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Efficient and accurate numerical simulation of 3D acoustic wave propagationin heterogeneous media plays an important role in the success of seismic fullwaveform inversion (FWI) problem. In this work, we employed the combined schemeand developed a new explicit compact high-order finite difference scheme tosolve the 3D acoustic wave equation with spatially variable acoustic velocity.The boundary conditions for the second derivatives of spatial variables havebeen derived by using the equation itself and the boundary condition for $u$.Theoretical analysis shows that the new scheme has an accuracy order of$O(\tau^2) + O(h^4)$, where $\tau$ is the time step and $h$ is the grid size.Combined with Richardson extrapolation or Runge-Kutta method, the new methodcan be improved to 4th-order in time. Three numerical experiments are conductedto validate the efficiency and accuracy of the new scheme. The stability of thenew scheme has been proved by an energy method, which shows that the new schemeis conditionally stable with a Courant - Friedrichs - Lewy (CFL) number whichis slightly lower than that of the Pad\'{e} approximation based method.

An Efficient and high accuracy finite-difference scheme for the acoustic wave equation in 3D heterogeneous media