seismic wave attenuation in the greater cairo region, egypt

12
Seismic Wave Attenuation in the Greater Cairo Region, Egypt AHMED BADAWY 1 and MAMDOUH A. MORSY 1 Abstract—In the present study, a digital waveform dataset of 216 local earthquakes recorded by the Egyptian National Seismic Network (ENSN) was used to estimate the attenuation of seismic wave energy in the greater Cairo region. The quality factor and the frequency dependence for Coda waves and S-waves were estimated and clarified. The Coda waves (Q c ) and S-waves (Q d ) quality factor were estimated by applying the single scattering model and Coda Normalization method, respectively, to bandpass-filtered seismo- grams of frequency bands centering at 1.5, 3, 6, 12, 18 and 24 Hz. Lapse time dependence was also studied for the area, with the Coda waves analyzed through four lapse time windows (10, 20, 30 and 40 s). The average quality factor as function of frequency is found to be Q c = 35 ± 9f 0.9±0.02 and Q d = 10 ± 2f 0.9±0.02 for Coda and S-waves, respectively. This behavior is usually correlated with the degree of tectonic complexity and the presence of heteroge- neities at several scales. The variation of Q c with frequency and lapse time shows that the lithosphere becomes more homogeneous with depth. In fact, by using the Coda Normalization method we obtained low Q d values as expected for a heterogeneous and active zone. The intrinsic quality factor (Q i -1 ) was separated from the scattering quality factor (Q s -1 ) by applying the Multiple Lapse Time Domain Window Analysis (MLTWA) method under the assumption of multiple isotropic scattering with uniform distribu- tion of scatters. The obtained results suggest that the contribution of the intrinsic attenuation (Q i -1 ) prevails on the scattering atten- uation (Q s -1 ) at frequencies higher than 3 Hz. Key words: Coda waves, quality factor, intrinsic, scattering, S-wave, cairo. 1. Introduction Seismicity of Egypt is mainly attributed to the relative motion of the Africa, Arabia, Eurasia plates and the Sinai sub-plate (BADAWY, 2005). During the last 5,000 years and particularly in the last century, Egypt has been affected by several earthquakes (e.g. an M = 6.9 earthquake in 1969; an M = 4.9 earth- quake in 1974; an M = 5.2 earthquake in 1981; and an M = 5.9 earthquake in 1992). In particular the moderate earthquake of 12 October 1992, southwest Cairo (M b = 5.9) was undeniably the most destruc- tive to ever hit Egypt and caused huge damage in northern Egyptian territories. This event resulted in 554 being killed, about 20,000 people being injured and over one billion US dollars reported as property loss. Earthquake damage is primarily caused by shear seismic waves and shaking is heavily influenced by the manner in which the seismic waves propagate through complex geological features. Since it is still out of ability to make relevant predictions of future earthquake activity. The economic and social effects of earthquake disasters can be reduced through comprehensive knowledge of attenuation and prop- erties of the source region. This is because the accurate definition of attenuation laws serves as a predictive tool for ground motion parameters at a particular site in future earthquakes. Attenuation of seismic waves is one of the basic physical parameters used in seismological and earthquake engineering studies, which are closely related to the seismicity and regional tectonics of particular area. Attenuation of seismic waves, described by the quality factor Q c , is a complex mechanism which depends on anelastic phenomena and scattering. The quality factor Q of seismic waves is mainly affected by energy absorption due to scat- tering and intrinsic attenuation. The main part of the body wave coda energy is believed to contain scat- tered S-waves and, therefore, it mainly describes the propagation effects on the S-waves (AKI, 1980a). Quantifying the relative contribution of scattering and intrinsic attenuation has been the subject of considerable interest among seismologists in the few 1 Earthquake Division, National Research Institute of Astronomy and Geophysics (NRIAG), Helwan, Cairo 11421, Egypt. E-mail: [email protected] Pure Appl. Geophys. 169 (2012), 1589–1600 Ó 2011 Springer Basel AG DOI 10.1007/s00024-011-0396-x Pure and Applied Geophysics

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Page 1: Seismic Wave Attenuation in the Greater Cairo Region, Egypt

Seismic Wave Attenuation in the Greater Cairo Region, Egypt

AHMED BADAWY1 and MAMDOUH A. MORSY

1

Abstract—In the present study, a digital waveform dataset of

216 local earthquakes recorded by the Egyptian National Seismic

Network (ENSN) was used to estimate the attenuation of seismic

wave energy in the greater Cairo region. The quality factor and the

frequency dependence for Coda waves and S-waves were estimated

and clarified. The Coda waves (Qc) and S-waves (Qd) quality factor

were estimated by applying the single scattering model and Coda

Normalization method, respectively, to bandpass-filtered seismo-

grams of frequency bands centering at 1.5, 3, 6, 12, 18 and 24 Hz.

