ABSTRACT

            Decay of earthquake ground motion with distance in Bangladesh is studied from published information and isoseismal maps. A total of seven earthquakes with magnitude varying from 5.1 to 8.1 are considered. Variation of attenuation of earthquake intensity in different directions is studied. A directional concept is used for developing an attenuation law for Bangladesh. Several publications have been examined for identifying appropriate isoseismal and related intensities. This field data is used to develop two equations representing attenuation of intensity: (i) in terms of magnitude and epicentral distance and (ii) in terms of magnitude and hypocentral distance. The second equation is somewhat questionable since it requires focal depth data which has uncertainty. The developed equations are compared with the field data. Finally comparisons are also made with other attenuation laws developed for different regions including NE India.

Introduction

In the last 150 years, Bangladesh has been affected by five earthquakes with magnitude 7 or greater. Two of them had their epicenters within Bangladesh, while others were not far from Bangladesh border. However, due to lack of seismic instrumentation inside Bangladesh, measured strong motion data for these earthquakes are not available. Alternatively, earthquake intensity data observed within the country may be used for the determination of attenuation relations for these major earthquakes. These historical earthquakes occurring during 1869 to 1930 are documented in some reports such as that of Oldham (1899) for 1897 Great Indian Earthquake (M=8.7) in Assam for the then Geological Survey of India. Such reports also give isoseismals in Oldham Intensity scale which is very different from other standard intensity scales such as Modified Mercalli Intensity (MMI) scale. Some later publications also describe these historical earthquakes. The older reports have been critically re-examined and changes in intensity levels have been suggested by some authors. Recently, Sabri (2001) developed intensity attenuation laws for NE India including Bangladesh as a function of hypocentral distance and magnitude. He considered 18 earthquakes; some of them were quite distant from Bangladesh. He considered average distance of isoseismals all around the source. Ambraseys and Bilham (2003) have reassessed 1897 Great Indian Earthquake effects, re-estimating its magnitude as well as intensity levels.

Probabilistic seismic hazard assessment studies require appropriate attenuation law for the region concerned. For the current study, attenuation of earthquake intensity for four of these historical major earthquakes and three additional significant earthquakes have been used in developing the intensity attenuation law for Bangladesh. Isoseismal maps and intensity descriptions for these earthquakes have been collected from various publications, critically examined and intensity level modified if deemed necessary. These isoseismal maps and intensity levels have been used for the determination of intensity based attenuation law. This paper presents attenuation laws representing decay of earthquake intensity with distance. Finally, some published intensity versus PGA (peak ground acceleration) relationships have been used to obtain the attenuation law in terms of PGA, for comparison with attenuation laws based on PGA.

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Comparison of Attenuation Model with Other Attenuation Laws

In order to make a comparison with standard attenuation laws based on peak ground acceleration (PGA), the intensity attenuation equations are converted into PGA attenuation relationship using standard intensity PGA relationships. The following intensity PGA relationships have been used:

log (PGA) = 0.14 + 0.300I       (Trifunac and Brady, 1975)        (4)

log (PGA) = -0.430 + 0.350I    (Murphy & O’brien, 1977)        (5)

            log (PGA) = 0.453 + 0.273I     (Wald et.al., 1999)                      (6)

 Figure 5: Comparison of developed PGA attenuation models with other attenuation laws.

   (a) Model-1(using epicentral distance), (b) Model-2 (using hypocentral distance).

