International Journal of Geosciences, 2011, 2, 549-561
doi:10.4236/ijg.2011.24058 Published Online November 2011 (http://www.SciRP.org/journal/ijg)
549
Site Dependence Earthquake Spectra Attenuation
Modeling: Nigerian Case Study
Adekunle Abraham Adepelumi1, Tahir Abubakar Yakubu2, Olatunbosun Adedayo Alao1,
Akinsola Yusuf Adebayo1
1Department of Geology, Obafemi Awolowo University, Ile-Ife, Nigeria
2Center for Geodesy and Geodynamics and Geodesy (CGG), Toro, Nigeria
Received June 23, 2011; revised August 7, 2011; accepted September 16, 2011
Abstract
Recent seismic events recorded in South-western Nigeria indicate that the country may not be aseismic as
had hitherto thought. Geologic and geodetic evidences suggest the existence of large fracture zones (Ro-
manche and Charcot) beneath the area. Considering the existence of these fracture zones, and the paucity of
seismicity information, the development (oil exploration and production) taking place in offshore Nigeria in
the last two decades and the ambitious planning for large future projects urgently call for the implementation
of a comprehensive earthquake ground motion modelling which is a useful tool in site-dependent seismic
hazard assessment in low to moderate seismicity region. In this study, ground-attenuation modelling based
on stochastic approach was applied to predict the expected peak ground velocity and acceleration and spec-
tral amplifications in two geologic settings. The seismic ground motion has been modelled using the Sep-
tember 11, 2009 earthquake of magnitude 4.8 (Mw) as case study. Synthetic seismic waveforms from which
parameters for engineering building design could be obtain have been derived. From the seismograms com-
puted, the seismic hazard for south-western Nigeria, expressed in terms of peak ground acceleration and peak
ground velocity have been estimated. The peak ground acceleration estimated for the study area ranges from
0.16 to 0.69 g, and the peak ground velocity from 18.0 to 58.3 m/sec. The high peak values of accelerations
and amplifications delineated are possibly due to the presence of the low velocity layers. In general, a good
correlation between the synthetic and field data was observed. These results attest to the efficacy of the mod-
elling exercise, and assessment of the seismic risk that the region would likely be subjected to. Also, the
earthquake engineering design parameters derived may be used to derive new civil engineering building
codes for the affected area.
Keywords: Ground-Motion, Modelling, Seismic, Fracture, Velocity, Acceleration
1. Introduction
Nigeria is supposedly said to be a region of low to mod-
erate seismicity but there has been course in the recent to
investigate the seismicity of Nigeria to be able to forecast
future occurrence of earthquake for engineering founda-
tion purposes. Earthquake all over the world are known
to always occur in regions of high seismicity along tec-
tonic plate boundaries, and are known as interplate
earthquakes, whilst earthquakes worldwide predomi-
nantly occur along tectonic plate boundaries (interplate
regions). Destructive earthquakes do occur away from
the plate margins and are known as intraplate earth-
quakes. The earthquake felt in Abeokuta on 11th Sep-
tember 2009 at by 03:10:30 am has a moment magnitude
of 4.8, and Intensity of 7. It was felt by the residents of the
area. The occurrence intraplate earthquakes in Nigeria is
seen to be characterized by the so called “high stress drop”
which has been interpreted recently as the result of high
velocity fault-slip in the generation of seismic waves at the
source of the earthquake [1]. High slip velocity is consid-
ered to be partly attributed to the thrust faulting mecha-
nisms typifying intraplate earthquakes.
The usual occurrences of these intraplate events ap-
pears random in both space and time and are often asso-
ciated with significant damage due to the vulnerability of

A. A. ADEPELUMI ET AL.
550
building stocks. These events in the case of Nigerian can
be classified as tremors and aftershocks of far and near
distant earthquakes. [2] used the peak ground accelera-
tion (PGA) or peak ground velocity (PGV) to scale the
spectrum to reflect the seismicity of site. His methodology
was adopted in this study. The model adopted has been
used in other part of the world that has experienced inter-
plate earthquakes like California and its application in a
region of assumed low seismicity is assumed conservative.
The response spectrum model which includes New-
mark and Hall model assumes a unique normalized re-
sponse spectrum for rock sites, which implies that the
spectral property of an earthquake depends solely on site
conditions and not on the earthquake source and path
only. In contrast, a uniform hazard spectrum displays
significant regional variations in shape of the response
spectra that are generated across the Nigeria plate. The
uniform hazard spectrum will possess a higher frequency
in the sedimentary regions than the metasediment regions.
These differences in frequency observed in the response
spectra of this region is believed to be results of the dif-
ferent wave transmission in the bedrock and the different
stress associated with the different faulting mechanism.
However, the relative importance of such of these factors
is still under investigation.
The derivation of a regional response spectrum from
first principles requires the analysis of a large number of
strong motion accelerograms representatives of the
whole range of source, path and site conditions. In aseis-
mic region such as Nigeria, Six (6) accelerograms re-
corded recently were used to undertake the empirical
numerical modelling carried out in this study.
The thrust of this paper is to model synthetic earth-
quake seismograms that will be generated by an earth-
quake having a magnitude greater than 4.5 and above on
the Richter scale; model the effect of various seismic
parameters on ground motions caused by this earthquake
using available seismological model; employ the sto-
chastic techniques for the numerical modelling; develop
a site specific design response spectra for Nigeria that
will be used in earthquake engineering studies for dy-
namic analyses (structural dynamic and structural engi-
neering) which may take the form of response spectral
analyses (RSA) or time-history analyses (THA). Com-
pare the response spectra derived from the synthetic
seismograms with those derived from the seismic event
that was recorded in three locations in Nigeria (Ile-Ife,
Kaduna and Nsukka) on 11th September 2009. Finally, an
attempt will be made to assess the seismic hazard of
these areas.
2. Geology of the Area
The principal investigated area covers Ile-Ife (basement
terrain) and Abeokuta (sedimentary terrain) both located
in South-western Nigeria. The former falls within the
Dahomey basin while the later fall within the basement
complex region. The surface geology of Abeokuta is
made up of the both the Ilaro Formation and the Recent
littoral alluvial to Coastal Plain sand deposits (Benin
Formation). The Ilaro Formation is best described by the
sandy strata between 22 m and 72 m penetrated by the
Ota borehole (GSN. BH. 927). The total thickness of the
type section is about 46m. The Ilaro Formation consists
of rather massive sandstone with local clay intercalations
(Figure 1). The Ilaro Formation is fine to medium
grained, and is fairly well sorted. The The Ilaro Forma-
tion lies conformably on the Oshoshun Formation (Lower
—Middle Eocene) and locally unconformably beneath the
Benin Formation (Oligocene-Pleistocene). The Ilaro For-
mation is mostly likely to be Middle to Upper Eocene in
age [3].
In the study area the thickness of the Benin Formation
is between 60 to 80 m. The Benin Formation consists of
continental sands with shale intercalations usually with
good groundwater potential. The Ilaro Formation is es-
timated to be about 70 m thick and shows rapid lateral
facies changes. This can affect the aquifer quality of the
Ilaro Formation [4]. However, the underlying Ewekoro
Formation is known to have good groundwater aquifer
(limestone).
Entire Ile-Ife and environs area is located within the
Ife-Ilesha schist belt, which is predominantly a migma-
tite gneiss-quartzite complex. [5] classified the rocks of
the Ife-Ilesha schist belt into the migmatite gneiss-
quartzite complex as slightly migmatized to non-mig-
matized meta-sedimentary and meta-igneous rocks, and
members of the older granite suite. The geology at the
campus is shown in Figure 1. The gray gneiss occurs in
the pediment area and is the oldest recognizable rock
within the migmatite-gneiss-quartzite complex. This unit
displays augen structures in some places. The slightly
migmatized to non-migmatized meta-sedimentary and
meta-igneous rocks of the campus belong lithologically
to mafic-ultramafic rocks. They occur in the southern
and eastern parts of the town. A dolerite dyke cuts across
the granite gneiss on hill 2 in the north-central part. Mi-
nor veins and pegmatites of various lengths and thick-
nesses cut across the country rock in both a concordant
and a discordant manner. Two prominent NE-trending
thrust faults (F1 and F2) occur in the northern and
south-central parts of the campus, respectively. Locally,
the rocks types found in Ile-Ife area is underlain overlain
by a relatively thick covering of weathered materials
made up of a sequence of lateritic clay (aquitards),
layey sand/sand, and weathered/fractured bedrock. c

