The accommodation of large strains in the upper crust is largely achieved by the accumulation of displacement on faults. Observation shows that as a fault accumulates displacement, it grows in size, i.e., its surface area and its length increase. Here we address the question: "For an increase in the amount of displacement on a fault, by how much would the length of the fault change?" It is argued by Cowie and Scholz [1992a] that the displacement on a fault is linearly related to the length of the fault. This simple result is expanded upon in this paper by assuming that a fault accumulates displacement by repeated earthquakes. Two different approaches are presented: The first approach considers the balance that must be achieved between the energy available for deformation and the work involved in creating new fault surface area as the fault grows. The available energy is provided by changes in strain energy when the fault slips. The second approach is to construct a geometrical model for fault growth using the scaling relationship between the slip during a single earthquake and the length of the rupture. The total displacement on a fault is the sum of the slips contributed by many earthquakes. The usefulness of these two approaches is that the growth of a fault over geologic time can be described by parameters that can be obtained from earthquake and fault data. The models presented here predict that (1) the maximum amount a fault can grow in a single earthquake that ruptures the entire fault is of the order of 1 % of its previous length and (2) the work of faulting may account for 10 % of the total energy available during an earthquake. The energy lost from the system is accounted for by work done against friction and seismic radiation. Consequences of fault growth for the segmentation and thus seismogenic potential of a fault over geologic time are discussed using predictions of the theory.
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