First Determination of Source Parameters of Moderate Earthquakes ( 4 . 1 ≤ M ≤ 5 . 1 ) in Morocco from Spectral Analysis

Recent installation of an array of broad band seismological stations in Morocco allowed us to study the records of five recent (2005-2008) moderate earthquakes (4.1 ≤ M ≤ 5.1) in order to determine their source parameters (seismic moment, fault slip, rupture area and stress drop) from P-wave spectra. We also studied the older Rissani events of 1992 using teleseismic data. Values of Mo, r, Δu and Δσ are, respectively, 1.1 × 1013 6 × 1016 Nm; 0.50 3.9 km; 0.8 5.8 cm and 0.3 1.49 MPa. The results are in accordance with the seismotectonic and geodynamic setting of Morocco as, for instance, the amount of slip along the faults with respect to the relative displacement of Nubia to Iberia (~4 mm∙yr−1) determined from GPS data, taking into account the period of stress accumulation. However, some events show very variable corner frequency and low-frequency amplitude values which lead to considerably higher stress drop and fault slip values, especially at the nearest stations, which may reflect some site effects or uncertainties on depth and take-off angles.


Introduction
Morocco is located at the westernmost extremity of the complex Ibero-Maghrebian area, where the Azores-Gi-braltar fault zone enters the continental lithosphere of the Betics-Rif-Alboran block.Along this boundary, the present-day convergent plate motion of the Nubian plate with respect to Iberia occurs along a NW-SE trend, as shown by plate kinematic, focal mechanism and GPS studies [1]- [11].The amount of convergence is about 4 mm•yr −1 , most of which is accommodated by earthquakes (Figure 1).Within this setting, a remarkable discrepancy is the NE-SW escape of the Central Rif block determined by GPS observations [4] [8] [12]- [14] and faultplane solutions [10] in conformity with geological studies e.g.[14] [15].
Although there is a large dataset on the fault-plane solutions of earthquakes in Morocco (see exhaustive compilation in [24]), little information exists on the other source parameters.The published studies were conducted only on the largest shocks, in particular on the 1994 and 2004 Al Hoceima, and the 1992 Rissani earthquakes, on the base of waveform analysis [4] [21] [25], but no studies based on spectral analysis were carried out, with the exception of that published by Bensaid et al. [26] on the Rissani earthquakes.
Since 2006, numerous broad band stations (BBS) were installed around the western Mediterranean in the context of international cooperation and projects ( [27] [28], Figure 2); these BBS provided high-quality digital data which allowed us to obtain a certain number of spectra, and therefore, to attempt determining the source parameters which have been done for other Mediterranean seismogenic areas from P-waves e.g.[29] [30] and Swaves e.g.[31].
In this paper, we expose the results of the study of the source parameters of 5 moderate shocks that occurred in Morocco during the period 2005-2008 together with two stronger shocks in 1992, corresponding to the Rissani earthquakes.Our leading objective was to attempt to determine the source parameters from these shocks from the P-wave spectra, such as the seismic moment, the fault dimension and displacement, the "stress drop", and to compare the results to available data on the kinematics and seismicity of the Africa-Iberia plate boundary.

Data and Processing
We selected 5 events with magnitude M ≥ 4 that occurred during the period 2005-2008 [10], and the Rissani events, two older shocks with magnitudes M ~ 5.2 which affected the Anti-Atlas area in 1992 [26] (Figure 2 and Table 1).
As exposed in a previous paper [10], the hypocentral relocations were determined using the revised version of the HYPO71 computer program [32], and a standard crustal model for Morocco with Vp/Vs = 1.74 [18].SEED data were read using Rdseed software, and then converted into SAC (Seismic Analysis Code) or ASCII formats.SAC software was used to accomplish all mathematical operations such as Fourier transform, spectral estimation, IIR and FIR filtering, decimation, interpolation correlation, seismic phase picking and graphical output.

Fault-Plane Solutions
Fault-plane solutions based on P-wave arrivals on the recordings of the selected events were already published in previous papers [10] [26].Summarizing, first motions of P-waves were read on available paper records and digital files of permanent and temporary stations.Take-off angles for stations at regional distances (less than 1000 km) were obtained for a crustal model formed by two flat layers (15 km each) with constant velocities 6.1 km•s −1 and 6.7 km•s −1 .The IASPEI model was used for stations at larger distances.Solutions were obtained us-ing the algorithm of Brillinger et al. [33].