Three equations representing horizontal PGA as a function of R and M are obtained for Attenuation Model-1 using Eq.(4), Eq.(5) and Eq.(6). In Fig.5a, these three equations of Attenuation Model-1 are compared with well-established attenuation laws of Abrahamson & Silva (1997), Ambraseys (1996) and Chapman (1999) for a M=7 magnitude earthquake. All three equations of Model-1 appear to be representing smaller attenuation of PGA, in other words greater PGA value compared to other laws. However Murphy and O’Brien (1977) relationship place Model-1 quite close to these attenuation laws. Wald et al. (1999) relationship places Model-1 far above these attenuation laws which appear to be very unrealistic. Intensity Attenuation Model-2 is also converted to PGA attenuation relationships for an assumed M=7 magnitude earthquake with a focal depth of 60 km. Fig.5b presents comparison of Model-2 PGA Attenuation using Eq.(4) and Eq.(5) with attenuation laws proposed by Atkinson & Boore (1995), Zare and Bard (1999) and Sabri (2001). It is observed that attenuation relationship of Sabri (2001) for NE India yield much higher PGA, representing lower attenuation. The Model-2 PGA Attenuation based on Murphy and O’Brien (1977) relationship falls between curves of Atkinson & Boore (1995) and Zare and Bard (1999). Although the developed laws need further verification from measured strong motion data in the country, in the absence of such data, both Attenuation Model-1 and Model-2 based on Murphy and O’Brien (1977) relationship may be used as an approximate first hand estimate of PGA based attenuation law for probabilistic hazard assessment studies in Bangladesh.

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Attenuation in Different Directions

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)
		Lat.	Long.			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.

Figure 4: Comparison of developed attenuation models with field intensity values

Figure 4: Comparison of developed attenuation models with field intensity values (continued)

Model 1 and Model 2 yield quite close results. Only at shorter distances for 1930 Dhubri earthquake, Model 2 underpredicts intensity significantly.

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Isoseismals

The isoseismal maps of different earthquakes have been obtained from different publications. Isoseismal map of five earthquakes (Fig.1) have been taken from Nandy (2001), which are 1918 Srimangal earthquake, 1930 Dhubri earthquake, 1945 Mikirhills earthquake and 1964 Medinipur earthquake. The isoseismal map of 1897 Great Indian Earthquake and mean epicentral distance of different isoseismals have been taken from Ambraseys and Bilham (2003). Isoseismal map for 1999 Moheshkhali earthquake is given by Ansary et al. (1999). Isoseismal map (Oldham Intensity Scale) of 1885 Bengal earthquake is given by Oldham (1899) and Islam (2003) converted these intensities to MMI Scale.

Figure 1: Isoseismal map for different earthquakes (after Nandy, 2001).

Some of the intensity levels have been modified to represent more realistic intensity levels. Ambraseys and Bilham (2003) gave re-estimated intensity values for different isoseismals of 1897 Great Indian earthquake in MKS scale which is equivalent to the MMI scale. In the new isoseismal map, intensity VIII has a mean radius of around 76 km. For the 1885 Bengal earthquake (M=7.0), while converting from Oldham isoseismals, the lower bound of intensities (in MMI scale) have been used considering the relatively large distances. As for example, the isoseismal for 403 km distance is taken as III intensity (MMI scale). The 1930 Dhubri earthquake (M=7.1) affected a large area of radius 233 km at intensity V inward Bangladesh. The 1918 Srimangal earthquake (M=7.6) has shown faster attenuation with an intensity of V at a distance of 119 km, which may be due to the smaller focal depth (14 km). The isoseismals of Dhubri and Srimangal earthquakes were converted into MMI Scale from RF Scale by conversion and qualitative assessment. Medinipur and Moheshkhali earthquakes of lower magnitudes affected smaller areas. Moheshkhali earthquake had shallow focal depth of 10 km and an intensity of V at a small distance of 17.5 km. 

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Regional Earthquakes

Brief description of earthquakes considered in this study are presented below:

1885 M=7.0 Great Bengal Earthquake: This earthquake with a magnitude of 7.0 occurred on 14^th August, 1885 with epicenter at 24.70°N, 89.55°E. The main shock was strong enough to destroy numerous houses and important public buildings. Poor quality constructions were one of the main causes of damage. The main shock was followed by a series of aftershocks and the earthquake was associated with significant ground rupture. The shaking was strongly felt in Sirajganj, Bogra, Rangpur, Sherpur, Mymensingh, Jamalpur, Dhaka, and Pabna where destruction to building was the greatest and loss of life had occurred. It extended westwards into Chota Nagpur and Bihar, Northwards into Sikhim and Bhutan and eastwards into Assam, Monipur and Burma. From the analysis of the macroseismic data, the isoseismal intensity at around 80 km distance was estimated as VII.

