Estimation of seismic moments from local magnitudes and coda durations for the Cairo earthquake aftershocks recorded at Kottamyia ( KEG ) Broadband station

The spectral analysis of fifty-five KEG VBB records from the October 12, 1992 Cairo earthquake source region was performed to obtain the seismic moment. We obtained this parameter in turn to develop empirical local magnitude (ML), seismic moment (Mo), coda duration (D) relations for that region. In this study the data consist of Lg-waves on the vertical component seismograms for the recorded earthquakes with ML ranging from 1.7 to 4.7. The derived empirical relation between the seismic moment (Mo) and magnitude ML for the aftershocks sequence with 1.7 ≤ ML < 3.5 is Log (Mo) = (0.96 ± 0.05) ML + (17.88 ± 0.13). We found a correlation between the coda duration (D) and Log of the moment (Log (Mo)) as follows: Log (Mo) = (2.35 ± 0.27) Log (D) + (16.33 ± 0.48). Mailing address: Dr. Hesham M. Hussein, National Research Institute of Astronomy and Geophysics (NRIAG), Seismology Department, Helwan 11421, Cairo, Egypt; e-mail: hesham6511421@yahoo.com


Introduction
On 12th of October 1992 a moderate size earthquake of Mw = 5.8 occurred at epicentral distance of about 25 km south west of Cairo city downtown in Dahshour region (fig.1) at a depth of 22 km.This earthquake was felt from Alexandria to Aswan.It registered a maximum observed intensity of 7 + in MSK intensity scale in Dahshour region (Maamoun et al., 1993).This shock caused considerable damage to the buildings in the eastern part of Cairo, Giza and the northern area of Fayoum.Significant damage was found mostly in adobe and old non-reinforced brick masonry buildings and non-engineering reinforced concrete buildings.In addition, extensive liquefaction of deltaic silty sand deposits (sand plumes) was observed in some cultivated fields of Giza Governerate located 19 km from the epicenter.According to eyewitnesses, sand and water continuously blew up to a height of 3 m for about 45 min (Maamoun et al., 1993).
The October 12, 1992 Cairo earthquake struck a previously known low seismicity zone.The only significant earthquake reported in this region during the historical period occurred in 1847.This mainshock was followed by an aftershock sequence.Within twenty two days after the occurrence of the Cairo earth-quake 55 shocks with 1.7 ≤ ML ≤ 4.7 were recorded by Kottamiya (KEG) Broadband station.The event data are given in table I. Figure 1 shows the distribution of the well located aftershocks of 1992 Cairo earthquake.Aftershocks sequence was recorded by a temporary seismic network installed by National Research Institute of Astronomy and Geophysics during the first twenty days of this sequence.Details about the seismic network and the procedure for determination of the hypocenters were described by Abou El Enein et al. (2000).However, the pattern of the aftershocks reflects a cluster rather than a clear trend of seismicity.
Teleseismic body wave inversion of the mainshock (Hussein, 1999) suggested a normal faulting mechanism with a small strike slip component on a plane striking EW to WNW-ESE and dipping to the east (fig.1).
The purpose of this study is to calculate the seismic moments of Cairo earthquake aftershocks recorded by the KEG Broadband station during the first three weeks after the occurrence of the mainshock using the ground displacement spectra of L g waves and to develop empirical formulas for estimating Mo from both ML and coda duration.

Data
Fifty-five Cairo earthquake aftershock sequences recorded during the three weeks after the occurrence of the mainshock of the October 12, 1992 earthquake were used in this study.Event data are given in table I.The local magnitude (M L) of these events varied from 1.7 to 4.7.All of these earthquakes are of crustal origin.Figure 1 shows the location of KEG station.KEG station is a part of the MEDNET project (Gardini et al., 1992).The seismic records were electronically digitized at a rate of 20 samples per second by STS-1 VBB velocity type sensor.For frequencies between 0.003 and 7 Hz the velocity response is flat with a full dynamic range of 140 dB.KEG station was the only available digital recording station in Northeast Africa and Egypt in 1992.

