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ORIGINAL PAPER

Attenuation relations of peak ground acceleration

and velocity in the Southern Dead Sea Transform region

Mahmoud Y. Al-Qaryouti

Received: 15 July 2008 / Accepted: 25 August 2008

#

Saudi Society for Geosciences 2008

Abstract Using the recorded earthquake strong ground

motion, the attenuation of peak ground acceleration (PGA)

and peak ground velocity (PGV) are deriv ed in the southern

Dead Sea Transform region. The expected values of strong

motion parameters from future earthquakes are estimated

from attenuation equations, which are determined by

regression analysis on real accelerograms. In this study,

the method of Joyner and Boor [Bull Seismol Soc Am 71

(6):2011–2038, 1981] was selected to produce the attenu-

ation model for the southern Dead Sea Transform region.

The dataset for PGA consists of 57 recordings from 30

earthquakes and for PGV 26 recordings from 19 earth-

quakes. The attenuation relations developed in this study

are proposed as replacement for former probabilistic

relations that have been used for a variety of earthquake

engineering applications. The comparison between the

derived PGA relations from this study with the former

relations clearly shows significant lower values than the

other relations.

Keywords PGA

.

PGV

.

Dead Sea Transform

.

Regression analysis

.

Accelerograms

.

Attenuation model

Introduction

Studies for empirical prediction of earthquake strong

ground motion usually evaluate attenuation curves to

determine maximum amplitude and spect rum of seismic

waves. During early stage of seismology, attenuation curves

were used to determine the magnitude for an earthquake by

empirical corrections of observed maximum amplitudes for

the distance from the source to the observation station

(Richter 1935 ; Tsuboi 1954). Variables of the attenuation

curve are usually magnitude and distance.

As many strong motion records have been accumulated,

many attenuation curves have been derived empirically

utilizing regression analysis (e.g., Fukushima and Tanaka

1990; Theodulidis and Papazachos 1992, 1994; Fukushima

and Irikura 1997; Douglas 2003 ; Gulkan and Kalkan 2004;

Ambraseys et al. 2005; Kanno et al. 2006). However, recent

advances in the studies of the attenuation of seismic waves

indicate that most of them have no distinct theoretical

background. A predictive model is needed. Such a model,

commonly referred to an attenuation relation, is expressed

as a mathematical function relating a strong-motion

parameter [e.g., peak ground acceleration (PGA) and peak

ground velocity (PGV)] to parameters characterizing the

earthquake, propagation medium, local site geology, and

engineering structure (Campbell 1985).

Estimation of ground motion either implicity through the

use of special earthquake codes or more specifically from

site-specific investigations is essential for the design of

engineered structures. The development of design criteria

requires, as a minimum, a strong-motion attenuation

relationship to estimate earthquake ground motions from

specific parameters characterizing the earthquake source,

geologic conditions of the site, and the length of the

propagation path between the source and the site.

The Dead Sea Transform (DST) system is tectonically

active zone. It is the dominant st ru ct ural elemen t of

transform type in the region. Many destructive earthquakes

occurred in the region durin g historic and prehis toric

periods. The instrumentally recorded earthquakes seem to

Arab J Geosci

DOI 10.1007/s12517-008-0010-4

M. Y. Al-Qaryouti (*)

Seismology Division, Natural Resources Authority,

Amman, Jordan

e-mail: almah2010@yahoo.com

have taken place in the form of sequences. Many of the

main shocks of the earthquake sequences are recorded by

accelerograph stations. These earthquake data are essential

for creating new empirical attenuation relations in the

region.

Previous attenuation relations

With no strong motion records predicted in Jordan, east of

the Dead Sea area, before August 2, 1993, isoseismal maps

were analyzed by Al-Tarazi (1992) to study the attenuation

of intensities with distance. Using three earthquakes

(25 November 1759, 1 January 1837, and 11 July 1927)

that occurred in the DST region, the following relation for

the region was derived:

IR; MðÞ¼1:8M 1:32 0:026R 0:313

ln R þ 25ðÞ ð2:1Þ

where I(R, M) is the intensity at a distance R in kilometer

from the epicenter and a magnitude M. This relation is used

to assess the probabilistic seismic hazard in the southern

DST region and its vicinity in terms of intensity. Other

attenuation relations of PGA have been derived for the

region (Amrat 1996; Malkawi and Fahmi 1996; Al-Tarazi

and Qadan 19 97 ). These relations were derived depending

mainly on historical earthquake data and, in general, have

the form:

YR; MðÞ¼c

1

e

c2m

R þ c

4

ðÞ

c3

ð2:2Þ

where Y(R, M) is the peak ground acceleration of an

earthquake epicenter with distance R in kilometer from the

epicenter and magnitude M. c

1

, c

2

, and c

3

are constants

appropriate to the region under consideration and to be

determined by the least-squares method, while c

4

is a

suitable chosen constant, usually 25 km. The constants of

c

1

, c

2

, c

3

, and c

4

of these equations are summarized in

Table 1.

