The occupation of a box as a toy model for the seismic cycle of a fault
Sketch of the box model. Balls are thrown at random until all the cells of the box are full. Then the box is emptied and a new cycle starts.
Discrete distribution function for the duration (in time steps, ) of the seismic cycle in the box model with .
Plot of the number of occupied cells during ten cycles of a box model with .
(a) Fit of the accumulative distribution of the box model to the accumulated histogram of the Parkfield earthquake sequence. (b) Residuals of the fit, evaluated at the midpoints of the horizontal segments of the accumulated histogram.
Yearly probability of the next characteristic earthquake at Parkfield, according to the box model.
(a) Fraction of errors , fraction of alarm time , and loss function as a function of for the forecasting strategy in a box model with . (b) Error diagram for this strategy. Each point on the curve is the result of using a different value of . The large dot corresponds to , for which the loss function reaches a minimum. The diagonal lines are isolines of . A random guessing strategy would render .
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