  The relic gravitational wave (RGW) generated during the inflation depends on
the initial condition via the amplitude, the spectral index $n_t$ and the
running index $\alpha_t$. CMB observations so far have only constrained the
tensor-scalar ratio $r$, but not $n_t$ nor $\alpha_t$. Complementary to this,
the ground-based interferometric detectors working at $\sim 10^2$Hz are able to
constrain the spectral indices that influence the spectrum sensitively at high
frequencies. In this work we give a proper normalization of the analytical
spectrum at the low frequency end, yielding a modification by a factor of $\sim
1/50$ to the previous treatment. We calculate the signal-noise ratios (SNR) for
various ($n_t,\alpha_t$) at fixed $r=0.2$ by S6 of LIGO H-L, and obtain the
observational upper limit on the running index $\alpha_t<0.02093$ (i.e, at a
detection rate $95\%$ and a false alarm rate $5\%$) at the default
$(n_t=0,r=0.2)$. This is consistent with the constraint on the energy density
obtained by LIGO-Virgo Collaboration. Extending to the four correlated
detectors currently running, the calculated SNR improves slightly. When
extending to the six correlated detectors of the second-generation in design,
the calculated SNR is $\sim 10^3$ times over the previous two cases, due to the
high sensitivities. RGW can be directly detected by the six 2nd-generation
detectors for models with $\alpha_t>0.01364$.
