Apparent clustering and apparent background earthquakes biased by undetected seismicity

Authors

  • Didier Sornette,

    1. Department of Earth and Space Sciences and Institute of Geophysics and Planetary Physics, University of California, Los Angeles, California, USA
    2. Laboratoire de Physique de la Matière Condensée, CNRS UMR6622, Université de Nice-Sophia Antipolis, Nice, France
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  • Maximillian J. Werner

    1. Department of Earth and Space Sciences and Institute of Geophysics and Planetary Physics, University of California, Los Angeles, California, USA
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Abstract

[1] In models of triggered seismicity and in their estimation from empirical data, the detection threshold md is commonly equated to the magnitude m0 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 m0md. By considering the branching structure of one complete cascade of triggered events, we derive the apparent branching ratio na (which is the apparent fraction of aftershocks in a given catalog) and the apparent background source Sa observed when only the structure above the detection threshold md is known due to the presence of smaller undetected events capable of triggering larger events. If, as several recent analyses have shown, earthquake triggering is controlled in large part by the smallest magnitudes, this implies that previous estimates of the clustering parameters may significantly underestimate the true values: For instance, an observed fraction of 55% of aftershocks is renormalized into a true value of 75% of triggered events.

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