Scattering and intrinsic attenuation in Cairo metropolitan areausing genetic algorithm

Mohamed F. Abdelwahed a,c, Ali K. Abdel-Fattah b,c,n

a King Abdulaziz University, Geohazards Research Center, Jeddah, Saudi Arabiab King Saud University, College of Science, Geology and Geophysics Department, Riyadh, Saudi Arabiac National Research Institute of Astronomy and Geophysics (NRIAG), 11421 Cairo, Egypt

a r t i c l e i n f o

Article history:Received 16 February 2014Received in revised form8 September 2014Accepted 25 October 2014

Keywords:Intrinsic absorptionScattering attenuationMLTW analysisCoda wavesGenetic algorithmGreater CairoEgypt

a b s t r a c t

A total number of 46 local earthquakes (2.0rMLr4.0) recorded in the period 2000–2011 by the Egyptianseismographic network (ENSN) were used to estimate the total (Qt

�1), intrinsic (Qi�1) and scattering

attenuation (Qsc�1) in Cairo metropolitan area, Egypt. The multiple lapse time window analysis (MLTWA)

under the assumption of multiple isotropic scattering with uniform distribution of scatters was firstlyapplied to estimate the pair of Le

�1, the extinction length inverse, and B0, the seismic albedo, in the frequencyrange 3–24 Hz. To take into account the effect of a depth-dependent earth model, the obtained values of B0and Le

�1 were corrected for an earth structure characterized by a transparent upper mantle and aheterogeneous crust. The estimated values of Qt

�1, Qsc�1 and Qi

�1 exhibited frequency dependences. Theaverage frequency-dependent relationships of attenuation characteristics estimated for the region are foundto be: Qt

�1¼(0.01570.008)f (�1.0270.02), Qsc�1¼(0.00670.001)f (�1.0170.02), and Qi

�1¼(0.00970.008)f (�1.0370.02); showing a predominance of intrinsic absorption over scattering attenuation. This findingimplies that the pore-fluid contents may have great effect on the attenuation mechanism in the upper crustwhere the River Nile is passing through the study area. The obtained results are comparable with thoseobtained in other tectonic regions.

& 2014 Elsevier Ltd. All rights reserved.

1. Introduction

The seismic wave attenuation, described by the quality factor Q,is one of the basic physical parameters used in seismologicaland earthquake engineering studies. It is a complex mechanismwhich depends on the intrinsic attenuation due to the medium anelasticity and the scattering attenuation associated with the hetero-geneities. Because of the combination of both mechanisms, codawaves are generated on the seismic waves traveling through theEarth medium.

The knowledge of the relative contributions of intrinsic (Qi�1)

and scattering (Qsc�1) attenuation is important for the appropriate

subsurface structure, tectonic interpretations and quantification ofthe ground motion (e.g. [28,8,19,11,12]). Therefore, quantifying therelative contribution of scattering and intrinsic attenuation hasbeen the subject of considerable interest among seismologists inthe past few decades and different methods have been developed(e.g., [7,48,24,32,27,38,47]). The Multiple Lapse Time WindowAnalysis (MLTWA), as proposed by Hoshiba et al. [32], is the most

common method used to separate intrinsic absorption from thescattering attenuation. The MLTWA method gives informationabout the temporal change of seismic energy during a wave'spropagation by considering the integral of the signal energycalculated in three successive time windows along the coda wavesof local earthquakes as a function of the hypocentral distance. Theintegrals of energy are evaluated on the basis of the radiativetransfer theory applied to elastic waves [41]. The attenuationproperties of (Qsc

�1) and (Qi�1) affect the distribution of the energy

within the seismic record. The wave scattering appears where theenergy accumulates directly after the direct S-wave or in the codawaves based on the effect of scattering heterogeneities along thepath between earthquake sources and recorded seismic stations.The intrinsic absorption (Qi

�1), however, produces a linear decayon the logarithm of the seismic wave field energy with distanceindependent on the coordinates. Therefore, the study of theenergy decay for each window versus hypocentral distance pro-vides an ideal framework that allows separating the influence ofeach attenuation parameter [14]. The theoretical model of seismicenergy propagation is proposed earlier by Hoshiba et al. [32]. Themodel describes the propagation of seismic waves in a half-spacemedium, heterogeneous, and isotropic. The MLTWA technique hasbeen widely applied to several areas in the world (e.g.[35,28,8,40,9,12,44,13]).

