Annals n.6/2003 ok 23/04 1209 ANNALS OF GEOPHYSICS, VOL. 46, N. 6, December 2003 Key words aftershocks – seismic moment – scaling 1. 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 liq- uefaction of deltaic silty sand deposits (sand plumes) was observed in some cultivated fields of Giza Governerate located 19 km from the epicenter. According to eyewitness- es, 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 oc- curred in 1847. This mainshock was followed by an aftershock sequence. Within twenty two days after the occurrence of the Cairo earth- Estimation of seismic moments from local magnitudes and coda durations for the Cairo earthquake aftershocks recorded at Kottamyia (KEG) Broadband station El-Sayed M. Abdelrahman (1), Mohamed M. Dessokey (2), Hesham M. Hussein (2) and Mohamed F. Abdelwahed (2) (1) Cairo University, Faculty of Science, Geophysics Department, Cairo, Egypt (2) National Research Institute of Astronomy and Geophysics (NRIAG), Seismology Department, Helwan, Cairo, Egypt Abstract 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 mag- nitude (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 Re- search Institute of Astronomy and Geophysics (NRIAG), Seismology Department, Helwan 11421, Cairo, Egypt; e-mail: hesham6511421@yahoo.com 1210 El-Sayed M. Abdelrahman, Mohamed M. Dessokey, Hesham M. Hussein and Mohamed F. Abdelwahed quake 55 shocks with 1.7 ≤ ML ≤ 4.7 were recorded by Kottamiya (KEG) Broadband sta- tion. The event data are given in table I. Figure 1 shows the distribution of the well located af- tershocks of 1992 Cairo earthquake. After- shocks sequence was recorded by a temporary seismic network installed by National Re- search Institute of Astronomy and Geophysics during the first twenty days of this sequence. Details about the seismic network and the pro- cedure for determination of the hypocenters were described by Abou El Enein et al. (2000). However, the pattern of the aftershocks re- flects a cluster rather than a clear trend of seis- micity. Teleseismic body wave inversion of the mainshock (Hussein, 1999) suggested a nor- mal 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 af- tershocks recorded by the KEG Broadband station during the first three weeks after the occurrence of the mainshock using the ground displacement spectra of Lg waves and to de- velop empirical formulas for estimating Mo from both ML and coda duration. 2. Data Fifty-five Cairo earthquake aftershock se- quences 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 (ML) 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. 3. Method of analysis In this work, a time window that started short- ly before the Lg arrival, depending on the size of earthquake was obtained from the vertical com- ponent 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 fre- quency 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 at- tenuation which is related to the quality factor Q (Nuttli, 1986) U Q f $ $ =c r (3.1) f is the wave frequency and U is the Lg-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 fre- quency spectral level was estimated. The low fre- quency level (Ωo) was estimated visually by fit- ting a straight line at the low frequency spectra. Fig. 1. Aftershocks of Dahshour earthquake of 1992 (open squares). The fault plane solution of the main shock (star) is also shown. 