seismic wave attenuation in the greater cairo region, egypt
TRANSCRIPT
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
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.
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
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.
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
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.
(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
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.
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
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.
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.
REFERENCES
ABDEL AAL, A., PRICE, J., VAITL, D.J., and SHRALLOW, A. (1994).
Tectonic evolution of the Nile Delta, its impact on sedimentation
and hydrocarbon. In: Twelfth Petroleum Exploration and Pro-
duction Conference, November 1994, pp. 19–34.
AKI, K. (1980a) Scattering and attenuation of shear waves in the
lithosphere. J. Geophys. Res. 85, 6496–6504.
AKI, K. (1980b) Attenuation of shear-waves in the lithosphere for
frequencies from 0.05 to 25 Hz. Phys. Earth. Planet. Interiors, 21,
50–60.
AKI, K. (1981) Attenuation and scattering of short-period seismic
waves in the lithosphere, in: Identification of seismic sources –
Earthquake or Underground Exploration, ed. by E. S. Husebye
and S. Mykkeltveit, pp. 515–541, D. Reidel, Dordrecht, Holland.
AKI, K. and CHOUET, B. (1975) Origin of Coda waves: source
attenuation and scattering effects. J. Geophys. Res. 80,
3322–3342.
AKINCI., N. and EYDOGAN, H. (2000). Scattering and anelastic
attenuation of seismic energy in the vicinity of north Anatolian
fault zone, eastern turkey. Phys. Earth planet Inter., 122,
229–239.
AKINCI, A., TAKTAK, A.G. and ERGINTAV, S. (1994). Attenuation of
Coda waves in Western Anatolia. Phys. Earth Planet. Int. 87,
155–165.
AMBRASEYS, N. N., MELVILLE, C. P. & ADAM, R. D., 1994. The
seismicity of Egypt, Arabia and Red sea: a historical Review.
Cambridge university press.
ARGYRIADIS, I, DE GRACIANSKY, P.C., MARCOUX, J., and RICOU, L.E.
(1980) The opening of the Meszoic Tethys between Eurasiaand
Arabia–Africa. Mem, Du Bureau de Recherches Geologiques et
Minieres 1 vol 115, pp. 199–214.
BADAWY, A. (1996). Seismicity and kinematic evolution of the Sinai
plate. Ph D thesis, pp 115, L. Eotvos Univ. Budapest.
BADAWY, A. (1999). Historical Seismicity of Egypt. Acta Geod.
Geoph. Hung., 34 (1–2), 119–135.
BADAWY A. (2005). Seismicity of Egypt. Seismolo. Res. Lett., 76(2),
149–160.
BADAWY, A., and HORVATH, F. (1999a). Seismicity of the Sinai
subplate region: Kinematic implications. J. Geodynam., 27,
451–468.
BADAWY, A. & HORVATH, F., 1999b. Sinai subplate and kinematic
evolution of the northern Red Sea. J. Geodynamics, 27: 433–450.
BARRON, T. (1907). The topography and geology of the area
between Cairo and Suez, Egypt, Surv. Dept., Cairo, p. 133.
BIANCO, F., DEL PEZZO, E., CASTELLANO, M., IBANEZ, J., and
DI LUCCIO, F. (2002). Separation of intrinsic and scattering
seismic attenuation in the Southern Apennine zone, Italy. Geo-
phys. J. Int., 150, 10–22.
BISWAS, N.N., and AKI, K. (1984). Characteristics of Coda waves:
central and southcentral Alaska. Bull. Seismol. Soc. Am. 74,
493–507.
CASTRO, R.R., MONACHESI, G., TROJANI, L., MUCCIARELLI, M., and
FRAPICCINI, M. (2002). An attenuation study using earthquakes
from the 1997 Umbria-Marche sequence. J. Seismol., 6, 43–59.
DUTTA, U., BISWAS, N.N., ADAMS, D.A., and PAPAGEORGIOU, A.
(2004). Analysis of S-wave attenuation in south central Alaska.
Bull. Seism. Soc. Am. 94, 16–28.
EL-HADIDY, S., ADEL, M. E., DEIF, A., ABU EL-ATA, A. S. &
MOUSTAFA, S. R., 2006. Estimation of frequency dependent Coda
wave attenuation structure at the vicinity of Cairo Metropolitan
Area, Acta Geophysica, 54, 177-186.
FRANKEL, A.A. (1991). Mechanisms of seismic attenuation in the
crust: scattering and anelasticity in New York State, South Africa
and Southern California. J. geophys. Res., 96, 6269–6289.
FRANKEL, A., and WENNERBERG, L. (1987). Energy flux model of
seismic coda: Separation of scattering and intrinsic attenuation.
Bull. Seismol. Soc. Am., 77, 1223–1251.
GIAMPICCOLO, E., TUVE, T., GRESTA, S. & PATANE, D., 2006. S-waves
attenuation and separation of scattering and intrinsic absorption
of seismic energy in southeastern Sicily (Italy). Geophys. J. Int.
165, 211-222.