Contents lists available at ScienceDirect

journal homepage: www.elsevier.com/locate/soildyn

Soil Dynamics and Earthquake Engineering

http://dx.doi.org/10.1016/j.soildyn.2014.10.0200267-7261/& 2014 Elsevier Ltd. All rights reserved.

n Corresponding author at: King Saud University, College of Science, Geology andGeophysics Department, Riyadh, Saudi Arabia.

E-mail addresses: aabdelfattah@ksu.edu.sa,ali_kamel@yahoo.co.uk (A.K. Abdel-Fattah).

Soil Dynamics and Earthquake Engineering 69 (2015) 93–102

Under the assumptions of multiple and isotropic scattering anduniform distribution of scatters, two parameters are calculated toevaluate scattering and intrinsic attenuation in the medium: theseismic albedo (B0), defined as the dimensionless ratio of thescattering loss to total attenuation (B0¼QSC

�1/Qt�1), and the extinc-

tion length (Le�1) that is the inverse of the distance (in kilometers)over which the primary S-wave energy is decreased by e�1. Severalauthors have solved the multi-parameterization problem byemploying a systematic grid search scheme (e.g. [31,26,13,43,25]).B0 ranges between 0 and 1 and was proposed by Wu [49] todescribe the proportions of energy loss dominated by intrinsicattenuation (B0o0.5) or scattering attenuation (B040.5).

Estimates of the Qi�1 and QSC

�1 are biased when the realisticEarth structure is far from being uniform. To overcome thedifficulty in analytical expressing the equations describing theseismic signal energy envelope for a realistic velocity model,Hoshiba [29,30], Hoshiba et al. [31] and Bianco et al. [13] usednumerical simulations of the radiative transfer equation in realisticearth media with velocity increasing and scattering coefficientdecreasing with depth. Their solutions implicitly show how largeis the bias associated with the estimates obtained in the uniformmodel assumption. Recently, Del Pezzo and Bianco [17] calculatedcorrections to be applied to the estimates obtained on the uniformassumption to reduce these biases. These corrections have beenobtained for a realistic earth model composed by an inhomoge-neous crust overlying a transparent mantle, with the velocityincreasing with depth. Applying these corrections, the scatteringproperties of the lithosphere in terms of separated Qi

�1 and QSC�1

can be routinely obtained in realistic assumptions, and manyalready existing data can be reinterpreted by applying thiscorrection [18].

Due to the importance of the respective region from seismologi-cal point of view, detailed information related to the attenuationmechanism and its behavior is required. For this purpose, we appliedthe MLTWA technique [32] to accurately quantify the separateamount of scattering (Qsc

�1) and intrinsic absorption (Qi�1) in

different frequency ranges. This method gives information aboutthe temporal change of seismic energy during a wave's propagationby considering the energy in multiple consecutive time windows as afunction of the hypocentral distance. The present study of coda waveattenuation in Cairo zone will enhance our knowledge about theattenuation characterization of seismic waves which is an importantcomponent of seismic hazard assessment in the study region. So far,few studies have investigated the attenuation properties of the coda-Q and S-wave attenuation in the region of interest (e.g., [21,1]).El-Hadidy et al. [21] estimated the frequency dependant coda waveattenuation structure in the frequency band of 1.5–18 Hz for theshallow crust, in terms of coda wave Q and proposed a regionalattenuation law as Qc¼85.66f 0.79. Abdel-Fattah [1] studied theattenuation of body waves in the crust beneath the vicinity of CairoMetropolitan area (Egypt), using the coda normalization technique toband passed filtered seismograms of frequencies ranging from 3.0 to24 Hz, in which the analysis showed a strong frequency dependencefor both body and shear waves. The estimated quality factor of P-wave Qα

�1 ranged from 10.7�10�4 to 72.9�10�4, while the S-wavequality factor Qβ

�1 ranged from 4.3�10�4 to 28.6�10�4. Thesevalues follow the frequency-dependent attenuation; Qα

�1¼(1972)�10�3f�0.870.1 and Qβ

�1¼(771)�10�3f�0.8570.1. He alsoconcluded that, the attenuation at higher frequencies is less pro-nounced than at lower frequencies and related this argument to thegeological conditions of the studied area, which is tectonicallycomplex with a high density of faults and pore fluids are alsoexpected. The detailed properties of the scattering and intrinsicattenuation in this region are not well known. The aim of this paperis to estimate the scattering (Qsc

�1) and intrinsic (Qi�1), attenuation

mechanisms in greater Cairo using the MLTWAmethod by proposing

an algorithm based on genetic algorithmmethod constrained with F-test distribution for the slandered division in the calculations.

