Today, full wavefield seismic imaging and full waveform inversion require the efficient and accurate numerical simulation of seismic waves through complex earth models. For this purpose higher-order Finite- difference (FD) methods are widely applied where the wave equation is discretized in both space and time. In this work we analyze the performance of a higher order accurate staggered Finite-Difference Time Domain (FDTD) method, in which the Adams-Bashforth third-order (M=3) and fourth-order (M=4) accurate time integrators are used for temporal discretization. The analysis shows that the numerical dispersion is much lower than that of the widely used second-order leapfrog method. Numerical dissipation is introduced by the ABS method which is significantly smaller for the ABS method of fourth-order accuracy. The ABS method does not require much additional floating point operations but the additional storage of M-1 perviously calculated time-levels of spatial derivative wave fields. In different simulation experiments we verify the convincing improvements of simulation accuracy of the fourth-order ABS method by comparisons with anal ... mehrytical solutions. We found that the ABS-method is straightforward to implement in 3-D elastic FDTD simulation codes. 3-D elastic numerical experiments confirm the improved efficiency of the new higher order ABS-FDTD method.