A. A. ADEPELUMI ET AL.
551
Figure 1. Geologic map of Nigeria (modified after obaje, 2009).
3. Methodology
The investigated area, South-western Nigeria is located
on a stable part of the Laurasian plate, and is in a region
of low seismicity. There has been no history of a major
earthquake occurrence in this region, but it has a several
potential sources of earthquake e.g. the Romanche and
Charcot fracture zones where future ground movement
may occur. The only history of earth movement (tremor)
in South-western Nigeria is that that occurred in Ijebu-
Ode on July 28, 1984. Also, very recently, an earth-
movement (tremor) of moment magnitude 4.8 and inten-
sity of seven (7) occurred on the 11th of September 2009
at about 03:11am (GMT). It was highly felt by the resi-
dents of Abeokuta and environs. This section treats an
overview of the ground modelling methods used in this
study. There are two main methods commonly used for
the generation of earthquake accelerograms. They are:
Deterministic methods and stochastic methods. However,
for this study, the stochastic method was adopted based
on the perceived robustness of the method.
For example, [6] performed a site effect seismic mod-
elling of the Tolmezzo-Ambiesta dam in North-eastern
Italy. They show that their numerical modelling output
compared favourably with the field results. Also, [7]
used an iterative Gauss-Newton to model and invert the
nonlinear problem displacement spectra of earthquakes
recorded by the French accelerometric network at re-
gional scale as the product of source, propagation (in-
cluding geometric and anelastic attenuation), and site
effects. A very robust site responses relative to an aver-
age rock-site response was derived, allowing them to
identify good reference rock sites. [8] performed a nu-
merical modelling of the attenuation of peak ground ve-
locity for intraplate earthquakes in Australia using the
CAM stochastic modelling approach. They obtained a
good agreement between both historical intensity data
and instrumental earthquake data with CAM model result.
[9] carried out a Stochastic simulations of the seismol-
ogical model for the magnitude 9.3 Aceh earthquake
(Indonesia) on the 26th of December in 2004, were per-
formed and compared with the response spectra recorded
on a rock site in Singapore. They further the attenuation
behaviour of earthquake ground shaking into three 1)
regional factors, 2) local factors, and iii) site factors.
In-addition, [10] used small-to-moderate earthquakes
located within 200 km of San Francisco to characterize
the scaling of the ground motions for frequencies ranging
between 0.25 and 20 Hz. They obtained results for geo-
metric spreading, Q(f), and site parameters. The results
of their analysis showed that, throughout the Bay Area,
the average regional attenuation of the ground motion
can be modeled with a bilinear geometric spreading
function with a 30-km crossover distance, coupled to an
anelastic function. Furthermore, [11] carried out a holis-
tic ground-motion modeling techniques for use in Global
Shake Map in different tectonic settings of the world. [12]
showed that ground-motion prediction is still affected by

