The spherical harmonic series expression of electromagnetic fields excited by ELF/SLF vertical electric dipole in the spherical earth-ionosphere cavity is derived when the earth and ionosphere are regarded as non-idea...The spherical harmonic series expression of electromagnetic fields excited by ELF/SLF vertical electric dipole in the spherical earth-ionosphere cavity is derived when the earth and ionosphere are regarded as non-ideal conductors.A method of speeding numerical convergence has been presented.The electromagnetic fields in the cavity are calculated by this algorithm,and the results show that the electromagnetic fields between the earth and the ionosphere are the sum of two traveling waves in the SLF band.Moreover,the results are in complete agreement with that of the well-known spherical second-order approximation in the SLF band.The electromagnetic fields in the cavity are a type of standing wave in the ELF band and the variation of the amplitude versus frequency coincides with Schumann’s resonance.展开更多
Given a continuous boundary value on the boundary of a ＂simply closed surface＂ as that encloses the whole Earth, a regular harmonic fictitious field V＊（P） in the domain outside an inner sphere Ki that lies inside...Given a continuous boundary value on the boundary of a ＂simply closed surface＂ as that encloses the whole Earth, a regular harmonic fictitious field V＊（P） in the domain outside an inner sphere Ki that lies inside the Earth could be determined, and it is proved that V＊（P） coincides with the Earth＇s real field V（P） in the whole domain outside the Earth. Since in the domain outside the inner sphere Ki and the fictitious regular harmonic function V＊（P） could be expressed as a uniformly convergent spherical harmonic series, it is concluded that the Earth＇s potential field could be expressed as a uniformly convergent spherical harmonic expansion series in the whole domain outside the Earth.展开更多
This paper deals with the order of magnitude of the partial sums of the spherical harmonic series and its convergence rate in Bessel potential spaces. The partial results obtained in the paper are the analogue of tho...This paper deals with the order of magnitude of the partial sums of the spherical harmonic series and its convergence rate in Bessel potential spaces. The partial results obtained in the paper are the analogue of those on the circle.展开更多
文摘The spherical harmonic series expression of electromagnetic fields excited by ELF/SLF vertical electric dipole in the spherical earth-ionosphere cavity is derived when the earth and ionosphere are regarded as non-ideal conductors.A method of speeding numerical convergence has been presented.The electromagnetic fields in the cavity are calculated by this algorithm,and the results show that the electromagnetic fields between the earth and the ionosphere are the sum of two traveling waves in the SLF band.Moreover,the results are in complete agreement with that of the well-known spherical second-order approximation in the SLF band.The electromagnetic fields in the cavity are a type of standing wave in the ELF band and the variation of the amplitude versus frequency coincides with Schumann’s resonance.
基金Supported by the National Natural Science Foundation of China （No.40637034, No. 40574004）, the National 863 Program of China （No. 2006AA12Z211）. The author thanks Prof. Dr. Sjoberg for his valuable comments on the original manuscript.
文摘Given a continuous boundary value on the boundary of a ＂simply closed surface＂ as that encloses the whole Earth, a regular harmonic fictitious field V＊（P） in the domain outside an inner sphere Ki that lies inside the Earth could be determined, and it is proved that V＊（P） coincides with the Earth＇s real field V（P） in the whole domain outside the Earth. Since in the domain outside the inner sphere Ki and the fictitious regular harmonic function V＊（P） could be expressed as a uniformly convergent spherical harmonic series, it is concluded that the Earth＇s potential field could be expressed as a uniformly convergent spherical harmonic expansion series in the whole domain outside the Earth.
文摘This paper deals with the order of magnitude of the partial sums of the spherical harmonic series and its convergence rate in Bessel potential spaces. The partial results obtained in the paper are the analogue of those on the circle.
