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Figure 1. a) Seismicity in a regional box of size
10o latitude by 10o longitude
centered on Los Angeles, CA (Figure 1a). Large red circles represent
earthquakes having magnitudes M>6.9. Smaller blue circles
are earthquakes with M>5.9. b) The timeseries of
earthquakes in that region since 1970, having magnitudes M
> 3.29. Blue curve is the exponential moving average (EMA)
with number of weights N = 36 [1]. c) Time series for the
mean number \(\mu(t)\) of small earthquakes as a function of time. The
mean is taken beginning in 1960, and is also shown since 1970. d)
Optimized state variable timeseries \(\Theta(t)\). State variable is the
EMA average of the small earthquakes, then adjusted using the current
mean number \(\mu(2022)\)of small earthquakes, using a constant of
proportionality \(\lambda\). e) The N -value and \(\lambda\)-value
are obtained by optimizing the ROC skill, which is shown as the total
area under the red curve. Skill for the random time series is shown as
the area under the diagonal line, thus random skill = 0.5.