  The time discretization of stochastic spectral fractional wave equation is
studied by using the difference methods. Firstly, we exploit rectangle formula
to get a low order time discretization, whose the strong convergence order is
smaller than $1$ in the sense of mean-squared $L^2$-norm. Meanwhile, by
modifying the low order method with trapezoidal rule, the convergence rate is
improved at expenses of requiring some extra temporal regularity to the
solution. The modified scheme has superlinear convergence rate under the
mean-squared $L^2$-norm. Several numerical experiments are provided to confirm
the theoretical error estimates.
