  In this paper, we consider the development and analysis of a new explicit
compact high-order finite difference scheme for acoustic wave equation
formulated in divergence form, which is widely used to describe seismic wave
propagation through a heterogeneous media with variable media density and
acoustic velocity. The new scheme is compact and of fourth-order accuracy in
space and second-order accuracy in time. The compactness of the scheme is
obtained by the so-called combined finite difference method, which utilizes the
boundary values of the spatial derivatives and those boundary values are
obtained by one-sided finite difference approximation. An empirical stability
analysis has been conducted to obtain the Currant-Friedrichs-Lewy (CFL)
condition, which confirmed the conditional stability of the new scheme. Four
numerical examples have been conducted to validate the convergence and
effectiveness of the new scheme. The application of the new scheme to a
realistic wave propagation problem with Perfect Matched Layer boundary
condition is also validated in this paper as well.