For this end, the estimates will be discussed and compared withprevious results obtained in the different tectonic areas over the worldwhich would suggest a broader knowledge for further researches onthe attenuation properties in Cairo metropolitan region.

2. Geologic and tectonic settings

Geographically, Cairo is situated on the Nile upstream of theRiver's Delta, about 250 km from the Mediterranean coastline anddownstream of the Aswan dam. From the viewpoint of geology,the area under study is located in the alluvial valley of the Nile.The Nile Valley is underlain by alluvial deposits consisting mainlyof sand and gravel silt with interbedded silt and clay sedimentswhich cover the whole area of thevalley as well as the northernparts of the cultivated lands of northern Egypt. However, thecrustal structure is rather heterogeneous and changes abruptlyfrom area to area, especially near the Nile Valley. Within the NileValley graben, loose water-saturated sedimentsoccupy the Nileflood plain region, including Cairo, and the desert fringes. How-ever, its thickness and water saturation decreases rapidly in bothdirections away from the graben ([22]). Consequently, the geolo-gical and morphological settingsof the upper crustin the regioncould bring a remarkable increasein the intrinsic effects on thepropagation of seismic waves.

Tectonically, the present-day seismic deformation in northernEgypt, where the study area is located, is attributed to the collisionbetween the African and Eurasian plates and the rifting along theRed Sea (Fig. 1). In addition, the Sinai sub-plate, local tectonicstructures of the Gulf of Suez and the Nile River has a key role in thedeformation process affecting the main tectonic regime in the studyarea. The recent geodetic data and GPS measurements imply thatthe African plate is moving NW with respect to Eurasia with avelocity of 6 mm/year [36] and the spreading rates along the RedSea decrease from 14 mm/year at 151N to 5.6 mm/year at 271N.Along the southernmost segment of Aqaba-Dead Sea fault, motionis a left-lateral strike-slip of 5.6 mm/year [37]. This left-lateralmotion shows a rate of about 2.8 mm/year at the northern segmentof the Dead Sea with slight spreading of the Suez rift [46]. Owing tothe complex tectonic, the region of northern Egypt and itssurroundings are geologically characterized by lateral heterogene-ities in crustal structures. For instance, the crustal thickness beneaththe Eastern Mediterranean varies from oceanic to continental. In thevicinity of the study area, the shear wave velocity, sedimentthickness and Moho depth derived from the dispersion curves ofsurface waves [20] showed lateral crustal heterogeneities. Theauthors concluded that the observed low velocities in the uppermantle of the Northern Africa that spanned to Crete might be anindication of serpentinized mantle from the subducting Africanlithosphere. On the other hand, the stretching and opening of theRed Sea could be the cause of the crustal faults and fractureswidespread along the study area. The crustal structure studies showthe presence of oceanic crust in the northern part of the Red Seaalong the Egyptian coastline ([34]). Meshref [39] reported that thecrust towards the respective area is continental, with a relativelysimple structure consisting of a sedimentary layer of 3 km withvelocity of 3.5 km/s, overlying a 30 km thickness of crust havingmoderate velocity changes from 6.0 to 6.35 km/s. The regionalattenuation tomography results [10] are also showing a lateralvariation east of the study area, indicating a possible change inthe crustal characteristics that are consistent with the residualgravity anomalies obtained by Seber et al. [42].

M.F. Abdelwahed, A.K. Abdel-Fattah / Soil Dynamics and Earthquake Engineering 69 (2015) 93–10294

3. MLTWA technique

The separation of intrinsic absorption and scattering attenua-tion in greater Cairo were obtained using the MLTWA method[32]. The MLTWA method analyzes the seismic time traces takinginto account that their characteristics strongly depend on Qsc

�1

and Qi�1 (e.g., [27,23,28,41]). In order to separate the intrinsic

absorption from the scattering attenuation, three consecutivetime windows are defined on the seismogram. The windowlength is chosen to be 15 s starting from the S-wave onset. Thefirst window mainly contains the contribution of the direct S-wave energy, while the other two windows mainly contain thecontribution of the scattered energy. The attenuation properties(Qsc

�1, Qi�1) affect the distribution of the energy within the three

windows with respect to the hypocentral distance. In particular,when scattering is weak most of the energy is concentrated in thefirst window. As scattering increases, more energy is accumu-lated in the second and third windows. The ratio at which theenergy should increase for the second and third window forthe different distances strongly depends on the value of Qsc

