Directional variation in distance decay

Given that geographers excel at measuring and explaining spatial variations in attributes, it is surprising that they are not more aware that relationships may vary over space. It is still normal practice, for example, to estimate a set of parameters in a model and to assume that the relationships represented by these values apply equally to all locations and in all directions. Recently, however, there have been several applications of Casetti's expansion method that have been focused on measuring anisotropic trends around locations. Here this technique is used to examine possible anisotropy in distance-decay relationships around origins. The authors attempt to answer the question: does the rate of distance decay vary with direction? The conclusions reached in previous research on this topic are only partially supported here. Via US migration data it is suggested that it is impossible to identify any overall trend across origins in directional variability. -from Authors