Lapse time dependence was also studied for the area, with the Coda

waves analyzed through four lapse time windows (10, 20, 30 and

40 s). The average quality factor as function of frequency is found

to be Qc = 35 ± 9f 0.9±0.02 and Qd = 10 ± 2f 0.9±0.02 for Coda

and S-waves, respectively. This behavior is usually correlated with

the degree of tectonic complexity and the presence of heteroge-

neities at several scales. The variation of Qc with frequency and

lapse time shows that the lithosphere becomes more homogeneous

with depth. In fact, by using the Coda Normalization method we

obtained low Qd values as expected for a heterogeneous and active

zone. The intrinsic quality factor (Qi-1) was separated from the

scattering quality factor (Qs-1) by applying the Multiple Lapse

Time Domain Window Analysis (MLTWA) method under the

assumption of multiple isotropic scattering with uniform distribu-

tion of scatters. The obtained results suggest that the contribution

of the intrinsic attenuation (Qi-1) prevails on the scattering atten-

uation (Qs-1) at frequencies higher than 3 Hz.

Key words: Coda waves, quality factor, intrinsic, scattering,

S-wave, cairo.

1. Introduction

Seismicity of Egypt is mainly attributed to the

relative motion of the Africa, Arabia, Eurasia plates

and the Sinai sub-plate (BADAWY, 2005). During the

last 5,000 years and particularly in the last century,

Egypt has been affected by several earthquakes (e.g.

an M = 6.9 earthquake in 1969; an M = 4.9 earth-

quake in 1974; an M = 5.2 earthquake in 1981; and

an M = 5.9 earthquake in 1992). In particular the

moderate earthquake of 12 October 1992, southwest

Cairo (Mb = 5.9) was undeniably the most destruc-

tive to ever hit Egypt and caused huge damage in

northern Egyptian territories. This event resulted in

554 being killed, about 20,000 people being injured

and over one billion US dollars reported as property

loss.

Earthquake damage is primarily caused by shear

seismic waves and shaking is heavily influenced by

the manner in which the seismic waves propagate

through complex geological features. Since it is still

out of ability to make relevant predictions of future

earthquake activity. The economic and social effects

of earthquake disasters can be reduced through

comprehensive knowledge of attenuation and prop-

erties of the source region. This is because the

accurate definition of attenuation laws serves as a

predictive tool for ground motion parameters at a

particular site in future earthquakes.

Attenuation of seismic waves is one of the basic

physical parameters used in seismological and

earthquake engineering studies, which are closely

related to the seismicity and regional tectonics of

particular area. Attenuation of seismic waves,

described by the quality factor Qc, is a complex

mechanism which depends on anelastic phenomena

and scattering. The quality factor Q of seismic waves

is mainly affected by energy absorption due to scat-

tering and intrinsic attenuation. The main part of the

body wave coda energy is believed to contain scat-

tered S-waves and, therefore, it mainly describes the

propagation effects on the S-waves (AKI, 1980a).

Quantifying the relative contribution of scattering

and intrinsic attenuation has been the subject of

considerable interest among seismologists in the few

1 Earthquake Division, National Research Institute of

Astronomy and Geophysics (NRIAG), Helwan, Cairo 11421,

Egypt. E-mail: [email protected]

Pure Appl. Geophys. 169 (2012), 1589–1600

� 2011 Springer Basel AG

DOI 10.1007/s00024-011-0396-x Pure and Applied Geophysics

Page 2: Seismic Wave Attenuation in the Greater Cairo Region, Egypt

last decades. Several investigators have discussed the

mechanisms underlying the observed coda attenua-

tion, and proposed methods to quantify the relation

between intrinsic and scattering attenuation (WU,

1984; FRANKEL and WENNERBERG, 1987; HOSHIBA,

1991; MCSWEENEY et al., 1991). AKI (1980a) single

scattering model is applied only to S-wave coda

records for hypocentral distances shorter than some

maximum value to ensure that only single scattering

effects are important. The volume of crust, from

which recorded Coda waves have scattered, is made

common to all records by using the same length of

coda window for each record in the analysis.

Coda-Q (AKI and CHOUET, 1975) and Multiple

Time Window Analysis (MLTWA), (HOSHIBA et al.,

1991) are the most common methods for attenuation

analysis in the frequency domain. The problem in the

Coda-Q method is the ambiguity in the interpretation

of the Coda-Q in terms of total attenuation, scattering

and intrinsic absorption. Nowadays, several methods

have been proposed to determine the relative contri-

bution of scattering attenuation and intrinsic

absorption to the total attenuation (AKI, 1980a; HOS-

HIBA et al., 1991; WENNERBERG, 1993). The MLTWA

method assumes multiple scattering and enables the

separation of intrinsic attenuation from scattering

effects by relating the energy in multiple consecutive

time windows to hypocentral distances.

The aim of this paper is to obtain the attenuation

properties of the crust beneath the Greater Cairo

region by using 216 local earthquakes and the esti-

mation of the quality factor of S-waves and Coda

waves. Previous studies on the attenuation in the

respective area have been published by EL-HADIDY

et al. (2006). They estimated the quality factor of

Coda waves using the waveform of relatively small

dataset that comprises of only 35 earthquakes

recorded by only three seismic stations. Based on

their estimates, Coda-Q varies between 118 and 841

in the frequency range of 1.5–18 Hz. To extend our

knowledge on the seismic attenuation in the study

area, we separate in details the intrinsic quality

factor (Qi-1) from the scattering coefficient (Qs

-1) by

applying the MLTWA method. Finally results in

light of differences and analogies observed among

different investigated areas in the world will be

discussed.