�1. Theintrinsic absorption (Qi

�1) produces a linear decay on the loga-rithm of the seismic wave field energy with distance independenton the coordinates. Therefore, the study of the energy decay foreach window versus hypocentral distance provides an idealframework that allows separating the influence of each attenua-tion parameter [14]. In this study, the integrated seismic energyfor the three windows was calculated by measuring the rootmean square (RMS) amplitudes over band pass filtered seismo-grams. Each integral was normalized to correct for the different

sources and site amplifications:

Eobsiðf ; rmÞ ¼eiðf ; rmÞ

Ecodaðf ; tref Þ; i¼ 1;2;3 ð1Þ

where Ecoda(f,tref)is the observed coda energy at the reference time trefselected at a lapse time of at least twice the S-wave travel time of thefarthermost distance (�45 s from origin time), ei(f,rm) is the RMSamplitude calculated as a function of frequency f and distance rmintegrated for the three consecutive time windows, and Eobsi(f,rm)represents the normalized observed seismic energy for the centralfrequency f and the ith time window [28]. Finally, the correction forthe geometrical spreading was performed by multiplying the inte-grated energy with the factor 4πr2. Under the assumption of multipleisotropic scattering and uniform distribution of scatters, the theore-tical curves of the energy density at a given lapse time andhypocentral distance, as described by Del Pezzo and Bianco [17],are expressed as:

Eðr; tÞffiE0expð�vtLe�1Þ

4πvr2δ t� r

v

h i

þE0H t� rv

h i 1� r2

v2t2

� �1=8

4πvt3Le � 1B0

� �3=2 exp �vtLe�1

h iG vtLe

�1B0 1� r2

v2t2

� �3=4" #

ð2Þ

GðxÞ ¼ exffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ2:026=x

pð3Þ

where E0 is the total incident wave energy, v the S-wave velocity, H isthe heaviside function, t is the travel time, r is the hypocentral

Fig. 1. Tectonic boundaries of the Eastern Mediterranean Region. Seismicity data (2oMbo6.8) was compiled after ENSN and NEIC from 1997 to 2007. The followingAcronyms represent: AEG-Aegean Sea; CY-Cyprus; ERA-Eratosthenes Seamount; FL-Florence; HER-Herodotus Basin, IB-Ionian Basin; MR-Mediterranean Ridge; LEV-Levantine Basin; LF-Levant Fault. Diamonds indicate the localities of Beni Suef and Cairo cities, after Abou Elenean and Hussein [5]. The studied area is enclosed by Yellowshadow square. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

M.F. Abdelwahed, A.K. Abdel-Fattah / Soil Dynamics and Earthquake Engineering 69 (2015) 93–102 95

distance. The estimation of the best-fit Le�1 and B0 was performed byusing the misfit function between observed data and model byHoshiba [27]:

MfitðLe�1; B0Þ ¼ ∑n

r ¼ 1∑3

w ¼ 1

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiEobsðr; twÞ�Eðr; twÞ½ �2

q=N ð4Þ

where Eobs(r,tw) are the energies measured from the observed data, asa function of the distance r and time window tw, E(r,tw) are thetheoretical ones and N is the total number of correlated points. Theminimum of the function Mfit(Le�1, B0) corresponds to the bestestimate of parameters Le�1 and B0 the sense of a global optimizationmethod. In the present study, we used the SGRAPH program [4] toperform the MLTW analysis using genetic algorithm. From the bestLe�1 and B0 values, the scattering Qsc

�1, intrinsic Qi�1, and total values Qt

were estimated by using the following relations:

Qsc�1 ¼ ðB0Le

�1Þ v2πf

;

Qi�1 ¼ ðLe�1�B0Le

�1Þ v2πf

;

Q �1t ¼ Qsc

�1þQi�1 ð5Þ

4. Data use and analysis

Local earthquakes recorded by the Egyptian National Seismo-graphic Network (ENSN) in the period from 2000 to 2013 were usedin this study. The ENSN includes over 69 signal-to-three componentseismographs operated by the National Research Institute ofAstronomy and Geophysics (NRIAG) since 1997. ENSN includesvelocity type short period 1-Hz seismometer and STS2 broadbandseismometers equipped with a 24-bit digitizer that provides a132 dB dynamic range. The data has been digitized with a samplingrate of 100 Hz. The arrival time data and the hypocentral para-meters are routinely reported by the ENSN operators.

