Physics-based ground-motion simulation requires the development of physically self-consistent source modeling tools to emulate the essential physics of earthquake rupture. Because of the high computational demand of full-dynamic rupture modeling, the kinematic description of earthquake source processes provides the most practical way of covering a wide range of rupture and wave propagation scenarios. We apply 2D spatial data analysis tools, commonly used in geostatistics, to characterizing earthquake rupture process and developing an effective source modeling tool for strong-motion prediction. The earthquake source process is described by key kinematic source parameters, such as static slip, rupture velocity, and slip duration. The heterogeneity of each source parameter is characterized with autocoherence while the linear dependency (coupling) between parameters is characterized with cross coherence. Both zero- and nonzero-offset spatial coherence can be considered in the form of cross coherence. We analyzed both synthetic and real dynamic rupture models to demonstrate the efficiency of these new techniques and found that many important features of earthquake rupture can be captured in this way, which may be difficult to analyze, or even detect by zero-offset coherence only. For instance, the correlation maximum between slip and rupture velocity can be shifted from the zero offset, that is, large slip may generate faster rupture velocity ahead of the current rupture front, which may be important for rupture directivity. We demonstrate that we can generate a number of realizations of earthquake source models to reproduce the target coherence using stochastic modeling techniques (e.g., sequential Gaussian simulation) once coherence structures in earthquake rupture are well understood. This type of coherence analysis may provide the potential for improved understanding of earthquake source characteristics and how they control the characteristics of near-fault strong ground motions.