Citation: Shalaby, I., T. Hayashida (2023), Ground motion simulation of a significant earthquake in Egypt,
Synopsis of IISEE-GRIPS Master’s Thesis.

GROUND MOTION SIMULATION OF ASIGNIFICANT EARTHQUAKE IN EGYPT
Ibrahim SHALABY1
MEE22702

Supervisor: Takumi HAYASHIDA2*

ABSTRACT
Destructive and significant earthquakes like the 1992 Dahshur Earthquake (Mb 5.8) in Egypt, whichcaused extreme damage to lives and property, high mortality, and severe injuries, may happen again
with similar or different magnitudes and intensities. Earthquake simulation requires three pieces of
information: source effect, wave propagation path, and site amplification factors. This study aims toseparate the source, site, and path effects of earthquakes recorded by the Egyptian Strong-Motion
Network (ESMN) to simulate ground motions from a significant earthquake that may recur in Egypt.
We applied the spectral inversion method (generalized spectral inversion technique; GIT) using the
ground motion records observed at 20 stations for 52 earthquakes (M3–7.8) to separate the factors. We
regarded station HLWN as a reference rock site and station ANSH as a divisor that recorded the
maximum number of events. Finally, we simulated the ground motions for a potential earthquake in
Cairo (Mw7.0), using the derived information from GIT and phase information from a small earthquake
in Cairo. The simulated waveform indicates peak ground accelerations of 58 cm/s2 at station HLWN,
about 35 km from the epicenter, suggesting the possibility of widespread strong ground motions in
populated areas. This study shows that GIT can provide physics-based ground motion estimations in
Egypt.
Keywords: Spectral inversion, Site amplification, Attenuation factor, Reference site, ESMN.
1. INTRODUCTION
The earthquake-induced ground shaking (i.e., earthquake ground motion) is mainly controlled by theearthquake source, propagation path, and site amplification factors. While seismic source characteristics
are related to the earthquake generation process associated with the fault rupture phenomenon,
propagation characteristics are related to the wave propagation of the seismic waves emitted from theseismic source. Site characteristics, also known as ground motion amplification characteristics, indicate
the effects of seismic wave amplification on shallow sediments. These characteristics contribute toground-motion prediction in a complex manner. Accordingly, science and engineering research is being
actively pursued. Many research findings were based on exhaustive surveys of damaged areas. In Egypt,
two earthquakes (in southwest Cairo on 12 October 1992, and Gulf of Aqaba on 22 November 1995)
caused damage in populated areas. During the 1992 Cairo earthquake, the most severely affected regions
were Old Cairo, Bulaq, and areas extending southwards along the Nile. This event resulted in thedestruction of 350 buildings and extensive damage to 9,000 others. Additionally, 216 mosques and 350
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National Research Institute of Astronomy and Geophysics (NRIAG)-Helwan-Cairo-Egypt.
International Institute of Seismology and Earthquake Engineering, Building Research Institute.

* Chief examiner1

schools suffered significant harm, leading to approximately 30,000 families being displaced from theirhomes.
The generalized spectral inversion technique (GIT) is employed to identify the spectral
shapes of the strong motions dividing earthquake records into the source, propagation path, and site
amplification factors. This method assists in deducing the physical factors that govern the mechanisms
considered in ground motion generation, and it facilitates the creation of accurate models by utilizing
information from the Fourier amplitude spectra (FAS). This study determined the strong ground motion
parameters observed by the Egyptian Strong Motion Network. We also attempted to estimate groundmotions at current seismic stations for a possible earthquake with a magnitude of Mw7.0.
2. DATAIn this work, 52 strong-motion earthquakes were gathered from 20 stations containing 206 acceleration
records. The magnitude ranged from 3 to 7.8. The events were recorded from 2008 (when the ESMN
was constructed) to 2023. The acceleration waveforms were recorded in unit m/s2 or count. The fileformats were seed, mseed, and ASCII, all converted to the sac format. This dataset was manually selectedfrom approximately 8000 local and regional earthquakes that happened in Egypt and around Egypt, andthat were recorded in the NRIAG bulletin and the GCMT catalog using the Compass 2014 software andby applying a band-pass filter to clear the events recorded in our stations. The file format was converted
to the SAC format using the same software. To convert the data from count to gal, we use the formulas
shown in Table 1. for each sensor.
Table 1. Conversion coefficients from count to gal (cm/s2).
Type of sensors
The equation used
Reftek