2. Geological and Tectonic Setting

The greater Cairo region undergoes severe exten-

sional stress resulting from the regional forces of the

neighboring plate boundaries including the African,

Arabian and Eurasian plate margins, the Red Sea

rifting system, and the Aqaba-Dead Sea fault system.

In addition, local tectonic structures of the Gulf of

Suez and the Nile River affect the tectonic regime of

northern Egypt. The fault pattern shows diverse fault

trends (Fig. 1) that are related to subsequent tectonic

phases from the early Mesozoic to the present. The

first tectonic phase, during the Triassic and Jurassic,

involved a left-lateral oblique extension in northern

Egypt, and the opening of the Tethys Sea as a result of

the westward movement of Eurasia relative to Africa

(ARGYRIADIS et al., 1980). This movement resulted in a

system of NE–SW to ENE–WSW trending faults

either as normal (ABDEL AAL et al., 1994) or strike-slip

faults with left lateral motion (MESHREF, 1990). Dur-

ing the period of the late Cretaceous to early Tertiary,

the NW-SE oblique contraction force was related to

the closing of the Tethys Sea (ORWIG, 1982). It also

resulted in ENE folding associated with thrust faults

(Syrian Arc Structure) and NW to NNW extension

faults parallel to the major contraction force affecting

northern Egypt (MESHREF, 1990). The last tectonic

phase began in the late Eocene and continued up to

recent times, and is dominated by two faults. The first

one is represented by the Gulf of Suez with NNW

trending normal faults in the late Eocene-Miocene.

The second is the NNE faults trend that is related to

the development of the Gulf of Aqaba rift which was

formed in the Miocene by a left-lateral oblique slip

movement.

The study area is covered by Miocene-Oligocene-

Eocene sediments (SAID, 1981). The petrology of the

Oligocene, Miocene and Pliocene rocks was studied

by BARRON (1907), SHUKRI (1953), SHUKRI and AKMAL

(1953), SHUKRI and EL AYOUTY (1956), and SAID

(1962). The cretaceous rocks are overlaid by Eocene

rocks made up of sandy brownish limestone with

sandstone beds. These beds are followed by Oligo-

cene deposits. Several basalt flows are reported from

all over the Cairo-Suez district. They are overlying

Oligocene sands and gravels and unconformable

overlaid by marine Miocene sediments. The Miocene

1590 A. Badawy, M. A. Morsy Pure Appl. Geophys.

Page 3: Seismic Wave Attenuation in the Greater Cairo Region, Egypt

sediments are subdivided into two units: a lower unit

made up of marine sediments and an upper unit made

up of non-marine fluviatile sediments. The recent

Nile deposits represented by silt and clay sediments

are covering the whole area in the Nile Valley as well

as the northern parts of the cultivated lands of

northern Egypt.

3. Data and Analysis

Data recorded during the period from January 1st

2000 to December, 31st 2005 by 12 stations of the

Egyptian National Seismic Network (ENSN) operat-

ing by the National Research Institute of Astronomy

and Geophysics (NRIAG) was analyzed. Each seis-

mic station is equipped with short period SS1

seismometer having a natural frequency of 1 Hz. The

waveform data is sampled with a sampling rate of

100 samples per second. We selected events exhib-

iting signal to noise ratio greater than 2 in all

frequency bands for S- and Coda waves. The selected

dataset consists of 2,592 vertical recorded waveforms

of 216 events with focal depths between 3 and 28 km

and magnitude ranging between 1.5 and 3.7. The

hypocentral distance of the events mainly ranges

from 5 to 60 km. Figure 1 shows a map of the studied

area with the epicentral locations of the analyzed

earthquakes and the twelve ENSN’s stations.

The lapse time windows for Qc analysis begins at

twice the travel time of the S-waves, and ends when

the S-wave coda falls to a fixed signal to noise level

ratio of two.. Such procedure might introduce an

amplitude distance dependence on the size of the

analysis window. Four window lengths are taken

from 10 to 40 s with a variation of 10 s to estimate

the attenuation at different lapse times for observing

its effect with depth. For all window lengths the

seismograms are band pass filtered at central fre-

quencies of 1.5, 3, 6, 12, 18 and 24 Hz. An increasing

frequency band is used for increasing central fre-

quency to avoid ringing and to take constant relative

band widths for getting equal amounts of energy go

into each band (HAVSKOV and OTTEMOLLER, 2003).