Method of analysis
In this work, a time window that started shortly before the Lg arrival, depending on the size of earthquake was obtained from the vertical component seismometer of KEG STS-1 VBB.The time window was nearly 10 s long.The digital data within the time window were corrected for the instrumental response, transformed to frequency domain using fast Fourier transformation.This spectrum was then integrated to obtain the displacement spectra.Typical spectrum examples are shown in fig. 2.
The spectrum was corrected for attenuation by multiplying it by the transfer function e −γ r where r is the distance from the source to the receiver and γ is the coefficient of anelastic attenuation which is related to the quality factor Q (Nuttli, 1986) f is the wave frequency and U is the L g-wave group velocity.Dessokey et al. (2000) obtained the γ value of 0.001497 km -1 for 1 Hz Lg in Dahshour region.
From the corrected spectrum, the low frequency spectral level was estimated.The low frequency level (Ωo) was estimated visually by fitting a straight line at the low frequency spectra.The seismic moments (Mo) were derived for the 55 recorded events from the low spectral level (Ωo) using Street et al. (1975)'s formula that was subsequently derived by means of theoretical model by Herrmann and Kijko (1983 where ρ is the density of the medium, β is the shear wave velocity, R is the epicentral distance and Ro is the reference distance.The reference distance R o is related to different kinds of Lgwaves geometric spreading.

Seismic moment coda duration and local magnitude
The seismic moment Mo is a measure of an earthquake strength defined in terms of parameters of double couple shear dislocation source model (Aki, 1966).It provides a better description of the real size of an earthquake.
On the basis of previous empirical results, the seismic moments of the events under study were estimated using eq.(3.2).Constant values corresponding to Cairo earthquake source region in eq. ( 3.2) were selected as follows: ρ = 2.7 gm/cm 3 , β = 3.5 km/s and Ro = 100 km.The seismic moment estimated was found to range from 3.5 × 10 19 to 2.5 × 10 22 dyne⋅cm.The calculated seismic moments using eq.( 3.2) are listed in table II.
The scatter for the events having a duration longer than 108 s (fig.3) is due to the small number of longer duration shocks.To obtain a more appropriate relation between the moment and the duration, a mathematical regression between the reported seismic moments and the corresponding coda durations D was made for 30 ≤ D ≤ 108 s.The coda duration in seconds used in this study was obtained from the available analog seismographic stations installed at the time of the earthquake.It was taken from the P arrival to the point in the coda where the seismic amplitude is nearly twice the back-   The seismic moment-local magnitude relation of the form Log (Mo) = CML + D should be carried out carefully (Shapira and Hofstetter, 1993).Bakum (1984) and Hanks and Boore (1984) detected a change in C value in this relation at ML ≈ 3.5, usually undetected due to a large number of ML < 5.0 and relatively small number of ML > 5.0 earthquakes.Using these recommendations, the moment magnitude relation is obtained for the selected 50 earthquakes in the range 1.7 ≤ ML < 3.5.In this work, a change in the moment magnitude relation at ML ≈ 3.5 could not be observed due to small number of larger events.Figure 4 shows the seismic moment versus local magnitude ML.  er et al., 1984), Hawaii (Savage and Mayer, 1985), California (Chen and Chen, 1989), Baltic shield (Kim et al., 1989) and Petlan, Mexico (Valdes et al., 1996).Randall (1973), Archuleta et al. (1982), and Fletcher et al. (1984) demonstrated that the slope of 1.0 for moment magnitude relations can be explained by the response of the Wood-Anderson instrument since the corner frequency of small events is greater than the cutoff frequency of 1.2 Hz Wood-Anderson instrument.

Conclusions
Seismic moment M o, logarithm of the coda duration and the local magnitude empirical relations were derived for the aftershocks of 1992 Cairo earthquake source area, providing a simple and straightforward way to quantify the source strength Mo through such relationships, which is superior to any magnitude scale.The resulting estimate of seismic moment, from local magnitudes and coda duration imply the following: -Seismic moment and local magnitude data are consistent with Log (Mo) = (0.96 ± 0.05) ML + + (17.88 ± 0.13).The rms precision in Log (Mo) is 0.028.
The derived empirical relationships are valid only for Cairo earthquake source region (Dahshour) as recorded at KEG broadband station.Their significance is only available in the 3.5 × 10 19 to 1.6 × 10 21 dyne⋅cm moment range and 1.7 to 3.4 local magnitude range.

Fig. 1 .
Fig. 1.Aftershocks of Dahshour earthquake of 1992 (open squares).The fault plane solution of the main shock (star) is also shown.

Table I .
List of earthquakes used in this study.

Table II .
Seismic moment of the events under study.