A. A. ADEPELUMI ET AL.
552
large, and only slowly decreasing, uncertainties even for
well-instrumented areas with long histories of strong-
motion observation (e.g. California). Also, [13] summa-
rised the importance of predicting the expected earth-
quake ground motions at sites of interest in Engineering
seismology. He concluded that an important considera-
tion when selecting the modelling parameters is the pos-
sible dependence of ground motions on geographical
region. [14] characterised and model the seismic re-
sponse at liquefied sites and a liquefiable site in China
using the JBF seismic attenuation model. They con-
cluded that for the two selected sites, the seismic re-
sponse spectra estimated from strong motion attenuation
model are the same.
4. Stochastic Methods
The generation of intraplate earthquake accelerograms
must consider random variabilities which can be ac-
counted for using stochastic methods. With the inven-
tions of computers and fast Fourier algorithms; the sto-
chastic methods which are basically dependent on fre-
quency domain analysis is less cumbersome and faster
for use to generate synthetic accelerograms of [15]. The
stochastic procedure typically consists of a deterministic
Target Fourier amplitude spectrum defining the fre-
quency content and a set of random phase angle defining
the phase arrivals. An amplitude function is used to
modulate the accelerograms to a realistic duration. Ka-
nai-Tajimi filter has developed within a stochastic frame
work to generate artificial accelerograms. More elaborate
Fourier spectrum models have been developed by [16]
and [17] using earthquake magnitude, source distance
and site classification as the controlling parameters. [18]
proposed a procedure which is a hybrid of stochastic and
deterministic methods. Furthermore, [19] applied the
stochastic technique to derive a tentative set of updated
hybrid empirical hard-rock ground motion estimates for
PGA, PGV and 5% damped linear elastic response spec-
tra for eastern North America. [20] successfully applied
this method in the West Coast of North America.. Also,
he was able to show that this method offers an alternative,
more empirically based, method for predicting near-
source ground motions from large-magnitude earth-
quakes in ENA and other stable continental regions.
GENQKE software version 1.0 was used for the nu-
merical computation. This software was used in deriving
the Fourier spectrum from a target response spectrum.
Synthetic accelerograms was generated to match code
response spectra using such a program. Whilst code de-
signed response spectra are typically smoothed and based
on implicit assumptions, empirical response spectrum
models addressing specific source, path and site condi-
tions and are more transparent. Also, a seismological
model originally developed by [21] and subsequently
modified by [22-24] identifies the important factors af-
fecting the properties of the earthquake ground motion
and distils these factors into few key parameters. The
advantage of this model is its generic, simple to use, and
its suitability for the modelling of seismic hazard in areas
of low seismicity areas where details of potential earth-
quake sources are generally unknown. The Fourier spec-
trum specified in the model is expressed as the product
of a source factor, a geometrical attenuation factor, a
whole path attenuation factor and factors representing
effects near the surface. Interestingly, the source factor
has been found to be consistent with Fourier transform of
the shear waves predicted by point shear dislocation the-
ory [25]. Ground motion parameters can be obtained
from the specified Fourier amplitude spectrum either
using random vibration theory according to [24] or by
generating synthetic accelerograms as described in chap-
ter four. Such parameters predicted by model generally
provide a good match with field observation, particularly
following recent modifications to the original source
function by [26]. Also, [27] showed that the seismologi-
cal model produces results which are comparable to the
previously described deterministic ray-theory method.
5. The Seismological Model
5.1. Overview
In the seismological model, the Fourier amplitude spec-
trum of displacement A(f) of seismic waves reaching the
exposed surfaces of bedrock may be expressed as the
product of a number of factor:
A(f) =C×Mo×S(f)×G×An(f)×V(f)×P(f) (1)
where
C is a scaling factor.
Mo is the seismic moment S(f) is the regional source
spectrum.
G is the regional geometric attenuation factor.
An(f) is the regional anelastic whole path attenuation.
V(f) is the local upper crust amplification filter.
P(f) is the local upper crust attenuation filter
5.2. Regional Source Factor S(f) and Mid Crust
Factor (mc

)
Regional and generic, source factors have been used to
generalize the average behaviour of seismic waves or
energy generated at the source of the earthquake to the
whole region. Countries like Nigeria which has not cap-
tured sufficient near-field strong motion data to develop

553 A. A. ADEPELUMI ET AL.
conventional (empirical) attenuation models of its own
have the option to adopt the alternative approach of un-
dertaking stochastic simulations of the seismological
model which is characterized by the separation of the
ground motion model into the “source”, “regional” (path)
and “local” components(the “local” component is not to
be confused with the “site” components which deal with
the effects of the surface sediments of the site). The heu-
ristic framework of resolving ground shaking into the
“source”, “path” and “local” components enables te-
lemetry data recorded by seismometers from long dis-
tances to be corrected for the path (and local) effects and
hence enable seismic waves radiated from the “source”
of the earthquake to be back-calculated. The stochastic
seismological methodology was pioneered in the low-
moderate seismicity regions of Central and Eastern North
America (CENA) where strong motion data was lacking
but sufficient telemetry data from the Eastern Canadian
Telemetry Network (ECTN) was available to construct
viable seismological models for the region, for example,
[25,28,29].
In this case study, the generic source factor of intra-
plate earthquakes as developed by [25] was used to rep-
resent the geological condition in our study area in Nige-
ria since they share similar features. Equations (2) to (8)
gives the generic source factor S(f) for displacement am-
plitude defining the Fourier spectrum of the seismic
shear energy generated at the source of earthquake:
S(f) = CMo[(1 – v)SA +
 SB] (2)
where S
A = 1/[1 + (f/fA)2] (3)
SB = 1/[1 + (f/fB)2] (4)
C = RpFV/4πρβ3 (5)
Mo is the seismic moment, Rp is the wave radiation
factor, F is the free surface amplification factor, V is the
factor partitioning seismic energy in the two orthogonal
directions. (the product of RpFV is 0.78), is the density of
the rock at depth of rupture is the shear wave velocity
(SWV) of the rock at the depth of rupture. The intraplate
source model was based on the generic hard rock condi-
tions obtained from a global database with = 2.8 t/m3 and
= 3.8 km/s at a depth approximately 12 km.
The magnitude-dependent corner frequencies fA, fB and
the proportioning factor V are listed as follows:
logfA = 2.41 – 0.533M (6)
logfB = 1.43 – 0.188M (7)
log
 =2.52 – 0.637M (8)
where M is the moment magnitude which has also been
denoted as Mw, the amplitude of S-wave generated from
the source of the earthquake is inversely proportional to
the shear wave velocity of the surrounding crust raised to
a power of 3, according to (5) above. Adjust to allow for
other parameter values can be made through the mid-
crust modification factor defined as:
3
mc
,8 8
3.8 2.8
S
V








