Small (1--10 km wide) grabens are ubiquitous tectonic structures that have been observed on the surfaces of all the terrestrial planets and satellites. In spite of their frequent occurrence, there is no fundamental understanding of how they form, other than that they are characteric of extensional terranes. This paper examines the mechanics of the initial stages of graben formation and demonstrates that the configuration of a pair of antithetically dipping normal faults (a graben) is the energetically most favorable fault configuration in elastic-brittle rocks subjected to pure extension. A corollary to this hypothesis is that the occurrence of synthetic normal faults is indicative of a stress field other than purely extensional, or of nonhomogeneous characteristics of the rock. The analysis proceeds by computing the stress field in the vicinity of a single initial normal fault using a two-dimensional finite element model. It is shown that slip on this fault substantially lowers the proximity to failure of the surrounding rocks except for two small regions, one near the surface of the downthrown block and the other near the fault tip. The region on the downthrown block is located a horizontal distance from the initial fault slightly less than the fault's depth.

The proximity to failure actually increases here, and a secondary fault develops. An antithetic secondary fault would link this region with the other failure zone near the fault tip. To demonstrate the preference for antithetic secondary faults more rigorously, we show that this fault configuration results in a smaller total strain energy than the synthetic configuration. In addition, a two-layer model is used to show that the graben's width is only weakly dependent upon the presence of mechanically distinct layers in the crust. Both weak-over-strong and strong-over-weak configurations are investigated. The depth of the initial fault and the thickness of the top layer are varied, and the width of the resulting graben is evaluated by computing the distance between the initial fault and the region of highest proximity to failure near the surface. This analysis indicates that the depth of the initial fault is the major factor controlling graben width. ¿ American Geophysical Union 1989