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A 3-dimensional calculation of atmospheric neutrinos flux is presented, andthe results are compared with those of a 1-dimensional one. In this study,interaction and propagation of particles is treated in a 3-dimensional wayincluding the curvature of charged particles due to the geomagnetic field,which is assumed to be a dipole field. The purpose of this paper is limited tothe comparison of calculation schemes. The updated flux value with newinteraction model and primary flux model will be reported in a separate paper.  Except for nearly horizontal directions, the flux is very similar to theresult of 1 dimensional calculations. However, for near-horizontal directionsan enhancement of the neutrino flux is seen even at energies as high as 1 GeV.The production height of neutrinos is lower than the prediction by1-dimensional calculation for near-horizontal directions, and is a littlehigher for near-vertical directions. However, the difference is not evidentexcept for near-horizontal directions.Comment: 22 pages, 15figure

Comparison of 3-dimensional and 1-dimensional schemes in the calculation of atmospheric neutrinos