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Intrinsic and scattering attenuation in the crust of the Abu Dabbab area in the eastern desert of Egypt
Physics of the Earth and Planetary Interiors 168 (2008) 103–112
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Intrinsic and scattering attenuation in the crust of the Abu Dabbab area in the eastern desert of Egypt Ali K. Abdel-Fattah a,∗ , M. Morsy a , Sh. El-Hady a , K.Y. Kim b,∗ , M. Sami a a b
National Research Institute of Astronomy and Geophysics, 11421 Helwan, Cairo, Egypt Department of Geophysics, Kangwon National University, Chuncheon, South Korea
a r t i c l e
i n f o
Article history: Received 13 September 2007 Received in revised form 6 May 2008 Accepted 13 May 2008 Keywords: Abu Dabbab earthquakes Coda wave Attenuation Egypt Single-scattering model
a b s t r a c t Fifty-five microearthquakes recorded by a digital-temporary seismic network in the Abu Dabbab area in the Eastern Desert of Egypt were used to estimate the direct S-wave (Q ), coda (Qc ), intrinsic (Qi ), and scattering quality factors (Qs ). Sato’s [Sato H., 1977] single-scattering assumption was used to fit the amplitude envelopes of the coda at seven central frequency bands (1.5, 3, 6, 9, 12, 18, and 24 Hz), obtaining a Qc varying with frequency as generally observed in tectonically active areas. Lapse time dependence was also studied for the area, with the coda waves analyzed at window lengths ranging from 10 to 40 s starting from the onset of the S-wave arrival. The direct S-wave Q was estimated using the coda normalization method [Aki, K., 1980a]. The frequency dependence of Q was investigated for the direct S-waves and coda waves. Results show a low quality factor and a high frequency parameter, indicating that the upper lithosphere of the Abu Dabbab area is seismically active and heterogeneous. Using the independent estimates of Qc and Q , the intrinsic quality factor Qi was separated from the scattering quality factor. The results suggest that intrinsic dissipation plays a predominant role with respect to scattering phenomena in the area; the obtained Q values seem closer to those reported by analyzing volcano-tectonic earthquakes. This finding reflects that the cause of Abu Dabbab earthquake swarms might be igneous activity where the magma is ascending through joints or serpentinized joints that are dewatering. © 2008 Elsevier B.V. All rights reserved.
1. Introduction Seismic activity in Egypt is attributed to the relative motion between the African, Arabian, and Eurasian plates. The seismicity of Egypt is spatially distributed along different earthquake source regions (Fig. 1). One of these earthquake source regions is Abu Dabbab, 24 km from the western margin of the Red Sea. That area is characterized by microearthquake activity accompanied by earthquake sounds (Morgan et al., 1981). These microearthquakes periodically occur as earthquake swarms. Earthquake swarms generally originate from volcanic, igneous, or tectonic activities. The extremely tight clustering of microearthquakes suggests that the seismicity in this area is not directly related to regional tectonics, and there is no obviously related structural feature (Daggett et al., 1986). In particular, Daggett et al. (1986) referred one possible explanation of the swarm activity to the magma intrusion into the Precambrian crust, but there are no surface occurrences supporting this hypothesis. El-Hady (1993) attributed the swarm activity
∗ Corresponding authors. E-mail addresses: ali [email protected] (A.K. Abdel-Fattah), [email protected] (K.Y. Kim). 0031-9201/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.pepi.2008.05.005
in the Abu Dabbab area to geothermal evolution. He determined the brittle-ductile transition depth in the area to be 9–10 km by the distribution of earthquake focal depths. However, the tectonic and magmatic processes in the area are still not well-known. It is also unclear if magma intrusion into the extensional faulting is temporally coupled or the tectonic and magmatic processes mechanically interact and potentially trigger each other. The magma intrusion in the crust is generally accompanied by high heat flows. The average value of eight heat flow measurements in the Abu Dabbab area is 92 mW/m2 , which is one of the highest values in the Eastern Desert of Egypt (Boulos et al., 1990). The heat anomaly may be derived from deep origins and conducted through fractures in basements. The attenuation of elastic waves depends strongly on temperature. Attenuation is quantified by the quality factor, Q, or internal friction, Q−1 , which typically varies by orders of magnitude between ambient temperature and rock solids (e.g., Kampfmann and Berckhemer, 1985). For shear waves, the quality factor must vanish before the rock liquids are reached. Seismic attenuation is therefore a useful parameter to characterize the physical state of rocks within a volcano, where melt fluids are thought to reside at shallow levels in the Earth’s crust. The attenuation of seismic waves is a complex mechanism controlled by the intrinsic dissipation factor and the scattering
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Fig. 1. Seismicity of Egypt from 1997 to 2007. The dashed square denotes the study area.
attenuation factor (Sato and Fehler, 1998). To estimate separately the amount of scattering and intrinsic losses from seismograms, it is necessary to study simultaneously the S-wave coda, which is generated by scattering processes inside the Earth, and the direct Swave train. Sato (1991) derived an analytic formula, which included multiple scattering of any order in 2D space. Zeng (1991) found an integral solution for the multiple scattering coda excitations in a 3D uniform random medium. Hoshiba (1993) separated the intrinsic from the scattering attenuation parameter using multiple lapse time window analysis (MLTWA) applied to short-period data in Japan. Using Zeng’s (1991) scattering model and the approximation of Abubakirov and Gusev (1990), Wennerberg (1993) introduced a method to estimate intrinsic (Qi ) and scattering quality factors (Qs ) from measurements of the direct S-wave (Q ) and coda wave (Qc ). In 2004, the temporary digital seismographic network was deployed around the Abu Dabbab area. Many earthquakes have been recorded, which provided an opportunity to measure the quality factor. In an attempt to establish the cause of peculiar seismicity in the area, we measured the intrinsic and scattering quality factors from independent estimates of Q and Qc using the approach described by Wennerberg (1993). The Q and Qc were estimated using the coda normalization method (Aki, 1980a) and the singlescattering model (Sato, 1977), respectively.
2. Area of study The study area in the present work is illustrated by the inset square in Fig. 1. The main geological zones by Conoco (1987) are shown in Fig. 2. The Eastern Desert in Egypt consists essentially of a backbone of high and rugged mountains parallel to the Red Sea Coast, and much of the area is covered by Late Proterozoic basement rocks of the Nubian Shield (Said, 1962). The basement rocks of the Eastern Desert of Egypt constitute the Nubian Shield that had been formed in the Arabian Peninsula before the opening of the Red Sea. It is generally accepted that the basement of the Nubian Shield was stabilized during the Pan African progeny around 570 Ma ago (El Gaby et al., 1988). The Precambrian basement complex, comprising about 10% of the total area of the country, is exposed mainly in the Eastern Desert and extends as a belt along the Red Sea Coast for a distance of about 800 km. The evolution of the Nubian Shield has been interpreted in terms of classical geosynclines and mountain-building cycles for many years (Akaad and El Ramly, 1960; Sabet, 1961; El Shazly, 1964). The craton is characterized by igneous and metamorphic rocks including widespread acidic igneous intrusions. With the advent of the concept of plate tectonics, several models were proposed for the development of the Nubian Shield. These models included
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Fig. 2. Geological map of the study area showing various surface faults.
