Geologists often see the Earth as homogeneous blocks separated by smooth curved boundaries. In contrast, computer modeling algorithms based on finite-difference schemes need to have the elastic constants of the Earth specified at the points of a regular grid. A common way of gridding a geological model is to lay the computer model grid down and use whatever elastic constants lie beneath each grid point. This naive method may result in artifacts; for example, a gently sloping interface will be modeled as a coarse staircase, which generates unwanted diffractions at the stair edges.