Strong motion database

Earthquake strong ground motion observation began in the

west of the Dead Sea area before 1979, while it began in

the east of the area in May 1990 when the Jordan

Seismological Observatory of Natural Resources Authority

operated the Kiemertric PDR-1 accelerograph stations. In

the second stage, it operated the kinemetric SSA-2 and Etna

accelerograph stations.

For field data retrieval and control of the SSA-2 and

Etna, all required an IBM PC compatible portable comput-

er, thus saving the expense of a specialized dedicated

playback system. For complete processing of strong motion

events recorded on the SSA-2 and Etna and for use with the

IBM (or 100% compatible) personal computer, a full set of

software is available from Kinemetrics system.

Despite the slow increase in the number of accelero-

graphs in the region, useful accelerograms were obtained.

Fortunately, recent intensive installation of digital accelero-

graph instru ments took place in different localities of

Jordan where, nowadays, the Jordan Strong Motion

Network consists of 27 digital accelerograph stations (see

Fig. 1).

Thirty earthquakes were recorded by the accelero-

graph stations in the southern DST region with a

magnitude range M=3.7–6.2 (see Table 2). Nineteen of

them occurred in the Gulf of Aqaba region. The first

interesting accelerograms have been obtained in Jordan

during the Dead Sea earthquake of August 2, 1993 with

local magnitude of 4. Peak ground accelerations and

velocities of the recorded earthquakes which have been

used in this study are given in Table 3. Th e largest

earthquake was recorded by the accelerograph stations in

the DST region is the 1995 Gulf of Aqaba earthquake.

With its 6.2 local magnitude (M

W

=7.3), it was located at

about 93 km south of Aqaba City with a depth of 12.5 km.

This event was recorded at six accelerograph stations in

Jordan and nine stations in the west of the Dead Sea area.

Aqaba Hotel Accelerograph Station (AQH) recorded the

largest peak ground acceleration (157 cm/s

2

) and peak

ground velocity (9.3 cm/s) during the 1995 Gulf of Aqaba

earthquake, while Aqaba Civil Defense Accelerograph

Station (ACD) recorded the largest displacement of

1.85 cm during the same earthquake.

Extraction of the attenuation relationship

As mentioned above, until now, all of the derived PGA

equations for Jordan and around were extracted depending

on historical earthquake data. Therefore, in this study, a

new attenuation equation of PGA and PGV using strong

motion records of earthquakes that occurred in and around

the southern DST region was utilized. The expected values

of strong motion parameters from future earthquakes are

estimated from attenuation equations which are determined

by regression analysis on real accelerogram s. The strong

Table 1 Constants of attenuation equations for the southern DST

region and around that derived by different sources

Reference c

1

c

2

c

3

c

4

Amrat (1996) 0.5 0.35 0.01 20

Malkawi and Fahmi (1996) 383.75 1.03 1.73 25

Al-Tarazi and Qadan (1997) 0.645 1.514 1.036 25

Arab J Geosci

motion parameter is predicted as a function of independent

parameters defining the earthquake source, the path to the

recording site, and the nature of the site itself. The two

independent parameter s that are always included in the

model are the magnitude of the earthquake and the distance

from the source to the site. The additional independent

parameter that is most commonly included is the geological

site.

The attenuation method of Joyner and Boore (1981) was

selected in this study to produce the attenuation model for

the southern DST region and around. This method applies a

two-step algorithm and uses a magnitude-independent

shape based on geo metrical spreading and anelastic

attenuation for the attenuation curve.

For simplicity, a linear atte nuation relation between

logarithmic acceleration and the distance in kilometers to

the closest approach of the zone of energy release was

applied to the data for each earthquake. The estimated

linear regression model is:

log A ¼b log RðÞþc ð4:1Þ

where A is the peak horizontal acceleration in cm/s

2

, R is

the distance between site and rupture in kilometer and, b

and c are the regression coefficients.

