# Stochastic Modeling of the Al Hoseima (Morocco) Aftershock Sequences of 1994, 2004 and 2016
## 8 Discussion  
In the present study, the stress pattern analysis revealed that all solutions had a maximum compressive horizontal stress (SHmax) between 142\({}^{\circ}\) N and 153\({}^{\circ}\) N, which is compatible with previous regional stress data as determined by previous studies. Furthermore, according to these results, the extension directions are clearly compatible with the Betic-Internal Rif's zone movement southwestward.  
The results for all the seismic sequences share horizontal stresses, showing a NW-SE compression and a NE-SW extension as a result of the regional setting. Nonetheless, some significant differences can be observed in the axial ratios and local stress regimes because of the series location in the main shear zone crossing the Alboran Sea and the activated structures in the main and secondary clusters. The three series induced a different fault system, also hosting seismicity, from which the sequence began.  
Concerning observed differences in the tectonic characteristics of the series, the 1994 sequence is mainly scattered along a NNE-SSW trending cluster over an almost vertical plane [32], the 2004 sequence is mainly scattered along a NE-SW strike slip fault, and the 2016 sequence is initially scattered along a NNE-SSW trending cluster over a subvertical strike-slip fault, then changing to N-S and finally distributed on a second rounded cluster with a dominant reverse focal mechanism solution [26]. The magnitude of completeness values considered in the current study were compared with those derived using Gft and mGft methods.  
Figure 13 shows plots of residuals vs. the minimum magnitudes for the three series. The results obtained matched the estimated values derived using the maximum curvature (Maxc) method. All approaches yield a result of 2.8 for the 1994 series. For the 2004 series,  
Figure 12: Cumulative released energy for the three sequences. Circles: observed values. Lines: mean \(\pm\)\(\sigma\) fitted model. Magnitudes of the events included in the sequences are also depicted. The inset shows the first ten days of the series.  
the difference was of the order of 0.1 using mGft, Gft5% and Maxc and 0.2 between Gft10% and Maxc. However, in the case of the 2016 series, the difference varies between 0.2 and 0.3. The results are 1.9 using Gft10%, 2.2 for Gft5%, 2.3 for mGft and 2.0 for Maxc.  
As discussed in this study, the RETAS model was used to study the gradual decay of the aftershock frequency based on the triggering magnitude \(M_{tr}\) assumption. The minimum value of the AIC parameter was used as a criterion for selecting the best-fit model. All possible models were estimated by varying the triggering magnitude \(M_{tr}\) from the threshold magnitude \(m_{c}\) (ETAS model) or \(m_{ms}\) (MOL model) to the mainshock magnitude. The results derived for the 1994 and 2004 series highlight and improve on the previous ones derived by [88]. For instance, for the 2004 aftershock sequence, as in [88], the minimum AIC value shows results for the best ETAS model. Considering that the 2016 sequence began on January 21 with an event of Mw 5.1, as suggested by some authors [26], the ETAS model was obtained as the best-fit model.  
Stochastic modeling of the energy revealed that the energy released over the series was outlined well by the proposed model in the 1994 and 2004 series. However, there were minor discrepancies in the 2016 sequence and the computed cumulative released energy did not match the model well. We deduced from the analysis that large aftershock clusters occurred more frequently and quickly after the main shock than they would if they occurred at random. This observation holds true for the Zemmouri, Algeria aftershock series of 2003 [88].