RESEARCH OF GEOGRAPHIC STRUCTURE AND EARTHQUAKE, VOL. 1, NO. 1, DECEMBER 2013
1
An Earthquake Study, Considering the Lack of
Data Existent, Sudan-Africa
F. Moradpouri, f.moradpouri@gmail.com
Faculty of Mining, Petroleum & Geophysics, Shahrood University of Technology, Shahrood, Iran.
M. Mojarab
School of Mining, College of Engineering, University of Tehran, Tehran, Iran.
Abstract— The seismic hazard is the most severe hazard from the natural environment to be considered in the design of different
structures in seismically active areas. Earthquake hazard is a multiple hazard as besides ground shaking, which is the main aspect
in seismic design codes and regulations, can trigger land- and rockslides into the area, etc. It is also a well-known fact that the
earthquake hazard is one of the least known hazards. Therefore, a very thorough investigation is needed for the estimate of the
ground motion of the different design earthquakes. Therefore probabilistic seismic hazard analysis (PSHA) is a commonly used
method to derive seismic hazard curve – a relationship between a ground motion parameter and its return period. The so-called
return period in PSHA is a modification of the recurrence intervals of earthquakes using the probabilities of ground motions. The
return period is not an independent temporal parameter, but it has been inappropriately treated as the mean recurrence interval of
an independent event (ground motion) and used in seismic hazard analysis. The current study is devoted to conduct the
probabilistic seismic hazard analysis at a site in Sudan-Africa, in terms of Peak Ground Acceleration (PGA), Peak Ground Velocity
(PGV), and Peak Ground Displacement (PGD) which is following by response spectra for the study area.
Keywords: Sudan-Africa; PGA; PGV; PGD; Response Spectra
I. INTRODUCTION
Sudan is a country in northeastern Africa with an 853 km
coastline bordering the Red Sea with an area of 2,505,810 km2.
It is bordered by Egypt to the north, the Red Sea to the
northeast, Eritrea and Ethiopia to the east, Kenya and Uganda
to the southeast, Congo and the Central African Republic to
the southwest, Chad to the west and Libya to the northwest.
The world's longest river, the Nile, divides the country
between east and west sides. The study area is located at
15.36º latitude and 32.33º east longitudes. Location map of the
study area can be seen in Fig.1.
A. Location and geology of the study area
The most important key to the understanding of the geology
is the understanding of its stratigraphy. This is the classical
area of the so-called Nubian Sandstone, which had the
reputation of being barren. Far from really being
unfossiliferous, these strata can be subdivided into formations
of Cambrian, Ordovician, Silurian, Devonian, Carboniferous,
Permotriassic to Early Jurassic, Late Jurassic to Early
Cretaceous, Middle and Upper Cretaceous age. One of the
difficulties to interpret the age of certain units results from the
fact that conditions of sedimentation and re-sedimentation
have been repeated under similar paleogeographical and
climatical circumstances several times within earth's history.
Consequently, similarities of facies and partly also of
paleontological remains between strata of different age are
frequent.
As can be seen in the geology map of Sudan in Fig. 2,
different stratigraphy units exist in it and in 200 km radius of
studied site, the dominant stratigraphy units is “Nubian
Sandston Formation” and “Gezira Formation”.
Nubian Sandston Formation located in north of study area
that had large development. Nubian Sandstones formation (N)
is Cretaceous period and including Continental clastic
sediments including: sandstones, siltstones, mudstones and
conglomerates. In addition to in south of study area there is
Gezira Formation that unconsolidated clays, silts and gravels.
This formation is time of Tertiary to Quaternary. Also
Ummrawaba formation is time of Tertiary to Quaternary that
unconsolidated sands with some gravels, clays and shales.
Recent units show with “A” that it is Alluviums, Wadi fills,
terraces, delta and swamp deposits. This unit located along
Nile River and Expansion is limited.