a juxtaposed volcanic arc resulting from the opening and closure of a limited basin (Garson and Shalaby, 1976), development of a rift ocean basin and subsequent phenomena (Church, 1979), and episodic and/or successive evolution of ensimatic island arcs, which were swept and welded together (Gass, 1977). The presence of silica detritus and granite pebbles in the metasediments of the Egyptian basement rocks contrasts with the ensimatic island arc model as a working hypothesis for the evolution of the Nubian
Shield (Hashad and Hassan, 1979). Botros (2002) suggested that the tectonic–magmatic evolution of the belt took place in three stages: namely the island-arc, orogenic, and post-orogenic stage. At the Arabian Red Sea margin, Cenozoic volcanoes are distributed among the outcropping Precambrian crystalline basements (Neumann Van Padang, 1963). Asymmetric distribution of the volcanoes with respect to the rift axis of the Red Sea suggested a possibility of leakage of igneous activity from the rift
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to the Egyptian margin. The Abu Dabbab area is covered by Precambrian basement rocks mainly composed of metasediments (metagreywackes, meta-effusives and siliceous schists), the oldest rocks in the area. These rocks are represented by alternating beds and lenses of quartz-feldspathic paraschists, metasandstone, metagreywacke, and metaconglomerates. Metavolcanic rock occurs as chains of beds, lens-like bodies of metaandesites, metabasalt and metarhyolites. Small intrusions and stock-like bodies of talkcarbonate serpentines and gabbroic rocks cut through these rocks. Gattarian granite bodies display clear cutting contacts with all the above-mentioned rocks followed by prophyritic dolerite dykes traversing the gneiss and cassiterite veins. Tertiary basaltic occurrences are distributed in the area (Meneisy, 1990). The presence of gold mineralization in the area is thought to be related to hydrothermal solutions associated with the emplacement of granite intrusions. The Abu Dabbab area is a part of the Red Sea mountain range (Zaghloul and Ghobrail, 1983). The rock masses in the area have elongated stock-like bodies with rough dissected surfaces. The contacts between the masses are usually accompanied by eruptive and tectonic breccias. Fig. 2 shows the lineaments of the study area located on a satellite image. Lineaments are modified from the geologic map of Egypt (Conoco, 1987). The local trends of major and minor faults and lineation are predominated by two directions; the major trend in the ENE–WSW direction and the minor in the NNW–SSE direction (Fig. 2). The major and minor trends are perpendicular and parallel to the dominant direction of the Red Sea rifting system, respectively. Meshref (1990) reported that no particular local anomalies in gravity and magnetic fields are found around Abu Dabbab, which means that there are no shallow magmatic materials. Considering the metamorphic dehydration of serpentine and the value of heat flow, low normal stresses are expected by enhancing the pore pressure in the lower crust, leading to the possibility of high seismicity. However, the Abu Dabbab area has mostly been characterized by microearthquakes till now, and dehydration of serpentine rocks is commonly associated with large active faults, such as the Motagua fault zone in Guatemala (Plafker, 1976) and along the San Andreas Fault. It is supposed that the presence of serpentine controls movement along the active faults (Allen, 1968). Earthquakes in the Abu Dabbab area have been reported by Morgan et al. (1981) as being accompanied by a sound of distinct rumbling similar to the sound of a distant quarry blast. This sound has been heard by Bedouins for several generations. The area has been monitored during three periods: May/June 1976, October/November 1976 and April/May 1977. During each period, a high rate of earthquake activity was recorded: 10–100 events per day occurred. The yearly rate of seismic activity releases a significant energy equivalent to an earthquake of magnitude 4 (Daggett and Morgan, 1977). The reconnaissance array recording carried out in the area using a relatively large diameter array of 55 km for a period of 16 days during October/November 1976 (Daggett et al., 1980, 1986) shows a clustering of microearthquakes in an area measuring about 50 km2 . 3. Method
is helpful to determine Coda Q from the early coda waves on the records where S-waves and coda waves are incorporated (Steck et al., 1989). This model incorporates the source–receiver offset and allows analysis of the coda starting from the S-wave arrival (NoveloCasanova and Lee, 1991). We used Sato’s formulation (1977) to estimate Qc through measurements of the amplitude decay of coda waves with time. Assuming discrete randomly-distributed heterogeneities and single isotropic scattering, the ratio of the mean energy density of the scattered (Ec ) waves to the primary S-wave energy (Es ) from a point source with short duration u, can be approximated at the frequency f by the square of the amplitude ratio [Ac (t)/As ]2 as Ec (r, t/f ) = Es (r/f )
A (t) 2 c
= n · u · ˇ · K(˛) · e2f (ts −t)/Qc
As
(1)
where r is the distance between the source and the receiver; t is the lapse time from the earthquake origin time; As is the maximum amplitude of the direct S-waves; Ac (t) is the Root Mean Square (RMS) amplitude of the coda around the time t; n is the effective scattering coefficient; ˇ is the S-wave velocity; Qc is the apparent quality factor; K(˛) = (1/˛)ln[(˛ + 1)/(˛ − 1)]; and ˛ = (t − t0 )/(ts − t0 ); with t0 as the origin time and ts the S-wave arrival time. Taking the natural logarithm of both sides and rearranging terms, we obtain:
ln
Ac (t) As
2
· K −1 (˛)
= C(f ) − b · (t − ts )
(2)
Where C(f) = ln(nˇ) is the source factor at frequency f, which for single frequency can be treated as a constant value. If we plot the left-hand side of Eq. (2) versus (t − ts ), a straight line in a leastsquare sense can fit the data with slope b = 2f/Qc , and then, Qc can be directly obtained at each particular frequency. 3.2. Coda normalization method The S-wave attenuation can be estimated using the coda normalization method (Aki, 1980a). The method is based on the experimental observation that the coda shape arises from scattering uniformly distributed in a volume surrounding the source, at least in the range 1–100 km from the source. Interpreting the Scoda as a random superposition of scattered S-waves (Aki, 1980b), the time average square of the S-coda spectral amplitude around a fixed lapse time tc at station j can be written as: −1
|Ac (f, tc )|2 ∝ WiS (f )|NjS (f )|2
e−2ftc ·Qc tcn
(3)
where Ac is the S-coda spectral amplitude at frequency f and fixed lapse time tc ; WiS (f ) is the energy radiation from source i in the same frequency band; |NjS (f )| is the S-wave site amplification factor for −1
site j; n is the geometrical spreading factor; and e−Qc 2ft is the attenuation function where Qc−1 is the S-coda wave attenuation. The square of the direct S-wave spectrum, As (f, t), for the ith source and jth station (at distance rij ) can be written as: WiS (f )
−2frij ·Q −1 /ˇ
For completeness of this paper, we briefly introduce theoretical background although they were appeared in many previous papers including Aki (1980b) and Sato (1977).
|As (f, t)|2 ∝
3.1. Estimate of Coda Q
assumes that the scattering coefficient in the region is constant and the focal mechanisms are random, the normalization of the direct S-wave amplitude to the coda amplitude measured at a fixed time, tc , leads to the elimination of the source and site effects from the
Based on the short recording seismograms that are produced by a local earthquake, Sato’s (1977) single isotropic scattering model
rij2
|NjS (f )|2 e

(4)
where Q−1 is the direct S-wave attenuation. Since the method
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observed spectra of the direct S-waves. On dividing Eq. (4) by Eq. (3) and taking the logarithm at fixed time tc we obtain
ln
rij · |As (f, t)|
|Ac (f, tc )|2
−f · rij + constant = Q (f ) · ˇ
see Aki (1982). 3.3. Separation of intrinsic and scattering quality factors Wennerberg (1993) described the possibility of reinterpreting the measured single-station Qc in terms of multiple scattering. He compared the shape of the coda envelope in the multiple-scattering hypothesis (Zeng, 1991) with the relationship describing the coda shape in the hypothesis of single scattering. It is possible to express the observed value of Qc in terms of intrinsic Qi and scattering Qs as: 1 1 1 − 2ı() = + Qc Qi Qs
(6)
Where 1 − 2ı() is −1/(4.44 + 0.738) with = ωt/Qs ; ω is the angular frequency; and t is the lapse time (the time measured from the earthquake origin time). The total attenuation factor can be expressed as the sum of the intrinsic dissipation factor and the scattering attenuation factor as: 1 1 1 = + QTotal Qi Qs
(6) and (7) as follows (e.g., Del Pezzo et al., 1995; Tselentis, 1998): 1 1 = Qs 2ı()
(5)
Here, the S-coda excitation term represented the coda decay shape as a function of lapse time has written as a constant for a fixed lapse time tc , independent of hypocentral distance. A least-square regression analysis of the left-hand side of Eq. (5) versus the hypocentral distance allows us to estimate Q−1 from the slope. For more details,
(7)
From the measured Q ∼ = QTotal for S-waves and Qc for coda waves as a function of lapse time t, it is possible to estimate easily the intrinsic and scattering attenuation parameters by rewriting Eqs.