Next, a general multiple regression analysis was per-

formed for th e whole dataset by assum ing the basic

regression model,

log A ¼ aM b log RðÞþc ð4:2Þ

where M is the magnitude, and a, b, and c are the regression

coefficients. To avoid the interaction between the coeffi-

cients a and b, a two-step stratified regression analysis

method using dummy variables has been found to be very

effective. In the firs t step, it is assumed that in Eq. 4.2, the

Accelerographsin Jordan

4 Accelerographsin Amman

Accelerographin Palestine area

Saudi Arabia

Syria

Iraq

Fig. 1 Accelerograph stations in the southern DST region that have been used in this study

Arab J Geosci

distance coefficient b (distance decay parameter) is uniquely

assigned for all earthquakes and the constant terms aM+c

are replaced by Σ d

i

l

i

for individual earthquakes. That is,

log A ¼b log RðÞþΣd

i

l

i

ð4:3Þ

where, l

i

is a dummy variables (equals 1 for the ith

earthquake, 0 otherwise) and d

i

is a coefficient for ith

earthquake.

As a second step, the attenuation model uses an equation

of the form:

log yðÞ¼c

1

þ c

2

M þ c

3

log RðÞþc

4

RðÞs P ð4:4Þ

where y is the ground motion parameter and c

1

, c

2

, c

3

, and

c

4

are the coefficients found by regression analysis. The

distance may be defined in many ways, sometimes being

the distance from epicenter or the hypocenter. The terms in

c

3

and c

4

in Eq. 4.4 represent, respectively, the geometric

and anelastic attenuation, and their coefficients must be

negative. The final term in Eq. 4.4 is as important as the

coefficients themselves and the mean value of y that they

predicted. There is always very considerable scatter in

the data with respect to the average behavior represented by

the predicted equation, and this scatter is measured by the

standard deviation σ; the residuals usually have a log-

normal distribution, so P simply represents the normal

distribution, taking a value of 0 for the 50 percentile and

1 for 84 percentile. The use of dummy variables to divide the

data into classes is a well-known technique in regression

analysis (Draper and Smith 1966; Weisberg 1980)

Data a nalysis and results

The dataset for peak ground acceleration consists of

57 recordings from 30 earthquakes and for peak ground

velocity 26 recordings from 19 earthquakes. Twenty-one of

the earthquakes in the peak acceleration dataset and 17 of

the earthquakes in the peak velocity data were recorded at

only one station. For peak values, the larger of the two

horizontal components has been used in this study (e.g.,

Table 2 Recorded earthquakes by the accelerograph stations in the southern DST region

Ser Date O.T. Lat. °N Long. °E M

L

Area

1 19790423 13:01 31.240 35.460 5 Dead Sea

2 19840824 06:02 32.660 35.180 5.3 Jordan Valley

3 19870427 20:41 31.290 35.487 4.2 Dead Sea

4 19871023 16:32 31.140 35.336 4.1 Dead Sea

5 19890103 17:10 32.479 35.461 3.9 Jordan Valley

6 19890106 10:59 32.456 35.483 3.7 Jordan Valley

7 19910928 00:43 31.077 35.505 3.9 Dead Sea

8 19930802 09:12 31.484 35.489 4.1 Dead Sea

9 19951226 06:19 28.890 34.610 5.0 Gulf of Aqaba

10 19970326 04:22 33.860 35.390 5.5 Lebanon

11 19970804 11:29 33.260 35.730 4.0 Lebanon

12 19930802 23:16 31.307 35.413 4.0 Dead Sea

13 19930803 12:31 28.938 34.747 5.0 Gulf of Aqaba

14 19930803 12:43 28.754 34.642 5.3 Gulf of Aqaba

15 19930803 13:23 28.684 34.736 4.3 Gulf of Aqaba

16 19930803 16:33 28.789 34.583 4.6 Gulf of Aqaba

17 19930820 23:10 28.568 34.782 4.6 Gulf of Aqaba

18 19940916 03:17 32.035 35.557 4.0 Gulf of Aqaba

19 19951122 04:15 28.758 34.628 6.2 Gulf of Aqaba

20 19951123 18:07 29.273 34.762 5.5 Gulf of Aqaba

21 19951124 16:45 29.172 34.735 5.4 Gulf of Aqaba

22 19951125 11:41 29.440 34.902 4.8 Gulf of Aqaba

23 19951129 08:10 29.238 34.833 4.7 Gulf of Aqaba

24 19951201 09:17 27.976 34.375 5.0 Gulf of Aqaba

25 19951202 00:47 29.291 34.879 4.7 Gulf of Aqaba

26 19960601 16:07 28.926 34.752 4.5 Gulf of Aqaba

27 19960703 20:11 29.231 34.869 4.4 Gulf of Aqaba

28 20000722 10:14 29.027 34.513 4.3 Gulf of Aqaba

29 20001225 01:57 28.522 34.572 4.5 Gulf of Aqaba

30 20010207 03:38 29.328 34.982 4.3 Gulf of Aqaba

O.T. origin time, M

L

local magnitude

Arab J Geosci

Table 3 Earthquake data used for the attenuation model of peak ground acceleration and peak ground velocity in the southern DST region