3.1. Method of Analysis

3.1.1 Single Scattering Model (Coda-Q Method)

The Single Backscattering model was proposed by

AKI and CHOUET (1975) to explain the time depen-

dence of the scattered energy density at the source

location in the 3-D space. The coda envelope may be

expressed as:

Acðf ; tÞ ¼ Aoðf Þ � t�c � e�pft=Qc ð1Þ

where f is the frequency, t-c is the geometrical

spreading function (c is taken as 1 for body waves),

Figure 1Map of the study area illustrated the topography, surface faults, 216-selected events and seismic stations

Vol. 169, (2012) Seismic Wave Attenuation 1591

Page 4: Seismic Wave Attenuation in the Greater Cairo Region, Egypt

Ao(f) is the coda source factor, t is the lapse time and

Qc is the quality factor for Coda waves. This model

assumes that the coda is composed of waves scattered

at uniformly distributed heterogeneities in a constant

velocity earth medium; moreover, it is assumed that

the scattering is weak enough so that multiple scat-

tering may be ignored. The relationship (1) is valid at

lapse times (measured from the earthquake origin

time) more than approximately twice the direct

S-wave travel time ts (RAUTIAN and KHALTURIN, 1978).

In order to analyze the early part of the coda, the

source-receiver distance must also be taken into

account, according to Sato’s single isotropic scatter-

ing model (SATO, 1977). Qc-1(f) can easily be

estimated from the recorded seismograms, by fitting

the envelopes of the filtered seismic traces to the

relationship (1) (AKI and CHOUET, 1975). Many

authors (e.g. BISWAS and AKI, 1984; HAVSKOV et al.

1986, 1989; MANDAL et al. 2004) have observed a

frequency dependent Qc in the range between 1 and

25 Hz which can be described by the power law

form:

Qcðf Þ ¼ Qoðf=foÞg ð2Þ

where Qo is the quality factor at the reference fre-

quency fo (generally 1 Hz) and g 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 model can not be used to

separate the effects of scattering and absorption.

3.1.2 Coda Normalization

For estimating the direct quality factor (Qd) we used

the Coda Normalization method (AKI, 1980a). This

method estimates (Qd) by comparing S and Coda

amplitudes of events at different distances from the

observer. It is based on the empirical observation that

Coda waves principally consist of S-waves scattered

at random heterogeneities in the Earth, at a lapse time

greater than the S-wave travel time the energy is

uniformly distributed in a volume surrounding the

source. The direct S-wave amplitude is normalized to

the coda amplitude measured at fixed time (tc)

leading to the elimination of the source power, site

effect and instrument response from the observed

spectra of the direct S-waves (for more details see

AKI, 1980a, 1981). Interpreting the S-coda 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:

Acðf ; tcÞj j2/ WSi ðf Þ NS

j ðf Þ���

���

2e�2pftc�Q�1c

tnc

ð3Þ

where Ac is the S-coda spectral amplitude at fre-

quency f and fixed lapse time tc; WiS(f) is the energy

radiation from source i in the same frequency band;

jNjS(f)j is the S-wave site amplification factor for site

j; n is the geometrical spreading factor; and e�Q�1c 2pft

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:

Asðf ; tÞj j2/ WSi ðf Þr2

ij

NSj ðf Þ

���

���

2

e�2pfrij �Q�1

db ð4Þ

where Qd-1 is the direct S-wave attenuation. Since the

method 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 observed spectra of the direct

S-waves. On dividing Eq. 4 by 3 and taking the

logarithm at fixed time tc we obtain

lnrij � Asðf ; tÞj jffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

Acðf ; tcÞj j2q

2

64

3

75 ¼

�pf

Qdðf Þ � b� rij þ const ð5Þ

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

Qd-1 from the slope.

3.1.3 Multiple Lapse Time Window Analysis

(MLTWA)

Several methods have been proposed to determine the

relative contribution of scattering attenuation and

1592 A. Badawy, M. A. Morsy Pure Appl. Geophys.

Page 5: Seismic Wave Attenuation in the Greater Cairo Region, Egypt

intrinsic absorption to the total attenuation (e.g. AKI,

1981; WENNERBERG 1993). WU’S (1985) formula

predicts the spatial distribution of the integral of

seismic energy over an infinite time length. It uses the

radiative transfer theory to separate the contribution

of scattering and intrinsic absorption based on a

theoretical model of seismic energy propagation,

where the scattering is assumed to be isotropic and

multiple scattering is included. HOSHIBA et al. (1991)

have developed a method called Multiple Lapse Time

Window Analysis (MLTWA) in which they consider

energy in three consecutive time windows as a

function of hypocentral distance. These data are then

matched to a set of model curves (ZENG, 1991). Each

model curve used in fitting is calculated based on an

input value for the seismic albedo (Bo) and the total

mean path, also known as extinction length (Le), the

seismic albedo being, Bo = gs/gs 1 gi and the extinc-

tion length coefficient Le = 1/gs 1 gi. The Le

describes the distance over which the amplitude of

the seismic signal decreases by e-1 and gs, gi

represent scattering and intrinsic factors.

Seismic albedo ranging from 0 to 1 was proposed

by WU (1985) to describe the proportions of energy

loss dominated by intrinsic attenuation (B0 \ 0.5) or

scattering attenuation (B0 [ 0.5). In particular, media

with strong heterogeneity and no intrinsic absorption

have high albedo, while homogeneous media have

zero seismic albedo.