The seismograms of the well-located events during the period2000–2013 were investigated to determine whether there were anyrecording problems such as noise, missed recordings, overlapping ofsuccessive earthquakes, or early cut-off of well-developed codawaves. About 46 well-recorded events were used having magnituderanges from M2.0 to M4.0 keeping good signal-to-noise ratio. The

analysis was preformed for the hypocentral distance ranges from 5 to90 km and focal depth ranges from 18 to 22 km as determined byAbdel-Fattah et al. [2] using the HypoDD algorithm. The data set usedin the present analysis was selected on the basis of (1) signal to noiseratio, at all the frequency bands for all successive windows, has to begreater than two for S-waves, and (2) the coda shape has to decayuniformly. The hypocental locations of the earthquakes and seismicstations used in the present study are shown in Fig. 2. A total numberof 280 vertical component seismograms were processed to obtainthe energy as a function of hypocentral distance for three successivewindows (W1,W2, andW3) with 15 s length starting at lapse times of0, 15, and 30 s from the S-wave arrival for W1, W2, and W3,respectively. The trend and mean values were removed and a 5%cosine taper was applied to each end of the time series before band-pass filtered at six central frequencies 3, 6, 9, 12, 18, and 24 Hz withbandwidth of 2, 4, 6, 8, 12, and 16 Hz, respectively. Further, theseismic energy for the three windows (W1, W2, and W3) wascalculated by integrating the squared amplitudes over time for thefiltered seismograms. A reference window (Wref) was also assigned aswell as a 5-s timewindow taken at a lapse time of 45 s from the origin

Fig. 2. Map showing the study area and geographical distribution of stations andepicenters. Triangles and stars denote the stations and earthquakes used in thepresent study, respectively. The inset area is marked with a red rectangle in theoverlaid map. (For interpretation of the references to color in this figure legend, thereader is referred to the web version of this article.)

Fig. 3. Screenshot of the MLTWA windowing procedure in the SGRAPH program [4] used in this study. Origin time (O.T.) is shown as the blue aligned lines. W1, W2, W3, andreference windows (Wref) are also shown in the figure. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of thisarticle.)

M.F. Abdelwahed, A.K. Abdel-Fattah / Soil Dynamics and Earthquake Engineering 69 (2015) 93–10296

time which is about twice the S-wave travel time of the fartherdistance (�90 km). The average shear-wave velocity is taken as3.45 km/s. The energy calculated was then normalized to correct theeffect of the earthquake source and site effects, as described in Eq. (1).This normalization is possible assuming that the coda waves areindependent on the source, site, and path effects [6,23,35]. Thenormalized energy was then corrected for the geometrical spreadingby multiplying with 4πr2 and fitted with theoretical seismic energies(Eq. 2) by using the genetic algorithm [15]. For each frequency band,the genetic algorithm with 500 generations, 4 populations anduniform crossover was performed. The search space is 0.001–0.1 forLe�1 parameter and 0.01–1.0 for the B0 parameter. We searched for the

minimum value of misfit function (Eq. (4)) in the grid of possiblevalues of the parameters B0 and Le

�1, corresponding to the bestsolution. Fig. 3 shows a typical screenshot of MLTWAwindows settingin the SGRAPH program [4] used in this study.

5. Results

Fig. 4 shows the best-fit curves of the observed and calculatedseismic energies at each frequency band, as the result of this studyfor the uniform velocity and scattering model. In general, a good

agreement between observed and theoretical energy is achievedfor the 6 frequency bands, particularly, at higher frequency bands.The first time window exhibits larger data scatter than the othertwo. This effect has commonly been observed in different areas(e.g., [23,35,40,9,12,25]) and can be attributed to many factors,among them the radiation pattern at source. This effect is in factaveraged out for late lapse times due to the natural averagingproduced by the scattering process. Moreover, at short lapse time,the effect of the uniform half-space assumption is stronger thanthat at late lapse times. In fact, the later coda waves sample greater

Fig. 4. Observed normalized energy for 0–15 (solid circles), 15–30 (open circles) and 30–45 s (triangles) laps time windows with the corresponding hypocentral distance.Best fit theoretical curve for each window is represented by a solid line; the corresponding best fit values of Le�1 and B0 are also given.

Table 1The results of the Le

�1 and B0 values for the different frequency bands using theassumption of uniform velocity and scattering.