(0.66×10-6 ) × (readings)

Titan(0.0625×10-6 ) × (readings)

Kinemetrics(0.119×10-6) × (readings)

Guralp(0.981×10-6) × (readings)

Two or three different sensor types were changed at the same station during themeasurement period, or the same sensor was replaced at a different station in a different period. All therecord names at the same station were renamed in this work, even with different sensor types, to only
one name for each station.
3. METHODOLOGY
3.1. Earthquake parameters separation
The GIT is based on a mathematics concept, in which the Fourier amplitude spectra of the ground motion
are expressed in the frequency domain as the product of three factors; 𝑆𝑖 (𝑓) the spectrum of the source
associated with the ith earthquake, 𝑃𝑖𝑗 (𝑓, 𝑋𝑖𝑗 ) is the function of distance and frequency accounting forthe path effects and 𝐺𝑗 (𝑓) is the site response function of the jth station as expressed in Eq. (1):𝐹𝑖𝑗 (𝑓, 𝑋𝑖𝑗)=𝑆𝑖 (𝑓) . 𝑃𝑖𝑗 (𝑓, 𝑋𝑖𝑗) . 𝐺𝑗 (𝑓)(1)

The term 𝑃𝑖𝑗 (𝑓, 𝑋𝑖𝑗 ) by Boore (1983) was presented as a function of S-wave velocity along
the path Vs, the frequency‐dependent quality factor 𝑄(𝑓) and hypocenter distance 𝑋𝑖𝑗 as follows:−𝜋𝑓𝑋𝑖𝑗1

𝑃𝑖𝑗 (𝑓, 𝑋𝑖𝑗 ) = 𝑋 𝑒𝑥𝑝 ( 𝑉 𝑄(𝑓) )
𝑖𝑗

𝑠

2

(2)

The following is obtained when substituting Eq. (2) in Eq. (1):−𝜋𝑓𝑋

−1𝐹𝑖𝑗 (𝑓, 𝑋𝑖𝑗 ) = 𝑆𝑖 (𝑓) . 𝐺𝑗 (𝑓) . 𝑋𝑖𝑗
𝑒𝑥𝑝 ( 𝑉 𝑄(𝑓)𝑖𝑗 )𝑠(3)

