Estimating spatiotemporal aggregation scales by revisiting the spatiotemporal L-function

As an important statistical tool for spatial data, the L-function is widely used in the estimation of the spatial aggregation scale. However, for heterogeneous spatiotemporal points, the formulation of the existing spatiotemporal L-function makes it liable to produce poor estimates of spatiotemporal aggregation scales, which is essential in revealing process evolutions, such as spatiotemporal scopes of seismic sequence and spatiotemporal spread extents of an epidemic. This technical note analyzes the mechanism whereby the existing L-function incorrectly estimates the spatiotemporal aggregation scales, and presents a modified spatiotemporal L-function that overcomes these issues. Moreover, a local version of the improved L-function is developed to identify aggregations for validation. The results of simulation experiments and a seismic case study demonstrate that our method estimates the spatiotemporal aggregation scales accurately, which verify the veracity of our corrections to the existing spatiotemporal L-function.