 
(9)
where ,8S and 8 V

is the crustal shear wave velocity
is the shear wave velocity and density respectively at 8
km depth.
5.3. Regional Geometrical Attenuation Factor
The geometrical G factor represent the attenuation of the
amplitude of the radiated seismic waves resulting purely
from the geometrical spread of energy as opposed to dis-
sipation of energy. The G factor in the near-field con-
forms to spherical attenuation and is independent of re-
gional conditions. The G factor becomes regionally de-
pendent in the far-field where the attenuation pattern is
influenced significantly by seismic waves reflected from
the Mohorovicic discontinuity which defines the inter-
face between the earth crust and the underlying litho-
sphere. The significance of the Mohorovicic discontinu-
ity reflection increases with decreasing thickness of the
earth crust, according to
 
30
GR,D for R1.5D
R


(10)
 
30
GR,D for 1.5DR2.5D
1.5D
 (11)
 
30 2.5D
GR,D for R2.5D
1.5D R
 (12)
where R is the source-site distance of the earthquake and
is crustal thickness.
5.4. Regional Whole Path Attenuation Factor
An(f)
Whole path attenuation is particularly important in the
modeling of ground motions from long-distant earth-
quake. Large-magnitude earthquakes generated at source-
site distance(R) exceeding 100km are typified by low-
frequency(long-period) seismic waves, since the high
frequency components have greatly diminished in am-
plitude as a result of energy absorption along the source-
site wave travel path. The attenuation mechanism may be
characterized by the value of seismological quality factor
Q (equivalent to Qo, namely Q at frequency of 1Hz) as
obtained from seismological monitoring in the region.
The value of Q may be substituted to develop the filter
function An(f) representing the effects of whole path at-

A. A. ADEPELUMI ET AL.
554
tenuation of seismic waves propagating within the
earth’s crust:


πR
QV
n
Ae
S
f
f
f


 (13)
where f is the wave frequency, R is the length of the
wave travel path and Vs is the shear wave velocity. The
Q(f) is then defined by:
Q(f) = Qof n (14)
Substitution of (14) into (13) yields the estimated
whole path attenuation factor. An empirical correlation
between Qo and Vuc has been developed, employing in-
formation obtained from global sources in conjunction
with that from local studies:
4.5
oucuc
Q1002.5V[V1.6 km/s] (15)
Further, an empirical correlation between

and Qo
based on global database has been developed:
2
oo
0.0000008Q 0.0014Q 0.93   (16)
5.5. Local upper Crustal Amplification Factor
V(f)
Upwardly propagating shear waves are amplified when
the waves cross from one medium to a lower velocity
medium and can be explained by principle of conserva-
tion of energy. Upper-crust amplification is a function of
the shear wave velocity profile (its value and gradient) in
the earth crust, particularly at shallow depths and is pe-
riod or frequency dependent. The extent of upper-crust
amplification may be predicted from [17], using and to
represent the rock density and SWV at the source depth,
which is typically assumed as z = D = 8 km and at a
depth corresponding to period of interest.

BB
S
AA
V
VV, =V

 (17)
To relate the period of interest to rock depth, the quar-
ter-wavelength approximation method is required. This
method allows the values of velocity (V) to be averaged
to a depth equivalent to the quarter-wavelength of the
upwardly propagating shear wave, for applying [17].
5.6. Local upper Crust Attenuation Factor P(f)
Wave transmission quality within bedrock is not uniform
with depth. Attenuation in the upper crust is a local phe-
nomenon and is represented by a local factor and the
mechanism occurs over a short transmission distance, as
for attenuation in soft sediments. The upper crustal at-
tenuation factor P(f) in the seismological model has been
defined by (18)


π
Pe
f
f
 
 (18)
Where

is measured from the Fourier transform of
seismic waves recorded from the very near-field. The
parameter

is generally difficult to measure in regions
of low and moderate seismicity because of magnitude or
epicentral distance requirement associated with the
measurements. A method for estimating is to make
inferences from the shear wave velocity near to rock
surface. Empirical correlation of with the average
shear-swave velocity of the upper crust Vuc (taken as the
upper 4 km depth), as well as at 30 km depth, have been
developed based on global sources:






uc uc
0.1450.12lnV0 V1.6 km/s   (19)

S
0.8
S
0.057 0.02 0.5 km/sV,0.03
V ,0.03
   (20)
5.7. Soil Site Response Function F(f)
Experiences gathered from previous earthquake has re-
peatedly shown that the intensity of damage produced
from ground shaking motions, are strongly influenced by
local site conditions, in particular the influence of rela-
tively shallow geologic material on nearly vertically
propagating body waves as soils behave nonlinearly
when subjected to strong levels of ground shaking, it is
more appropriate to account separately for site effects
from bedrock and soil layers, and hence a site response
transfer function F(f) can be added to (1). It is worth
mentioning that soil site response function F(f) is not
single value for specific site, as it depends on the level of
soil damping and is, in turn, related to the shaking level.
Together with different resonant conditions, which are
interactive effects arising between the earthquake sce-
nario and site condition, the soil site response factor
would vary for different earthquake events. That repre-
sents a unique and distinctive feature of using the com-
bination of seismological model and site response func-
tion as the attenuation model. For this study, a new Mat-
lab script was written for the stochastic modelling, while
the earthquake events recorded in September 2009 was
used for the numerical modelling and computations.
6. Results and Discussion
The result obtained from the seismological computation
and modeling has shown that ground motion modelling
is a useful tool in site-dependent seismic hazard assess-
ment in low to moderate seismicity region. It helps in
giving ideas on the type of earthquake signature to be