The parameters are separated by taking the natural logarithm of the left and right sides. We
applied for four Fortran programs following Iwata & Irikura (1988), developed by Dr. Hayashida(IISEE-BRI). Only S-wave was used for the treatment; hence, the first program extracted the S-wave
part, in which the first 10.24 s from the S-wave onsets. Fast Fourier transform (FFT) was also performed
for the selected data to obtain the Fourier spectra and horizontal-to-vertical (H/V) spectral ratios of theextracted waves. The second program was implemented to create the matrices using the accepted dataset.
The third program stabilizes the inversion problem by choosing some known parameters. From H/Vresults, we assumed station HLWN as a reference rock site, assuming the amplification factor as
𝐺𝑗 (𝑓) = 2, and station ANSH as a divisor site. The final program derives the estimated source, site
amplification, and attenuation path factor by conducting a linear inversion analysis.
3.2. Simulation of potential earthquake
This study mainly aimed to simulate an earthquake in Egypt that may recur at the source, similar to thatof the historically significant and destructive earthquakes in Egypt. The most recent major earthquake isthe 1995 Gulf of Aqaba earthquake (Mw7.3), but the small earthquake ground motion records that
occurred near the epicenter, which are necessary to reproduce it, are not included in our data set. On theother hand, we assumed a Mw7.0 earthquake in Cairo for the simulation.
Earthquake simulation requires the recorded data of a smaller earthquake (i.e., target
earthquake) at the same location. We did not have a record of the 1992 earthquake, but we have the datafrom three stations for the 202012111547 event. By comparison, this event was the closest to the 1992
Dahshur Earthquake, bearing only a small location difference. Hence, it was considered herein as a target
earthquake.
The following parameters to simulate the waveforms should be estimated: Fourier amplitude
spectra for the target large earthquake and phase spectra from the small earthquake. Three parameters
were needed to model the amplitude spectra, namely, the source, path (Q factor), and site effects. For thesource effect, we had the pseudo-point source models (Nozu, 2012) that followed the assumption of anomega square model based on the earthquake source model proposed by Brune (1970). The flat level(Ωo) and the corner frequency (fo) were estimated from the seismic moment (Mo) to define the source
spectrum of the simulated event. The formula of Hanks and Kanamori (1979) was used to calculate theseismic moment (Mo) from moment magnitude Mw, from Eq. (4) we assumed (Mw=7) we found Mo =3.55e + 26 dyne.cm. where:
Mo = 101.5 ( 𝑀𝑤+10.7 )(4)The corner frequency (fo) was estimated by following the empirical formula of Kawase &Matsuo (2004) Eq. (5) by substitute with Mo, we found 𝑓0 = 0.035 Hz.
Mo = 8.0 × 1022 × 𝑓0 −2.5015(5)

All these parameters were employed to determine the source effect for the potential
earthquake follow formula of David & Boore, (1983):
𝑀0
S (f) = Rθϕ . fs . PRTITN . 4𝜋𝜌𝛽3 .

3(2𝜋𝑓)2
1+(

𝑓 2
)
𝑓0

(6)

where, 𝑆(𝑓) is Fourier amplitude spectra, 𝑅𝜃𝜙 = 0.55 is the radiation pattern, 𝑓𝑠 = 2 is the free𝟏
surface effect, 𝑃𝑅𝑇𝐼𝑇𝑁 =is coefficient that separate the horizontal motion into two component,√𝟐𝜌=2.4 g/cm3 is the density and 𝛽=3.55 km/s is the S-wave velocity.
Now we have the phase of the simulated earthquake where it is the same as the target
earthquake. From Eq. (6), we obtained the source spectrum of the target earthquake, and we considered
the estimated site effect and Q-factor to model the amplitude spectra at the given site. Our target stationsare HLWN, KOTM, and DABA.
By compiling the Fourier amplitude spectra and the corresponding phase of the potential
earthquake with magnitude Mw7.0 at the location of the 1992 Dahshur Earthquake. The spectra wereconverted to the time domain at the station that recorded the target earthquake.
4. RESULTS AND DISCUSSION
4.1. Earthquake parameters separation
By applying the four Fortran programs with some characteristic and changing the characteristics andtrying again, the programs exclude some data, finally we get the suitable results by using 137 records at
15 stations from 19 events. As clear in Figure 1. The estimated site amplification factors assuming the
HLWN station as a reference site. We plotted the amplification spectra in the frequency range of 0.2 to
10 Hz for each station. Almost all the station site amplifications decreased when the frequency increased.
This was mainly observed in frequencies higher than 1.0 Hz. In addition, some stations presented strangesite effect values higher than 10, which may be attributed to the data rarity and sensor history in thesesites, where each sensor had a different conversion equation from count to gal (cm/s2), as shown in Table
1. Also, the results show that at some sites the amplification factor estimated is similar to the H/Vspectral ratio.

DABA
KOTM
HLWN
Stations
3 ≤ m<44 ≤ m<55 ≤ m<6
6 ≤ mFigure 1. Epicenters of the events used inthis study (circles) and the ESMN stations(triangles).

Figure 2. Estimated site amplification factors at
each frequency at each station.