Under the assumption of multiple isotropic scatter-

ing and uniform distribution of scatterers, the

theoretical curves of the energy density at a given

lapse time and hypocentral distance can be obtained by

means of the equation described by ZENG et al. (1991):

Eðr; tÞ ffi E0e�gvt dt ¼ r

v

� �

4pvr2þ gs

H t ¼ rv

� �

4pvrtln

1þ rvt

1� rvt

� �

þ cH t ¼ r

v

� 3gs

4pvt

�32

e�3gsr2

4vt �givt

ð6Þ

with:

c ¼ E0

1 ¼ 1þ gsvtð Þe�gsvt½ �4ffiffippRffiffiffiffiffiffi3gsvtp

2

0e�a2a2da

and E(r, t) is the scattered energy density; E0 is the

energy a t = 0; r is the position of the receiver; g is

the coefficient of total attenuation; gs is the coeffi-

cient of scattering attenuation; m is the S-wave

velocity; H is the Heaviside function and

a ¼ vt

r:

ZENG (1991) called the solution of Eq. 6 hybrid-

single scattering-diffusion solution. We adopted the

hybrid-single-scattering-diffusion approximation to

model absorption and scattering in the crust of the

analyzed area.

After modeling the theoretical curves in terms of

Le-1 and B0, we follow the approach described in

BIANCO et al. (2002), to compare the experimental

curves to the theoretical ones in order to obtain a

separate estimate of intrinsic and scattering

attenuation.

4. Results

The single scattering model (AKI and CHOUET,

1975) and Coda normalization method (AKI, 1980a)

were applied to a dataset composed of 216 selected

seismic events to investigate in detail on Qc fre-

quency dependence and possible variations of seismic

attenuation with source-station path.

4.1. Coda Waves Quality Factor

For the quality factor of Coda waves we obtained

an average attenuation law Qc = 35 ± 9f0.9±0.02. The

resulting values of Qc are plotted in Fig. 2 and listed

in Table 1. They show how the Qc values for local

Average Q at different Lapse Time

0

100

200

300

400

500

600

700

800

900

0 5 10 15 20 25 30

Frequency

Q-V

alu

e

10 sec

20 sec

30 sec

40 sec

Figure 2Estimates of Qc obtained at different lapse time

Vol. 169, (2012) Seismic Wave Attenuation 1593

Page 6: Seismic Wave Attenuation in the Greater Cairo Region, Egypt

earthquakes in the greater Cairo region are clearly

frequency and lapse time dependent.

Generally, the quality factor increases with

frequency (MITCHELL, 1995). The obtained results of

Qc follow formula (2). This relationship indicates that

the attenuation of seismic waves at different distances

from the source varies with frequency. For greater

Cairo region we obtained Qc ¼ 17� 3f 1:1�0:03

Qc ¼ 23� 6f 1:0�0:04, Qc ¼ 32� 10f 1:0�0:05 and,

Qc ¼ 40� 15f 0:9�0:08 at 10, 20, 30, and 40 s lapse

times respectively. These results are twice lower than

that obtained by EL-HADIDY et al. (2006). This may be

due to the use of small number of earthquakes and

stations in EL-HADIDY et al. (2006) and they stated

that their results ‘‘are only preliminary; verification

by the computational results of data for other regions

and theoretical explanation are still needed’’.

The value of Qc increases with the lapse time

length. Also, a test for the model misfit variations of

coda Q is estimated for the geometrical spreading

factor v 0.5 and 1.0. The frequency dependence

relationship is interpreted as a tectonic parameter. In

this study, the obtained frequency dependence rela-

tionship indicates that the attenuation at higher

frequencies is less pronounced than at lower frequen-

cies. So far this is characterized tectonically active

area distinguished by complex structure (AKI 1980a;

AKINCI and EYDOGAN, 2000; GIAMPICCOLO et al., 2006).

The values of quality factor (Qo) and frequency

parameter (g) are listed in Table 2 and Fig. 3 shows

the Qo versus exponent g for selected values of the

geometrical spreading factor v.

Focal-depths dependence was also studied,

obtaining a frequency dependent relation Qc ¼33� 13f 0:9�0:13, Qc ¼ 30� 11f 0:9�0:03, and Qc ¼29� 10f 0:9�0:05, for earthquakes zoned at centered

focal depths 5, 15 and 25 km, respectively. The

obtained relationships indicate that Qc does not

appear to depend on focal depth.