A. A. ADEPELUMI ET AL.
555
expected in various geologic settings. In this study,
ground-attenuation modelling based on ground motions
stimulated stochastically in accordance with seismologi-
cal model was carried out over two geological settings:
sedimentary terrain and the basement complex. The re-
sults obtained were compared in order to determine the
efficacy of the modelling exercise carried out. Ground
motion modelling has to be taken into consideration in
Nigeria especially the Southwestern region in order to
address seismic risks, and develop effective mitigation
measures in view of its high population density, recent
development and concentration of commercial activities
and local engineering practices that have not embraced
aseismic design principles.
6.1. Seismological Parameter Used
The mean focal depth or depth to the epicentre is taken
as h = 20 km in the seismological modelling. With this
depth range, it is considered that ρ = 2.8 t/m3 and β = 3.7
km/s, which is consistent with values obtained from [30].
The mid-crust modification factor is accordingly equal to
1.0 - 1.1. The data from [30] gave value of D for Nigeria
to be 30km.The quality factor Qo = 121 and the upper
crustal attenuation factor κ = 0.02 have been obtained
from the regional shear wave velocity parameter (of the
upper 4 km depth).
To develop representative local factors representing
the 2 mechanisms, the shear-wave velocity profile of the
crustal rock has been designed based on [30] and the
methodology of constructing rock SWV profiles.
6.2. Comparism of Simulated with Instrumented
Recorded Data
Synthetic accelerogram have stimulated stochastically
using computer program GENQKE. The response spec-
tra calculated from six (6) accelerograms with random
phase angles are averaged for different earthquake sce-
narios. The average response spectra computed are
shown in Figures 2-4. The response spectra recorded on
a rock site in Ile-Ife and Abeokuta area have been plotted
on same graph for direct comparison.
It is worth-mentioning that the earth tremor of 11th
September 25, 2009 was also recorded at Nsukka and
Kaduna respectively. For comparison sake, we would
briefly compare the earthquake field data obtained at
these locations also with our model results. The model
results shown in Figures 2-4 correlate reasonably well
with the recorded three components tremor data at three
major locations in Nigeria at Ile-Ife, Nsukka and Kaduna
(See Figure 5). From this figures, it is evident that the
model result is comparable in magnitude to the event
recorded at Ile-Ife; this offered the opportunity to test the
robustness of the stochastic model. The site-source dis-
tance of this second event from Kaduna was only about
588 km (which is 0.6 times the site-source distance of the
Abeokuta earthquake).The recorded model comparison
of the second event displays a similar level of consis-
tence as with the first event. The very different site-
source distance of the Abeokuta and Kaduna earthquake
means that significant record model would have surfaced
with one of the events had the adopted attenuation pa-
rameters (the quality factor in particular) been not repre-
sentative of real conditions of the wave travel path.
6.3. Computed Synthetic Accelerograms
Sample acceleration time-histories on “rock” conditions
characteristics of some parts Nigeria are presented in
Figures 2, 3 and 4 to show the increase in the duration of
the accelerogram with earthquake magnitude and dis-
tance in accordance with the relationship defined in [31].
These accelerograms can be modified to represent the
filtering effects of soil sediments using well-established
standard procedures in which bedrock accelerograms are
Figure 2. Time history of simulated accele rograms for earthquake sce nario of M > 2.9 < 5 for on rock c harac teristic of Ile -Ife,
Southwestern Nigeria.

A. A. ADEPELUMI ET AL.
556
Figure 3. Time history of simulated accelerograms for earthquake scenario of M > 2.9 < 5, R = 466 km on rock characteristic
of Nsukka, Eastern Niger i a.
Figure 4. Time history of simulated accelerograms for earthquake scenario of M > 2.9 < 5, R = 588 km on rock characteristic
of Kaduna, Northern Nigeria.
Figure 5. Earthquake seismogram recorded on September
11, 2009 for Ife, Kaduna and Nsukka seismic stations.
used as the input motion. Ground shaking could be sig-
nificantly prolonged on soft soil sites (sedimentary re-
gions) increasing the risk of damage to structures.
7. Response Spectra
Time History Analyses is considered to provide a more
realistic representation of the actual response of the
structure than Response Spectra Analyses (RSA) par-
ticularly when the response is characterized by non-lin-
ear (inelastic) behavior or significant torsional coupling
behavior. When time-history analyses are performed in
earthquake engineering studies, several representative
ground motions should be used in order that the sensitiv-
ity of the response of the structure to random variations
in the excitations can be deciphered. Large number of
accelerograms representing a range of conditions was
used in this study for multiple analyses is to be done.
Accelerograms that were recorded locally in Nigeria
were typically taken from small magnitude events, after-
shocks, or from long epicentral distances. Near-field mo-
tions of engineering significance are very difficult to
capture due to the infrequent characteristics of intraplate
earthquakes and also the insufficiency of strong ground
motion data in Nigeria which does not meet seismic de-
sign requirements and earthquake studies. Strong motion
accelerograms if recorded from outside Nigeria may
misrepresent local conditions even though the records
could be taken from regions that have low to moderate

557 A. A. ADEPELUMI ET AL.
seismicity. The use of accelerograms generated artifi-
cially by computer based on stochastic simulations has
become a viable alternative for THA. In this section, we
intend to present the result of synthetic accelerograms
that have been generated for engineering applications
using program called GENQKE that was developed at
the University of Melbourne [31-33] In view of the fur-
ther occurrence of ground motion, our emphasis is on
examining the peak ground velocity and response spec-
tral properties of the accelerograms which is more useful
in the engineering aspect. The simulation methodology
used has been well established and review articles on this
subject can be found in the literature [31].
It is shown that separate modelling is required for i)
“hard rock” conditions and “rock” conditions of some
regions in Nigeria. Response spectra of the generated
accelerograms have also been calculated. Results were
averaged and presented systematically for one magnitude
and varying distances. The verification analyses also
compared data collected from the 11th of September 2009
Abeokuta earthquake against computer simulations. Re-
sults of the comparative analyses provide support to the
claim that the generated accelerograms are generally
consistent with local conditions as seen from Figure 5.
Further verification analyses addressing the long-period
behaviour of the accelerograms are presented in Figure 6.
Response spectra for both rock and soft soil conditions
are presented for comparison with the design response
spectra are shown in Figure 7.
7.1. Sensitivity Study on Sample Size
Initially, the response spectrum of an individual simu-
lated accelerogram was calculated. This response spec-
trum based on a single accelerogram was then compared
with the average of six (6) accelerograms. Results of this
comparative study are shown in Figures 2-5—for a
Figure 6. Sample size comparison of average response ve-
locity and acceleration spectra.
Figure 7. Displacement spectral Responses for the three
Seismic stations. The left panels’ show the results for Ife,
Nsukka and Kaduna, while the right panel is the average
displacement for the simulation for the three stations.
Magnitude M = 4.8, R = 140 km earthquake. The irregu-
lar appearance of the response spectrum based on a sin-
gle simulation is clearly noticeable, indicating a signifi-
cant bias at certain periods. It is the opinion of the au-
thors that a minimum of 4 - 6 randomly generated accel-
erograms has to be included in the analyses to effectively
suppress the biases (as evidenced by the smoothness of
the averaged response spectra associated with larger
sample sizes).
7.2. Response Spectra of Accelerograms
Simulated
Six random simulations have been produced for each
earthquake scenario defined by a magnitude-distance
(M-R) combination for the “rock” conditions of South-
Western Nigeria. A response spectrum was then calcu-
lated for each simulation and results were averaged. A
selection of the averaged response spectra is presented in
Figure 6.
Estimation of this ground motion parameter either im-
plicitly through the use of special earthquake codes or
more specifically from site-specific investigations is es-

