Spatio-temporal slip model

Our method is based on the intuitive assumption that larger slip takes longer time to accumulate. This assumption follows from the well-known linear scaling relation between stress drop and slip velocity, which given that stress drop is basically independent of scalar seismic moment, implies that slip velocity is also essentially constant over the range of seismic moment and may be estimated by assuming regionally appropriate values of rigidity and shear wave velocity.

In practice, a spatially variable slip model is defined by a grid of point sources on a fault plane with rupture duration given by multiple time windows. We use empirical relations to define the average and minimum rise time and assume the scalar seismic moment Mo from seismic or geodetic estimates. The regions with smallest slip take the minimum rise time to finish slipping, while the regions with larger slip require multiple time window based on the ratio of the spatially variable slip to the constant slip velocity. For a given level of slip, a larger assumed stress drop implies that more slip occurs in each of the time windows resulting in a shorter overall duration (Figure 13.40). A circular rupture front initiates at the hypocenter given by seismic estimates and propagates with constant assumed rupture velocity. Slip is triggered when the rupture front reaches each point source and has a duration determined by the number of time windows appropriate for the level of slip at that point.

Figure 13.40: A schematic diagram showing how to determine the number of time windows for a variable-slip model. Left column shows the variable slip model on its rupture plane. White star indicates hypocenter of Northridge event. Two small panels on the right indicate necessary time windows (solid gray triangles) and final rise time curve (thick black) associated with slip patches indicated on slip distribution model.
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