Urban gravity model based on cross-correlation function and Fourier analyses of spatio-temporal process

This paper is devoted to gaining a new insight into urban physics in the right perspective. The conventional urban gravity model based on Newton's Law of Universal Gravitation is made into a new expression based on a cross-correlation function. Endowed with a time-lag parameter and time functions, the developed model can integrate temporal dimension into spatial process of cities. A pair of gravity spectra can be given for spatial interaction of any two cities with Fourier transform, and the series of attraction quantity are proved to be the average values of interaction volumes from the traditional model. The method is applied to four cities in China, illustrating how to employ the improved model to characterize the spatio-temporal process of urban interaction. The new gravity model reveals the relationship between the concept of energy and the notion of interaction, and suggests asymmetric interaction between cities, commonly observed in the real world.