# Stochastic Modeling of the Al Hoseima (Morocco) Aftershock Sequences of 1994, 2004 and 2016
## 4 Seismic Series Stress Regime  
The IGN database, international agencies and numerous studies aimed at analyzing these seismic series were used to obtain earthquake focal mechanisms for the selected series. Figure 4 shows earthquakes with magnitudes greater than 3.0, from the 1994 Al Hoseima sequence, as well as the focal mechanism of aftershock events computed by [32] (Figure 4A); different solutions for the focal mechanism of the main shock (Figure 4B) from the Global Centroid Moment Tensor (GCMT), International Seismological Centre (ISC); and specific works by [38; 39; 40; 41] (for both a pre-event and the main quake) and [29]. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Sequence** & **n** & **M\({}_{\text{min}}\)** & **m\({}_{\text{c}}\)** & **a \(\pm\)\(\sigma\)** & **b \(\pm\)\(\sigma\)** & **Sequence** \\ \hline
1994 & 263 & 2.0 & 2.8 & 5.05 \(\pm\) 0.02 & 1.01 \(\pm\) 0.07 & 1994 \\
2004 & 969 & 1.5 & 3.4 & 6.56 \(\pm\) 0.02 & 1.14 \(\pm\) 0.05 & 2004 \\
2016 & 2577 & 0.8 & 2.0 & 4.86 \(\pm\) 0.03 & 0.82 \(\pm\) 0.02 & 2016 \\ \hline \end{tabular}
\end{table} 
Table 1: Number of events (n), minimum recorded magnitude (M\({}_{\text{min}}\)), computed threshold magnitude (m\({}_{\text{c}}\)) using the Maxc method and a and b-parameters. Figure 3: Temporal evolution of the studied series (magnitudes above 2.0). Starting of the x-axis does not always correspond to the occurrence of the main event. Figure 5A depicts the distribution of events with magnitudes greater than 3.0, which were included in the 2004 series, as well as the estimated focal mechanisms of the largest events. In addition, Figure 5B shows the earthquakes and computed focal mechanisms of the so-called \"eastern cluster\" from [34]. Figure 6 shows events with magnitudes more than 3.0 as well as estimated focal mechanism solutions for the 2016 Al H  
Figure 4: **(A)** 1994 seismic sequence showing earthquakes with magnitude above 3.0 and computed focal mechanisms for aftershocks [32]. **(B)** Different focal mechanism solutions for the mainquake. GCMT: Global Centroid Moment Tensor; T&al. : [40]; M&R: [38]; ISC: International Seismological Centre; B&B-I and B&B-II: [41], for a pre-event and the main quake, respectively; B&al. : [29]; EA&al. : [32,39]. Figure 5: **(A)** 2004 seismic sequence showing earthquakes with magnitude above 3.0 and computed focal mechanisms for the biggest events. **(B)** Earthquakes with magnitude above 1.0 and focal mechanism solutions for the biggest events (m\({}_{\text{b}}\) 1.9–3.0) of the “eastern cluster” studied by [34]. The stress pattern from the inversion of the available focal mechanism data was used to characterize the three seismic series. It is worth noting that for the inversion process, it was not necessary to select between two available nodal planes. To estimate the different parameters of the reduced stress tensor, we used the improved right dihedron method [42] combined with the iterative rotational dihedron method [43]. Our aim was to calculate the four parameters of the reduced stress tensor, \(\sigma_{1}\), \(\sigma_{2}\), \(\sigma_{3}\) and the stress ratio, \(\text{R}=(\sigma_{2}-\sigma_{3})/(\sigma_{1}-\sigma_{3})\). According to [19], this method allows for estimating previous parameters and the extraction of filtered focal mechanism data by deleting nodal planes that are incompatible with the average stress regime. The compatible focal mechanisms and the calculated stress tensor produced at this point were then employed as the direct starting point for the rotational optimization technique. The iterative grid-search rotational optimization process is based on a controlled grid search of the stress tensor using the Win-TensorTM code to reduce the so-called misfit (F5) [44]. According to [45], the nodal plane best explained by the stress tensor was chosen as the actual fault plane from the two planes of the focal mechanism. Consequently, the final inversion examines the focal planes that a uniform stress field best fits [46].