Apparent clustering and apparent background earthquakes biased by undetected seismicity

In models of triggered seismicity and in their estimation from empirical data, the detection threshold m(d) is commonly equated to the magnitude m(0) of the smallest triggering earthquake. This unjustified assumption neglects the possibility of shocks below the detection threshold triggering observable events. We introduce a formalism that distinguishes between the detection threshold md and the minimum triggering earthquake m(0)