1211 Seismic moments estimation Table I. List of earthquakes used in this study. Event Date Origin time Lat. Long. Depth MD ML No. y.m.d h min s °N °E (km) (HLW) 1 1992.10.12 13 50 9.65 29-46.94 31-13.66 10.93 2.5 2 1992.10.12 14 11 8.64 29-43.33 31-9.12 18.84 2.3 3 1992.10.12 14 15 7.43 29-57.23 30-57.28 25.09 2.8 4 1992.10.12 14 58 14.73 29-52.55 31-14.55 22.32 1.8 5 1992.10.12 15 07 42.05 29-53.52 31-6.80 26.85 2.3 6 1992.10.12 15 25 24.65 29-52.48 31-6.83 29.55 4.7 7 1992.10.12 15 52 50.77 29-51.24 31-9.94 22.77 2.3 8 1992.10.12 16 55 9.79 29-50.29 31-11.01 25.59 2.4 9 1992.10.12 18 31 42.36 29-47.89 31-9.82 21.14 2.2 10 1992.10.12 19 55 59.20 29-51.15 31-13.38 19.10 2.2 11 1992.10.12 21 31 34.22 29-40.00 31-7.06 20.73 4.2 12 1992.10.12 21 46 16.02 29-43.61 31-13.10 9.83 2.9 2.5 13 1992.10.12 23 34 22.50 29-55.72 31-16.90 17.10 3.0 2.7 14 1992.10.12 23 46 24.42 29-44.40 31-10.38 21.78 2.9 2.1 15 1992.10.13 18 09 8.14 29-52.44 31-10.98 22.39 3.4 3.7 16 1992.10.13 18 34 54.26 29-50.62 31-13.15 20.72 3.2 17 1992.10.13 23 27 56.39 29-53.00 31-7.37 32.02 2.4 2.2 18 1992.10.14 02 44 23.14 29-52.16 31-9.69 30.25 3.1 2.8 19 1992.10.14 03 50 14.53 29-46.63 31-6.43 29.49 3.4 2.8 20 1992.10.14 09 40 27.04 29-43.49 31-1.28 27.64 4.0 4.2 21 1992.10.14 10 41 57.34 29-46.67 31-7.99 22.95 2.6 1.9 22 1992.10.14 12 09 15.72 29-43.34 31-5.99 20.53 3.0 23 1992.10.14 13 46 39.47 29-50.45 31-10.37 28.51 3.5 3.2 24 1992.10.14 14 23 44.67 29-41.18 31-14.42 20.22 3.1 2.4 25 1992.10.14 14 31 27.90 29-43.41 31-6.98 24.97 3.3 2.9 26 1992.10.14 20 16 11.05 29-49.25 31-9.74 20.94 2.6 2.3 27 1992.10.15 12 13 41.41 29-48.25 31-9.02 25.52 2.6 2.0 28 1992.10.16 03 28 51.46 29-47.29 31-5.79 24.12 2.5 2.0 29 1992.10.16 05 56 11.84 29-47.31 31-3.17 30.70 3.1 2.9 30 1992.10.16 09 57 46.87 29-47.50 31-5.51 26.25 3.3 3.1 31 1992.10.16 18 07 53.12 29-51.50 31-7.49 24.20 2.6 2.4 32 1992.10.17 01 35 28.51 29-45.06 31-8.25 25.44 2.6 2.0 33 1992.10.18 08 12 16.12 29-43.38 31-8.40 20.74 3.4 2.9 34 1992.10.18 13 04 28.44 29-42.75 31-13.80 18.50 3.0 2.6 35 1992.10.19 10 46 30.95 29-42.67 31-9.58 21.58 2.9 2.2 36 1992.10.19 12 30 16.44 29-44.22 31-6.30 25.20 3.2 3.0 37 1992.10.19 14 59 50.43 29-44.50 31-8.87 18.68 3.3 3.2 38 1992.10.20 06 00 30.77 29-32.36 31-4.27 22.28 2.7 1.7 39 1992.10.20 17 28 28.44 29-40.39 31-9.24 20.62 2.5 2.0 40 1992.10.20 23 14 47.46 29-43.08 31-7.65 17.20 3.1 3.1 41 1992.10.21 18 09 27.53 29-46.47 31-2.00 14.65 2.7 2.0 42 1992.10.22 08 28 58.70 29-44.83 31-6.53 21.90 3.4 3.4 43 1992.10.22 17 38 57.30 29-40.62 31-5.68 22.88 3.9 4.6 44 1992.10.23 02 40 5.43 29-44.21 31-5.46 22.85 2.6 2.2 45 1992.10.23 15 12 10.08 29-41.39 31-10.00 22.40 3.8 3.3 46 1992.10.23 16 02 4.12 29-44.78 31-7.38 21.70 2.4 1.7 47 1992.10.25 09 05 4.64 29-40.09 31-10.71 22.05 3.1 2.8 48 1992.10.25 12 26 15.06 29-39.93 31-5.95 24.12 3.1 2.7 49 1992.10.25 16 21 05.28 29-38.35 31-6.70 22.92 2.9 2.3 50 1992.10.25 19 45 34.56 29-40.97 31-8.52 23.78 2.3 3.2 51 1992.10.26 06 45 23.96 29-52.40 31-6.49 27.45 3.4 3.3 52 1992.10.26 08 43 52.01 29-40.55 31-5.75 28.25 2.8 2.4 53 1992.10.28 06 20 54.90 29-37.30 31-3.63 24.63 2.9 2.5 54 1992.10.28 18 25 56.28 29-50.64 31-16.07 19.46 2.8 2.5 55 1992.10.30 14 08 11.19 29-40.70 31-5.09 25.71 3.0 2.7 1212 El-Sayed M. Abdelrahman, Mohamed M. Dessokey, Hesham M. Hussein and Mohamed F. Abdelwahed Fig. 2. Displacement spectra for Lg-waves for some selected events. 