Expansions of the double product of the global gravity field

Summary Four fundamental forms of expansion of the double product of the gravity function into an infinite series are derived. Two isotropic parts are separated, one is expressed by Legendre polynomials and the other by invariants of Wigner's D-matrices.

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¶rt; m n¶rt;mau ¶rt; au ¶rt; nu¶rt;uaumau uu ¶rt;. ¶rt; ¶rt; umn amu, na aam n nu a¶rt;a u ma n uauam amu ua.

     

A more precise mechanical theory of askania gravity meters

Summary The measuring systems of Askania gravity meters are assumed to have 3 degrees of freedom. The axis of rotation of the beam can also be displaced in the vertical and horizontal directions. The equations of equilibrium of this system (25)–(27) were used to derive the expressions for the effect of displacing the calibration ball, for the scale equation and for the sensitivity of the gravity meter. Equations (33), (34) and (39) refer to gravity meters with a photoelectric transducer, and Eqs (46), (47) and (49) to gravity meters with a capacitive transducer.

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uum umaum au n¶rt;naam 3 mnu ¶rt;. au aa m m nam mua uuma anau. au au m um (25)–(27) ¶rt; au ¶rt; ¶rt;mu nu au aua, ¶rt; aua a u ¶rt; mummuauma. aum mmuu mm m au (33), (34), (39), ¶rt;aum m mm au (46), (47), (49).

     

Magnitude calibrating functions for a multidimensional homogeneous system of reference stations

Calibrating functions play a substantial role in the determination of earthquake magnitudes. Their shape and character is closely connected with the internal structure of the Earth, the distribution of velocities and attenuation of seismic waves in the Earth's body. These facts have been considered during the establishment of the Eurasian Homogeneous Magnitude System (EuHMS). The paper summarizes the procedures used for constructing the new complete set of calibrating functions for body and surface waves (vertical and horizontal components of P, S and L waves from medium period instruments, and vertical component of P waves from short period instruments).The calibrating functions were derived in the distance range between 20° and 100°, being based on several thousands of homogeneous observations for each wave type. The application of a HMS gives a possibility to derive the magnitude calibrating functions with a considerable degree of reliability due to the method of simultaneous optimization of the calibrating functions and the systems of station corrections. The magnitude calibrating functions for EuHMS represent the first complete set of calibrating functions, which are derived by the same standard method and initial observational material. A comparison with the existing calibrating functions shows that the application of σ and Q functions, presently used in the seismological practice for magnitude determinations, may lead to errors exceeding of magnitude unit at certain epicentral distances, specific for each wave type. It appears that the internationally recommended Q functions are not admissible for magnitude determinations from short-period P waves.     

Changes in the shape of the circumpolar vortex due to heating from above

Summary Based on model considerations it is shown that, under certain assumptions, zonalization of tropospheric circulation may be expected in the region of the auroral oval as a result of heat released at the time energetic electrons penetrate from the Sun into the lower stratosphere.

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a auu ¶rt; a¶rt;u naa, m nu m n¶rt;nu u¶rt;am auau mn uuu amu aa aa mam ¶rt;u mna nuu mumu m u a u mam.

     

On the expanding earth hypothesis

Summary The hypothesis of an expanding Earth is discussed on the basis of lunar laser ranging It is provcd that the given data do not indicate a secular increase in the principal moment of the Earth's inertia which would have to occur if the Earth were really expanding.

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¶rt;amunma au u mu u ammuu a¶rt;u u ¶rt;a n a auu . aam, m n mu ¶rt;a m umamu amaua ma uuu u, m ¶rt; nmmam auu, u n¶rt; u m.

     

Effect of cofactors of adjusted and unadjusted quantities on their functions

aamuam uu am a (m u naamuu n) u u (a) uu a uu mu uu. mam (19), (28) naam, m amua am mau u m ¶rt; am amu: a) na ¶rt;um am, n n a uu am u uu a uu; ) ma ¶rt;um am, m aam uu a uu.     

Earthquake distribution and volcanism in Kamchatka,Kurile Islands,and Hokkaido Part 3: Southern Kuriles and Hokkaido

Summary The morphology of the Wadati-Benioff zone in the region of Southern Kuriles and Hokkaido, based on the distribution of 4015 earthquake foci, verified the existence of an intermediate depth aseismic gap and its relation to active andesitic volcanism. A paleosubduction zone activated by an intermediate depth collision with the active subduction zone was found and described.

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u Wadati-Benioff amu uu - u a¶rt;, aa a an¶rt;uu 4015 a mu, nm¶rt;ua mau n¶rt; au u amu a¶rt;um au. a a¶rt;a u nuaa a na¶rt;uu, amuuuaa nmu mu amu ¶rt;uu.

     

Magnetic susceptibility anisotropy of deformed rocks

¶rt;au uu aum nuuumu u aumnuu ¶rt; aa aam n¶rt; am amuu u namuu ¶rt;au. amu uu aumnuu nuuumu, a amu ¶rt;au, m ¶rt;mu au ma nma aaumu m¶rt; ¶rt;a, m a amu uu aum m mnu n¶rt;u ¶rt; mm uaum amua n¶rt; ¶rt;au. u aumnuu nu a namu ¶rt;auu(<1%) a uuu m nuuumu _i uaum amua. u aumnuu ¶rt;mu uu uum aauuau ¶rt;ua am m uu, m, m ¶rt; u au namu ¶rt;auu.     

Travel time curves for complex inhomogeneous slightly anisotropic media

Summary The linearization approach is used to compute the travel times in inhomogeneous slightly anisotropic media. The basic formulae are outlined and their accuracy demonstrated in comparison with the exact solution based on the zero-order ray theory and the Backus formula (1965). The linearization is extended also to complex media with curved interfaces. The computer program for calculating travel times in 2D, inhomogeneous, slightly anisotropic, complex media is briefly described. The numerical results obtained for a realistic situation and various types of waves are presented to enable the effects of anisotropy and the effects of inhomogeneity on the resulting travel times to be compared.

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na uauua n¶rt;¶rt; ¶rt; ama¶rt;aa , anmau aaumn ¶rt;a. ¶rt; u n¶rt; au m u n muu nuuuu u m¶rt; aa (1965). a uauua n¶rt;¶rt; ¶rt; a ¶rt; uuuauau a¶rt;a. am nuaa uuma naa ¶rt; ama¶rt;a ¶rt; ¶rt;. u mam ¶rt; a mun ¶rt;am m um m aumnuu u m ¶rt;¶rt;mu a a anmau .