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1 1 = Qi 2ı()
1 1 − Q Qc ()
and
1 2ı() − 1 + Q Qc ()
(8)
Estimates of Qi and Qs can be obtained by applying Eq. (8) after changing into ωt/Qs . 4. Data used and analysis To monitor earthquake activity occurring in the Red Sea, a permanent seismic station belonging to the Egyptian Seismographic Network (ESN) was installed in the Abu Dabbab area (25.351◦ N, 34.6238◦ E). This station displays an annual rate of more than 700 microearthquakes triggered in the Abu Dabbab area, Egypt. This led NRIAG to install a telemetric seismological network to gain information about the seismotectonics in the area. This portable network was installed for 6 months beginning in May 2004. Fig. 3 shows the locations of the seismographic network and earthquake epicenters with local magnitude greater than 1.0. The network comprises 11 remote stations: 10 are single component stations, and the other one has three components. Each station is equipped with a velocity-type 1-Hz seismometer (Mark-Product L4C), GPS timing, 16 bit-RD3 digitizer of 100 Sample/s, and VHF radio waves transmitter. The three-component station has 24-bit RD24 digitizer of 100 Sample/s. The array covered an area of about 90 km2 . We used the eleven vertical ground motion components in the present study. The seismograms of the well-located events during the monitored period were investigated to determine whether there were any recording problems such as noise, missed recordings, overlapping of successive earthquakes, or early cutoff of well-developed coda waves. We analyzed 864 microearthquakes and selected 55 for this study. The magnitude of these events ranged from 1.3 to 3.6. The depth range of the earthquakes is 5–15 km and the average hypocentral distance is about 13 km. The data set was selected on
Fig. 3. Locations of earthquakes (empty circles) used in the present study and the digital portable seismic stations (solid triangles).
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Fig. 4. Plot of the event recorded at S03 station 16 km away from the epicenter on 16/08/2004. (a) Unfiltered data trace with coda waves, (b) waveform of the coda (c) displacement amplitudes in the 30 s coda window after application of band-pass filters with bandwidths of 1–2 and 16–32 Hz, respectively, and (d) the RMS amplitude values multiplied K(˛) and their best fits in the selected coda window at central frequencies of 1.5 and 24.0 Hz, respectively. The Qc is determined from the slope of fitting lines.
the following base: (1) signal-to-noise ratio greater than 2 in all the frequency bands greater than 2 for the S and coda windows, and (2) the coda shape of uniform decays. To estimate Qc , four windows of 10, 20, 30, and 40 s started from the lapse time of the S-wave arrival, which is measured from the earthquake origin time, were selected to examine the decay pattern of coda waves in the present study (Fig. 4). However, the coda window can increase or decrease based on the available data set. Signals are filtered by the Butterworth band-pass filter with center frequencies 1.5, 3, 6, 12, 18, and 24 Hz. A bandwidth of f ± f/3 has been used to filter the coda. An increasing frequency band is used for increasing central frequency to avoid ringing and to take constant relative bandwidths to get an equal amount of energy into each band, as suggested by Havskov and Ottemoller (2003). The RMS amplitude of the last 5 s data of the time lapse window is divided by the noise data of the same length before the onset of the P-wave to calculate the signal-to-noise ratio. To estimate Q , the spectral amplitude of S-waves and coda waves can be estimated by selecting two windows over the seismogram: the first one centered over the direct wave arrival time, and the second centered over the coda wave at a fixed lapse time tc to calculate As (f) and Ac (f) of the relationship in Eq. (5). As the first step in processing, the baseline was corrected by subtracting the mean from the raw data in order to remove long-period biases before applying the FFT. Then, the data were corrected for the effect of the instrument response. A width of 5% cosine taper was used for the S-wave. The waveform data analysis was done in the frequency domain in different frequency bands with a bandwidth of f ± f/3 Hz. At each frequency band, As was estimated as the RMS of the amplitude with a window length of 2 s. Then, we normalized As for the average coda amplitude Ac computed at lapse time tc = 8 s. Taking the logarithm of the ratio between As and Ac for all the station-event couples (i, j), Q can be linearly inverted using Eq. (6). Assuming that the signal and noise are statistically inde-
pendent and that the noise is stationary, the noise power spectrum started at a lapse time 2 s before the onset of P wave was subtracted from the spectral amplitudes of the S and coda waves. 5. Results and discussions 5.1. Coda Q In Fig. 4, there is an example of the analysis used to measure Qc in the present article. The Qc was calculated from the slope of linear regression curve of ln((As /Ac (t))2 ·K(˛)) and lapse time. The RMS amplitude of a 1-s window before the P-wave arrival is taken as a correction value of noise background from the RMS amplitude of the coda wave. Sato (1977) introduced the K(˛) factor to incorporate the source–receiver offset in the single-scattering model. This model allows the analysis of coda wave starts after the arrival of the shear wave. In the present study, a series of data windows with a length of 1 s are taken to calculate the RMS amplitude of the window center starting from the direct S-wave arrival. The lapse time was measured from the origin time. The time window is successively moved with 0.5-s increments. To obtain reliable Qc values, the criterion of the correlation coefficient ≥0.65 is applied in fitting the data log to a straight line. Generally, the quality factor increases with frequency (Mitchell, 1981). The obtained values of Qc and Q follow the frequency dependence relationship of the form Q = Qo
f fo
(9)
Where Qo is the quality factor at the reference frequency fo (generally 1 Hz) and is the frequency-dependency coefficient, which is close to 1 and varies from region to region based on heterogeneity of the medium (Aki, 1980a). This relationship indicates that the attenuation of seismic waves, at different distances from the
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Fig. 5. Linear regression of quality factors at the station O for four different coda duration intervals, showing the frequency dependent relationship, Qc = Qo fn as in the Sato’s model (1977).
source, varies with frequencies. Hence, the seismic data are firstly filtered by a Butterworth band-pass filter at central frequencies 1.5, 3, 6, 12, 18, and 24 Hz. Then, the attenuation of coda waves is calculated at each central frequency after band-pass filtering. A regression analysis is carried out on the average Qc values calculated at each central frequency, as shown in Fig. 5, indicating the following frequency dependence of Qc values: Qc = 9 ± 1f1.1±0.03 , Qc = 16 ± 1f1.0±0.03 , Qc = 22 ± 1f0.9±0.03 and Qc = 29 ± 1f0.9±0.04 at 10, 20, 30, and 40 s, respectively. Average values of Qo and frequency parameter are plotted in Fig. 6. Regions of high tectonic and volcanic activities are characterized by low Qc compared to stable regions where Qc is high (Singh and Herrmann, 1983; Paul et al., 2003). On the other hand, the frequency dependence relationship is interpreted as a tectonic parameter. The frequency dependence relationship obtained in this study indicates that the attenuation at higher frequencies is less pronounced than at lower frequency. That is characteristic of tectonically active areas distinguished by complex structures (e.g., Aki, 1980a; Akinci and Eydogan, 1996; Giampiccolo et al., 2002, 2004). As shown in Fig. 6, the trend of average Qo increases with lapse time, while the trend of decreases. This means that the upper lithosphere is tectonically active and more heterogeneous in the Abu Dabbab area. However, the differences in attenuation among the stations are relatively small and probably due to real crustal differences in terms of coda Q. This indicates that the attenuation properties and the scatters in the study area have different patterns. Fig. 7 shows a comparison of the Qo values among the stations. The attenuation at S00, S03, and S08 is higher than those at other stations (S02, S04, S06, S07, and S10). This may be due to differences in heterogeneity at the epicentral area rather than its surroundings. Station S05 is located on the valley deposits and is located far from the heterogeneous area.
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Fig. 6. Average values of Qo and as functions of lapse time. Standard deviations are shown error bars.
Fig. 7. Quality factor Qo with Standard deviation at the seismic stations in the Abu Dabbab for four lapse times.
