Focal mechanism provides a reasonable approximation to an earthquake's rupture mechanics in terms of its fault plane orientation and direction of slip. The first part of this dissertation explores focal mechanism as a means to describe the anisotropic spatial distribution of aftershocks. Based on empirical analysis of aftershock patterns in Southern California seismicity, a spatial distribution for the relative location of aftershocks with respect to mainshock focal mechanism is proposed. When compared to alternative models for aftershock and seismicity patterns, the proposed model appears to offer superior fit to Southern California seismicity.

The second part proposes a general framework for extending space-time earthquake point process models to incorporate focal mechanism data via an anisotropic spatial kernel. Using the proposed model for relative aftershock locations as an example, the effectiveness of using focal mechanism in modeling earthquake occurrences is assessed. In addition, a new residual method is proposed for assessing the relative performance of models to spatial and spatial-temporal point process data. This graphical tool is used to illustrate the advantages and disadvantages of extended ETAS models compared to alternative models and appears quite effective.