## 2 Methods
### Event Coincidence Analysis  
In ECA [1], two event time-series labeled by \(A\) and \(B\) defined as two ordered event sets with timings \(\{t_{1}^{A},t_{2}^{A},\ldots,t_{N_{A}}^{A}\}\) and \(\{t_{1}^{B},t_{2}^{B},\ldots,t_{N_{B}}^{B}\}\), respectively, are considered. Thus, there are \(N_{A}\) events of type A and \(N_{B}\) events of type B that cover the time interval \([t_{0},t_{f}]\), such that \(t_{0}\leq t_{1}^{A},t_{1}^{B}\) and \(t_{f}\geq t_{N_{A}}^{A},t_{N_{B}}^{B}\). ECA is based on counting (possibly lagged) coincidences between events of the two different types but it should be stressed that B type events are considered as possibly influencing the timings of A type events, and not vice versa [1; 3]. The assumption to be quantified and tested by ECA is that the events of B precede the events of A. This is made by introducing an instantaneous coincidence if two events with timings \(t_{i}^{A}\) and \(t_{j}^{B}\) (\(t_{i}^{A}\geq t_{j}^{B}\)) are closer in time than a coincidence interval \(\Delta T\), that means \(t_{i}^{A}-t_{j}^{B}\leq\Delta T\), and generalizing it to a lagged coincidence if  
\[(t_{i}^{A}-\tau)-t_{j}^{B}\leq\Delta T, \tag{5}\]  
holds, where \(\tau\geq 0\) is the time lag parameter. For the quantification of the strength of the interrelations between the two event series, two variants of the coincidence rate addressing B type events as either precursors or trigger have been introduced [1]: The precursor coincidence rate  
\[r_{p}(\Delta T,\tau)=\frac{1}{N_{A}}\sum_{i=1}^{N_{A}}\Theta\left[\sum_{j=1}^ {N_{B}}1_{[0,\Delta T]}(t_{i}^{A}-\tau-t_{j}^{B})\right], \tag{6}\]  
where \(\Theta(x)\) is the Heaviside unit step function (equal to 0 for \(x\leq 0\) and 1 for \(x>0\)) and \(1_{I}(x)\) is the indicator function for the interval \(I\) (equal to 1 for \(x\in I\), and 0 otherwise), which measures the fraction of A type events that are preceded at least by one B type event (i.e., multiple B type events within \(\Delta T\) are counted once) and the trigger coincidence rate  
\[r_{t}(\Delta T,\tau)=\frac{1}{N_{B}}\sum_{j=1}^{N_{B}}\Theta\left[\sum_{i=1}^ {N_{A}}1_{[0,\Delta T]}(t_{i}^{A}-\tau-t_{j}^{B})\right], \tag{7}\]  
which measures the fraction of B type events that are followed by at least one A type event (i.e., multiple A type events within \(\Delta T\) are counted once). The distinction between precursor and trigger coincidence rates allows the introduction of a notion of directionality while the parameter \(\tau\) explicitly takes into account lagged interrelations between B type and A type events. Based on appropriate assumptions for example for the inter-event time distributions [1] various statistical tests can be made to examine whether B type events are precursors to A type events for a risk enhancement test [4] or whether B type events are triggers for A type events trigger test [4]. Typical examples are the climate-related disasters as risk enhancement factor for armed conflicts in ethnically fractionalized countries [4] or the role of flood events as triggers of epidemic outbreaks [1]. Here, we made use of the CC.eca.es function of the CoinCalc package [3] for R [67] that implements ECA and compared against the (default) Poisson test, though it is well known that EQs appear in sequences in view of aftershocks (cf. CC.eca.es function allows two additional tests called \"shuffle\" and \"surrogate\". For the first case, the significance test is based on an empirical cumulative distribution function of the coincidence ratesestimated by a large number of randomly shuffled time series having the same number of events like the original time series--thus numerically simulating a Poisson process--whereas for the second case, the significance test is based on a similar calculation for a large number of surrogate time series having the same waiting time distributions as the original data).