# Stochastic Modeling of the Al Hoseima (Morocco) Aftershock Sequences of 1994, 2004 and 2016
## 1 Introduction  
Seismic events can be classified into three main types based on their distribution over time [1]: (1) mainshock followed by a number of aftershocks decreasing in frequency, (2) slow build-up of seismicity leading to a type (1) sequence and (3) gradual increase and decay of seismicity without a distinct mainshock (seismic swarm), which occurs in areas with complex tectonic structures.  
The decrease in aftershock occurrences caused by a strong earthquake can be studied using a wide range of methods, according to [2]. The Omori law model is the most typically adopted model [3], which [4] adapted into the modified Omori formula (MOF) by assuming that the fluctuation of the stress field of the mainshock initiates all the events in the sequence.  
The trigger events are conditionally independent and follow a non-stationary stochastic Poisson process. Considering the complex behavior of some earthquake series, particularly in the presence of secondary events, [5] introduced the epidemic type aftershocksequence (ETAS) model, by increasing the capacity to generate secondary events for each event in the sequence. There are several triggering models between these two limit situations: the MOF and ETAS models being two of them [6; 7]. The RETAS model [8] was developed by applying the principle of Bath's law [9; 10] to the subsequences caused by principal events, such as the mainshock. It is worth mentioning that the magnitude difference between the mainshock and the strongest aftershock is commonly considered to be constant, ranging between 1.2 and 1.4 on average, depending on the criterion [11], although with a lot of variability between individual aftershock sequences [12].  
In this study, we focus on three sequences of type (1) designated as the aftershock sequences of Al H conceima 1994, 2004 and 2016, occurring near the city of Al H conceima, in Morocco (Figures 1 and 2). The multifractal properties of these sequences have already been investigated in the framework of the spatial modeling of many seismic series in the Ibero-Maghrebian region [13]; however, even more temporal, energy and stress evaluations are required. Therefore, this study aims to examine three aftershock series using stochastic modeling.  
Figure 1: Geologic sketch map of the Betic-Rif region and location of the Al H conceima study area. Bk: Bokoya Massif; Ra: Ras Afrou; Rt Tas Tarf; Tf: Tres Forcas Cape. Internal Zone includes Sebtides and Ghomarides in the Rif and Nevado-Filabrides, Alpujarrides and Malaguides in the Betics.  
This contribution includes the first section, which describes the regional geological context. In the second section, as suggested by [14], the three aftershock sequences are analyzed, and the stress regime in each series is comprehensively described. The Gutenberg-Richter relationship analysis, performed in a later section, attempts to derive reliable threshold magnitude values and \(b\)-value estimates for each sequence. A stochastic point process modeling analysis was performed in the previous two sections. As described previously, the aftershock decay rate was comprehensively studied using the RETAS model. The identified best-fit model was then integrated into a stochastic analysis of strain release. A comparison between the real values of the cumulative energy release and the expected modeled values is also examined and addressed.