Basement Complex includes Px and Ps. Px Undifferentiated
Basement Complex and Ps Undifferentiated Schist Group.
Only unit Intrusive Rocks is γz that is Younger Granites.
B. Seismicity of Sudan
Sudan is generally considered a country of low seismic
activity. However; recent seismic activities in different regions
within the Sudan warrant seismic hazard assessment of the
Sudan. The country and its vicinity experienced one of the
largest earthquake in recent history: The May 20, 1999, 7.4
earthquake and its aftershocks that hit Southern Sudan is the
one of the largest in continental Africa in the instrumental era
of earthquake recording [18]. In additional to the Southern
Sudan, major portions in Central Sudan also experienced
earthquake recently, for example Earthquakes stroke Kordofan
State in August 1, 1993 with a magnitude of 5.5 and in
November 15, 1993 with a magnitude of 4.3 [18].
Sources of earthquakes that affect most parts of Sudan are
located in (1) the southernmost portion of Sudan around Aswa
fault, (2) central Sudan from several rifts, (3) the Red Sea
coast near the Afro- Arabian fault, (4) eastern Sudan from
Afar Depression in Eritria and also from the East African Rift
2
RESEARCH OF GEOGRAPHIC STRUCTURE AND EARTHQUAKE, VOL. 1, NO. 1, DECEMBER 2013
System, and (5) the included earthquake source in Lake Nassir
(High Dam) in southern Egypt [2].
Seismic studies [1, 3] have shown that Sudan is relatively
stable with occasional earthquakes of low to moderate
magnitude that can give rise to damaging intensities. They
also noted that the Southern States of Sudan are frequently
subjected to moderate to high intensities of earthquakes.
Figure 1: Location map of the study area
II. PROBABILISTIC SEISMIC HAZARD ANALYSIS
PSHA is the most used method to assess seismic hazard and
risk for input into various aspects of public and financial
policy. PSHA was originally developed by Cornell in 1968 for
estimating engineering risk in comparison with the analogous
flood or wind problem. A similar method was also developed
by [17]. Ref.[10] extended his method to incorporate the
possibility that ground motion at a site could be different for
different earthquakes of the same magnitude at the same
distance (i.e., ground motion uncertainty). A FORTRAN
algorithm of Cornell’s method [10] was developed by
McGuire in 1976 and has been the standard PSHA ever since.
There is a fundamental difference between the formulations in
[9] and those in [10]; the former does not include
ground-motion uncertainty, whereas the latter does, but
incorrectly. In PSHA, an annual probability of exceedance (γ)
of a ground-motion amplitude y is [16].
(y) =
∑ v ∫∫∫ f
i
M
(m) fR (r) fΕ (ε )P[Y > y | m, r, ε ]dm dr d ε
(1)
Figure 2: Geology map of the study area
where νi is the activity rate for seismic source i; fM(m),
fR(r), and fε(ε) are earthquake magnitude, source-to-site
distance, and ground motion density functions, respectively; ε
is ground motion uncertainty; and P[Y>y|m,r,ε] is the
probability that Y exceeds y for a given m and r. The triple
integration in equation (1) is very complicated, and a
numerical solution is required.
For characteristic seismic sources, Eq. (1) can be
simplified as:
1
(2)
γ (y) =
P (Y > y)
∑T
i
i
i
Where Ti is the average recurrence interval of the
characteristic earthquake for source i, and Pi(Y ≥ y) is the
probability that the ground motion (Y) from source i will
exceed y.
The inverse of annual probability of exceedance (1/γ),
called the return period, is often used: for example, a
2,500-year return period (the inverse of annual probability of
exceedance of 0.0004). The return period has been
erroneously equated to the average recurrence interval (τ) of
earthquakes and used to calculate seismic risk [11, 12, 13]. As
shown in Eq.(1) and Eq.(2), the return period is a function of
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B. Earthquake catalogue, seismic sources and seismicity
parameters
Selection of the appropriate catalogue is an important step in
estimation of the seismicity parameters. Earthquakes catalogue
including the records located in a circle of 200 km radius far
from the site in question listed in Table 2 based on catalogues
that prepared by Ref. [3].