P-Wave Spectra
The bulk seismograms were cut at the onset of the P-and S-waves.The mean and the linear tendency were removed in order to centre the signal at zero and to stabilize the numerical operations respectively.Since the signal corresponds to velocity, data were integrated to obtain displacements (Figure 3).Once picked, the seismogram was deconvoluted by the velocity response of the recording instrument.Spectra were obtained from the original digital records using software SAC (Figure 3).Finally, the low-frequency (plateau) part (Ω o ) and the corner frequency f c were automatically obtained from the signal using software KIV, and subsequently the source parameters.
As spectra can be affected by attenuation, we used two to six stations at variable epicentral distances in order to obtain a mean value.

Source Parameters
The source dimensions and scalar seismic moment were determined by spectral analysis using the circular fault model [34] [35], which is the most suitable for small/moderate earthquakes generated along short faults that generally do not crosscut the Earth's surface and do not show a well-defined aftershock pattern [36].
The radiation pattern (R) for each station was computed from the fault-plane solution, and the scalar seismic moment M 0 was estimated using the amplitude spectra of P-waves [37].
( ) ( ) ( ) where ρ is the density, a is the fault radius, r is the distance from the focus to the receiving station, g(∆) is the geometric attenuation, C(i o ) is the effect of free surface on amplitude, Ω o is the spectral amplitude at low frequency of P-wave displacement, ω is the angular frequency, Q is the quality factor of P-wave (taken here as 300) and ( ) is the radiation factor corresponding to the source orientation given by , , φ δ λ , i h where φ is the azimut of the station with respect to the fault, δ is the dip of the fault-plane, λ is the rake and i h is the take-off angle.
The dimension of the rupture (a) was evaluated from the corner frequency (f c ) [37]: where α is the P-wave velocity.
The average displacement and stress drop were estimated from the scalar moment (M 0 ) and dimensions [38]: The stress drop σ ∆ was determined using the equation [34]- [37] [39]: Computations were performed at the Complutense University (Madrid) using softwares KIV and SAC (IRIS [40]) to obtain the spectra of the P-wave, and MOS2 for determining M 0 and source dimensions.The epicentral distance, azimut, and take-off angle were determined with the help of subroutine CASSOL.The radiation pattern R was obtained with MECSTA.The choice of the software was based on its availability at Madrid University and because it is the same than that used by Spanish researchers who have installed the WM network in Morocco.

Focal Mechanisms
The fault-plane solutions and numerical parameters of the studied earthquakes [10] are respectively shown in Figure 4 and Figure 5 and listed in Table 2 respectively.In the central and eastern Rif (solutions 3 and 5), the solutions correspond to either almost-pure normal faulting or to strike-slip faulting with a normal component.The T-axes have an E-W trend.The solutions determined in the Middle Atlas chain and in the Meseta (solutions 4, 6 and 7) show almost-pure reverse faulting in two cases and strike-slip faulting with a normal component in another.In the three cases, the P-axis is oriented NW-SE.Finally, the solutions south of the High Atlas correspond to strike-slip faulting with a NW-SE oriented P-axis.

Source Parameters from P-Wave Spectra
The characteristics of 29 spectra of the studied earthquakes such, as the low-frequency spectral amplitudes and the corner frequencies observed are indicated in Table 3. Selected examples for each event are shown in Figure 6.The source parameters (seismic moment, fault radius, moment magnitude, fault displacement and stress drop) calculated from these data are given in Table 4.For the largest events (#1 and 2), which correspond to the Rissani twin earthquakes of 23 and 30 October 1992, the fault radii are close to 4 km, the displacements are about 4 cm and the stress drops are 0.3 -0.4 MPa.The three smallest events show very similar parameters with fault radii close to 0.6 km, fault displacements of 1.26 to 2.41 cm and stress drops of 0.96 to 2.45 MPa.However, the parameters of the 22 March 2005 event ap- pear to be too high with respect to the other events, certainly because of the small number of available spectra.We also had to remove station M010 from the calculations of the 28 September 2008 source parameters, because it led to too high values.
In contrast, the M ~ 5 event that occurred in the Middle Atlas on 11 August 2007 shows very variable values of fault displacement (0.8 cm at ECEU to 87 cm at IFR) and stress drops (0.52 MPa at ECEU to 63 MPa at IFR), although the fault radii values are homogeneous (0.83 to 0.99 km).Therefore, we recalculated the source parameters shown in Table 4 without taking into account stations IFR and AVE, which provided too large values.