Ser Date O.T. M

L

PGA PGV Δ

a

Station

1 790423 13:01 5.0 11.4 – 39.6 MIZ

2 790423 13:01 5.0 11.2 – 56.2 KFR

3 790423 13:01 5.0 24.5 – 71.8 BNR

4 840824 06:02 5.3 29.3 – 17.8 IZR

5 840824 06:02 5.3 46.6 – 19.2 HAT

6 870427 20:41 4.2 7.3 – 10.1 DA2

7 871023 16:32 4.1 16.9 – 0.9 TUG

8 871023 16:32 4.1 19.9 – 7.0 DA1

9 871023 16:32 4.1 17.2 – 10.1 DA2

10 871023 16:32 4.1 8.6 – 16.3 DA3

11 890103 17:10 3.9 8.8 – 4.8 BET

12 890106 10:59 3.7 8.5 – 5.2 BET

13 910928 00:43 3.9 10.3 – 13.4 MIF

14 910928 00:43 3.9 9.3 – 16.4 NET

15 930802 09:12 4.1 12.3 – 34.0 ALM

16 930802 09:12 4.1 8.3 – 40.0 JER

17 930802 23:16 4.0 8.1 0.29 34.2 KRK

18 930803 12:31 5.0 2.0 0.28 70.8 ACD

19 930803 12:43 5.3 19.9 2.22 93.5 ACD

20 930803 13:23 4.3 11.8 0.65 98.0 ACD

21 930803 16:33 4.6 12.4 0.61 92.3 ACD

22 930820 23:10 4.6 1.7 0.12 109.4 AQH

23 940916 03:17 4.0 10.1 0.25 28.8 KTD

24 940916 03:17 4.0 17.9 0.34 45.7 MSH

25 940916 03:17 4.0 3.4 0.14 78.1 SRF

26 951122 04:15 6.2 157.0 8.56 93.3 AQH

27 951122 04:15 6.2 73.0 7.93 93.6 ACD

28 951122 04:15 6.2 93.0 – 94.4 EIL

29 951122 04:15 6.2 33.7 – 245.4 SVT

30 951122 04:15 6.2 36.8 – 320.4 ASQ

31 951122 04:15 6.2 14.4 – 321.3 MIZ

32 951122 04:15 6.2 18.9 3.18 330.6 HMM

33 951122 04:15 6.2 15.2 – 346.3 ALM

34 951122 04:15 6.2 3.1 0.42 377.2 AM6

35 951122 04:15 6.2 19.4 – 413.4 HAD

36 951122 04:15 6.2 5.9 0.81 436.7 YAU

37 951122 04:15 6.2 5.1 0.75 439.7 WAD

38 951122 04:15 6.2 9.3 – 443.3 ALN

39 951122 04:15 6.2 11.9 – 452.5 HAC

40 951122 04:15 6.2 5.2 – 505.5 GOS

41 951123 18:07 5.5 33.5 2.40 37.1 ACD

42 951123 18:07 5.5 42.1 – 36.5 EIL

43 951124 16:45 5.4 33.6 1.66 47.8 ACD

44 951125 11:41 4.8 6.3 0.45 14.3 ACD

45 951129 08:10 4.7 1.3 0.32 36.4 AQH

46 951201 09:17 5.0 3.0 0.32 183.4 AQH

47 951202 00:47 4.7 3.4 0.23 29.3 AQH

48 951226 06:19 5.0 8.7 – 81.0 EIL

49 960601 16:07 4.5 6.1 0.22 54.8 APS

50 960703 20:11 4.4 4.8 0.12 19.3 APS

51 970326 04:22 5.5 9.2 – 74.6 KIT

52 970326 04:22 5.5 9.3 – 75.0 GOS

53 970326 04:22 5.5 8.1

– 99.6 ZEF

54 970804 11:29 4.0 6.3 – 14.0 KIT

55 000722 10:14 4.3 13.0 0.21 59.3 APS

56 001225 01:57 4.5 3.1 0.11 103.0 APS

57 010207 03:38 4.3 5.3 0.15 5.8 APS

PGA peak ground acceleration (cm/s

2

), PGV peak ground velocity (cm/s)

a

Epicentral distance (km)

Arab J Geosci

Cramer and Darragh 1994), while others (e.g., Campbell

1981; Fukushima and Tanaka 1990) have used the mean of

the two components. The earthquakes used in this study are

listed in Tables 3 and 4. The M and R values are taken to be

local magnitude and epicentral distance, respectively.

