2005PASJ...57..769N

begin{HTML} We calculate cyclotron lines in a neutron star slab assuming a non-dipole surface magnetic field. We consider the influences of a non-dipole surface field on the properties of the cyclotron resonant scattering lines. When the magnetic field strength decreases with height in the line-forming region, the ratios of the higher harmonics to the fundamental at the peak energies of the cyclotron lines become less than classical harmonic ratios, 1 : 2 : 3... . On the other hand, when the magnetic field strength increases with height in the line-forming region, the ratios at the peak energies of the cyclotron lines become more than the classical harmonic ratios. The deviation from the harmonic ratios, which has actually been observed in some accretion-powered X-ray pulsars, is more significant than that expected from a relativistic effect in the cyclotron resonant energy. This may suggest the line-forming region is threaded by a strong non-dipole magnetic field in some accreting X-ray pulsars. In observations, the ratios are more or less than the classical harmonic ratios. This could imply that the magnetic field strength in the line-forming region decreases or increases with the altitude or the horizontal distance from an emission region.