Figure 4 shows the spatial distribution of the Qc

values at the greater Cairo region. It is obvious that

Qc values are relatively little higher to the east

Table 1

Average values of coda attenuation Qc estimates different frequency bands and lapse time

1.5 3 6 12 18 24

10 75 ± 22 111 ± 34 123 ± 47 209 ± 70 319 ± 102 419 ± 129

20 88 ± 26 122 ± 42 160 ± 54 271 ± 71 383 ± 106 538 ± 154

30 100 ± 31 132 ± 56 191 ± 66 332 ± 86 492 ± 113 649 ± 169

40 104 ± 36 137 ± 61 207 ± 77 386 ± 100 573 ± 122 772 ± 187

Table 2

The Quality factor (Qo) at reference frequency(1 Hz) and the frequency parameter (g) values at the greater Cairo region

Length 10 s 20 s 30 s 40 s

Station Qo g Qo g Qo g Qo g

BNS 15 ± 1 1.1 ± 0.028 20 ± 1 1.1 ± 0.019 26 ± 1 1 ± 0.014 38 ± 1 1.0 ± 0.08

AYT 10 ± 1 1.0 ± 0.036 12 ± 1 1.1 ± 0.027 19 ± 1 1.0 ± 0.024 26 ± 2 1.0 ± 0.021

FYM 13 ± 1 0.9 ± 0.009 15 ± 1 1.0 ± 0.011 18 ± 1 1.1 ± 0.011 22 ± 1 1 ± 0.008

HAG 17 ± 1 1.1 ± 0.019 21 ± 1 1.0 ± 0.016 31 ± 2 1.0 ± 0.02 44 ± 2 0.9 ± 0.016

KOT 15 ± 01 1.2 ± 0.033 18 ± 2 1.2 ± 0.029 37 ± 3 1.0 ± 0.023 48 ± 4 0.9 ± 0.028

MYD 14 ± 1 0.9 ± 0.034 18 ± 2 1.0 ± 0.038 28 ± 4 1.0 ± 0.052 32 ± 3 1.0 ± 0.031

SQR 16 ± 1 0.9 ± 0.063 17 ± 1 1.1 ± 0.023 27 ± 1 1.0 ± 0.017 38 ± 2 0.9 ± 0.018

GLL 26 ± 2 0.8 ± 0.020 33 ± 2 0.9 ± 0.024 40 ± 3 0.9 ± 0.028 46 ± 4 0.9 ± 0.03

KHB 25 ± 1 0.9 ± 0.012 27 ± 3 0.8 ± 0.032 30 ± 2 0.9 ± 0.019 31 ± 1 0.9 ± 0.014

NAT 12 ± 1 1.1 ± 0.020 15 ± 1 1.1 ± 0.015 23 ± 2 1.1 ± 0.024 33 ± 2 1.0 ±0.024

SAF 31 ± 4 0.9 ± 0.044 45 ± 4 0.8 ± 0.090 58 ± 2 0.9 ± 0.120 64 ± 2 0.9 ± 0.029

HLW 15 ± 1 1.0 ± -0.020 32 ± 1 0.9 ± 0.013 44 ± 1 0.9 ± 0.006 56 ± 2 0.8 ± 0.011

1594 A. Badawy, M. A. Morsy Pure Appl. Geophys.

Page 7: Seismic Wave Attenuation in the Greater Cairo Region, Egypt

(HLW, SAF, HAG, KOT, BNS and GLL stations) of

the Nile River than to the west (AYT, FYM, MYD,

SQR, KHB and Nat stations). This may be attributed

to the marine limestone beds in the eastern bank of

the Nile River and the recent Nile deposits along the

Fayoum depression in the west (SAID, 1962, 1981).

Moreover, within the Nile Valley graben, loose

sediments are thicker with water saturation than

outside the graben and rapidly decrease in both

directions away from the graben. Consequently, high

degree of structure heterogeneities created by seismic

activity is expected and could bring remarkable

increase of seismic wave attenuation. Generally, the

estimation values of Qc at the greater Cairo region are

relatively lower than those obtained at different

tectonics areas (e.g. AKINCI et al., 1994; GUPTA

et al., 1998).

4.2. S-Waves Quality Factor

We also estimated Qd by using the same dataset

selected for Qc. We calculated the quantity in the left-

hand side of Eq. 5 for different frequencies bands

centered at 1.5, 3, 9, 12, 18 and 24 Hz assuming

3.5 km/s s-wave velocity. The estimated quantity for

each frequency band is plotted as a function of

hypocentral distance together with the best fitting

linear regression (Fig. 5). Frequency-dependent of Qd

can be fitted by the well known relationship (Eq. 2).

For the greater Cairo region, we obtained

Qd = 10±2f0.9±0.02 relatively smaller than that esti-

mated for Coda waves.

If we compare the average attenuation law of

Coda waves Qc = 35±9f0.9±0.02 and S-waves

Qd = 10±2f0.9±0.02 calculated at a lapse of the same

order of the S-waves travel path, we observed that the

frequency dependence of the Coda-Q is roughly the

same as the S-wave Q. According to the energy flux

model (FRANKEL, 1991), the similarity between the

coda and the S-wave decay at one frequency implies

that the intrinsic attenuation is the dominant cause of

attenuation at that frequency. The results of our study

show that the coda and amplitude decay of S-waves

with distance are comparable. This indicates that

intrinsic attenuation become important at all studied

frequencies from 1.5 to 24 Hz (for more details see

the next section)

4.3. Scattering Attenuation and Intrinsic Absorption

We apply Multiple Lapse Time Window Analysis

(MLTWA) to the same dataset for a detailed sepa-

ration of scattering attenuation (Qs-1) from intrinsic

absorption (Qi-1). The obtained results indicate that

the intrinsic absorption dominates over scattering in

the attenuation process at all frequencies except at

3 Hz they seem to be of the same order. The seismic

albedo (Bo) defines as the dimensionless ratio of the

scattering loss to the total attenuation and ranges

between 0 and 1 (WU, 1985). The energy loss is

dominated by intrinsic absorption (Bo \ 0.5) or

scattering attenuation (Bo [ 0.5). In particular, media

with strong heterogeneities and no intrinsic absorp-

tion have high seismic albedo, while homogeneous

media have zero seismic albedo.