1213 Seismic moments estimation 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 the- oretical model by Herrmann and Kijko (1983) / < / M R R R R R R R 4 / o o o o o o o o o o 3 3 1 2 = rtb Ω M R R R4 $= rtb Ω ^ ^ h h (3.2) 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 Ro is related to different kinds of Lg- waves geometric spreading. 4. Results 4.1. Seismic moment coda duration and local magnitude The seismic moment Mo is a measure of an earthquake strength defined in terms of param- eters of double couple shear dislocation source model (Aki, 1966). It provides a better descrip- tion 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 re- gion in eq. (3.2) were selected as follows: ρ = 2.7 gm/cm3, β = 3.5 km/s and Ro = 100 km. The seismic moment estimated was found to range from 3.5 × 1019 to 2.5 × 1022 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 be- tween 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 avail- able 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- Table II. Seismic moment of the events under study. Event Duration ML Mo No. (s) (dyne ⋅ cm) 1 2.5 1.942783E + 20 2 2.3 2.267175E + 20 3 2.8 2.836813E + 20 4 1.8 5.468023E + 19 5 2.3 7.922314E + 19 6 279 4.7 2.267175E + 22 7 2.3 8.386375E + 19 8 2.4 1.225617E + 20 9 2.2 1.28611E + 20 10 2.2 1.520192E + 20 11 169 4.2 7.825914E + 21 12 57 2.5 1.021348E + 20 13 65 2.7 7.1504E + 20 14 2.1 8.689964E + 19 15 161 3.7 2.028367E + 21 16 1992 3.2 7.671786E + 20 17 37 2.2 6.70293E + 19 18 56 2.8 3.1557E + 20 29 2.8 4.717935E + 20 20 237 4.2 5.429151E + 21 21 1.9 5.667937E + 19 22 34 3.0 3.666106E + 20 23 3.2 4.157197E + 20 24 2.4 4.071058E + 20 25 69 2.9 4.769604E + 20 26 45 2.3 6.387174E + 19 27 35 2.0 6.550127E + 19 28 2.0 3.571662E + 19 29 108 2.9 5.07458E + 20 30 62 3.1 7.187676E + 20 31 2.4 2.237957E + 20 32 35 2.0 6.845436E + 19 33 78 2.9 4.614945E + 20 34 63 2.6 3.037181E + 20 35 39 2.2 9.024836E + 19 36 85 3.0 7.510935E + 20 37 79 3.2 6.659202E + 20 38 1.7 2.856025E + 19 39 30 2.0 5.832978E + 19 40 87 3.1 9.421127E + 20 41 2.0 6.235795E + 19 42 94 3.4 1.637872E + 21 43 4.6 2.522325E + 22 44 34 2.2 1.227609E + 20 45 3.3 1.490997E + 21 46 1.7 3.499786E + 19 47 55 2.8 4.527036E + 20 48 68 2.7 5.052129E + 20 49 38 2.3 1.011922E + 20 50 3.2 7.076904E + 20 51 99 3.3 1.602396E + 21 52 34 2.4 1.00893E + 20 53 59 2.5 2.729787E + 20 54 50 2.5 1.03903E + 20 55 2.7 3.834036E + 20 1214 El-Sayed M. Abdelrahman, Mohamed M. Dessokey, Hesham M. Hussein and Mohamed F. Abdelwahed Fig. 3. Seismic moment (Mo)-coda duration relation of Dahshour aftershocks. Fig. 4. Plot of seismic moment versus local magnitude. 