A. A. ADEPELUMI ET AL.
558
sential for engineered structures. An important parameter
used in earthquake engineering characterizing each re-
sponse spectra is the notional peak ground velocity (PGV)
which is defined herein as the highest point on the aver-
aged velocity response spectrum divided by 1.8. Thus,
the peak ground acceleration estimated for the study area
ranges from 0.16 to 0.69 g, and the peak ground velocity
from 18.0 to 58.3 m/sec (Figures 6 and 7). The values
presented as the peak ground acceleration (PGA) and
peak ground velocity (PGV) are minute. Also, a good
agreement has been found between computer simulations
and field measurements [32].
Furthermore, spectral displacement is highly depend-
ent upon seismic moment of the seismic shear wave
whereas the spectra acceleration is mainly dependent on
stress drop parameter of the earthquake ground motion
and to a lesser extent on seismic moment. A particular
threshold frequency called corner frequency is the fre-
quency that dictates acceleration amplitude and in turn
controls the frequency content of earthquake ground mo-
tion at the source. Thus the stress drop is believed to
have contributed to high frequency content observed in
intraplate earthquakes generally. This further confirms
the information that displacement amplitude is controlled
by low frequency while acceleration amplitude is con-
trolled by high frequency. Stress drop of intraplate earth-
quakes is well correlated with very low slip rate of intra-
plate fault. Interestingly, observed stress drops did not
show any significant difference between normal, reverse
and strike-slip faulting system among intraplate earth-
quakes around the world.
The Abeokuta, Nigeria earthquake that occurred on
the 11th of September 2009 was deduced to be triggered
of by the Romanche fracture zone. It is one of the largest
offsets striking East-West that marks the Mid-Atlantic
Ridge in the Atlantic Ocean. It is a normal fault with
length of over 1000km, width of 200km, and occurs as a
narrow break near the equator. We deduce that the seis-
mic moment of the seismic shear wave of this earthquake
ground motion possibly got attenuated in the sedimentary
terrain of Nigeria. Displays of the displacement obtained
are shown in Figure 7.
On the other hand, Figure 8 shows the attenuation plot
for the seismic wave derived for the investigated area in
Nigeria. A is simulated for a magnitude 3 earthquake,
and B is for a magnitude 4.8 earthquake. The plot im-
plies that there is moderate attenuation of the seismic
waves in the study area. A general exponential decay of
the curve is observed. This is in conformity with what is
obtained around the world. We adjudged that the relation
obtained from this study is the most plausible representa-
tion model that possibly corresponds to real ground mo-
tions for this affected area. It is well known that soils
Figure 8. Attenuation plot for the seismic waves propagated
on 11th September 2009.
behave non-linearly when subjected to strong level of
ground shaking. Soil site response function is not a sin-
gle value for a specific site due to the soil having mem-
ory as it is dependent on soil damping and in turn related
to the shaking level at crustal rock and overlying soil
sediment interface.
From the resultant attenuation curves obtained from
this study shown in Figure 8, it is pertinent to note that
there is no obvious difference in the trend which is ap-
parent among the different irrespective of the variation of
the magnitude value. We envisaged that the decay curve
accounts for damping effects of the soil which is very
important in structural engineering for structural dy-
namic analyses. This is based on the fact that civil struc-
tures dissipate viscous energy on rock medium as a result
of the damping effect. This decay is usually caused by
the spherical spreading of the seismic shear waves gen-
erated by the earthquake at the Mohorovicic discontinu-
ity and spherical spreading at the Gutenberg.
7.3. Seismic Hazard Assessment
The peak ground acceleration and velocity computed for
the investigated area ranges from (0.16 - 0.69) g and
(18.0 - 58.3) m/s, respectively. Using the peak ground
values obtained and the amplifications computed from
the numerical modeling, the investigated areas has been
divided into three main hazard zones called low, moder-
ate and high damage potential zones (Figure 9). The
estimated PGA and PGV values obtained from this study
were used in deriving the seismic hazard map for the
study area. The seismic ground motion of Nigeria has
been computed, and the hazard zones assessed based on
the computations from synthetic accelerograms that take
simultaneously into account the source, path and site
effects. The parameters obtained from the accelerograms
and response spectra allow us to estimate the seismic
hazard of some parts of Nigeria.
Areas underlain by unconsolidated sediments (having
ow mechanical strength) are classified as the maximum l