A proper definition of seismic source zones is an essential
key to calculate and assign the seismicity parameters to the
seismic sources. Therefore the following factors are
considered to select the sources, (1) to include more important
earthquakes into the calculation, (2) to cover the seismicity
around some important faults.
In the current study based on the proper criteria for the
disputed site and the above description, four seismic sources
are chosen , two sources as regional sources, and the rest as
line sources which are shown in Fig. 3. As can be seen, Fig.3
includes the faults and the occurred historical and instrumental
earthquakes in the study area as well.
Afterwards, a crucial part of seismic hazard analysis is to
calculate β and λ values. Due to the lack of enough appropriate
data in the study area, previous studies which was done by
Ref.[2] are used to calculate a- value and b- value and the
results are presented in Table3 including seismicity
parameters for the selected sources.
MORADPOURI ET AL: AN EARTHQUAKE STUDY, CONSIDERING THE LACK ..
the recurrence intervals of earthquakes and the probabilities in
which the ground motion will exceed a specific value if the
earthquakes occur. In other words, the return period is a
modification of the recurrence intervals (time-domain
characteristics) of earthquakes using the uncertainty of
ground-motion measurement at a site (spatial characteristics)
without physical basis [20, 21, 22]. This can be clearly seen
for a single characteristic seismic source:
P[Y > y]
T
(3)
γ (y) =
or return period =
T
P[Y > y]
As shown in Eq. 3, the return period is equal to the actual
recurrence interval of an earthquake divided by the probability
of ground motion. These calculations clearly show that the
return period defined in PSHA is not equivalent to the
recurrence interval of earthquakes.
A. Seismic hazard assessment
An alternative method, called seismic hazard assessment
(SHA), was proposed by Ref[23] and is briefly described
here. Similar to flood occurrences in hydrology, earthquake
occurrences follow the well-known Gutenberg-Richter
magnitude-frequency relationship:
(4)
N = 10 (a−bM )
(4.a)
ln(n) = a ln(10) − b ln(10)M
(4.b)
α = a ln(10) = 2.303a and β = b ln(10) = 2.303b
(4.c)
ln N = α − β M
Where N is the cumulative number of earthquakes with
magnitude equal to or greater than M occurring yearly, and a
and b are constants (α and β called seismicity parameter of the
region). As discussed earlier, the average recurrence rate (1/t)
of earthquakes with magnitudes is equal to or greater than a
specific size (M). Therefore
(5)
1 / τ = N = e2.303a−2.303bM
Estimations of the expected ground motion at a site are
given by assuming a ground-motion attenuation relationship,
which describes a relationship between a ground-motion
parameter (Y) and magnitude of an earthquake (M) and
epicentral distance (R) [7,8]. Generally, the attenuation
relationship follows the functional form of:
(6)
lnY = a0 + f (M , R) + ε
Where ε is uncertainty (a0 is a constant). The uncertainty (ε)
can be modeled using a log normal distribution with a
standard deviation (σ). From Eq. (3), M can be expressed as a
function of R, lnY, and ε:
(7)
M = f (R,lnY , ε )
Combining Eq. (5) and (7) results in:
1 / τ = e2.303a−2.303bf ( R,lnY ,ε ) or τ = e−2.303a+2.303bf ( R,lnY ,ε ) (8)
Eq. (8) describes a relationship between the ground motion
(lnY), with an uncertainty (ε) and its annual recurrence rate
(1/t) or recurrence interval (t) at a distance (R), i.e., a hazard
curve. Eq. (8) can be used to estimate ground motion at a site
or in a region. Three ground motion models (attenuation
relationships), used in this study are presented in Table 1.
