We obtain numerical results which agree with results obtained by other methods.     

On the propagation of finite Love Waves

Summary The problem of the propagation of finite Love Waves in a heterogeneous elastic half space lying over a homogeneous elastic half space, using the quasilinear stress-strain relation due toS. Ferhst [4] is considered in detail. The variations of the parameter in the layer assumed to be of the form 1= 0e ^z, 0e ^z where is a constant andz is distance measured from the surface into the layer.     

Scientific objectives of the Solar Mesosphere Explorer mission

The 1981–82 Solar Mesosphere Explorer (SME) mission is described. The SME experiment will provide a comprehensive study of mesospheric ozone and the processes which form and destroy it. Five instruments will be carried on the spinning spacecraft to measure the ozone density and its altitude distribution from 30 to 80 km, monitor the incoming solar ultraviolet radiation, and measure other atmospheric constituent which affect ozone. The polar-orbiting spacecraft will be placed into a 3pm-3 am Sun-synchronous orbit. The atmospheric measurements will scan the Earth's limb and measure: (1) the mesospheric and stratospheric ozone density distribution by inversion of Rayleigh-scattered ultraviolet limb radiance, and the thermal emission from ozone at 9.6 m; (2) the water vapor density distribution by inversion of thermal emission at 6.3 m; (3) the ozone photolysis rate by inversion of the O₂(¹g) 1.27 m limb radiance; (4) the temperature profile by a combination of narrow-band and wide-band measurements of the 15 m thermal emission by CO₂; and, (5) theNO₂ density distribution by inversion of Rayleighscattered limb radiance at 0.439 m. The solar ultraviolet monitor will measure both the 0.2–0.31 m spectral region and the Lyman-alpha (0.1216 m) contribution to the solar irradiance. This combination of measurements will provide a rigorous test of the photochemical equilibrium theory of the mesospheric oxygen-hydrogen system, will determine what changes occur in the ozone distribution as a result of changes in the incoming solar radiation, and will detect changes that may occur as a result of meteorological disturbances.     

Transmission of Rayleigh waves over the surface of a heterogeneous medium

Summary The frequency equation of Rayleigh waves propagating over the free surface of an isotropic, perfectly elastic, heterogeneous semi-infinite medium with material properties varying as = ₀ e ^az , = ₀ e ^az , = ₀ e ^az (a>0) has been obtained. Solution of the frequency equation in closed form is obtained in two cases (i) =0, (ii) =, and the Rayleigh wave dispersion curves for phase and group velocities drawn. In both the cases the medium yields single Rayleigh modes which cannot propagate below certain cut-off frequencies. It is found that in case (i), <c<c ₀ and 0.87500 <c _g <c ₀, and in case (ii), 1.03082 <c<c ₁ and 0.90850 <c _g <c ₁, wherec andc _g denote phase nad group velocities respectively, is the constant shear wave velocity of the mediumc ₀ andc ₁ are the corresponding Rayleigh wave velocities of the homogeneous medium of the same Poisson's ratio. The motion of the surface particles is found to be retrograde elliptical as in the homogeneous case, but the ratic of the major and minor axes now becomes frequency dependent and is plotted against frequency. In both the cases (i) and (ii), the ratio starts at a lower value at the cut-off frequency and approaches the corresponding value of the homogeneous medium at high frequencies.     

Frequency-dependent Shear-wave Q Models for the Crust of China and Surrounding Regions

— Starting with fundamental-mode Rayleigh-wave attenuation coefficient values (_R) predicted by previously determined frequency-independent models of shear-wave Q (Q), we have obtained frequency-dependent Q models that explain measured values of _R as well as of Lg coda Q and its frequency dependence at 1 Hz (Q_o and , respectively) for China and some adjacent regions. The process combines trial-and-error selection of a model for the depth distribution of the frequency dependence parameter () for Q with a formal inversion for the depth distribution of Q at 1 Hz. Fifteen of the derived models have depth distributions of that are constant, or nearly constant, between the surface and a depth of 30 km. distributions that vary with depth in the upper 30 km are necessary to explain the remaining seven models. values for the depth-independent models vary between 0.4 and 0.7 everywhere except in the western portion of the Tibetan Plateau where they range between about 0.1 and 0.3 for three paths. These low values lie in a region where Q_Lg and crustal Q are very low and suggest that they should also be low for high-frequency propagation. The models in which varies with depth all show a decrease in that value ranging between 0.55 and 0.8 in the upper 15 km of the crust and (with two exceptions where =0.0) between 0.3 and 0.55 in the depth range 15–30 km. The distribution of values between 0.6 and 0.8 (the higher part of the range) in the upper crust indicates that high-frequency waves will propagate most efficiently, relative to low-frequency waves, in a band that includes, and strikes north-northeastward from the path between event 212/97 and KMI to the path between event 180/95 and station HIA in the north.Acknowledgement. We thank Lianli Cong for providing his code for plotting crustal Q models and Robert Herrmann for writing the mode summation code for computing Lg synthetics used in this study. Our work benefited from helpful discussions with Jack Xie at Lamont-Doherty Earth Observatory of Columbia University. This research was sponsored by the Defense Threat Reduction Agency Contract No. DTRA-01-00-C-0213.