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West Africa is considered a region of low seismicity. However, the monitoring of earthquake activity by local seismic arrays began very early (as early as 1914) in West Africa but seismic catalogs are very incomplete. In 1991, Bertil studied the seismicity of West Africa based on networks of seismic stations in Ivory Coast and neighboring countries. The reference work of Ambraseys and Adams as well as the recent earthquakes given by the international data centres on the seismicity of West Africa were also used for the computations of earthquake hazard parameters. Different earthquake event data have been compiled and homogenised to moment magnitude (
M_{w}
). The obtained catalog covers a period of over four centuries (1615-2021) and contains large historical events and recent complete observations. The complete catalog part has been subdivided into four complete subcatalogs with each a level of completeness. The minimum magnitude and the maximum observed magnitude are equal to 2.89 and 6.8 respectively for the whole catalog. The seismic code software developed by Kijko was used to calculate the earthquake hazard parameters. The results give a
b
value of 0.83 ± 0.08 for the whole period and preliminary seismic hazards curves are also plotted for return periods 25, 50 and 100 years. This is a good and practical example showing that this procedure can be used for seismic hazard assessment in West Africa.

West Africa spans the area between latitude 0˚N to15˚N and longitude 20˚W to 10˚E. It corresponds to a vast complex that includes the West African Craton, the Pan-African mobile belt and the Mauritanides fold belt (

The edification of West Africa has developed grabens, horsts, and tectonic lineaments which are superimposed on older structures. The tectonics of the Western Africa plate have revealed several continental or oceanic fracture zones. These fracture zones are often interpreted as Atlantic passive margins, the site of seismic strain rates and active deformation [_{w} ≥ 6.0) and can be associated with the Romanche, Chain and Saint Paul transform faults [

Bertil [

of weakness: continental faults systems and oceanic fracture zones. Although several major historical and recent earthquakes were recorded in the region, the seismicity of West Africa is infrequent according to the geological context. Using the geological and geophysical features, Meghraoui et al. [

The purpose of this work is to assess the seismic hazard level in this province from an incomplete seismic catalog compiled from the available data gathered from previous works and international data centres during the period 1615 to 2021. The seismic parameters are estimated using the computer code describing the probabilistic approaches of Kijko and Sellevoll [

The geological history of West Africa begins with the Archaean era (about 2.5 billion years old). Its different deformation processes correspond to main geodynamic events that affected this region during successive orogenic cycles. West Africa is characterized by formation of craton and its borders, western (Atlantic passive margin) and eastern (area of the active intracontinental rift system of Central and West Africa).

The West African craton has remained stable since the Liberian orogeny. It was partly reworked during Eburnean and Pan-African cycles [

The western and northern edges of the craton contain any evidence of significant deformations undergone during the Variscan orogeny [

The Archean and Paleoproterozoic domains of craton are located in two broad shields (the Reguibat Shield to North and the Man-Leo Shield to the south). They are separated by the vast intracratonic Precambrian basin of Taoudeni with its sedimentary cover, as well as mobile belts of late Precambrian age, locally affected by a Paleozoic imprint. At the extreme north of the craton is the Anti-Atlas (thrust and fold belt), which represents the northern end of the West African Craton. Just below the Anti-Atlas, is the Tindouf basin whose sedimentary filling is predominantly Paleozoic, with a basal cover of upper Proterozoic age. The western end of the Reguibat Shield consists of the Mauritanides, which are a portion of the Variscan chain in north-west Africa [

West Africa is a seismotectonic area yet poorly known in terms of the current faulting activity, crustal deformation, and their geodynamic causes. However, this region is also seismically active (

The historical and instrumental regional seismicity data used in our study was obtained from the seismic catalogs prepared during the studies of intraplate seismicity in West Africa from 1615-1991 [

centres such as IRIS, USGS, BGS and ISC. Ambraseys and Adams [_{w}). According to the approximations carried out by Musson [_{w}. Local magnitude values of Bertil catalog (M_{L}) were converted to moment magnitude through the relation derived by Grünthal et al. [

M w = 0.0376 M L 2 + 0.646 M L + 0.53 . (1)

Finally, this seismicity catalog was divided into incomplete historical data and complete observations (

Thus, the earthquake hazard parameters of West Africa are estimated from an algorithm developed by Kijko and implemented in Matlab. The applied procedure provides a maximum likelihood estimate of earthquake hazard parameters, together with their uncertainties, by combining historical and instrumental data. In the description of this analytical method, the moment magnitude (M_{w}) is reported as m; we have chosen to do this because it will be easier to include it in the formulae than to use the conventional notation M_{w}.

The theoretical background assume that the historical part contains n 0 largest seismic events, each with a magnitude m 0 k ( k = 1 , ⋯ , n 0 ) such as m 0 k ≥ m 0 and m 0 ≥ m min , m min being overall minimum magnitude of the whole catalog. The time span of the historical part of the catalog t 0 can be expressed as the sum of the time intervals t 0 k between the historical events. The complete part can be divided into s subcatalogs (s being the number of subcatalogs), each one complete has n i earthquakes, each with a magnitude m i k ( i = 1 , ⋯ , s ;

k = 1 , ⋯ , n i ) such as m i k ≥ m min ( i ) , m min ( i ) is threshold magnitude of subcatalog with a time span t i . The maximum likelihood procedure require that the temporal and magnitude distributions of seismicity for a specified source are respectively described by the Poisson process [

log 10 N = a − b m , (2)

where a and b are parameters, m is the magnitude and N denotes the number of earthquakes of magnitude greater than or equal to the level of completeness magnitude m min . The probability that a total of n earthquakes will be observed during the specified time interval t within a given area by the formula:

