Before revision:  In order to solve the local problems in DAT, we shall propose a compact finite difference scheme with arbitrarily high accuracy order and low numerical dispersion for piecewise smooth coefficients and variable wave numbers.
After revision:  In order to solve the local problems in DAT, we shall propose a compact finite difference method (FDM) with arbitrarily high accuracy order and low numerical dispersion for piecewise smooth coefficients and variable wave numbers.