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.
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 [
Earthquakes in Morocco have shallow foci [
Although there is a large dataset on the fault-plane solutions of earthquakes in Morocco (see exhaustive compilation in [
Since 2006, numerous broad band stations (BBS) were installed around the western Mediterranean in the context of international cooperation and projects ([
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.
We selected 5 events with magnitude M ≥ 4 that occurred during the period 2005-2008 [
As exposed in a previous paper [
Seismicity of northern Morocco and adjacent area for the period 1990-2010, magnitudes > 3.5 (after [10] )
Location of the earthquakes (stars) and Moroccan and southern Spanish stations (dots) used in the present study. See Table 1 for earthquake parameters
. List of studied earthquakes.
Ref | Date (dd/mm/yy) | Time | Latitude | Longitude | Magnitude | Depth in km | Location |
---|---|---|---|---|---|---|---|
1 | 23/10/1992 | 09:11:08 | 31.36 | −4.18 | 5.2 | 2 | Rissani |
2 | 30/10/1992 | 10:43:58 | 31.28 | −4.34 | 5.1 | 2 | Rissani |
3 | 22/03/2005 | 09:03:15 | 35.05 | −2.97 | 4.7 | 5 | Nador |
4 | 11/08/2007 | 20:46:01 | 33.14 | −5.21 | 5.1 | 7 | Khénifra |
5 | 21/01/2008 | 02:24:03 | 35,12 | −3.94 | 4.1 | 8 | Al Hoceima |
6 | 25/01/2008 | 13:19:40 | 33.01 | −5.36 | 4.3 | 6 | Khénifra |
7 | 28/09/2008 | 02:11:21 | 33.59 | −5.89 | 4.5 | 22 | Tiflet |
Data in Standard for Exchange of Earthquake Data (SEED) format (FDSN) were retrieved from files of digital stations located in Morocco (Institut Scientifique, ING-CNRST, Siberia and WM networks), Algeria (GEOFON) and Europe (IGN network and German stations) at various epicentral distances between 43 and 2454 km.
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 based on P-wave arrivals on the recordings of the selected events were already published in previous papers [
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 (
As spectra can be affected by attenuation, we used two to six stations at variable epicentral distances in order to obtain a mean value.
The source dimensions and scalar seismic moment were determined by spectral analysis using the circular fault model [
The radiation pattern (R) for each station was computed from the fault-plane solution, and the scalar seismic moment M0 was estimated using the amplitude spectra of P-waves [
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 Ωo and corner frequency fc
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(io) is the effect of free surface on amplitude, Ωo 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
The dimension of the rupture (a) was evaluated from the corner frequency (fc) [
where α is the P-wave velocity.
The average displacement and stress drop were estimated from the scalar moment (M0) and dimensions [
The stress drop
Computations were performed at the Complutense University (Madrid) using softwares KIV and SAC (IRIS [
The fault-plane solutions and numerical parameters of the studied earthquakes [
Location of the fault-plane solutions of the studied earthquakes, after [10]
Detailed fault-plane solutions of the studied earthquakes (see Table 2 for 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
. Fault-plane solutions of the studied earthquakes, after [10] .
Ref | Date (D/M/Y) | Lat. N Lon. W | M | Depth (km) | Fault planes (˚) (Φ, δ, λ) | P axis (˚) (Tr; pl) | T axis (˚) (Tr; pl) | N | Score (%) |
---|---|---|---|---|---|---|---|---|---|
1 | 23/10/1992 | 31.36˚; 4.18˚ | 5.2 | 2 ± 5.2 | A: 359 ± 9; 71 ± 9; 1 ± 11 B: 89 ± 11; 89 ± 10; −161 ± 9 | 316 ± 10; 14 ± 10 | 223 ± 09; 13 ± 09 | 30 | 97 |
2 | 30/10/1992 | 31.28˚; 4.34˚ | 5.1 | 2 ± 6.0 | A: 9 ± 11; 73 ± 14; 7 ± 11 B: 277 ± 12; 83 ± 10; 163 ± 14 | 324 ± 12; 7 ± 12 | 232 ± 11; 16 ± 12 | 13 | 100 |
3 | 22/03/05 | 35.05˚; 2.97˚ | 4.7 | 5 ± 4 | A: 33 ± 59; 40 ± 38; −44 ± 53 B: 160 ± 35; 63 ± 20; −121 ± 52 | 25 ± 43; 59 ± 45 | 272 ± 37; 13 ± 19 | 29 | 97 |
4 | 11/08/07 | 33.14˚; 5.21˚ | 5.1 | 7 ± 3.7 | A: 14 ± 13; 59 ± 20; −7 ± 35 B: 108 ± 24; 84 ± 29; −149 ± 21 | 336 ± 14; 26 ± 19 | 237 ± 24; 17 ± 31 | 23 | 91 |
5 | 21/01/08 | 35.12˚; 3.94˚ | 4.1 | 8.2 ± 3.0 | A: 200 ± 9; 70 ± 12; −9 ± 20 B: 293 ± 12; 82 ± 19; −159 ± 12 | 158 ± 9; 20 ± 16 | 65 ± 11; 8 ± 15 | 19 | 95 |
6 | 25/01/08 | 33.01˚; 5.36˚ | 4.3 | 5.6 ± 3.5 | A: 80 ± 6; 40 ± 4; 69 ± 13 B: 233 ± 24; 53 ± 4; 107 ± 16 | 335 ± 7; 7 ± 3 | 90 ± 30; 75 ± 10 | 12 | 100 |
7 | 28/09/08 | 33.59˚; 5.89˚ | 4.5 | 21.8 ± 2.7 | A: 80 ± 7; 21 ± 2; 66 ± 8 B: 234 ± 4; 71 ± 2; 99 ± 3 | 331 ± 4; 25 ± 2 | 130 ± 7; 63 ± 2 | 13 | 85 |
The characteristics of 29 spectra of the studied earthquakes such, as the low-frequency spectral amplitudes and the corner frequencies observed are indicated in
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-
. Spectral characteristics obtained from the stations for each studied earthquakes. R: radiation pattern; Ωo: flat low- frequency amplitude; fc: corner frequency.