C. Proposed Values for the PGA, PGV and PGD
A seismic hazard analysis is carried out to estimate the
ground motion parameters using attenuation relationships
presented in Table 1. As a result, final PGA values for the
return periods of 75, 475, 975 and 2475 are presented in Table
4. It is clear that, in order to correctly identify the seismic
displacement demand, it is necessary to account for the design
PGV at the site. Thus, PGV and PGD values, regarding to
PGA values and the following equations are calculated and
presented in Table 5.
v = c1
a
g
d = c2
v2
g
(9)
Where v is PGV, a is PGA (cm/s2), d is PGD and c1, c2 are
constant.
Ultimately, several hazard curves such as PGA, PGV
and PGD are computed and shown in Fig. 4, 5 and 6.
Table 1: The List of attenuation relationships used in this study. r =
hypocentral distance (km), d & R = epicentral distance (km); h = depth of
focus (km), M = magnitude; c, b1, b2, b3, b5 and b7 are constant
Author
Attenuation Relationship (Ground Motion Model)
Boore & Joyner
Ln Y = b1 + b2 (M-6) + b3 (M– 6)2 + b5 ln r + b7 (Vs/
& Fumal (1997):
VA) where r = (d2 + h2)1/2, Y is in g (acceleration
gravity), VS= shear wave velocity
Ambraseys
(1996)
Campbell &
Bozorgnia (2008)
NGA USGS 2008
log Y = C1+C2 M+C3 r+C4 Log(r)
where r = (d2 + h2)1/2
where Y is in g (acceleration gravity), C1 = −1.48,
C2= 0.266, C4 = −0.922, h = 3.5
ln Y = fmag+fdis+ffit+fhng+fsit+fsed
Due to comprehensive details, refer to summery of
strong ground motion attenuation relationships for
peak ground acceleration and spectral ordinate,
J.douglas, ESEE reports,
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RESEARCH OF GEOGRAPHIC STRUCTURE AND EARTHQUAKE, VOL. 1, NO. 1, DECEMBER 2013
75 0.071 0.058 0.092 0.049 No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
Table 2: Earthquake Catalogue
year Lat.
Long. Ms
Ref 1854 15.57 32.55 Amb. 1922 15.57 32.55 Amb. 1944 15.57 32.55 Amb. 1993 15.4116 31.6656 5.10 ISC 1993 15.635 31.7495 4.50 ISC 2004 15.726 31.404 3.50 ISC 2004 15.393 32.357 2.10 ISC 2004 15.035 32.218 2.90 ISC 2004 16.857 32.071 2.90 ISC 2004 15.659 32.553 2.40 ISC 2005 15.659 32.553 1.00 ISC 2005 15.93 32.749 1.90 ISC 2006 15.631 32.048 3.30 ISC 2006 14.011 32.373 3.10 ISC 2006 15.321 32.658 1.00 ISC 2006 15.289 32.628 0.90 ISC 2006 15.252 32.555 1.10 ISC 2006 16.437 31.580 2.40 ISC 2007 14.486 32.831 2.10 ISC 2007 14.539 32.989 2.50 ISC 2007 16.596 33.279 1.90 ISC 0.138 0.133 0.165 0.094 975 0.176 0.177 0.205 0.123 2475 0.233 0.25 0.257 0.161 No. 1 Table 5: PGV and PGD values
Return Period
PGV (cm/s) PGD (cm) (year) 75 2.003 0.733 2 475 4.039 2.064 3 975 5.248 2.789 4 2475 6.98 4.117 III. PROPOSED RESPONSE SPECTRA
Table 3: Seismicity parameters for the selected seismic sources
Source Source 1 Source 2 F1 F2 475 β λ Mmax 1.842 0.488 4.9 1.842 1.255 6.2 1.842 1.186 5.2 1.842 1.744 5.3 Figure 3: Location map of the faults, earthquakes and seismic sources in
200 km radius of the studied site
Table 4: PGA values (acceleration gravity coefficients, g (cm/s2))
Boor –
Campbell & Joyner
Return
Amberseys et
Mean Bozorgnia – Fumal period al (1996) (2008) (1997) For the seismic design of a structure, earthquake ground
motions are usually characterized by PGA, response spectra
and acceleration time histories. In previous sections, PGA
values are obtained for traditional static force analysis. The
earthquake ground motions for dynamic analysis, however,
should be specified in terms of response spectra or
acceleration time histories. Response spectra shows the
maximum values of acceleration, velocity, and/or
displacement response of an infinite series of single
degree-of-freedom systems subject to a time dependent
dynamic excitation such as ground motion. The maximum
response values are expressed as a function of the undamped
natural period for a given damping. The values of response
spectra of ground motion can be defined by using standard or
site-specific procedures. Site-specific response spectra
corresponds to those expected on the basis of seismological
and geological calculations using either the deterministic or
the probabilistic seismic hazard analysis method [19]. As
mentioned above, the seismic sources and earthquake activity
are well identified and recognized in the area under study.
