Aftershocks do not uniformly surround a mainshock, and instead occur in spatial clusters. Spatially variable physical properties of the crust may influence the spatial distribution of aftershocks. I study four aftershock sequences in Southern California (1992 Landers, 1999 Hector Mine, 2010 El Mayor—Cucapah, and 2019 Ridgecrest) to investigate which physical properties are spatially correlated with aftershock occurrence. I find that aftershocks correlate with several properties, including measures of stress and stress change from the mainshock, fault structure, kinematics, seismic velocity, and heat flow. Aftershock spatial density exhibits an order of magnitude or more variation as a function of these properties. I determine simple empirical relations between each of the properties and the aftershock spatial density, and use these relations to construct new spatial models that describe aftershock locations. The new spatial models are a significant improvement over a simple base model, but do not fully capture the dense spatial clustering of aftershocks. Numerous spatially varying physical properties exhibit no (or poor) correlation with aftershock spatial density, including temperature, rock composition, and rheological properties that might be expected to control aftershock occurrence. These results suggest that while spatially variable physical properties appear to influence aftershock locations, more work is necessary in order to establish the connections between aftershock occurrence and the causative physical properties.