F(Hz) Le�1(km�1) B0 g0(km�1) Qsc

�1 Qi�1 Qt

�1

3 0.027170.003 0.42670.04 0.0116 0.00202 0.00270 0.004756 0.027570.007 0.42970.06 0.0117 0.00103 0.00137 0.002409 0.026670.003 0.43970.03 0.0117 0.00068 0.00087 0.00155

12 0.024770.003 0.43970.03 0.0108 0.00047 0.00060 0.0010818 0.024370.003 0.42270.03 0.0103 0.00030 0.00041 0.0007124 0.025270.003 0.43770.02 0.0110 0.00024 0.00031 0.00055

M.F. Abdelwahed, A.K. Abdel-Fattah / Soil Dynamics and Earthquake Engineering 69 (2015) 93–102 97

volumes and average over a greater number of scatters with ahigher degree of azimuth-distribution around the source andreceivers [40,25]. In addition, the integration over the entireevent-station paths yields scatters due to the differences inattenuation behavior. According to this result, the B0 is found tovary between 0.422 and 0.439, while the Le

�1 varies between0.0243 and 0.0275 (Table 1). The error intervals in Le

�1 and B0parameters were calibrated using the F-distribution test for 25, 50,75, and 95 percent confidence level (e.g. [12,13]). Fig. 5 shows therange of possible solutions of the Le

�1 and B0 pairs with theresiduals estimated using the F-distribution; corresponding to25, 50, 75 and 95 percent confidence levels. It is obvious thatthe 95 percent confidence level decreases with frequency that

complies with the fact that high frequency bands are less scat-tered, as shown in Fig. 4. The Le

�1 and B0 numerical values, withtheir corresponding standard errors, are shown in Table 1. Ingeneral, Le�1 value ranges from 0.02470.003 to 0.02870.007 andthe B0 value ranges from 0.4070.02 to 0.4370.04 for allfrequency bands higher than 3.0 Hz. The F-distribution test carriedover the GA search proves the reliability of the Le

�1 and B0solutions for the entire frequency bands since they are beyondthe rejection limit for 95 percent confidence. The Qsc

�1, Qi�1, and

Qt�1 values for each frequency band corresponding to the uniform

model are calculated using Eq. (5) and listed in Table 1.To retrieve more realistic estimates, the uniform model values of

B0 and Le�1 were corrected for the effects of the depth-dependent

Fig. 5. Map of the residuals normalized to their minimum at all frequency bands for the hypocentral distance range 5–90 km. Gray cross indicates the pair Le�1 and B0 ofminimum residual. Solid circles represent the searching points with the size varying with the normalized fitness. The white circle is the resulted B0 and Le

�1 valuescorresponding to the global maximum fit with the corresponding confidence interval. The 95 percent confidence area is shown in gray. The cross symbol of red color refers tothe minimal residual. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

M.F. Abdelwahed, A.K. Abdel-Fattah / Soil Dynamics and Earthquake Engineering 69 (2015) 93–10298

earth model estimated by Del Pezzo and Bianco [17] which is closelyrelated to our region. In this model, the earth structure is character-ized by a transparent upper mantle and a heterogeneous crust. TheMoho depth is 40 km, S-wave velocity is 3.45 and 4.6 km/s in thecrust and mantle, respectively. The velocity-depth pattern isdescribed through a continuous function with a sharp gradientaround the Moho. In the same way, the scattering coefficient patternas a function of depth is described through a continuous functionhaving a strong gradient around the Moho depth and approachingtwo different constant values, respectively for the depth increasingto infinity and depth decreasing to zero. The seismogram energyenvelope as a function of source-receiver distance is then synthe-sized by the numerical simulation method [50] for a suite ofreasonable values of B0 and Le

�1. Finally, the MLTW is applied tothese synthetic envelopes to obtain a correspondence map of theuniform B0 and Le

�1 and their corresponding depth dependentvalues, see Del Pezzo and Bianco [17] for more detail. In our study,we used the coefficients resulting from this simulation to calculatethe corrected values (B0corr and Le

�1corr) corresponding to the hetero-

geneous model, as shown in Table 2. Fig. 6 shows the B0–Le�1 vector

map for the changed values. It is found that the average Le�1 and B0

values decreased by a factor of 1.1 and 1.3, respectively from thecorresponding uniform model values.

Using Eq. 5, the Qsc�1,Qi

�1 and Qt�1 values for heterogeneous model,

as a function of frequency, were calculated and listed in Table 3. TheQ�1-frequency plot for the scattering, intrinsic, and total attenuation,as the result of this study, is shown in Fig. 7. For the uniform modelthe Q�1-frequency relation (Q�1¼Q0

�1f�η) are found to be0.00670.0005f�1.0170.02, 0.00970.008f�1.0370.02, and 0.01570.008f�1.0270.02 for Qsc

�1, Qi�1, and Qt

�1, respectively. For the hetero-geneous model, the Q�1-frequency relations are found to be0.00570.0005f�1.1170.02, 0.00870.008f�0.9970.02, and 0.01270.008f�0.9970.02 for the corrected Qsc

�1, Qi�1, and Qt

�1, respectively,as reported in Table 3.