Hence, it is possible to specify site-specific values of response
spectra for the site.
Generally, response spectra obtained is based on statistical
analysis of strong motion recordings. The general approach
used for this method was described by Kimball, 1983. This
method consists of conducting statistical analysis of a suite of
strong motion recordings from earthquakes having magnitudes
and distance ranges similar to the target magnitude. Before the
statistical analysis is conducted, these recordings are first
adjusted or modified for differences in magnitude, distance,
and style of faulting, site conditions, and other factors between
the site-specific conditions and the recording conditions.
Typically, these records must be selected to have similar
conditions to those of the project, but usually due to lack of
good records some modifications are needed for differences in
site conditions.
As pointed out above, when the target design ground
motion earthquake is specified, the available appropriate
recording from earthquakes with magnitudes close to the
target magnitude is analyzed statistically to obtain estimates of
the site-specific spectra.
COPYRIGHT © SCIENTIFIC ONLINE PUBLISHING
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probabilistic hazard spectra for 475 year return period (see
Fig.5), using weighted mean of attenuation equations as can
be seen in Fig. 6.
MORADPOURI ET AL: AN EARTHQUAKE STUDY, CONSIDERING THE LACK ..
For our case, due to the low seismicity of Sudan, no seismic
recording s found to implement the approach as described
above. Hence, In order to define response spectra for design
purposes, the design response spectra is developed based on
Figure 4: Hazard curves using weighted mean of attenuation equations. (a) PGA (cm/s2) hazard curve. (b) PGV (cm/s) hazard curve. (c) PGD (cm) hazard curv
Figure 5: Probabilistic hazard spectra for 75, 475, 975 & 2475 years return
period using weighted mean of attenuation Equations
Figure 6: Response Spectra target region
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RESEARCH OF GEOGRAPHIC STRUCTURE AND EARTHQUAKE, VOL. 1, NO. 1, DECEMBER 2013
IV. CONCLUSION
In designing new structures and evaluating seismic
performance of existing structures, it is important to construct
an accurate uniform hazard response spectrum at a selected
site. To construct a uniform hazard response spectrum this
study uses available earthquakes. Earthquakes that occur
within 200 km of the site are considered.
Furthermore, in this paper, a probabilistic seismic hazard is
conducted in Sudan-Africa. Although we confront with the
lack of proper data, the results seem to be reliable and
appropriate to design the structure. As the low seismicity of
Sudan proved, the results obtained for the study area, also
show the low values of PGA, PGV and PGD which are
compatible to the seismicity of the study area.
Also the choice of the attenuation relationships used in this
study may have some biases. The developments of regional
ground motion prediction models, as well as the testing of
applicability of the recently proposed generalized worldwide
ground-motion models, are a matter of high importance.
[9]
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