A. A. ADEPELUMI ET AL.
559
Figure 9. Seismic hazard map of some parts of Nigeria derived from the PGA and PGV values obtained in this study.
damage potential zone. The presence of low velocity
sediments possibly contributed to the high peak values
and amplifications obtained. Whilst those underlain by
meta-sediments are said to be the moderate damage po-
tential zone, and highly consolidated geological forma-
tion, that is, areas having very high mechanical proper-
ties) are classified as low damage potential zone. Build-
ings in these areas classified as the maximum damage
potential zone, and should be designed to resist such high
ground acceleration. As development within the me-
tropolis is generally not controlled or planned, it makes
the area a recipe for major disaster in the event of a
strong earthquake. Buildings are poorly designed and
constructed and the building codes are not adhered to
strictly.
It is inferred that areas that lies within the moderate to
high damage potential zones are more likely susceptible
to severe damage if another ground movement having
high PGA values should occur, it is envisaged that struc-
tures and buildings would be destroyed with loss of
lives and property when an earthquake of such intensity
strikes the area. The maximum peak ground acceleration
estimated is located in areas denoted as zones with low
velocity geological formations such as continental and
marine deposits in the especially the low-lying coastal
regions where a lot of and local construction practices
are in progress. Also, areas characterized by highly con-
solidated geological materials are classified as low dam-
age potential zones are the areas that will be least af-
fected by any earthquake or tremor.
The results of the numerical simulation have been ex-
tended to all other areas with similar geological forma-
tion. It is now possible to define realistic seismic pa-
rameters for the already built area. Damage in such heav-
ily populated area. The ground motion parameters ob-
tained is useful for urban planning, retrofitting of the
built environment, for earthquake preparedness and risk
reduction. Civil Engineers can use the parameters as
seismic input for the design of structures in future con-
struction works of civil structures. This is a prerequisite
to curtail the negative impact of any strong earthquake
on structures in the investigated areas.
8. Conclusions
Nigeria is known to be on a stable part of the African

A. A. ADEPELUMI ET AL.
560
shield, and a reliable assessment of seismic risk in this
region requires knowledge and understanding of both the
seismicity and the attenuation of strong ground motion.
The seismic ground motion of the south-western Nigeria
has been computed using stochastic modelling technique
and the hazard zones assessed. The results obtained were
correlated with field events recorded on 11th September
2009. A good correlation between the two was obtained.
This showed that stochastic modelling could be effec-
tively used as a predictive tool both for the basement
complex and sedimentary terrain of Nigeria. The peak
ground acceleration estimated for the study area ranges
from 0.16 to 0.69 g, and the peak ground velocity from
18.0 to 58.3 m/sec. These correspond to intensity ranging
from VII to IX on the MM Intensity scale of Bolt (2004).
The high peak values of accelerations and amplifications
delineated are possibly due to the presence of the low
velocity sediments. Also, the resultant spectra attenua-
tion curves generated synthetically across three (3)
different stations with a distance of 466km (Nsukka) and
588km from Ile-Ife represent typical spectral for the
basement complex and sedimentary terrains. It is con-
cluded that the differences between the three (3) curve
types obtained for the three cities showed that distance is
a more important factor than magnitude in determining
the shape of spectra attenuation. We observe that the
maximum peak ground acceleration is located in areas
having low velocity layers. In terms of seismic vulner-
ability, the investigated area is classified into maximum
(sedimentary), moderate (meta-sediments) and low
damage potential (basement rocks). Therefore, buildings
in these areas should be designed to resist such high
ground acceleration. The seismic ground motion pa-
rameters computed is useful to future urban planning
development and structural design.
9. Acknowledgements
The Third World Academy of science is appreciated for
the research grant that enabled us carry out this research.
Also, the research grant support (11801BOW) of the
University Research Council at Obafemi Awolowo Uni-
versity, Ile-Ife, Nigeria is acknowledged. Also, the Cen-
ter for Geodesy and Geodynamics and Geodesy (CGG),
Toro, Bauchi State Nigeria appreciated for the technical
assistance.
10. References
[1] I. A. Beresnev and G. M. Atkinson, “Modelling Fi-
nite-Fault Radiation from the Spectrum,” Bulletin of the
Seismological Society of America, Vol. 87, No. 1, 1997,
pp. 67-84.
[2] N. M. Newmark and W. J. Hall, “Earthquake Spectra and
Design,” Earthquake Engineering Research Institute Mo-
nograph Series, 1982.
[3] M. E. Omatsola and O. S. Adegoke, “Tectonic Evolution
and Cretaceous Stratigraphy of the Dahomey Basin,”
Journal of Mining and Geology, Vol. 18, No. 1, 1981, pp.
130-137.
[4] N. G. Obaje, “Geology and Mineral Resources of Nige-
ria,” In S. Bhattacharji, et al., Eds., Lecture Notes in Earth
Sciences, Springer-Verlag, Berlin, 2009, pp. 1-219.
[5] M. A. Rahaman and O. O. Ocan, “On Relationship in the
Precambrian Migmatite Gneiss of Nigeria,” Journal of
Mining and Geology, Vol. 15, 1978, pp. 23-30.
[6] C. Barnaba, E. Priolo, A. Vuan and M. Romanelli, “Site
Effect on the Strong Motion Site at Tolmezzo-Ambiesta
Dam in Northeastern Italy,” Bulletin of the Seismological
Society of America, Vol. 97, No. 1B, 2007, pp. 339-346.
doi:10.1785/0120060077
[7] S. Drouet, S. Chevrot, F. Cotton and A. Souriau, “Simul-
taneous Inversion of Source Spectra, Attenuation Pa-
rameters, and Site Responses: Application to the Data of
the French Accelerometric Network,” Bulletin of the
Seismological Society of America, Vol. 98, No. 1, 2008,
pp. 198-219. doi:10.1785/0120060215
[8] N. Lam, C. Sinadinovski, R. Koo and J. Wilson, “Peak
Ground Velocity Modelling for Australian Intraplate
Earthquake,” Journal of Earthquake Engineering &
Structural Dynamics, Vol. 5, No. 2, 2003, pp. 11-22.
[9] H. H. Tsang, N. T. K. Lam and S. H. Lo, “Site-Depend-
ent Response Spectral Attenuation Modelling: A Case
Study of Long Distance Earthquakes Affecting Singa-
pore,” International Journal of Geology, Vol. 1, No. 1,
2007, pp. 6-10.
[10] L. Malagnini, K. Mayeda, R. Uhrhammer, A. Akinci and
B. R. Herrmann, “A Regional Ground-Motion Excita-
tion/Attenuation Model for the San Francisco Region,”
Bulletin of the Seismological Society of America, Vol. 97,
No. 3, 2007, pp. 843-862. doi:10.1785/0120060101
[11] T. I. Allen and D. J. Wald, “Evaluation of Ground-Mo-
tion Modeling Techniques for Use in Global Shake-
Map—A Critique of Instrumental Ground-Motion Pre-
diction Equations, Peak Ground Motion to Macroseismic
Intensity Conversions, and Macroseismic Intensity Pre-
dictions in Different Tectonic Settings,” US Geological
Survey Open-File Report 2009-1047, 2009, p. 114.
[12] J. Douglas, “On the Regional Dependence of Earthquake
Response Spectra,” ISET Journal of Earthquake Tech-
nology, Vol. 44, No. 1, 2007, pp. 77-99.
[13] J. Douglas, “Investigating Possible Regional Dependence
in Strong Ground Motions,” Earthquake Data in Engi-
neering Seismology, Vol. 14, Part 1, 2011, pp. 29-38.
[14] J. Zhang and C. Yang, “Characteristics of Seismic Re-
sponses at Liquefied and Non-Liquefied Sites with Same
Site Conditions,” Journal of Modern Transportation, Vol.
19, No. 2, 2011, pp. 134-142.
[15] E. H. Vanmarcke, “Seismic Risk and Engineering Deci-
sions, Chapter 8,” Elsevier Publishing Co., New York,

