Expansion of geoid heights into a spherical harmonic series

Summary An algorithm is derived to compute the coefficients of a spherical harmonic series for the geoid radius vector that are a solution to a system of linear equations, containing Stokes' constants of the geopotential.     

The effect of ordered vertical velocities and of the Earth's surface on the trajectories of particles of polluted air in the atmosphere

Summary The possibilities of improving of the construction of trajectories of air particles polluted by antropogeneous admixtures are discussed. With this in view attention is devoted to the ordered vertical velocities of dynamic origin and a simple method of approximate construction of the trajectories in the boundary layer of the atmosphere, where the flow is markedly affected by the Earth's surface, is discussed.     

The origin of garnet-cordierite-sillimanite bearing rocks from Chandos Township,Ontario

Garnet-cordierite-sillimanite bearing rocks from the contact aureole of the Precambrian Loon Lake pluton in Chandos Township, southeastern Ontario were analyzed for the major and rare-earth elements. In comparison with the associated Apsley biotite gneisses, they are rich in Al, Mg, and Fe, low in Si, Na, and K and their REE distribution patterns show a depletion of light REE with a negative Eu anomaly. These rocks are probably residuum left after partial melting of biotite gneiss. Leucogranite associated with the GCS rocks may represent the extracted anatectic material. It is suggested that some of the garnet cordierite-sillimanite gneisses which frequently occur in high-grade regionally metamorphosed areas of the Grenville Province of the Canadian Shield may also be of a similar residual origin as proposed by Lal and Moorhouse (1969).     

Frequency-time analysis of geomagnetic beating-type pulsationsPc3

Summary The mechanism of beating of Pc3 type pulsations is studied. Using the method of numerical computation of a sonagram (the method of frequency-time analysis) a set of samples of pulsations from the Budkov Observatory is treated (1968–1969) mostly at K-indices equal to 2–3. By comparing f–t diagrams with the spectra of the samples an attempt has been made at interpreting the beating as a superposition of the frequency components, contained in the pulsation signal. In most observed cases it is possible to determine two close frequencies, the difference of which is on the average =5.4 mHz. The average carrier frequency of the samples was =37.6 mHz, and the average frequency of the beating =2.7 mHz. The interval of observed values of f_B amounted to 1–5 mHz. A tendency was observed for f_B to increase with increasing degree of disturbance of the geomagnetic field.     

Computation of spectra of some simple functions using various types of Windows

Summary In the introductory part of the paper, a method of computing spectra by computer is described, which cuts down the computer time required without using the Fast Fourier Transformation. Windows which can be used to adjust the resultant spectrum are described. The spectra of a constant, a linear function, a sine function, of the superposition of two sine functions and of the superposition of a sine function with a constant and linear function are described in detail and it is demonstrated how these spectra change when different types of windows are used. The suitability of the separate windows for various purposes is discussed. Finally, in the case of the superposition of two sine oscillations it is shown under what conditions the two frequency components can be distinguished.     

Construction of Green's function for the Stokes boundary-value problem with ellipsoidal corrections in the boundary condition

Green's function for the boundary-value problem of Stokes's type with ellipsoidal corrections in the boundary condition for anomalous gravity is constructed in a closed form. The `spherical-ellipsoidal' Stokes function describing the effect of two ellipsoidal correcting terms occurring in the boundary condition for anomalous gravity is expressed in O(e <sup>2</sup> <sub>0</sub>)-approximation as a finite sum of elementary functions analytically representing the behaviour of the integration kernel at the singular point ψ=0. We show that the `spherical-ellipsoidal' Stokes function has only a logarithmic singularity in the vicinity of its singular point. The constructed Green function enables us to avoid applying an iterative approach to solve Stokes's boundary-value problem with ellipsoidal correction terms involved in the boundary condition for anomalous gravity. A new Green-function approach is more convenient from the numerical point of view since the solution of the boundary-value problem is determined in one step by computing a Stokes-type integral. The question of the convergence of an iterative scheme recommended so far to solve this boundary-value problem is thus irrelevant. Received: 5 June 1997 / Accepted: 20 February 1998     

Relation between the field of surface heat flow and the distribution ofP n -wave velocities for continents

Summary The dependence between P_n-wave velocities and the surface heat flow, temperature at the core-mantl boundary and thickness of the Earth's crust for continents (Europe, Asia, North America and Australia) was investigated statistically in connection with the problem of lateral inhomogeneities in the upper mantle. The relations obtained were compared with those determined under laboratory conditions. The conclusion is that temperature and pressure effects may provide additional explanations of the regional variations of P_n-wave velocities observed in most continents.

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auum ¶rt;auu mu n¶rt; a nmu uua(P_n ), nm mn nm, mnam a u m mum a u¶rt;aa u n uuuma ¶rt;¶rt;m mu P_n. nua ¶rt;a mama aam u¶rt;au nu m n¶rt; amuu u u ¶rt;au u mnam a¶rt;um mmmuu mamau n¶rt;aa am. am ¶rt;, m ua uu m P_n- ¶rt; amu muma n¶rt;m auu m¶rt;uauu u a nmu muua.

     

Normal density earth models

Summary Models of the Earth's density, close to thePREM model, have been derived, they reproduce the external normal gravitational field of the Earth and its dynamic flattening, and are referred to as normal density models. The Earth's surface is approximated by an ellipsoid of the order of the flattening, or of its square. Of the group of normal models sgtisfying the solution of the inverse problem, the normal density modelHME2 is recommended. The spherically symmetric density modelPREM, which was corrected in the course of solving the inverse problem, thus creating the modifiedPREM-E2 model, was used as the a priori information.

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¶rt; ¶rt;u an¶rt;u nmmu uu ¶rt;uPREM (m. a. a ¶rt;u nmmu), aumau n m u¶rt;mu na¶rt;am auaumau n u. m u annuum am unu¶rt; au. uau amu a ¶rt; mam H==0.003 273 994. ma ¶rt; a ¶rt; ¶rt;m ¶rt;HME2. am anu u a ¶rt; nmmu a unaa ¶rt; a¶rt;ua umua ¶rt;PREM. ¶rt;aam ¶rt;uuau m ¶rt;u n¶rt; aauPREM-E2.