Using the above procedure, the following attenuation

relation of peak horizontal acceleration and peak horizontal

velocity, respectively, for the southern DST region are

derived:

log A ¼3:45092 þ 0:49802M 0:38004 log RðÞ

0:00253 RðÞ0:313P ð4:5Þ

log V ¼3:28773 þ 0:79450M 0:21966 log RðÞ

0:00278 RðÞP ð4:6Þ

where V is the peak ground velocity. The other parameters

are as defined above.

Discussion and conclusions

Seismic hazard assessment is an effort to evaluate the

likelihood of an earthquake occurrence and its magnitude

and intensities in and around locatio n of interest and

severity of strong ground motions expected for a certain

return period. In the last decades, seismic strong motion

studies have been newly e valuated to elucidate the

processes of seismic wave generation and propagation as

well as site effect characteristics due to large earthquakes.

The reliable assessment of seismic risk in a region

requires knowledge and understanding of both the seis mic-

ity and the attenuation of strong ground motion. The recent

expansion of accelerograph stations throughout the DST

region resulted in the recording of several accelerograms in

the near-source region of moderate to large earthquakes, an

area where data have been severely lacking in the past. The

attenuation relation developed in this study for estimating

peak ground acceleration and peak ground velocity in the

southern DST region are proposed as replacement for

former probabilistic relations that used historical data. Both

deterministic and probabilistic approaches are often used

3 6 10 60 100301 300 600 1000

Distance (km)

1

0.5

0.2

0.1

0.05

0.02

0.01

0.005

0.002

0.001

Peak Ground Acceleration (g)

M 5

M 6

M 7

Fig. 2 Attenuation curves of peak horizontal acceleration from 57

recordings of 30 earthquakes (1979–2001) in the southern Dead Sea

Transform region for magnitudes 5, 6, and 7

Table 6 Peak ground acceleration (cm/s

2

) from different equations for

M

L

=7 and three selected epicentral distance

Reference PGA at

Δ=10 km

Δ=50 km Δ=100 km

Amrat (1996) 661.5

a

258.8

a

81

a

198.4

b

77.7

b

24.3

b

Malkawi and

Fahmi (1996)

1153.4 308.6 127.5

Al-Tarazi and

Qadan (1997)

690 313.3 184.6

This study 362.6 155.8 89

a

For alluvium site

b

For limestone site

Table 4 Peak ground acceleration (cm/s

2

) from different equations for

M

L

=5 and three selected epicentral distance

Reference PGA at Δ=

10 km

Δ=50 km Δ=100 km

Amrat (1996) 132

a

51.6

a

16.2

a

39.6

b

15.5

b

4.9

b

Malkawi and

Fahmi (1996)

70 18.7 7.7

Al-Tarazi and

Qadan (1997)

11.2 5.1 3

This study 43 18 10.6

a

For alluvium site

b

For limestone site

Table 5 Peak ground acceleration (cm/s

2

) from different equations for

M

L

=6 and three selected epicentral distance

Reference PGA at

Δ=10 km

Δ=50 km Δ=100 km

Amrat (1996) 295.5

a

115.6

a

36.2

a

88.7

b

34.7

b

10.9

b

Malkawi and

Fahmi (1996)

341.8 91.5 37.8

Al-Tarazi and

Qadan (1997)

115.6 52.5 30.9

This study 135.5 58.2 33.4

a

For alluvium site

b

For limestone site

Arab J Geosci

for a variety of earthquake engineering as well as

engineering seismology.

The method used in this study to derive attenuation

relations in the southern DST region is based on the strong

motion records. It would be expected to produce the most

representative model corresponding to real ground motions.

The resultant attenuation curves of peak ground accelera-

tion are shown in Figure 2 for three different magnitude

classes. No obvious differences in trend are apparent among

the different magnitude classes, giving no support to the

idea that the shape of the attenuation curves depends upon

magnitude. Tables 4, 5, and 6 summarize the comparison

between the derived peak ground acceleration equation

from this study with the aforementioned equations for

selected local magnitude of 5, 6, and 7 and three epicentral

distances. The peak ground acceleration equation of this

study clearly shows significant lower values than the other

equations.

Acknowledgments An anonymous reviewer sent extensive and very

useful comments and suggestions. The support and encouragement of

all these people is gratefully acknowledged.

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