1215 Seismic moments estimation ground noise amplitude. The linear regression fitting of the data as shown in fig. 3 indicates the following relation: . . . . . Log LogM D D 2 35 0 27 16 33 0 48 30 108 o ! ! # # = + + ^ ^ ^ ^ ^ h h h h h (4.1) Estimation of seismic moment from a simple parameter such as coda duration is very use- ful, as it allows the estimation of the source size of local earthquakes for the moment range 3.5 × 1019 to 1.6 × 1021 dyne ⋅ cm. Our linear moment magnitude relation over the available duration range results in mean root square error of 0.05 in Log (Mo). The obtained relation for all the available moment range is insufficient for meaningful comparison with the published Log (Mo)-Log (D) relations in different tectonic provinces. The seismic moment-local magnitude re- lation of the form Log (Mo) = CML + D should be carried out carefully (Shapira and Hofstet- ter, 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 rela- tively small number of ML > 5.0 earthquakes. Using these recommendations, the moment magnitude relation is obtained for the select- ed 50 earthquakes in the range 1.7 ≤ ML < 3.5. In this work, a change in the moment magni- tude relation at ML ≈ 3.5 could not be ob- served due to small number of larger events. Figure 4 shows the seismic moment versus lo- cal magnitude ML. The least square fitting gives the following equation: . . . . . < . . M M M Log 0 96 0 05 17 88 0 13 1 7 3 5 o L L ! ! # = + + ^ ^ ^ ^ h h h h (4.2) This relation is valid for earthquakes with 1.7 ≤ ≤ ML < 3.5 and seismic moment in the range 3.5 × 1019 to 1.6 × 1021 dyne⋅cm. The average root mean square difference in the estimated Log (Mo) is 0.028. The relation is in a fair agreement with Log Mo = 1.1 ML + 17.9 for ML ≤ 4.1, this relation was obtained by Fletcher et al. (1984) for aftershocks of Orville, California earthquake. Performing a least square fitting of Log Mo versus ML for ML ≤ 4.1 yields almost identical values to eq. (4.2) Log (Mo) = (0.95 ± 0.05)ML + (17.90 ± ± 0.13). The slope of the least square fitting between Log (Mo) and ML is near one. A slope of about 1.0 for the moment-magnitude rela- tionship seems to be similar to those obtained in many proposed moment magnitude rela- tions for Mammoth lakes, California (Archu- leta et al., 1982), Oroville, California (Fletch- 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) demon- strated that the slope of 1.0 for moment mag- nitude relations can be explained by the re- sponse 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. 5. Conclusions Seismic moment Mo, logarithm of the co- da 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 relation- ships, which is superior to any magnitude scale. The resulting estimate of seismic mo- ment, from local magnitudes and coda dura- tion 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. – Coda durations are related to seismic mo- ment by the following linear relation: Log (Mo) = = (2.35 ± 0.27) Log (D) + (16.33 ± 0.48) with a rms precision of 0.05 in Log (Mo). The derived empirical relationships are valid only for Cairo earthquake source region (Dahshour) as recorded at KEG broadband sta- tion. 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. 1216 El-Sayed M. Abdelrahman, Mohamed M. Dessokey, Hesham M. Hussein and Mohamed F. Abdelwahed REFERENCES ABOU EL ENEIN, K.M., H.M. HUSSEIN, A.S. ABU EL ATA and E.M. IBRAHIM (2000): Seismological aspects of the Cairo earthquake, 12 October 1992, Ann. Geofis., 43 (3), 485-504. AKI, K. (1966): Generation and propagation of G waves from the Niigate earthquake of June 16, 1964. Part 2. Estimating of earthquake movement, release energy, and stress-strain drop from G wave spectrum, Bull. Earthquake Res. 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