Spherical harmonic analysis and Fourier transformation

Summary The paper deals with the computation of spherical harmonic coefficients from surface measurements of the magnetic or gravity field of the Earth when the measurements are distributed regularly. The Fourier representation of associated Legendre functions which this procedure makes use of, then enables the harmonic analysis to be transformed to Fourier analysis which has better numerical properties.

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ama na ama uu uu uum n nm uu aum uuaumau n u a, ¶rt;a mu uu an ammu ma. ¶rt;mau n a¶rt; , m unm mm n¶rt;¶rt;, nm nmauu aau naam aau , m a¶rt;am uu uumu mau.

     

The relation between the heat flow field and the distribution ofP n -wave velocities for the European continent

Summary The dependence of P_n-wave velocities on the heat flow, temperature at the crustmantle boundary and the thickness of the Earth's crust in Europe was investigated in relation to the problem of lateral inhomogeneities in the upper mantle. A map was constructed of the distribution of P_n-wave velocities on the territory of Europe. The relations these investigations yielded, were compared with the results of laboratory experiments and all the results are discussed from the physical point of view. The conclusion drawn is that that temperature and pressure effect provide a sufficient explanation of the observed regional changes of P_n-wave velocities for the European continent.

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auum ¶rt;auu mu n¶rt; ¶rt; nmu uua (P_n) u mn nm, mnam a nmu amuu u m a mumuu n a u¶rt;aa u numa ¶rt;¶rt;m amuu. mumuu n a maa a uu m P_n- a nmu uua. u¶rt;u umam ¶rt;a mama aam u¶rt;au uuu m n¶rt; amuu u u ¶rt;au u mnam mmmm mama n¶rt;aa am. ¶rt;a ¶rt;, m ua uu m P_n- a n mum ¶rt;mam um uuu mnam u ¶rt;au a nmu uua.