Ref | Event (dd/mm/yy) | Number of spectra | Stations | Epicentral distance (km) | Take-off angle | R (θ, φ) | Ωo (m) | fc (Hz) | ||
---|---|---|---|---|---|---|---|---|---|---|
1 | 23/10/92 | 4 | FUR AQU WET TAM | 2439 1980 2439 1350 | 32 39 30 42 | 0.595 0.811 0.624 0.638 | 5 × 10−6 1 × 10−5 1 × 10−6 2 × 10−6 | 0.5 0.8 0.6 0.5 | ||
2 | 30/10/92 | 4 | FUR AQU WET TAM | 2294 1980 2454 1357 | 32 33 30 43 | 0.025 0.812 0.040 0.610 | 5 × 10−6 1 × 10−5 3 × 10−6 3 × 10−6 | 0.5 0.6 0.5 0.5 | ||
3 | 22/03/05 | 2 | EALB ECOG | 100 254 | 62 41 | −0.6035 −0.7285 | 1 × 10−6 1 × 10−7 | 4 5 | ||
4 | 11/08/07 | 5 | IFR AVE EALB ECEU EMIJ | 43 206 370 380 383 | 85 42 42 42 42 | −0.3500 0.3700 −0.4100 −0.7500 −0.6900 | 1 × 10−5 1 × 10−5 1 × 10−7 1 × 10−7 2 × 10−7 | 3 2 3 3 3 | ||
5 | 21/01/08 | 6 | M006 M008 M014 M012 M018 IFR | 79 114 134 145 175 211 | 71 61 56 43 43 43 | 0.7619 −0.1388 −0.8301 0.2695 −0.4706 −0.2073 | 1 × 10−7 1 × 10−7 1 × 10−7 1 × 10−7 1 × 10−7 2 × 10−7 | 6 4 6 3 5 3 | ||
6 | 25/01/08 | 4 | M011 M017 M018 IFR | 61 98 109 111 | 75 63 60 59 | −0.37019 −0.75248 0.35968 −0.51466 | 1 × 10−7 1 × 10−7 1 × 10−7 1 × 10−7 | 5 4 5 4 | ||
7 | 28/09/08 | 5 | M010 M018 M006 M019 | 81 133 184 225 | 81 51 51 51 | −0.8458 0.6701 −0.0758 0.6397 | 3 × 10−7 1 × 10−7 1 × 10−8 3 × 10−8 | 6 6 3 4 | ||
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
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 (
Selected examples of P-wave spectra for the studied earthquakes
. Spectral characteristics obtained from the stations for each studied earthquakes. R: radiation pattern; Ωo: plateau amplitude; fc: corner frequency.
Ref | Event | Mean M0 (Nm) | Mean r (km) | Mw | N | Δu (cm) | (MPa) |
---|---|---|---|---|---|---|---|
1 | 23/10/92 | 6.03 ± 3.03 × 1016 | 3.90 ± 0.70 | 5.1 | 4 | 4.00 ± 2.10 | 0.4 ± 0.20 |
2 | 30/10/92 | 5.07 ± 2.28 × 1016 | 3.70 ± 0.60 | 5.0 | 4 | 3.70 ± 1.85 | 0.3 ± 0.16 |
3 | 22/03/05 | 1.1 ± 0.6 × 1015 | 0.50 ± 0.00 | 4.00 | 2 | 4.31 ± 2.38 | 3.8 ± 0.00 |
4 | 11/08/07 | 5.8 ± 4.6 × 1015 | 0.88 ± 0.07 | 5.00 | 3 | 5.80 ± 4.80 | 1.30 ± 0.57 |
5 | 21/01/08 | 9.1 ± 0.88 × 1014 | 0.60 ± 0.26 | 3.90 | 6 | 2.04 ± 1.13 | 1.49 ± 0.62 |
6 | 25/01/08 | 4.3 ± 0.22 × 1014 | 0.59 ± 0.05 | 3.70 | 4 | 1.26 ± 0.63 | 0.96 ± 0.51 |
7 | 28/09/08 | 2.6 ± 0.73 × 1014 | 0.62 ± 0.16 | 3.74 | 3 | 0.80 ± 0.44 | 0.70 ± 0.50 |
3) The use of the circular fault model of Brune [
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.
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 [
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 [
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.
This study has been partially supported by the Universidad Complutense de Madrid, project AE1/09-16586 to I. Bensaid. We are deeply grateful to Professor Elisa Buforn (Universidad Complutense, Madrid) for having provided the calculation programs and receiving I.B. for numerous training stays. We also thank Professors Mimoun Harnafi (IS Rabat) for providing part of the data used in this work, and Taj-Eddine Cherkaoui for allowing us to publish his seismic maps.