Influence of the Quality of Data and Processing on the Obtained Results
Our study was initially intended to attempt determining the source parameters of the Moroccan moderate events for seismotectonic analysis.However, the results show that the variability of the parameters that lead to them may have a large influence on the obtained values.
First, it appears that the corner frequency values obtained from the spectra are not always homogeneous for the same event, especially at the nearest stations which display large discrepancies, as for instance in the case of stations IFR and AVE for the event recorded on 11 August 2008.This may be due to several parameters such as: 1) Site effects related to the geological composition of the basement, which may also have an influence on the stress drop.
2) Uncertainty on the hypocentral depth (Table 2), which may dramatically influence the estimation of the radiation pattern and subsequent calculations.Such discrepancies may currently be observed even within closely spaced stations, but within 30% of the mean value [41].3) The use of the circular fault model of Brune [34] [35], because we consider that a rectangular fault surface would be more realistic tectonically, but it was impossible to use it because of several parameters such as the small size of the earthquakes, the large depth of some of them and therefore the absence of an aftershock series which could have provided more information on the fault surface.
Therefore, we consider that a more systematic study, using a larger number of stations by event is needed in order to constraint the role of each parameter in the determination of the spectrum.

Seismotectonic Implications and Risk Assessment
As exposed in the first section, the amount of convergence of Nubia to Iberia is about 4 mm•yr −1 in Morocco according to the recent GPS studies [4] [5] [8] [11]- [13].The Rif and High Atlas chains accomodate ~1 mm•yr −1 by earthquakes of low to moderate magnitude (maximum Mw = 6.3 at Al Hoceima in 2004), while the Alboran area, the Mesetas and the Anti Atlas accommodate the remaining.
Our results show that the moderate earthquakes are associated to fault slip values of 1 -4 cm, which may represent 10 to 40 years of stress accumulation at a strain rate of 1 mm•yr −1 or less at a higher strain rate.This may be a suitable explanation for the diffuse distribution of the Moroccan earthquakes, especially in the Atlas chains, where the shocks occur randomly which indicates that stress may be released at different segments.
Another point is that our results can be used for seismic hazard assessment in Morocco, obviously together with other methods such as Coulomb stress; for instance, it appears that for moderate earthquakes (M = 4 -5), stress is released on faults by slip of about 4 mm to 4 cm.Recent GPS monitoring studies show that in several areas in Morocco, the relative motion of fault blocks can be more or less precisely evaluated.This is the case of the SW-displacement of the Rif units onto their foreland, with velocities of 1 -4 mm•yr −1 .If the date of the last significant earthquake in a given area can be known, the magnitude of the next one can be predicted on the base of the time interval.For instance, we can predict that an earthquake of magnitude M = 4 can occur each year in an area showing relative (convergence) velocities of 4 mm•yr −1 , or each two years if it is 2 mm•yr −1 , and that larger ones with M = 5 each 10 years in a 4 mm•yr −1 displacement area, as for instance near the city of Fès [14].

Conclusion
In this paper, we exposed the first results of the use of P-wave spectra obtained from broad band station recordings in Morocco for determining the source parameters of some moderate earthquakes that occurred in the country.The main conclusion is that the spectra can be useful for determining the source parameters, and provide results which are in accordance with the seismotectonic and geodynamic setting of Morocco.For instance, the amount of slip along the faults with respect to the relative displacement of Nubia to Iberia and that of Morocco to Nubia can be evaluated for earthquakes whose faults do not reach the surface.However, some events show very variable corner frequencies and low frequency amplitudes which lead to considerably higher values of source parameters such as stress drop and fault slip, especially at the nearest stations, which may reflect some site effects or uncertainties on depth and take-off angles.Therefore, it appears necessary to increase the number of studied spectra in order to improve the values of the source parameters.

Figure 2 .
Figure 2. Location of the earthquakes (stars) and Moroccan and southern Spanish stations (dots) used in the present study.See Table1for earthquake parameters.

Figure 3 .
Figure 3. P-wave amplitude spectrum at station AVE for the event of 11 January 2008.(a) chosen window in the velocity record; (b) obtained displacement record after removing the instrument effect and integration; (c) amplitude spectrum showing plateau Ω o and corner frequency f c .

Figure 4 .
Figure 4. Location of the fault-plane solutions of the studied earthquakes, after [10].

Figure 5 .
Figure 5. Detailed fault-plane solutions of the studied earthquakes (see Table2for the numerical parameters).Full circles = compression; empty circles = dilatation; squares = direct arrivals; P = pressure axis; T = tension axis; dashed traces in solutions 1 and 2 = solutions given by Harvard.

Figure 6 .
Figure 6.Selected examples of P-wave spectra for the studied earthquakes.

Table 1
for earthquake parameters.

Table 1 .
List of studied earthquakes.

Table 3 .
Spectral characteristics obtained from the stations for each studied earthquakes.R: radiation pattern; Ω o : flat lowfrequency amplitude; fc: corner frequency.

Table 4 .
Spectral characteristics obtained from the stations for each studied earthquakes.R: radiation pattern; Ω o : plateau amplitude; fc: corner frequency.