We found that the seismic albedo (Bo) is less than

0.5 at all investigated frequencies (1.5–24 Hz). This

indicates that the intrinsic absorption dominates over

scattering attenuation. Indeed, the seismic albedo (Bo)

seems to be very close to 0.5 at 3 Hz frequency

(Table 3) which reflects both intrinsic and scattering

are of the same order. However, at GLL station the

value of seismic albedo (Bo) is equal to or little bit

Figure 3Values of Qo and g as function of lapse times

Vol. 169, (2012) Seismic Wave Attenuation 1595

Page 8: Seismic Wave Attenuation in the Greater Cairo Region, Egypt

higher than 0.5 (Table 3). This may reflect a very

local geological site condition/effect.

5. Discussion and Conclusions

Comprehensive assessment of seismic hazard and

information on earthquake source parameters in a

given area requires a good knowledge of attenuation

and properties of the medium. Especially information

on high-frequency seismic wave attenuation in the

lithosphere is of particular interest (YOSHIMOTO et al.,

1993). The region under study is not well known

from the viewpoint of seismic wave attenuation.

Therefore, the present results are of considerable

interest for seismic hazard assessment in the Egyptian

territories which is characterized by a moderate

hazard and high risk (BADAWY, 2005). In Egypt the

population as well as the archaeological sites and

sensitive construction are concentrated within a nar-

row belt around the Nile Valley and buildings are not

designed to resist earthquakes. Therefore, relatively

Figure 4Spatial distribution of Qc along the greater Cairo region. a At 10 s lapse time, b 20 s lapse time, c 30 s lapse time and d 40 s lapse time

1596 A. Badawy, M. A. Morsy Pure Appl. Geophys.

Page 9: Seismic Wave Attenuation in the Greater Cairo Region, Egypt

moderate earthquakes can be source of huge socio-

economic disasters (BADAWY, 2005). The spatial dis-

tribution of recent seismicity indicates that both

interplate and intraplate earthquakes hit Egypt. Most

earthquakes are concentrated in northern Egypt

(BADAWY, 1996; BADAWY and HORVATH, 1999a, b).

Egypt has a history of being repeatedly shaken by

similar-size earthquakes (AMBRASEYS et al., 1994;

BADAWY, 1999).

The loss or absorption of energy in a seismic

wave propagating through a rock mass is attributed to

many mechanisms including: geometrical spreading,

scattering, dispersion and energy loss due to heat or

thermal frication. Aside from geometrical spreading

these mechanisms result from attenuation properties

of the rock mass. We have made a systematic esti-

mate of seismic shear wave attenuation in the greater

Cairo region, separating intrinsic absorption from

scattering attenuation. By this separation it is possible

to improve understanding of the physical mechanisms

governing attenuation properties in the crust in this

region.

We applied the Single Scattering Model (AKI and

CHOUET, 1975) to a dataset composed of 216 events to

investigate Coda-Q frequency and laps-time depen-

dence. Coda-Q appears to be almost linear with

frequency and is lapse-time dependent. All attenua-

tion parameters are frequency dependent and the

coefficient (g) ranges from 0.8 to 1.2 (Table 2). The

value of Qc increases with the lapse time length.

Increasing values of Coda-Q with lapse time

which can be reasonably interpreted in terms of non-

uniform medium and depth-decreasing intrinsic

attenuation in the crust were found. A possible

interpretation is that the model fitting for the

observed energy-distance relation at multiple lapse

time windows did not work well at all distances.

Moreover, the assumption of uniform distribution of

Figure 5Plots of Coda Normalization method for different frequency bands versus hypocentral distance

Vol. 169, (2012) Seismic Wave Attenuation 1597

Page 10: Seismic Wave Attenuation in the Greater Cairo Region, Egypt

scatters may be unrealistic because it is widely

accepted that heterogeneity decreases with increasing

depth. At any depth-dependent attenuation mecha-

nism in the crust will cause the departure from the

idealized uniform and homogenous case.

The quality factor for direct S-waves (Qd) has

been measured as a function of frequency for a dis-

tance interval up to 60 km for the same dataset by

applying the Coda-normalization method (AKI,

1980a). The frequency dependence fits the widely

used empirical relationship (formula 2). The com-

parison between the attenuation relations of S-waves

and Coda waves with the student t-test in the range of

1.5–24 Hz shows that the difference between the

S-wave and Coda-wave attenuation is statistically

non-significant. The similarity between the coda and

the S-wave decay at one frequency implies that the

intrinsic attenuation is the dominant cause of atten-

uation at that frequency (FRANKEL, 1991). The results

of our study show that the coda and amplitude decay

of S-waves with distance are comparable. This indi-

cates that intrinsic attenuation become important at

all studied frequencies from 1.5 to 24 Hz. Moreover,

the closeness in frequency dependence between the

S-wave and Coda-wave suggests that the coda is

primarily composed of S-waves (AKI 1980b).

