We define a seismicity model based on (1) the epidemic‐type aftershock sequence model that accounts for earthquake clustering, and (2) a closed slip budget at long timescale. This is achieved by not permitting an earthquake to have a seismic moment greater than the current seismic moment deficit. This causes the Gutenberg–Richter law to be modulated by a smooth upper cutoff, the location of which can be predicted from the model parameters. We investigate the various regimes of this model that more particularly include a regime in which the activity does not die off even with a vanishingly small spontaneous (i.e., background) earthquake rate and one that bears strong statistical similarities with repeating earthquake time series. Finally, this model relates the earthquake rate and the geodetic moment rate and, therefore, allows to make sense of this relationship in terms of fundamental empirical law (the Gutenberg–Richter law, the productivity law, and the Omori law) and physical parameters (seismic coupling, tectonic loading rate).

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