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The estimated Q factors are plotted in Figure 3 in the frequency range of 0.2 to 10
Hz. The attenuation model (Q factor) is derived as a function of the frequency Q(f) = B fα using
the least square method. Accordingly, B = 186.86 and α = 1.5 are obtained. The estimated Q
factors show frequency dependency.
Concerning source factors, we plot theestimated source factors as a function of the frequency
from 0.2 to 10 Hz for all events accepted in the inversion
using the reference site constraint. The source spectral
decay shows that all estimated source spectra for all
events rapidly decrease at a frequency greater than 1 Hz.
The source spectra illustrate frequency dependence. We
did not examine the seismic moment (M0), where thefrequency band is limited, as shown in Figure 4.

Figure 4. Estimated source
factors for all accepted events.

4.2. Simulation of potential earthquake
The simulated and target
earthquakes
were
approximately at the same
location, 35 km fromHLWN station, 78 kmfrom KOTM station and
320 km from DABA
station. The peak groundamplitudes (PGA) at
station DABA show smallvalues; 1.7 gal and 2.2 gal
in
N-S
and
E-W
components, respectively.
Station KOTM is locatedfarther than station HLWN
from the epicenter, but theestimated PGAs are 65 gal
and 70 gal in N-S and E-W
component, respectively.
The PGAs at station
HLWN, the PGA values
are 58 gal and 50.4 gal in
N-S and E-W component,
respectively, implying thatstation KOTM is locatedon soft sediment.

Figure 3. Estimated Q-factor

58 gal50.4 gal(E-W) HLWN

(N-S) HLWN

70 gal

65 gal(E-W) KOTM

(N-S) KOTM

2.2 gal

1.7 gal(E-W) DABA

(N-S) DABA

Figure 5. Simulated waveform and PGA values for an M7
earthquake (Mw7.0) at the E–W and N–S components of the
HLWN, KOTM and DABA stations (see location in Figure 1).

5. CONCLUSIONSThis study focused on separating the source, path, and site effects from the recorded strongmotion data in the ESMN from 2013 to 2023. The spectral inversion method was applied toseparate the three factors of source, path, and site. It used the S-wave portion of the observed

5acceleration Fourier spectra to estimate the site amplification and the Q factor in the 0.2 to 10
Hz frequency range.
The HLWN station was chosen as a reference rock site, to stabilize the inversion,considering the S-wave H/V ratio information. The estimated amplification factor in the HLWN
station also confirmed its ability to be a reference site.
Estimating the source factors resulted in the 0.2 to 10 Hz frequency range for all theevents used in the inversion, which employed the reference site constraint. The source spectral
decay showed that all estimated source spectra for all events rapidly decreased at a frequency
greater than 1 Hz. The source spectra displayed frequency dependence. The Q factor was
calculated where the Q(f) = 186.86 f1.5, which clearly showed frequency independent.
Finally, we simulated ground motions waveforms for the potential earthquake in
Cairo (Mw=7.0). The Fourier amplitude spectra at the three sites target were obtained from thesite, path, and source effect parameters for the potential earthquake. The Fourier phase spectra
were obtained from the small earthquake recordings at the same location. The estimatedwaveforms show that PGAs at station KOTM are larger than station HLWN located closer tothe epicenter, implying a larger site amplification. Our estimates suggest that the groundmotions around Cairo will be large for the potential earthquake due to subsurface soils,
indicating the importance of evaluating ground motions at many sites, considering the detailed
source model and site amplification factors.
ACKNOWLEDGEMENTS
This research was conducted during the individual study period of the training course “Seismology,
Earthquake Engineering and Tsunami Disaster Mitigation” by the Building Research Institute, JICA,
and GRIPS. I would like to thank all professors and the administration staff of these entities. Also, I
would like to express my sincere gratitude to my supervisor Dr. Takumi Hayashida for his valuable
support and experience which helped me to complete my research successfully. And thank my instituteprofessors and colleagues who provide me with data.
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