In order to accurately quantify the separate

amount of scattering (Qs-1) and intrinsic absorption

(Qi-1) in the frequency range from 1.5 to 24 Hz we

applied MLTWA approach (HOSHIBA et al., 1991). At

all frequencies intrinsic absorption predominates over

scattering attenuation except at 3 Hz frequency where

they are of the same order. According to the model of

FRANKEL (1991), the comparison between the coda

and the S-wave attenuation values implies that the

intrinsic attenuation dominates attenuation mecha-

nism at higher frequencies (C3.0 Hz). Moreover, our

results show that the seismic albedo (Bo) is less than

0.5 (Table 3) which reflects a predominant of intrin-

sic absorption.

Several authors have tried to separately estimate

(Qi-1) and (Qs

-1) in different regions worldwide by

applying the MLTWA method. Our results are in

agreement with those obtained in many other regions

which show intrinsic attenuation at least at frequen-

cies higher than 3 Hz (HOSHIBA, 1991; PUJADES et al.,

1997; BIANCO et al., 2002) On the other hand, many

Table 3

The total attenuation (QT), scattering (Qs-1) and intrinsic (Qi

-1)

values at frequencies range 1.5–24 Hz along the greater Cairo

region

Station 1.5 3 6 12 18 24

Scattering (Qs-1)

BNS 71 84 111 198 312 407

AYT 50 68 81 147 230 292

FYM 32 68 90 148 222 274

HAG 121 157 173 231 347 464

KOT 112 236 132 245 385 500

MYD 63 102 131 194 286 363

SQR 24 61 74 138 211 266

GLL 86 132 143 338 597 974

KHB 39 107 110 172 255 312

NAT 35 65 101 195 303 392

SAF 77 171 191 272 399 523

HLW 27 86 142 226 281 354

Absorption (Qi-1)

BNS 66 115 175 325 501 689

AYT 79 92 127 266 425 589

FYM 55 90 128 261 404 554

HAG 76 118 173 329 509 690

KOT 98 124 176 329 509 696

MYD 66 96 151 313 475 646

SQR 65 110 141 272 418 561

GLL 87 106 159 319 488 657

KHB 51 88 137 278 428 575

NAT 60 94 148 306 475 655

SAF 103 145 158 314 481 648

HLW 60 118 246 448 668 909

Total (QT)

BNS 137 199 286 523 813 1096

AYT 129 160 208 413 655 881

FYM 87 158 218 409 626 828

HAG 197 275 346 560 856 1154

KOT 210 360 308 574 894 1196

MYD 129 198 282 507 761 1009

SQR 89 171 215 410 629 827

GLL 173 238 302 657 1085 1631

KHB 90 195 247 450 683 887

NAT 95 159 249 501 778 1047

SAF 180 316 349 586 880 1171

HLW 87 204 388 674 949 1263

Seismic albedo (Bo)

BNS 0.5 0.4 0.4 0.4 0.4 0.4

AYT 0.4 0.4 0.4 0.4 0.4 0.3

FYM 0.4 0.4 0.4 0.4 0.4 0.3

HAG 0.6 0.6 0.5 0.4 0.4 0.4

KOT 0.5 0.7 0.4 0.4 0.4 0.4

MYD 0.5 0.5 0.5 0.4 0.4 0.4

SQR 0.3 0.4 0.3 0.3 0.3 0.3

GLL 0.5 0.6 0.5 0.5 0.6 0.6

KHB 0.4 0.5 0.4 0.4 0.4 0.4

NAT 0.4 0.4 0.4 0.4 0.4 0.4

SAF 0.4 0.5 0.5 0.5 0.5 0.4

HLW 0.3 0.4 0.4 0.3 0.3 0.3

1598 A. Badawy, M. A. Morsy Pure Appl. Geophys.

Page 11: Seismic Wave Attenuation in the Greater Cairo Region, Egypt

studies showed that scattering attenuation becomes an

important factor contributing the attenuation at fre-

quencies lower than 3.0 Hz (PUJADES et al., 1997;

BIANCO et al., 2002; CASTRO et al., 2002; DUTTA et al.,

2004; GIAMPICCOLO et al., 2006).

Acknowledgments

The authors are grateful to the editor-in-Chief Prof.

Brian Mitchell and the two anonymous reviewers for

their critical reviews which have greatly helped to

improve the paper. This work has been carried out at

Earthquake Division of the National Research Insti-

tute of Astronomy and Geophysics (NRIAG), the

authors are also grateful to the all staff members of

the ENSN. Great thanks to Prof. D. Kossy at Imperial

College, London, for reviewing the revised version of

the manuscript.

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(Received February 13, 2011, revised June 23, 2011, accepted June 25, 2011, Published online August 19, 2011)

1600 A. Badawy, M. A. Morsy Pure Appl. Geophys.