6. Discussion and conclusion

In the present study, the multiple lapse time window analysis(MLTWA) technique in conjunction with genetic algorithm [15] isused to determine the attenuation characteristics in the greaterCairo region, a tectonically active area in Egypt. A total of 280waveforms (5oΔo90 km) from 46 earthquakes (2.0oMo4.0)are used. The hypocentral depth ranges from 18 to 22 km. Thehypocentral parameters range is found to be optimal for theMLTW assumptions [16] and suitable for the attenuation of seismicwaves of these frequency bands within the crust. The attenuationcharacteristics in terms of the extension length (Le�1), the seismicalbedo (B0), the scattering attenuation (Qsc

�1), the intrinsic absorp-tion (Qi

�1), and the total attenuation (Qt�1) are estimated for both

the uniform and depth-dependent models for the frequency bands3–24 Hz.

It is remarkable that Qi�1 is greater than the Qsc

�1. However, theaverage B0

corr value is less than the 0.5 (0.33) for all frequencyranges higher than 3.0 Hz indicating that the intrinsic absorptionslightly predominates over scattering attenuation at all frequency

Table 2The corrected results of the Le

�1 and B0 values and their corresponding Qsc�1, Qi

�1

and Qt�1 for the different frequency bands taking into account the effects of a

depth-dependent earth model.

F(Hz) Le�1Corr(km�1) B0

Corr g0 Corr(km�1) Qsc�1 Corr Qi

�1 Corr Qt�1 Corr

3 0.02349 0.335 0.0079 0.00139 0.00278 0.004186 0.02366 0.335 0.0079 0.00070 0.00140 0.002109 0.02364 0.334 0.0079 0.00047 0.00093 0.00140

12 0.02314 0.334 0.0077 0.00034 0.00068 0.0010318 0.02268 0.335 0.0076 0.00023 0.00045 0.0006724 0.02323 0.334 0.0078 0.00017 0.00034 0.00052

Fig. 6. Vector map of the B0–Le�1 values before and after the depth-dependent

model correction.

Table 3Q-frequency relationships of Qsc

�1, Qi�1 and Qt

�1 for the uniform model with theirstandard errors compared with the corresponding depth-dependent values, as theresult of this study.

Uniform model Depth-dependent model

Qsc�1 0.00670.005f�1.0170.02 Qsc

�1 0.005f�1.11

Qi�1 0.00970.008f�1.0370.02 Qi

�1 0.008f�0.99

Qt�1 0.01570.008f�1.0270.02 Qt

�1 0.012f�0.99

Fig. 7. Plot of intrinsic, scattering and total attenuation versus frequency.

M.F. Abdelwahed, A.K. Abdel-Fattah / Soil Dynamics and Earthquake Engineering 69 (2015) 93–102 99

bands higher than 3.0 Hz [9]. The average Le�1 and B0 values are

found to decrease by a factor of 0.9 and 0.8, respectively from thecorresponding uniform model values. This finding is consistentwith Abdel-Fattah [1] suggesting that seismic waves are stronglyaffected by intrinsic absorption through their propagation ingreater Cairo region and its vicinity. The low value of seismicalbedo (o0.5) may be attributed to the pore pressure effect offluid saturation in active faults that can exhibit strong intrinsicattenuation [45,14]. This in turn, yields a high intrinsic loss(Qi

�140.0003–0.0014) and/or lower degree of heterogeneities.The Q�1-frequency dependent parameters for the uniform and

heterogeneous models are shown in Fig. 7 and listed in Table 3.The coefficient η is 1.11, �0.99 and �0.99 for the corrected Qsc

�1,Qi

�1, and Qt�1, respectively. The coefficient η for the Qsc

�1 relationwith frequency increased from 1.01 to 1.11 after correction.Whereas, the corresponding η value for the Qt

�1 decreased from1.02 to 0.99. It is also observed that the corrected value mainlyaffects the Qsc

�1 values which decreased significantly; however, theQi

�1 values are nearly fixed. As a result, the Qt�1 decreased slightly

after the correction, see Fig. 7. This variation of the η value impliesa complex structure in the area and significant changes in theattenuation parameters with depth. Generally, the frequencydependence of the intrinsic absorption, probably, depends on thecomposition and distribution of the fluids in the upper crust of thestudy area. A decrease of the Qsc

�1 faster than f�1 with increasingfrequency implies that the medium is characterized by a Gaussian

autocorrelation function [49,25]. Several authors (e.g., [35,8,9,25])suggested that the strong frequency dependence could be relatedto the size of heterogeneities.