The values of Qc obtained from this study are compared with those reported in tectonic and volcanic regions of the world (Table 1). From the comparison, we found that in the Abu Dabbab area Qc values are significantly lower than in tectonic areas and are relatively similar to those observed in volcanic regions
Table 1 Frequency dependence of Qc for different tectonic and volcanic areas in the world Zone Deception Island volcano (Antarctica) Southeastern Sicily (Italy) Mt. Etna (Italy) Southeastern Canada Charlevoix Region Anatolian Highlands Granada Basin (Spain) Koyna Region (India)
Q = Qo fn 0.9
20f 48f1.0 29f0.9 126f0.95 91f0.95 51f1.01 75f0.87 96f1.09
Lapse time (s)
Authors
20 20 20 20–40 20–40 30 30 30
Martinez-Arevalo et al. (2003) Giampiccolo et al. (2002) for S1 Sato’s model Del Pezzo et al. (1995) Woodgold (1994) Woodgold (1994) Akinci et al. (1994) Ibanez et al. (1990) Gupta et al. (1998)
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such as Mt. Etna (Del Pezzo et al., 1995) and the Deception Island volcano (Martinez-Arevalo et al., 2003). Wong et al. (2001) have investigated the coda wave attenuation for the Tres Virgenes volcanic area, Baja California Sur, Mexico. They estimated an average Qc = 50 ± 3f0.65±0.2 except the location of a stream production well. They estimated the anomalous low Qc = 4.3 ± 0.6f1.33±0.05 for this location and related it to the presence of a highly conductive body in the crust. In general, Q values are significantly lower for volcanic environments than for tectonic areas. The low value of Qo and a high frequency-dependency coefficient have been suggested to be due to seismic activity and heterogeneities in the upper part of the lithosphere in the brittle-ductile zone, which is the effect of tectonic stress loading in brittle-ductile transition (Aki, 2003). 5.2. Qˇ The quantity in the left-hand side of Eq. (5) estimated for each frequency band is plotted as a function of the hypocentral distance together with the best-fit linear regression (Fig. 8). The resulting slope from the linear least-squares fit of Eq. (5) is equal to f/Q (f)ˇ. Thus, an estimate of Q can be done for different frequency bands, assuming the S-wave velocity is 3.5 km/s. The retrieved values of Q present frequency dependence and are fitted by the following well-known empirical relationship Q = Qo (f/fo ) . The regression has been carried on the Q values calculated at central frequencies 12, 18, and 24 Hz and indicates that the attenuation law of Q is 13 ± 2f0.89±0.04 . The number of data in the low-frequency ranges is smaller than those in the high-frequency ranges. Therefore, in the frequency band lower than 12 Hz the regression line shows a positive gradient leading to negative Q values caused by an insufficient number of data where at short distance stations separation of the S-wave is very difficult.
Fig. 8. Plots of the left-hand side term in Eq. (5) against the hypocentral distance for S-wave amplitudes. The regression lines from the least-squares estimate are drawn with the solid lines.
Table 2 Measures of Qc , Q , Qi and Qs estimated in the present study Frequency (Hz)
Q
Qc (20 s lapse)
1.5 3 6 12 18 24
– – – 134 ± 29 208 ± 41 271 ± 48
32 47 84 170 254 339
± ± ± ± ± ±
11 10 8 15 23 33
Qi
Qs
– – – 161 243 323
– – – 588 1145 1288
The Q values are similar to the Qc values estimated at time window 20 s. The similarity between the Q determined from S-waves and the Qc determined by applying the single-scattering model found in this study has been noted in several other cases (Rautian and Khalturin, 1978; Herrmann, 1980; Aki, 1980a; Roecker et al., 1982; Rovelli, 1982; Campillo et al., 1985; Kvamme and Havskov, 1989; Hatzidimitriou, 1995). Observations of Q measured using shear waves have been shown to be frequency dependent, proportional to f , where is between 0.5 and 0.9 for frequencies between 1 and 30 Hz (Fedotov and Boldyrev, 1969; Aki, 1980b; Console and Rovelli, 1981; Sato, 1990), and the value of 0.89 found for the Abu Dabbab area using vertical component records is in agreement with those reported for Q . 5.3. Intrinsic and scattering Q The separation of intrinsic and scattering effects is based on the independent estimations of the Q coda and of Q for the same set of data. Since we do not have available the Q variation with the travel time, we evaluate the values of coda Q at a lapse time of 20 s and direct Q for events with the same order of the S-wave travel time (less than 10 s in the present study). The results have been interpreted as an average in the volume; thus, small differences between the lapse time used and the longest available travel times would produce second-order effects (e.g., Del Pezzo et al., 1995; Giampiccolo et al., 2004). Results obtained using a multiplescattering model show that intrinsic dissipation is dominant over scattering attenuation in the frequency range analyzed 12–24 Hz. Table 2 lists the measured values of Qi and Qs . Moreover, the results in Fig. 9 shows that Qi is close to Qc for the frequency range ana-
Fig. 9. Pattern of Qi , Qs , Q and Qc with frequency. Standard deviations for Q and Qc values are represented by error bars.
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those measured in several tectonically active and heterogeneous zones. Using the independent estimates of Qc and Q of the same data set, we separated the intrinsic from the scattering attenuation parameter. The results suggest that, in the Abu Dabbab area, intrinsic dissipation plays a predominant role with respect to scattering phenomena. Comparing our results with those obtained worldwide, the pattern of the intrinsic dissipation and scattering attenuation parameter are comparable to the results obtained by analyzing volcano-tectonic earthquakes at Mt. Etna. It is worth stressing that the previous work in the Abu Dabbab area by Ibrahim and Yokoyama (1998) concluded that the origin of the Abu Dabbab earthquake swarms is probably igneous. They estimated the Ishimoto and Iida (1939) m-parameter, which is related to the Gutenberg and Richter (1944) b-parameter by m = b + 1. The relationship between maximum trace amplitude and frequency were discussed for the purpose of studying characteristics of the earthquake swarms. The m-values of the swarms range between 1.9 and 2.5, slightly higher than normal for tectonic earthquakes and smaller than volcanic earthquakes of low frequency content. The m-values observed by Ibrahim and Yokoyama (1998), the continental crustal structure of 33-km thickness derived by (Marzouk, 1988), and the geological settings in the Abu Dabbab area indicate that the swarms are not related to immature volcanic area. Acknowledgments
−1 Fig. 10. Comparison of (a) Qi−1 and (b) Qsc from different regions; Southern California (Jin et al., 1994), Mt. Etna and Granada Basin (Del Pezzo et al., 1995), Western Greece (Tselentis, 1998), Almeria Basin (Pujades et al., 1997), Erzincan Region (Akinci and Eydogan, 2000), Southeastern Sicily (Giampiccolo et al., 2004), NW Himalayas (Mukhopadhyay et al., 2006), and Abu Dabbab area (this study).
lyzed and is in good agreement with theory and observations (e.g., Jin et al., 1994; Akinci et al., 1995; Del Pezzo et al., 1995; Canas et al., 1998; Bianco et al., 2002). Fig. 10a and b show a comparison between Qi and Qs obtained from this study and other areas over the world. The results seem closer to the values obtained by analyzing volcano-tectonic earthquakes at Mt. Etna. 6. Conclusions The seismic attenuation of coda waves and the direct S waves were studied in the Abu Dabbab area, with the purpose of quantifying the amount of intrinsic dissipation and scattering attenuation. The coda Q estimated using the single-scattering model of Sato (1977) exhibits a strong frequency dependence according to the power law Qc = Qo (f/fo ) , with the average around 0.97. This indicates that the attenuation at higher frequencies is less pronounced than at lower frequencies. The analysis of coda waves at different window lengths of lapse time indicates that Qc is time-lapse dependent in the region. In particular, the Qc value increases with the time window length for lapse times ranging from 10 to 40 s. This result may be due to the fact that Qc increases with depth. This pattern may be explained by a decrease in the heterogeneity of the medium with depth increases. The Q has been computed by using the same data set selected for the estimate of Qc . The obtained Q values exhibit frequency dependence with around 0.89. This indicates that the attenuation at higher frequencies is less pronounced than at lower frequencies. The obtained Q seems close to that estimated for coda waves at 20 s of lapse time. The obtained Q values are generally comparable with
Authors acknowledge assistance of the many people at NRIAG who participated in the Abu Dabbab temporal seismic network instrument deployment and preliminary data analyses. We are indebted to Elisabetta Giampiccolo for her comments and revisions, which improved the manuscript. The comments by Prof. George Hellffrich and two anonymous reviewers were very helpful in improving the paper. References Abubakirov, I.R., Gusev, A.A., 1990. Estimation of scattering properties of the lithosphere of Kamchatka based on Monte Carlo simulation of record envelope of a near earthquake. Phys. Earth Planet. Int. 64, 52–67. Allen, C.R., 1968. The tectonic environments of seismically active and inactive areas along the San Andreas fault system. Stanford Univ. Publ. Geol. Sci. 11, 70–80. Akaad, M.K., El Ramly, M.F., 1960. Geological history and classification of the basement rocks of the central Eastern Egypt. Geol. Surv. Egypt Pap. 9, 24. Aki, K., 1980a. Attenuation of shear-waves in the lithosphere for frequencies from 0.05 to 25 Hz. Phys. Earth Planet. Int. 21, 50–60. Aki, K., 1980b. Scattering and attenuation of shear waves in the lithosphere. J. Geophys. Res. 85, 6496–6504. Aki, K., 1982. Scattering and attenuation. Bull. Seismol. Soc. Am. 72, S319–S330. Aki, K., 2003. Seismology of earthquake and volcanic prediction. In: Proceedings of the Seventh Workshop on Non-Linear Dynamics and Earthquake Prediction, The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy, H4.SMR/1519-10. Akinci, A., Del Pezzo, E., Ibanez, J., 1995. Separation of scattering and intrinsic attenuation in Southern Spain and western Anatolia (Turkey). Geophys. J. Int. 121, 337–353. Akinci, A., Eydogan, H., 1996. Frequency-dependent attenuation of S and coda waves in Erzincan (Turkey). Phys. Earth Planet. Int. 97, 109–119. Akinci, A., Eydogan, H., 2000. Scattering and anelastic attenuation of seismic energy in the vicinity of north Anatolian fault zone, eastern Turkey. Phys. Earth Planet. Int. 122, 229–239. Akinci, A., Taktak, A.G., Ergintav, S., 1994. Attenuation of coda waves in Western Anatolia. Phys. Earth Planet. Int. 87, 155–165. Bianco, F., Del Pezzo, E., Castellano, M., Ibanez, J., Di Luccio, F., 2002. Separation of intrinsic and scattering seismic attenuation in the southern Apennine zone. Italy. Geophys. J. Int. 150, 10–22. Botros, N.Sh., 2002. Metallogeny of gold in relation to the evolution of the Nubian Shield in Egypt. Ore Geol. Rev. 19, 137–164. Boulos, F.K., Henin, S.F., El-Sayed, Toppozada, T.R., 1990. Regional earthquakes in Egypt identified during recording aftershocks of 14 November 1981 Aswan earthquake. Ann. Geol. Surv. Egypt 16, 275–280. Campillo, M., Plantet, J.-L., Bouchon, M., 1985. Frequency-dependent attenuation in the crust beneath central France from Lg waves: data analysis and numerical modeling. Bull. Seismol. Soc. Am. 75, 1395–1411.
