The AMR concept and data

It has been found that an increase in the number of intermediate earthquakes occurs before a large event which produces a regional increase in the cumulative Benioff strain. This cumulative Benioff strain can be fit by a power law time-to-failure relation (Bowman et al., 1998) which has the following form: $\epsilon(t)=A+B(tc-t)^m$

and

$\epsilon(t)=\sum_{i=1}^{N(t)} \sqrt{E_{i}(t)}$

where $\epsilon(t)$ is the Benioff strain, N is the number of earthquakes considered, E is the energy of individual earthquakes, tc is the time of the large earthquake and A is the value of the Benioff strain when t=tc. The energy of each particular seismic event is defined as: log(E)=4.8+1.5Ms

To quantify the AMR, we examine the ratio called c-value between the root-mean-square of a power-law time-to-failure function versus a linear fit to the cumulative energy of events. When the c-value is smaller than 0.7, we may consider a case of AMR. The cumulative Benioff strain is then better fit by a power law than by a linear trend.

In the case of using a circular search area for AMR, several parameters (magnitude range, area surrounding the events, time period prior to large earthquake) are required according to the choice of the mainshock studied and the AMR results depends on them.

We study the seismicity of southern California obtained from the ANSS catalog between 32N and 40N latitude since 1910 with a minimum magnitude 3.5. We extract events for AMR calculations following the systematic approach employed in previous studies. We use Nutcracker, a stress and seismicity analysis software to perform all the AMR calculations.

Berkeley Seismological Laboratory
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