A comparison of Qsc�1, Qi

�1, Qt�1, B0, Le�1, and g0 for the study

area with that obtained worldwide is shown in Fig. 8. Firstly, theQsc

�1,Qi�1, and Qt

�1values estimated in this study is comparablewith the coda-Q results of studies conducted in the same area[1,21]. It is found that our results agree well with those obtained inother tectonic regions which show dominant intrinsic attenuationat frequencies higher than 3.0 Hz. In particular, the results ofSouthern Italy [43]; Central Italy [18]; Southeastern Sicily [25];Southern Netherland [26]; and Eastern Turkey [9] are the mostcomparable. As a matter of fact, those studies are different in themodels used and the data ranges, however, the tectonic frame-work are closely related. For instance, the Central Italy and SouthNetherland lie in a continental plate characterized by low tomoderate seismicity similar to the Greater Cairo region. On theother hand, the estimates of North Colombia is quite far from ourestimates. This is attributed to the tectonic setting of NorthColombia which constitutes of an extensive zone of continentaldeformation with a complex geological and tectonic configurationresulting from the relative motion of three plates, Nazca, SouthAmerica and Caribbean [45]. This complicated framework exhibitsa significant increase of Qi�1 and Qsc

�1 relative to the value of ourregion (Fig. 8). Similarly, South Eastern Sicily, characterized byextensional tectonic with high seismic risk and volcanisms, shows

Fig. 8. Comparison of (a) Le�1, (b) B0, (c) g0, (d) Qsc�1, (e) Qi

�1, and (f) Qt�1 from different regions; Southern Netherland [26]; Eastern Turkey [9]; Southeastern Sicily [25];

Northwestern Colombia [45]; Southern Iberia [40]; Northeastern Italy [13]; Southern Italy [43]; Central Italy [18]; South Korea [33]; Cairo (El-Hadidy, 2006); Cairo [1]; Abu-Dabbab area [3]; and Greater Cairo (this study).

M.F. Abdelwahed, A.K. Abdel-Fattah / Soil Dynamics and Earthquake Engineering 69 (2015) 93–102100

higher Qsc�1 and Qi

�1 values. Abou-Dabbab region is significantlydifferent as well. This region is located near the eastern cost ofEgypt and seismically active with the doubt of existence ofvolcanic activity [3].

The values of B0, Le�1, and g0 are found to be within the rangeof all the compared results and are mostly insensitive to frequency(Fig. 8a–c). This indicates that the seismic wavelengths are lower thanthe average size of the heterogeneities in the study region. The valueof g0 calculated in this study (Fig. 8c) is about 0.011–0.0079 km�1

before and after correction, respectively, which agrees well with thatobserved in other tectonic regions (e.g., Central Italy, [18]; Southeastern Sicily, [25]; Eastern Turkey, [9]).

Hence, the result of this study is found to provide newinformation on the attenuation characteristics of the Cairo metro-politan region which is helpful for better understanding theseismic activity and the seismic hazards in this region. However,it is noted that the correction for the depth dependent model isnecessary for the MLTW analysis. This raises the importance oftaking into account a realistic Earth's model for such kind ofmeasurements. It is crucial to use larger number of data in thisstudy with a proper depth-dependent model. Moreover, it isrecommended to conduct this study on broadband data toinvestigate the broader frequency bands less than 3.0 Hz withsmaller frequency intervals to cover deeper structures.

In conclusion, this study provides crucial information on theattenuation properties in the Cairo metropolitan region. Theattenuation parameters resulted in this study are sufficiently largeexhibiting significant changes in the attenuation parameters withdepth. This reflects the nature of the geological and morphologicalenvironment of the study region which is tectonically active withhigh density of faults and a complex regime of fluid distributionand composition. The intrinsic absorption dominates over thescattering attenuation which may be attributed to the porepressure effect of fluid saturation in active faults.

Acknowledgments

The authors wish to thank David L. Carroll for offering the GAcode. We appreciate the National Research Institute of Astronomyand Geophysics (NRIAG), Helwan, Egypt for maintaining andsupplying the high quality waveform data used in this study. Thesoftware of Generic Mapping Tools (GMT) by Wessel and Smithwas used for plotting some of the figures. This work wassupported by King Saud University, Deanship of ScientificResearch, College of Science Research Centre.

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