  Long-term hard X-ray monitoring observations on high mass X-ray binary Vela
X-1 from 2003 -- 2011 have been performed by INTEGRAL. I systematically
analyzed the average hard X-ray spectra of Vela X-1 from 3 -- 200 keV, with
main aims to detect cyclotron resonant scattering features and study their
variation patterns with accreting luminosities and orbital phases. The
cyclotron scattering lines of Vela X-1 at $\sim 22 - 27$ keV and $49 - 57$ keV
are confirmed in the average spectra of Vela X-1. But in the flare states with
hard X-ray luminosity higher than $\sim 5\times 10^{36}$ erg s$^{-1}$ (3 -- 100
keV), the fundamental line cannot be detected. This feature suggests that a
fan-like beam radiation pattern is expected in high luminosity ranges of Vela
X-1. Variations of the cyclotron line energies and depths are discovered, which
may change with continuum spectral properties. Both cyclotron line energies
show no correlations with X-ray luminosity. The fundamental line energy shows
no significant correlations with photon index and cutoff energy. While, the
first harmonic energy shows a positive correlation with photon index and
exponential cutoff energy. The energy ratio of two cyclotron lines always
higher than 2 has the weak correlation with photon index and cutoff energy.
These relations support that the X-ray spectral properties of accreting X-ray
pulsars are affected by cyclotron resonance scattering. In the case of Vela
X-1, the broader and deeper first harmonic would play the main role to cause
the spectral variations. The positive correlations between the ratio of line
width to energy and the corresponding depth for both two lines support a
cylindrical column accretion geometry in Vela X-1.