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Intrinsic and scattering attenuation in the crust of the Abu Dabbab area in the eastern desert of Egypt Ali K. Abdel-Fattah a,∗ , M. Morsy a , Sh. El-Hady a , K.Y. Kim b,∗ , M. Sami a a b
National Research Institute of Astronomy and Geophysics, 11421 Helwan, Cairo, Egypt Department of Geophysics, Kangwon National University, Chuncheon, South Korea
a r t i c l e
i n f o
Article history: Received 13 September 2007 Received in revised form 6 May 2008 Accepted 13 May 2008 Keywords: Abu Dabbab earthquakes Coda wave Attenuation Egypt Single-scattering model
a b s t r a c t Fifty-five microearthquakes recorded by a digital-temporary seismic network in the Abu Dabbab area in the Eastern Desert of Egypt were used to estimate the direct S-wave (Q ), coda (Qc ), intrinsic (Qi ), and scattering quality factors (Qs ). Sato’s [Sato H., 1977] single-scattering assumption was used to fit the amplitude envelopes of the coda at seven central frequency bands (1.5, 3, 6, 9, 12, 18, and 24 Hz), obtaining a Qc varying with frequency as generally observed in tectonically active areas. Lapse time dependence was also studied for the area, with the coda waves analyzed at window lengths ranging from 10 to 40 s starting from the onset of the S-wave arrival. The direct S-wave Q was estimated using the coda normalization method [Aki, K., 1980a]. The frequency dependence of Q was investigated for the direct S-waves and coda waves. Results show a low quality factor and a high frequency parameter, indicating that the upper lithosphere of the Abu Dabbab area is seismically active and heterogeneous. Using the independent estimates of Qc and Q , the intrinsic quality factor Qi was separated from the scattering quality factor. The results suggest that intrinsic dissipation plays a predominant role with respect to scattering phenomena in the area; the obtained Q values seem closer to those reported by analyzing volcano-tectonic earthquakes. This finding reflects that the cause of Abu Dabbab earthquake swarms might be igneous activity where the magma is ascending through joints or serpentinized joints that are dewatering. © 2008 Elsevier B.V. All rights reserved.
1. Introduction Seismic activity in Egypt is attributed to the relative motion between the African, Arabian, and Eurasian plates. The seismicity of Egypt is spatially distributed along different earthquake source regions (Fig. 1). One of these earthquake source regions is Abu Dabbab, 24 km from the western margin of the Red Sea. That area is characterized by microearthquake activity accompanied by earthquake sounds (Morgan et al., 1981). These microearthquakes periodically occur as earthquake swarms. Earthquake swarms generally originate from volcanic, igneous, or tectonic activities. The extremely tight clustering of microearthquakes suggests that the seismicity in this area is not directly related to regional tectonics, and there is no obviously related structural feature (Daggett et al., 1986). In particular, Daggett et al. (1986) referred one possible explanation of the swarm activity to the magma intrusion into the Precambrian crust, but there are no surface occurrences supporting this hypothesis. El-Hady (1993) attributed the swarm activity
∗ Corresponding authors. E-mail addresses: ali [email protected] (A.K. Abdel-Fattah), [email protected] (K.Y. Kim). 0031-9201/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.pepi.2008.05.005
in the Abu Dabbab area to geothermal evolution. He determined the brittle-ductile transition depth in the area to be 9–10 km by the distribution of earthquake focal depths. However, the tectonic and magmatic processes in the area are still not well-known. It is also unclear if magma intrusion into the extensional faulting is temporally coupled or the tectonic and magmatic processes mechanically interact and potentially trigger each other. The magma intrusion in the crust is generally accompanied by high heat flows. The average value of eight heat flow measurements in the Abu Dabbab area is 92 mW/m2 , which is one of the highest values in the Eastern Desert of Egypt (Boulos et al., 1990). The heat anomaly may be derived from deep origins and conducted through fractures in basements. The attenuation of elastic waves depends strongly on temperature. Attenuation is quantified by the quality factor, Q, or internal friction, Q−1 , which typically varies by orders of magnitude between ambient temperature and rock solids (e.g., Kampfmann and Berckhemer, 1985). For shear waves, the quality factor must vanish before the rock liquids are reached. Seismic attenuation is therefore a useful parameter to characterize the physical state of rocks within a volcano, where melt fluids are thought to reside at shallow levels in the Earth’s crust. The attenuation of seismic waves is a complex mechanism controlled by the intrinsic dissipation factor and the scattering
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Fig. 1. Seismicity of Egypt from 1997 to 2007. The dashed square denotes the study area.
attenuation factor (Sato and Fehler, 1998). To estimate separately the amount of scattering and intrinsic losses from seismograms, it is necessary to study simultaneously the S-wave coda, which is generated by scattering processes inside the Earth, and the direct Swave train. Sato (1991) derived an analytic formula, which included multiple scattering of any order in 2D space. Zeng (1991) found an integral solution for the multiple scattering coda excitations in a 3D uniform random medium. Hoshiba (1993) separated the intrinsic from the scattering attenuation parameter using multiple lapse time window analysis (MLTWA) applied to short-period data in Japan. Using Zeng’s (1991) scattering model and the approximation of Abubakirov and Gusev (1990), Wennerberg (1993) introduced a method to estimate intrinsic (Qi ) and scattering quality factors (Qs ) from measurements of the direct S-wave (Q ) and coda wave (Qc ). In 2004, the temporary digital seismographic network was deployed around the Abu Dabbab area. Many earthquakes have been recorded, which provided an opportunity to measure the quality factor. In an attempt to establish the cause of peculiar seismicity in the area, we measured the intrinsic and scattering quality factors from independent estimates of Q and Qc using the approach described by Wennerberg (1993). The Q and Qc were estimated using the coda normalization method (Aki, 1980a) and the singlescattering model (Sato, 1977), respectively.
