Attenuation in Different Directions ~ Earthquake

Attenuation in Different Directions

Epicentral distances have been measured along different directions and it is observed that the distance for the same isoseist is often different in different directions. Fig.2 shows the attenuation of three different earthquakes in different directions. From Fig.2, for 1885 Bengal earthquake it is observed that the intensity in the direction west shows much smaller attenuation. For 1930 Dhubri earthquake, South and S45⁰W directions represent greater attenuation. For 1918 Srimangal earthquake, S45⁰W and east directions show greater attenuation. So the directions affecting Bangladesh (see Fig.3) in general show greater attenuation than some other directions.

Figure 2: Attenuation of different earthquakes in different directions.

Development of Attenuation Law

For the establishment of Intensity-attenuation relationship, seven earthquakes have been selected as mentioned earlier. Because of the directional difference in intensity attenuation (Fig.2), directions have been chosen which are affecting Bangladesh mainly. Six out of seven earthquakes have been considered for which average epicentral distances along these directions are determined for each isoseismal. Chosen directions for these earthquakes are shown in Fig.3.

Figure 3 Directions considered for determining average epicentral distances of isoseismals for six earthquakes (except 1897 Assam earthquake)

Table 1 presents the epicentral distance data considered for different isoseismals of different intensities (MMI scale). Also shown are relevant earthquake data (date, epicenter location and depth, and magnitude). The epicentral distance data for 1897 Assam earthquake is taken from the average radius data given by Ambraseys and Bilham (2003), since the isoseismals are of very irregular shape (Fig.1a). The directional average distance of the isoseismals from the epicenter is estimated for the other six earthquakes. The Table 1 data is used for developing attenuation law.

Table 1: Epicenter location and mean directional epicentral distance data of selected earthquakes:

No.	Date	Earthquake Epicenter		M	Depth (km)	Mean Directional* Epicentral Distance (km) of Isoseismals for Different Intensities (MMI)
No.	Date	Lat.	Long.	M	Depth (km)	III	IV	V	VI	VII	VIII	IX	X
1	14/07/1885	24.70⁰N	89.55⁰E	7.0	72	403	-	238	-	88	-	-	-
2	12/06/1897	25.84⁰N	90.38⁰E	8.1	60	-	576	381	250	172	75	-	-
3	08/07/1918	24.25⁰N	91.80⁰E	7.6	14	-	-	119	74	-	39	-	18
4	02/07/1930	25.95⁰N	90.04⁰E	7.1	60	-	-	233	139	-	58	16	-
5	08/07/1945	25.8⁰N	92.3⁰E	6.7	-	-	260	185	105	-	-	-	-
6	15/04/1964	21.7⁰N	88⁰E	5.5	36	162	90	50	-	-	-	-	-
7	22/07/1999	21.61⁰N	91.96⁰E	5.1	10	-	-	17	8	4	-	-	-

* Epicentral distance of isoseismals for 1897 earthquake is taken not on directional basis due to irregular shape of isoseismal, but from tabulated average values given by Ambraseys and Bilham (2003)

Attenuation Model 1 (Using Epicentral Distance)

The attenuation law for intensity is assumed to be of the standard form of Eq.(1):

I=a+b*(M)+c*(R)+d*log(R)+σP (1)

where a, b, c, d are coefficients, M is the earthquake magnitude (Richter scale or equivalent), R is the mean epicentral distance, I is the intensity (MMI), σ is the standard deviation of I. The constant P takes a value zero for 50 percent probability that the parameter will exceed the real value and one for 84 percent probability.

Then coefficients a,b,c,d are determined by fitting Eq.(1) to the earthquake data set M and selected (I, R) pairs listed in the Table 1. The regression analysis is performed using a program developed in Matlab 7.0, details of which is given by Islam (2009). The data set consists of 25 (I, R) pairs for seven earthquake events. The following equation is obtained for Attenuation Model 1 using epicentral distance:

I=1.0249+1.4863*(M)-0.0042*(R)-2.4518*log(R)+1.001P (2)

with standard deviation σ = 1.001

Attenuation Model 2 (Using Hypocentral Distance)

Eq.1 can also be used with hypocentral distance replacing epicentral distance. Considering focal depth, the hypocentral distances are calculated for use in the regression analysis. The 1945 Mikirhills earthquake was excluded from the data set due to unavailability of focal depth. The following equation is obtained for Attenuation Model 2 using hypocentral distance R_hyp:

I=1.9626+1.4906*(M)-0.0042*( R_hyp)-2.826*log(R_hyp) + 1.0812P (3)

with standard deviation σ = 1.0812

Validation of Attenuation Models with Field Data

The attenuation equations are validated by comparing predicted intensities with the earthquake data of Table 1. Fig.4 presents comparison for all earthquakes except Moheshkhali earthquake. The comparison yields reasonably good agreement for all earthquakes except for 1918 Srimangal earthquake. The difference is appreciable at larger distances, and the models overestimate the intensity. The Srimangal earthquake with shallow focal depth has relatively faster attenuation compared to other earthquakes which could not be represented well by the models.