Solutions to heterogeneous media wave propagation problems are often computed using numerical methods. The accuracy of such solutions is affected not only by spatial and temporal discretization errors but also by errors associated with the source injection schemes, absorbing boundary conditions, and approximations to the heterogeneous media. This paper presents a methodology for estimating order-of-accuracy (OOA) for the overall numerical simulator. As the discretization intervals in space and time decrease, the solution computed using a consistent scheme approaches the analytic solution ever more closely. The methodology shows whether this, in fact, happens, and if so, the rate of convergence. The paradigm for estimating accuracy is based on an analytic Taylor series expansion of the exact solution. Since the analytic solution is not known, a reference solution computed using a fine grid is chosen as the benchmark against which coarser solutions are compared. The order-of-accuracy of a Lax–Wendroff finite difference scheme illustrates the method. Starting with the Taylor series paradigm, a numerical estimate of OOA is formulated using an errorenergyratio. While the underlying Lax–Wendroff difference scheme is second-order accurate in a homogeneous material, the numerical estimate of OOA for scattering from an ice edge shows that the convergence is superlinear, though not quadratic. The short fall in rate of convergence is attributed to heterogeneity, absorbing boundaries, added dissipation near internal boundaries, and source injection errors.