2. Area of study The study area in the present work is illustrated by the inset square in Fig. 1. The main geological zones by Conoco (1987) are shown in Fig. 2. The Eastern Desert in Egypt consists essentially of a backbone of high and rugged mountains parallel to the Red Sea Coast, and much of the area is covered by Late Proterozoic basement rocks of the Nubian Shield (Said, 1962). The basement rocks of the Eastern Desert of Egypt constitute the Nubian Shield that had been formed in the Arabian Peninsula before the opening of the Red Sea. It is generally accepted that the basement of the Nubian Shield was stabilized during the Pan African progeny around 570 Ma ago (El Gaby et al., 1988). The Precambrian basement complex, comprising about 10% of the total area of the country, is exposed mainly in the Eastern Desert and extends as a belt along the Red Sea Coast for a distance of about 800 km. The evolution of the Nubian Shield has been interpreted in terms of classical geosynclines and mountain-building cycles for many years (Akaad and El Ramly, 1960; Sabet, 1961; El Shazly, 1964). The craton is characterized by igneous and metamorphic rocks including widespread acidic igneous intrusions. With the advent of the concept of plate tectonics, several models were proposed for the development of the Nubian Shield. These models included
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Fig. 2. Geological map of the study area showing various surface faults.
a juxtaposed volcanic arc resulting from the opening and closure of a limited basin (Garson and Shalaby, 1976), development of a rift ocean basin and subsequent phenomena (Church, 1979), and episodic and/or successive evolution of ensimatic island arcs, which were swept and welded together (Gass, 1977). The presence of silica detritus and granite pebbles in the metasediments of the Egyptian basement rocks contrasts with the ensimatic island arc model as a working hypothesis for the evolution of the Nubian
Shield (Hashad and Hassan, 1979). Botros (2002) suggested that the tectonic–magmatic evolution of the belt took place in three stages: namely the island-arc, orogenic, and post-orogenic stage. At the Arabian Red Sea margin, Cenozoic volcanoes are distributed among the outcropping Precambrian crystalline basements (Neumann Van Padang, 1963). Asymmetric distribution of the volcanoes with respect to the rift axis of the Red Sea suggested a possibility of leakage of igneous activity from the rift
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to the Egyptian margin. The Abu Dabbab area is covered by Precambrian basement rocks mainly composed of metasediments (metagreywackes, meta-effusives and siliceous schists), the oldest rocks in the area. These rocks are represented by alternating beds and lenses of quartz-feldspathic paraschists, metasandstone, metagreywacke, and metaconglomerates. Metavolcanic rock occurs as chains of beds, lens-like bodies of metaandesites, metabasalt and metarhyolites. Small intrusions and stock-like bodies of talkcarbonate serpentines and gabbroic rocks cut through these rocks. Gattarian granite bodies display clear cutting contacts with all the above-mentioned rocks followed by prophyritic dolerite dykes traversing the gneiss and cassiterite veins. Tertiary basaltic occurrences are distributed in the area (Meneisy, 1990). The presence of gold mineralization in the area is thought to be related to hydrothermal solutions associated with the emplacement of granite intrusions. The Abu Dabbab area is a part of the Red Sea mountain range (Zaghloul and Ghobrail, 1983). The rock masses in the area have elongated stock-like bodies with rough dissected surfaces. The contacts between the masses are usually accompanied by eruptive and tectonic breccias. Fig. 2 shows the lineaments of the study area located on a satellite image. Lineaments are modified from the geologic map of Egypt (Conoco, 1987). The local trends of major and minor faults and lineation are predominated by two directions; the major trend in the ENE–WSW direction and the minor in the NNW–SSE direction (Fig. 2). The major and minor trends are perpendicular and parallel to the dominant direction of the Red Sea rifting system, respectively. Meshref (1990) reported that no particular local anomalies in gravity and magnetic fields are found around Abu Dabbab, which means that there are no shallow magmatic materials. Considering the metamorphic dehydration of serpentine and the value of heat flow, low normal stresses are expected by enhancing the pore pressure in the lower crust, leading to the possibility of high seismicity. However, the Abu Dabbab area has mostly been characterized by microearthquakes till now, and dehydration of serpentine rocks is commonly associated with large active faults, such as the Motagua fault zone in Guatemala (Plafker, 1976) and along the San Andreas Fault. It is supposed that the presence of serpentine controls movement along the active faults (Allen, 1968). Earthquakes in the Abu Dabbab area have been reported by Morgan et al. (1981) as being accompanied by a sound of distinct rumbling similar to the sound of a distant quarry blast. This sound has been heard by Bedouins for several generations. The area has been monitored during three periods: May/June 1976, October/November 1976 and April/May 1977. During each period, a high rate of earthquake activity was recorded: 10–100 events per day occurred. The yearly rate of seismic activity releases a significant energy equivalent to an earthquake of magnitude 4 (Daggett and Morgan, 1977). The reconnaissance array recording carried out in the area using a relatively large diameter array of 55 km for a period of 16 days during October/November 1976 (Daggett et al., 1980, 1986) shows a clustering of microearthquakes in an area measuring about 50 km2 . 3. Method
is helpful to determine Coda Q from the early coda waves on the records where S-waves and coda waves are incorporated (Steck et al., 1989). This model incorporates the source–receiver offset and allows analysis of the coda starting from the S-wave arrival (NoveloCasanova and Lee, 1991). We used Sato’s formulation (1977) to estimate Qc through measurements of the amplitude decay of coda waves with time. Assuming discrete randomly-distributed heterogeneities and single isotropic scattering, the ratio of the mean energy density of the scattered (Ec ) waves to the primary S-wave energy (Es ) from a point source with short duration u, can be approximated at the frequency f by the square of the amplitude ratio [Ac (t)/As ]2 as Ec (r, t/f ) = Es (r/f )
A (t) 2 c
= n · u · ˇ · K(˛) · e2f (ts −t)/Qc
As
(1)
where r is the distance between the source and the receiver; t is the lapse time from the earthquake origin time; As is the maximum amplitude of the direct S-waves; Ac (t) is the Root Mean Square (RMS) amplitude of the coda around the time t; n is the effective scattering coefficient; ˇ is the S-wave velocity; Qc is the apparent quality factor; K(˛) = (1/˛)ln[(˛ + 1)/(˛ − 1)]; and ˛ = (t − t0 )/(ts − t0 ); with t0 as the origin time and ts the S-wave arrival time. Taking the natural logarithm of both sides and rearranging terms, we obtain:
ln
Ac (t) As
2
· K −1 (˛)
= C(f ) − b · (t − ts )
(2)
Where C(f) = ln(nˇ) is the source factor at frequency f, which for single frequency can be treated as a constant value. If we plot the left-hand side of Eq. (2) versus (t − ts ), a straight line in a leastsquare sense can fit the data with slope b = 2f/Qc , and then, Qc can be directly obtained at each particular frequency. 3.2. Coda normalization method The S-wave attenuation can be estimated using the coda normalization method (Aki, 1980a). The method is based on the experimental observation that the coda shape arises from scattering uniformly distributed in a volume surrounding the source, at least in the range 1–100 km from the source. Interpreting the Scoda as a random superposition of scattered S-waves (Aki, 1980b), the time average square of the S-coda spectral amplitude around a fixed lapse time tc at station j can be written as: −1
|Ac (f, tc )|2 ∝ WiS (f )|NjS (f )|2
e−2ftc ·Qc tcn
(3)
where Ac is the S-coda spectral amplitude at frequency f and fixed lapse time tc ; WiS (f ) is the energy radiation from source i in the same frequency band; |NjS (f )| is the S-wave site amplification factor for −1
site j; n is the geometrical spreading factor; and e−Qc 2ft is the attenuation function where Qc−1 is the S-coda wave attenuation. The square of the direct S-wave spectrum, As (f, t), for the ith source and jth station (at distance rij ) can be written as: WiS (f )
−2frij ·Q −1 /ˇ
For completeness of this paper, we briefly introduce theoretical background although they were appeared in many previous papers including Aki (1980b) and Sato (1977).
|As (f, t)|2 ∝
3.1. Estimate of Coda Q
assumes that the scattering coefficient in the region is constant and the focal mechanisms are random, the normalization of the direct S-wave amplitude to the coda amplitude measured at a fixed time, tc , leads to the elimination of the source and site effects from the
Based on the short recording seismograms that are produced by a local earthquake, Sato’s (1977) single isotropic scattering model
rij2
|NjS (f )|2 e

(4)
where Q−1 is the direct S-wave attenuation. Since the method
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observed spectra of the direct S-waves. On dividing Eq. (4) by Eq. (3) and taking the logarithm at fixed time tc we obtain
ln
rij · |As (f, t)|
|Ac (f, tc )|2
−f · rij + constant = Q (f ) · ˇ
see Aki (1982). 3.3. Separation of intrinsic and scattering quality factors Wennerberg (1993) described the possibility of reinterpreting the measured single-station Qc in terms of multiple scattering. He compared the shape of the coda envelope in the multiple-scattering hypothesis (Zeng, 1991) with the relationship describing the coda shape in the hypothesis of single scattering. It is possible to express the observed value of Qc in terms of intrinsic Qi and scattering Qs as: 1 1 1 − 2ı() = + Qc Qi Qs
(6)
Where 1 − 2ı() is −1/(4.44 + 0.738) with = ωt/Qs ; ω is the angular frequency; and t is the lapse time (the time measured from the earthquake origin time). The total attenuation factor can be expressed as the sum of the intrinsic dissipation factor and the scattering attenuation factor as: 1 1 1 = + QTotal Qi Qs
(6) and (7) as follows (e.g., Del Pezzo et al., 1995; Tselentis, 1998): 1 1 = Qs 2ı()
(5)
Here, the S-coda excitation term represented the coda decay shape as a function of lapse time has written as a constant for a fixed lapse time tc , independent of hypocentral distance. A least-square regression analysis of the left-hand side of Eq. (5) versus the hypocentral distance allows us to estimate Q−1 from the slope. For more details,
(7)
From the measured Q ∼ = QTotal for S-waves and Qc for coda waves as a function of lapse time t, it is possible to estimate easily the intrinsic and scattering attenuation parameters by rewriting Eqs.