A. A. ADEPELUMI ET AL.
561
1977.
[16] R. K. McGuire, “A Simple Model for Estimating Fourier
Amplitude Spectra of Horizontal Ground Acceleration,”
Bulletin of the Seismological Society of America, Vol. 68,
No. 3, 1978, pp. 803-822.
[17] M. D. Trifunac, “Dependence of Fourier Spectrum Am-
plitudes of Recorded Earthquake Accelerations on Mag-
nitude, Local Soil Conditions and on Depth of Sedi-
ments,” Earthquake Engineering Structure Dynamics,
Vol. 18, No. 7, 1989, pp. 999-1016.
doi:10.1002/eqe.4290180706
[18] G. Gibson, “Artificial Ground Motions,” Proceedings of
a Seminar Held by the Australian Earthquake Engineer-
ing Society of The Institute for Engineers Australia, Mel-
bourne, 1993, pp. 83-86
[19] K. W. Campbell, “The Dependence of Peak Horizontal
Acceleration on Magnitude, Distance, and Site Effects for
Small-Magnitude Earthquakes in California and Eastern
North America,” Bulletin of the Seismological Society of
America, Vol. 79, No. 5, 1989, pp. 1311-1346
[20] G. M. Atkinson and D. M. Boore, “Ground Motion Rela-
tions for Eastern North America,” Bulletin of the Seis-
mological Society of America, Vol. 85, 1995, pp. 17-30.
[21] J. N. Brune, “Tectonic Stress and the Spectra of Seismic
Shear Waves from Earthquakes,” Journal of Geophysical
Research, Vol. 75, No. 26, 1970, pp. 4997-5009.
[22] D. M. Boore, “Stochastic Simulation of High-Frequency
Ground Motions Based on Seismological Model of the
Radiated Spectra,” Bulletin of the Seismological Society
of America, Vol. 73, No. 6, 1983, pp. 1865-1894.
[23] D. M. Boore and G. Atkinson, “Stochastic Prediction of
Ground Motion and Spectral Response Parameters at
Hard-Rock Sites in Eastern North America,” Bulletin of
the Seismological Society of America, Vol. 73, 1987, pp.
1865-1894.
[24] T. C. Hanks and R. K. McGuire, “The Character of
High-Frequency Strong Ground Motion,” Bulletin of the
Seismological Society of America, Vol. 71. No. 6, 1981,
pp. 2071-2095.
[25] G. Atkinson and W. Silva, “An Empirical Study of Earth-
quake Source Spectra for Californian Earthquakes,” Bul-
letin of the Seismological Society of America, Vol. 87, No.
1, 1997, 97-113.
[26] I. A. Beresnev and G. M. Atkinson, “Source Parameter of
Earthquakes in Eastern and Western North America
Based on Finite-Fault Modelling,” Bulletin Seismological
Society of America, Vol. 92, No. 2, 2002, pp. 695-710.
doi:10.1785/0120010101
[27] G. Atkinson and P. Somerville, “Calibration of Time
History Simulation Methods,” Bulletin of the Seismol-
ogical Society of America, Vol. 84, 1994, pp. 400-414.
[28] A. M. Chandler, N. T. K. Lam and H. H. Tsang “Re-
gional and Local Factors in Attenuation Modelling: Hong
Kong Case Study,” Journal of Asian Earth Sciences, Vol.
27, No. 6, 2006, pp. 892-906.
doi:10.1016/j.jseaes.2005.09.005
[29] G. M. Atkinson and D. M. Boore, “Evaluation of Models
for Earthquake Source Spectra in Eastern North Amer-
ica,” Bulletin of the Seismological Society of America,
Vol. 88, 1998, pp. 917-934
[30] CRUST2.0, Institute of Geophysics and Planetary Phys-
ics, University of California, San Diego, 2001.
http://mahi.ucsd.edu/Gabi/rem.dir/crust/crust2.html
[31] N. T. K. Lam, J. L. Wilson and G. L. Hutchinson, “Gen-
eration of Synthetic Earthquake Accelerograms Using
Seismological Modelling: A Review,” Journal of Earth-
quake Engineering, Vol. 4, No. 3, 2000, pp. 321-354.
doi:10.1080/13632460009350374
[32] N. T. K. Lam, J. L. Wilson, A. M. Chandler and G. L.
Hutchinson, “Response Spectral Relationships for Rock
Sites Derived from the Component Attenuation Model,”
Earthquake Engineering and Structural Dynamics, Vol.
29, No. 10, 2000, pp. 1457-1489.
doi:10.1002/1096-9845(200010)29:10<1457::AID-EQE9
69>3.0.CO;2-Q
[33] N. T. K. Lam, J. L. Wilson, A. M. Chandler and G. L.
Hutchinson, “Response Spectrum Modelling for Rock
Sites in Low and Moderate Seismicity Regions Combin-
ing Velocity, Displacement and Acceleration Predictions,”
Earthquake Engineering and Structural Dynamics, Vol.
29, No. 10, 2000, pp. 1491-1526.
doi:10.1002/1096-9845(200010)29:10<1491::AID-EQE9
70>3.0.CO;2-T