GUPTA, S.C., TEOTIA, S.S., RAI, S.S., and GAUTAM, N. (1998). Coda
Q estimates in the Koyna region, India. Pure Appl. Geophys.,
153, 713–731.
HAVSKOV, J., KVAMME, L., and BUNGUM H. (1986). Attenuation of
seismic waves in the Jan Mayen island area. Marine Geophys.
Res., 8, 39–47.
HAVSKOV, J., MALONE, S., MCCLURG, D., and CROSSON, R. (1989).
Coda Q for the state of Washington. Bull. Seismol. Soc. Am., 79,
1024–1037.
HAVSKOV, J., and OTTEMOLLER, L. (2003). SEISAN: The Earthquake
Analysis Softwares forWindows, Solaris and Linux, Version 8.0.
Institute of Solid Earth Physics, University of Bergen, Norway.
HOSHIBA, M. (1991). Simulation of multiple scattered Coda wave
excitation based on the energy conservation law. Phys. Earth
Planet Inter. 67, 123–136.
HOSHIBA, M., SATO, H., and FEHLER, M. (1991). Numerical basis of
the separation of scattering and intrinsic absorption from full
seismogram envelop- a Monte Carlo simulation of multi isotropic
scattering. Paper Metrol. Geophys., 42, 65–91.
MANDAL, P., JAINENDRA, JOSHI, S.,KUMAR, S., BHUNIA, R., RASTOGI,
B.K., 2004. Low coda Qc in the epicentral region of the 2001
Bhuj earthquake of Mw 7.7. Pure Appl. Geophys. 161,
1635–1654.
Vol. 169, (2012) Seismic Wave Attenuation 1599
MCSWEENEY, T.J., BISWAS, N.N., MAYEDA, K., and AKI, K. (1991).
Scattering and anelastic attenuation of seismic energy in central
and south central Alaska. Phys. Earth Planet. Inter., 67, 115–122.
MESHREF, W.M. (1990). Tectonic framework, ed. by in SAID, R. The
geology of Egypt: Rotterdam, A. A. Balkema, pp. 112–155.
MITCHELL, B.J. (1995). Anelastic structure and evolution of the
continental crust and upper mantle from seismic surface wave
attenuation. Rev. Geophys., 33, 441–462.
ORWIG, E. R. (1982). Tectonic framework of northern Egypt and the
eastern Mediterranean. EGPC: 5th Exploration Seminar, Cairo,
Egypt, p. 20.
PUJADES, L.G., UGALDE, A., CANAS, J.A., NAVARRO, M., BADAL, F.J.,
and CORCHETE, V. (1997). Intrinsic and scattering attenuation
from observed seismic codas in the Almeria Basin (southeastern
Iberian Peninsula). Geophys. J. Int. 129, 281–291.
RAUTIAN, T.G., and KHALTURIN, V.I. (1978). The use of the coda for
determination of the earthquake source spectrum. Bull. Se-
ism.Soc. Am. 68, 923–948.
SAID, R. (1962). The geology of Egypt. Elsevier Pub. Co., New
york, 337 pp.
SAID, R. (1981). The geological evolution of the River Nile. Elsevier
Pub. Co., Amsterdam & New York, 180 pp.
SATO, H. (1977). Energy propagation including scattering effects:
single scattering approximation. J. Phys. Earth, 25, 27–41
SHUKRI, N.M. (1953). The geology of the desert east of Cairo. Bll.
Inst. Desert d’ Egypt, vol. 3(2), 89–105.
SHUKRI, N.M.and Akmal, M.G. (1953). The geology of Gebel el
Nassuri and Gebel El Anqabia district, Cairo-Suez. Bull. Soc.
Geogr. Egypt, 26, 246.
SHUKRI, N.M., and EL AYOUTY, M.K. (1956). The geology of Gebel
Oweibid-Gafra area, Cairo-Suez district. Bull. Soc. Geogr.
Egypt, 29, 67–109.
WENNERBERG, L. (1993). Multiple scattering interpretations of coda
Q measurements. Bull. Seism. Soc. Am., 83, 279–290.
WU, R.S. (1984). Seismic wave scattering and the small scale
inhomogeneities in the lithosphere. Ph.D. thesis, Massachusetts
Institute of Technology, Cambridge, 305 pp.
WU, R.S. (1985). Multiple scattering and energy transfer of seismic
waves—separation of scattering effect from intrinsic attenuation.
I. Theoretical modeling. Geophys. J. R. Astr. Soc., 82, 57–80.
YOSHIMOTO, K., SATO, H., and OHTEKA M. (1993). Frequency-
dependent attenuation of P and S-waves in Kanto area, Japan
based on coda-normalization method. Geophys. J. Inter., 114,
165–174.
ZENG, Y. (1991). Compact solutions for multiple scattered wave
energy in time domain. Bull. Seism. Soc. Am., 81, 1022–1029.
ZENG,Y., SU, F., AKI, K. (1991). Scattering wave energy propa-
gation in the random isotropic scattering medium 1. Theory J.
Geophys. Res., 96, 607–619.
(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.