This study investigates the accuracy of a density-tapering approach for modeling the seismic response of free-surface topography on a fourth-order staggered finite-difference grid. The accuracy of the boundary condition near the free-surface and at-depth is rigorously tested in 2D where noise artifacts are identified and characterized. This technique is then modified using spatial density filters, to reduce the noise artifacts while retaining the accuracy, stability, and computational efficiency of the original algorithm. The modified density- tapering boundary condition is accurate down to 15 points per wavelength (PPW) with noise levels below 5% in almost all instances. This multi-step technique adjusts only the material properties near the taper zone allowing it to remain a preprocessing technique, applied prior to the finite-difference calculation.