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1 1 = Qi 2ı()
1 1 − Q Qc ()
and
1 2ı() − 1 + Q Qc ()
(8)
Estimates of Qi and Qs can be obtained by applying Eq. (8) after changing into ωt/Qs . 4. Data used and analysis To monitor earthquake activity occurring in the Red Sea, a permanent seismic station belonging to the Egyptian Seismographic Network (ESN) was installed in the Abu Dabbab area (25.351◦ N, 34.6238◦ E). This station displays an annual rate of more than 700 microearthquakes triggered in the Abu Dabbab area, Egypt. This led NRIAG to install a telemetric seismological network to gain information about the seismotectonics in the area. This portable network was installed for 6 months beginning in May 2004. Fig. 3 shows the locations of the seismographic network and earthquake epicenters with local magnitude greater than 1.0. The network comprises 11 remote stations: 10 are single component stations, and the other one has three components. Each station is equipped with a velocity-type 1-Hz seismometer (Mark-Product L4C), GPS timing, 16 bit-RD3 digitizer of 100 Sample/s, and VHF radio waves transmitter. The three-component station has 24-bit RD24 digitizer of 100 Sample/s. The array covered an area of about 90 km2 . We used the eleven vertical ground motion components in the present study. The seismograms of the well-located events during the monitored period were investigated to determine whether there were any recording problems such as noise, missed recordings, overlapping of successive earthquakes, or early cutoff of well-developed coda waves. We analyzed 864 microearthquakes and selected 55 for this study. The magnitude of these events ranged from 1.3 to 3.6. The depth range of the earthquakes is 5–15 km and the average hypocentral distance is about 13 km. The data set was selected on
Fig. 3. Locations of earthquakes (empty circles) used in the present study and the digital portable seismic stations (solid triangles).
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Fig. 4. Plot of the event recorded at S03 station 16 km away from the epicenter on 16/08/2004. (a) Unfiltered data trace with coda waves, (b) waveform of the coda (c) displacement amplitudes in the 30 s coda window after application of band-pass filters with bandwidths of 1–2 and 16–32 Hz, respectively, and (d) the RMS amplitude values multiplied K(˛) and their best fits in the selected coda window at central frequencies of 1.5 and 24.0 Hz, respectively. The Qc is determined from the slope of fitting lines.
the following base: (1) signal-to-noise ratio greater than 2 in all the frequency bands greater than 2 for the S and coda windows, and (2) the coda shape of uniform decays. To estimate Qc , four windows of 10, 20, 30, and 40 s started from the lapse time of the S-wave arrival, which is measured from the earthquake origin time, were selected to examine the decay pattern of coda waves in the present study (Fig. 4). However, the coda window can increase or decrease based on the available data set. Signals are filtered by the Butterworth band-pass filter with center frequencies 1.5, 3, 6, 12, 18, and 24 Hz. A bandwidth of f ± f/3 has been used to filter the coda. An increasing frequency band is used for increasing central frequency to avoid ringing and to take constant relative bandwidths to get an equal amount of energy into each band, as suggested by Havskov and Ottemoller (2003). The RMS amplitude of the last 5 s data of the time lapse window is divided by the noise data of the same length before the onset of the P-wave to calculate the signal-to-noise ratio. To estimate Q , the spectral amplitude of S-waves and coda waves can be estimated by selecting two windows over the seismogram: the first one centered over the direct wave arrival time, and the second centered over the coda wave at a fixed lapse time tc to calculate As (f) and Ac (f) of the relationship in Eq. (5). As the first step in processing, the baseline was corrected by subtracting the mean from the raw data in order to remove long-period biases before applying the FFT. Then, the data were corrected for the effect of the instrument response. A width of 5% cosine taper was used for the S-wave. The waveform data analysis was done in the frequency domain in different frequency bands with a bandwidth of f ± f/3 Hz. At each frequency band, As was estimated as the RMS of the amplitude with a window length of 2 s. Then, we normalized As for the average coda amplitude Ac computed at lapse time tc = 8 s. Taking the logarithm of the ratio between As and Ac for all the station-event couples (i, j), Q can be linearly inverted using Eq. (6). Assuming that the signal and noise are statistically inde-
pendent and that the noise is stationary, the noise power spectrum started at a lapse time 2 s before the onset of P wave was subtracted from the spectral amplitudes of the S and coda waves. 5. Results and discussions 5.1. Coda Q In Fig. 4, there is an example of the analysis used to measure Qc in the present article. The Qc was calculated from the slope of linear regression curve of ln((As /Ac (t))2 ·K(˛)) and lapse time. The RMS amplitude of a 1-s window before the P-wave arrival is taken as a correction value of noise background from the RMS amplitude of the coda wave. Sato (1977) introduced the K(˛) factor to incorporate the source–receiver offset in the single-scattering model. This model allows the analysis of coda wave starts after the arrival of the shear wave. In the present study, a series of data windows with a length of 1 s are taken to calculate the RMS amplitude of the window center starting from the direct S-wave arrival. The lapse time was measured from the origin time. The time window is successively moved with 0.5-s increments. To obtain reliable Qc values, the criterion of the correlation coefficient ≥0.65 is applied in fitting the data log to a straight line. Generally, the quality factor increases with frequency (Mitchell, 1981). The obtained values of Qc and Q follow the frequency dependence relationship of the form Q = Qo
f fo
(9)
Where Qo is the quality factor at the reference frequency fo (generally 1 Hz) and is the frequency-dependency coefficient, which is close to 1 and varies from region to region based on heterogeneity of the medium (Aki, 1980a). This relationship indicates that the attenuation of seismic waves, at different distances from the
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Fig. 5. Linear regression of quality factors at the station O for four different coda duration intervals, showing the frequency dependent relationship, Qc = Qo fn as in the Sato’s model (1977).
source, varies with frequencies. Hence, the seismic data are firstly filtered by a Butterworth band-pass filter at central frequencies 1.5, 3, 6, 12, 18, and 24 Hz. Then, the attenuation of coda waves is calculated at each central frequency after band-pass filtering. A regression analysis is carried out on the average Qc values calculated at each central frequency, as shown in Fig. 5, indicating the following frequency dependence of Qc values: Qc = 9 ± 1f1.1±0.03 , Qc = 16 ± 1f1.0±0.03 , Qc = 22 ± 1f0.9±0.03 and Qc = 29 ± 1f0.9±0.04 at 10, 20, 30, and 40 s, respectively. Average values of Qo and frequency parameter are plotted in Fig. 6. Regions of high tectonic and volcanic activities are characterized by low Qc compared to stable regions where Qc is high (Singh and Herrmann, 1983; Paul et al., 2003). On the other hand, the frequency dependence relationship is interpreted as a tectonic parameter. The frequency dependence relationship obtained in this study indicates that the attenuation at higher frequencies is less pronounced than at lower frequency. That is characteristic of tectonically active areas distinguished by complex structures (e.g., Aki, 1980a; Akinci and Eydogan, 1996; Giampiccolo et al., 2002, 2004). As shown in Fig. 6, the trend of average Qo increases with lapse time, while the trend of decreases. This means that the upper lithosphere is tectonically active and more heterogeneous in the Abu Dabbab area. However, the differences in attenuation among the stations are relatively small and probably due to real crustal differences in terms of coda Q. This indicates that the attenuation properties and the scatters in the study area have different patterns. Fig. 7 shows a comparison of the Qo values among the stations. The attenuation at S00, S03, and S08 is higher than those at other stations (S02, S04, S06, S07, and S10). This may be due to differences in heterogeneity at the epicentral area rather than its surroundings. Station S05 is located on the valley deposits and is located far from the heterogeneous area.
