It is very difficult to resolve the oscillation frequencies of slowly pulsating
B-type (SPB) stars by the ground-based observations. Therefor，the research of
slowly pulsating B-type (SPB) stars still at the early stage. And there are many
questions of the stellar interiors. Asteroseismology is a powerful tool for probing
stellar interiors and constraining the relative physical processes. Our goal is to
probing internal structure and physical process of SPB stars by using the method
of astroseismology. At first，this paper introduces the slowly pulsating B-type (SPB) stars，the
theory of stellar oscillation，and the oscillation properties of SPB stars. Then we
take KIC 11971405 as the object of this research, which is a fast rotational SPB
star observed by Kepler satellite. A preliminary asteroseismic analysis was made
by P apics et al. for the SPB star KIC 11971405. And they obtained some fundamental
parameters. Based on their results, we obtain a period series constituted
by 36 modes (l=1,m=0) by using a method of fitting the period spacings with a
linear function. We select the best-fitting model by using the chi-squared method
when doing model fittings in this work. Finally, we find that the frequency and
amplitude of the oscillation pattern in the period spacings determined by the outline
of the element abundances. And our analytic result shows that KIC 11971405
must be a late-type SPB star with a central hydrogen mass fraction Xc < 0.5. In
addition, we conclude that this star has an exponentially decaying core convection
overshooting with parameter fov = [0.014,0.016].
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