Spatial aliasing is a vexing issue of numerical analysis. The Kirchhoff codes shown here do not work as expected unless the space mesh size is suitably more refined than the time mesh.
Spatial aliasing means insufficient sampling of the data along the space axis. This difficulty is so universal, that all migration methods must consider it.
Data should be sampled at more than two points per wavelength. Otherwise the wave arrival direction becomes ambiguous. Figure 5 shows synthetic data that is sampled with insufficient density along the x-axis.
Figure 5 Insufficient spatial sampling of synthetic data. To better perceive the ambiguity of arrival angle, view the figures at a grazing angle from the side.
You can see that the problem becomes more acute at high frequencies and steep dips.
There is no generally-accepted, automatic method for migrating spatially aliased data. In such cases, human beings may do better than machines, because of their skill in recognizing true slopes. When the data is adequately sampled however, computer migrations give better results than manual methods.