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Fig. 6. Average values of Qo and as functions of lapse time. Standard deviations are shown error bars.
Fig. 7. Quality factor Qo with Standard deviation at the seismic stations in the Abu Dabbab for four lapse times.
The values of Qc obtained from this study are compared with those reported in tectonic and volcanic regions of the world (Table 1). From the comparison, we found that in the Abu Dabbab area Qc values are significantly lower than in tectonic areas and are relatively similar to those observed in volcanic regions
Table 1 Frequency dependence of Qc for different tectonic and volcanic areas in the world Zone Deception Island volcano (Antarctica) Southeastern Sicily (Italy) Mt. Etna (Italy) Southeastern Canada Charlevoix Region Anatolian Highlands Granada Basin (Spain) Koyna Region (India)
Q = Qo fn 0.9
20f 48f1.0 29f0.9 126f0.95 91f0.95 51f1.01 75f0.87 96f1.09
Lapse time (s)
Authors
20 20 20 20–40 20–40 30 30 30
Martinez-Arevalo et al. (2003) Giampiccolo et al. (2002) for S1 Sato’s model Del Pezzo et al. (1995) Woodgold (1994) Woodgold (1994) Akinci et al. (1994) Ibanez et al. (1990) Gupta et al. (1998)
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such as Mt. Etna (Del Pezzo et al., 1995) and the Deception Island volcano (Martinez-Arevalo et al., 2003). Wong et al. (2001) have investigated the coda wave attenuation for the Tres Virgenes volcanic area, Baja California Sur, Mexico. They estimated an average Qc = 50 ± 3f0.65±0.2 except the location of a stream production well. They estimated the anomalous low Qc = 4.3 ± 0.6f1.33±0.05 for this location and related it to the presence of a highly conductive body in the crust. In general, Q values are significantly lower for volcanic environments than for tectonic areas. The low value of Qo and a high frequency-dependency coefficient have been suggested to be due to seismic activity and heterogeneities in the upper part of the lithosphere in the brittle-ductile zone, which is the effect of tectonic stress loading in brittle-ductile transition (Aki, 2003). 5.2. Qˇ The quantity in the left-hand side of Eq. (5) estimated for each frequency band is plotted as a function of the hypocentral distance together with the best-fit linear regression (Fig. 8). The resulting slope from the linear least-squares fit of Eq. (5) is equal to f/Q (f)ˇ. Thus, an estimate of Q can be done for different frequency bands, assuming the S-wave velocity is 3.5 km/s. The retrieved values of Q present frequency dependence and are fitted by the following well-known empirical relationship Q = Qo (f/fo ) . The regression has been carried on the Q values calculated at central frequencies 12, 18, and 24 Hz and indicates that the attenuation law of Q is 13 ± 2f0.89±0.04 . The number of data in the low-frequency ranges is smaller than those in the high-frequency ranges. Therefore, in the frequency band lower than 12 Hz the regression line shows a positive gradient leading to negative Q values caused by an insufficient number of data where at short distance stations separation of the S-wave is very difficult.
Fig. 8. Plots of the left-hand side term in Eq. (5) against the hypocentral distance for S-wave amplitudes. The regression lines from the least-squares estimate are drawn with the solid lines.
Table 2 Measures of Qc , Q , Qi and Qs estimated in the present study Frequency (Hz)
Q
Qc (20 s lapse)
1.5 3 6 12 18 24
– – – 134 ± 29 208 ± 41 271 ± 48
32 47 84 170 254 339
± ± ± ± ± ±
11 10 8 15 23 33
Qi
Qs
– – – 161 243 323
– – – 588 1145 1288
The Q values are similar to the Qc values estimated at time window 20 s. The similarity between the Q determined from S-waves and the Qc determined by applying the single-scattering model found in this study has been noted in several other cases (Rautian and Khalturin, 1978; Herrmann, 1980; Aki, 1980a; Roecker et al., 1982; Rovelli, 1982; Campillo et al., 1985; Kvamme and Havskov, 1989; Hatzidimitriou, 1995). Observations of Q measured using shear waves have been shown to be frequency dependent, proportional to f , where is between 0.5 and 0.9 for frequencies between 1 and 30 Hz (Fedotov and Boldyrev, 1969; Aki, 1980b; Console and Rovelli, 1981; Sato, 1990), and the value of 0.89 found for the Abu Dabbab area using vertical component records is in agreement with those reported for Q . 5.3. Intrinsic and scattering Q The separation of intrinsic and scattering effects is based on the independent estimations of the Q coda and of Q for the same set of data. Since we do not have available the Q variation with the travel time, we evaluate the values of coda Q at a lapse time of 20 s and direct Q for events with the same order of the S-wave travel time (less than 10 s in the present study). The results have been interpreted as an average in the volume; thus, small differences between the lapse time used and the longest available travel times would produce second-order effects (e.g., Del Pezzo et al., 1995; Giampiccolo et al., 2004). Results obtained using a multiplescattering model show that intrinsic dissipation is dominant over scattering attenuation in the frequency range analyzed 12–24 Hz. Table 2 lists the measured values of Qi and Qs . Moreover, the results in Fig. 9 shows that Qi is close to Qc for the frequency range ana-
Fig. 9. Pattern of Qi , Qs , Q and Qc with frequency. Standard deviations for Q and Qc values are represented by error bars.
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those measured in several tectonically active and heterogeneous zones. Using the independent estimates of Qc and Q of the same data set, we separated the intrinsic from the scattering attenuation parameter. The results suggest that, in the Abu Dabbab area, intrinsic dissipation plays a predominant role with respect to scattering phenomena. Comparing our results with those obtained worldwide, the pattern of the intrinsic dissipation and scattering attenuation parameter are comparable to the results obtained by analyzing volcano-tectonic earthquakes at Mt. Etna. It is worth stressing that the previous work in the Abu Dabbab area by Ibrahim and Yokoyama (1998) concluded that the origin of the Abu Dabbab earthquake swarms is probably igneous. They estimated the Ishimoto and Iida (1939) m-parameter, which is related to the Gutenberg and Richter (1944) b-parameter by m = b + 1. The relationship between maximum trace amplitude and frequency were discussed for the purpose of studying characteristics of the earthquake swarms. The m-values of the swarms range between 1.9 and 2.5, slightly higher than normal for tectonic earthquakes and smaller than volcanic earthquakes of low frequency content. The m-values observed by Ibrahim and Yokoyama (1998), the continental crustal structure of 33-km thickness derived by (Marzouk, 1988), and the geological settings in the Abu Dabbab area indicate that the swarms are not related to immature volcanic area. Acknowledgments
−1 Fig. 10. Comparison of (a) Qi−1 and (b) Qsc from different regions; Southern California (Jin et al., 1994), Mt. Etna and Granada Basin (Del Pezzo et al., 1995), Western Greece (Tselentis, 1998), Almeria Basin (Pujades et al., 1997), Erzincan Region (Akinci and Eydogan, 2000), Southeastern Sicily (Giampiccolo et al., 2004), NW Himalayas (Mukhopadhyay et al., 2006), and Abu Dabbab area (this study).
lyzed and is in good agreement with theory and observations (e.g., Jin et al., 1994; Akinci et al., 1995; Del Pezzo et al., 1995; Canas et al., 1998; Bianco et al., 2002). Fig. 10a and b show a comparison between Qi and Qs obtained from this study and other areas over the world. The results seem closer to the values obtained by analyzing volcano-tectonic earthquakes at Mt. Etna. 6. Conclusions The seismic attenuation of coda waves and the direct S waves were studied in the Abu Dabbab area, with the purpose of quantifying the amount of intrinsic dissipation and scattering attenuation. The coda Q estimated using the single-scattering model of Sato (1977) exhibits a strong frequency dependence according to the power law Qc = Qo (f/fo ) , with the average around 0.97. This indicates that the attenuation at higher frequencies is less pronounced than at lower frequencies. The analysis of coda waves at different window lengths of lapse time indicates that Qc is time-lapse dependent in the region. In particular, the Qc value increases with the time window length for lapse times ranging from 10 to 40 s. This result may be due to the fact that Qc increases with depth. This pattern may be explained by a decrease in the heterogeneity of the medium with depth increases. The Q has been computed by using the same data set selected for the estimate of Qc . The obtained Q values exhibit frequency dependence with around 0.89. This indicates that the attenuation at higher frequencies is less pronounced than at lower frequencies. The obtained Q seems close to that estimated for coda waves at 20 s of lapse time. The obtained Q values are generally comparable with
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