1897 M=8.1 Great Indian Earthquake: The powerful Great Indian Earthquake of 12^th June 1897 occurred with epicenter at 25.84°N, 90.38°E in Assam. The focal depth was reported to be 60 km. Although the initial magnitude was reported to be 8.7, it was later reported as 8.0-8.1 by Ambraseys and Bilham (2003). The earthquake almost totally destroyed settlements and small towns on the western part of the Shillong Plateau, and caused heavy damage in surrounding districts, chiefly due to the extensive liquefaction of the ground. Ambraseys and Bilham (2003) re-estimated the intensity levels, intensity in Dhaka for this earthquake was VI. They maintained that Oldham's intensities (Oldham, 1899) were unsuspectingly inflated by 1.5-3 intensity units. The large area over which loose deposits liquefied and the size of the area over which the shock was felt, are similar to those produced by other large earthquakes of New Madrid 1811, Bihar-Nepal 1934 and Assam 1950. The epicentral area is in the west-central part of the Shillong Plateau, with intensities decaying to the north and south at the same rate.

1918 M=7.6 Srimangal Earthquake, 1918: The Srimangal earthquake of July 8, 1918 occurred at 24.25°N, 91.80°E. Reported focal depth was around 14 km. Magnitude was reported to be 7.6. The main shock which lasted about 12 secs damaged almost every house in the epicentral area. The greatest damage occurred in the tea garden areas of the Balisera, Doloi and Luskerpore valleys. With few expectations all brick buildings were found to be destroyed within this area. Water and sand spouted up to a height of several feet. Most of the area where the earthquake was violent enough damaged all or nearly all brick buildings.

1930 M=7.1 Dhubri Earthquake: The Great Dhubri Earthquake of July 1930 occurred at. 25.95°N, 90.04°E. Reported focal depth was around 60 km. Magnitude was reported to be 7.1. Aftershocks occured at regular intervals throughout the July 1930. The earthquake caused total destruction or heavy damage to most of the constructions in the area around the villages of Dhubri. Ground fissure and liquefaction-induced damages were majority in the zone covering the towns of Rangpur, Lalmanirhat, Cooch Bihar, Alipur Duar, eastern region of Brahmaputra River, and Tura town in Garo hills. This earthquake had disastrous result in northern Bengal and in Western Assam and was felt very distinctly over a wide area, extending from Dibrugarh and Manipur in the east to Chittagong and Calcutta  in the South to Patna in the west and beyond the frontiers of Nepal, Sikkim and Bhutan in the North.

1945 M=6.7 Mikirhills Earthquake: The Earthquake was felt during 8^th July, 1945. Magnitude was reported to be 6.7. The Epicenter was 25.8°N, 92.3°E. The epicentral distance of the third isoseist (IV-MMI) was considered as 260 km.

1964 M=5.5 Medinipur Earthquake: The Earthquake occurred on 15^th April, 1964 with a reported magnitude of 5.5. Focal depth was reported to be around 36 km. The Epicenter was 21.7°N, 88°E in the coastal area. The mean epicentral distance of the third isoseist (III-MMI) was considered as 162 km.

1999 M=5.1 Moheshkhali Earthquake, 1999: The Earthquake of magnitude 5.1 and focal depth 10 km occurred on 22th July, 1999. The Epicenter was 21.61°N, 91.96°E near Moheshkhali island. The mean epicentral distance of the third isoseist (V-MMI) was considered as 17.5 km.

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