P n ( λ , t ) = ( λ t ) n n ! exp ( − λ t ) , n = 0 , 1 , 2 , ⋯ (3)

λ ≡ λ ( m min ) refers to the Poisson distribution parameter and describes the area-characteristic, mean seismic activity rate of earthquakes with magnitudes greater than or equal to m min . The standard seismic hazard analysis procedure requires that earthquake events are independent [

Considering both models (2) and (3), the classic probability density function (PDF) of earthquake magnitude defined by Aki [

f M ( m ) = β e − β ( m − m min ) for m ≥ m min , (4)

while the cumulative distribution function (CDF) of earthquake magnitude is also given by Aki [

F M ( m ) = 1 − e − β ( m − m min ) for m ≥ m min , (5)

where the magnitudem is a continuous variable which may take any value greater or equal to than the completeness level m min and β = b ln ( 10 ) . The most seismic-hazard assessment procedures do not integrate the temporal variations of seismicity [

f X ( x ) = x ( q − 1 ) p q Γ ( q ) exp ( − p x ) with x , p , q > 0 . (6)

In Equation (6), Γ ( q ) denotes gamma function [

Γ ( q ) = ∫ 0 ∞ y q − 1 exp ( − y ) d y , q > 0 (7)

where p and q are related to the mean μ x ( μ x = q p ) and the variance σ x 2 ( σ x 2 = q p 2 ) of the distribution.

The coefficient of variation expresses the uncertainty related to the variation of a given parameter relative to its mean is given by:

υ x = σ x μ x

The Bayesian CDF of earthquake magnitudes derived from Equations (5) and (6) will take the form of the Bayesian Exponential-Gamma distribution, as described by [

F M ( m | υ β , m min ) = C β [ 1 − ( p β p β + m − m min ) q β ] . (8)

In which p = β ¯ / ( σ β ) 2 , q = ( β ¯ / σ β ) 2 with β ¯ and σ β being respectively the mean value and the standard deviation of the parameter β . C β being a normalizing coefficient of the form:

C β = [ 1 − ( p β p β + m max − m min ) q β ] − 1 (9)

The poisson distribution (3) combined with the gamma distribution (6) will become the Poisson-gamma Bayesian distribution:

P n ( λ ¯ , t , υ λ ) = Γ ( n + q λ ) n ! Γ ( q λ ) ( p λ t + p λ ) q λ ( t t + p λ ) n , (10)

where p λ = λ ¯ / σ λ 2 and q λ = ( λ ¯ / σ λ ) 2 are the parameters of gamma distribution (6), λ ¯ the mean value of the activity rate λ .

As q λ = λ ¯ p λ and q β = β ¯ p β Equations (8) and (10) may respectively be rewritten in the form [

F M ( m | υ β , m min ) = C β [ 1 − ( q β q β + β ¯ ( m − m min ) ) q β ] (11)

P n ( λ ¯ , t , υ λ ) = Γ ( n + q λ ) n ! Γ ( q λ ) ( q λ λ ¯ t + q λ ) q λ ( λ ¯ t λ ¯ t + q λ ) (12)

In this case, the normalizing coefficient takes the form:

C β = [ 1 − ( q β q β + β ¯ ( m max − m min ) ) q β ] − 1 , (13)

and ( λ ¯ , β ¯ ) are calculated by applying the maximum likelihood procedure.

Using Equations (11) and (13), the Bayesian PDF of earthquake magnitudes are defined as [

f M ( m | υ β , m min ) = C β β ¯ ( q β q β + β ¯ ( m − m min ) ) q β + 1 (14)

The maximum likelihood estimators of the parameters λ ¯ and β ¯ respectively denoted λ ¯ ^ and β ¯ ^ are the values of λ ¯ and β ¯ that maximizes the likelihood function L ( Θ ) for a given maximum area-characteristic earthquake magnitude m max . Thus, maximization of the likelihood function is obtained by

solving the system of two equations ∂ l ∂ λ ¯ = 0 and ∂ l ∂ β ¯ = 0 , in which l = ln [ L ( Θ ) ] . The uncertainties of the parameters λ ¯ and β ¯ expressed as a formal estimate of the variance of ( λ ¯ ^ , β ¯ ^ ) are given from the equations describing the approximate variance-covariance matrix of vector ( λ ¯ ^ , β ¯ ^ ) such as [

D ( λ ¯ ^ , β ¯ ^ ) = − [ ∂ 2 l ∂ λ ¯ 2 ∂ 2 l ∂ λ ¯ ∂ β ¯ ∂ 2 l ∂ β ¯ ∂ λ ¯ ∂ 2 l ∂ β ¯ 2 ] − 1 , (15)

in which derivatives are calculated at the point λ ¯ = λ ¯ ^ and β ¯ = β ¯ ^ . Equation (15) provides a good approximation of the event variance-covariance matrix for sufficiently largen. It should be noted that the formulation (15) does not provide estimation of the standard error of the estimator of m max denoted m ^ max .

The likelihood function L ( Θ ) calculated from all available data is the product likelihood functions, based on the historical and complete parts of the catalog, as

L ( Θ ) = L H ( Θ ) × L C ( Θ ) (16)

In Equation (16), the likelihood function L H ( Θ ) of the parameters λ ¯ and β ¯ for the historical events is [

L H ( Θ ) ≡ L H ( Θ | m 0 , t 0 , v ) = ∏ k = 1 n 0 f M max ( m 0 k | υ β , m 0 , t 0 k ) ,

in which f M max ( m 0 k | υ β , m 0 , t 0 k ) which denotes the PDF of the largest earthquake magnitude within the time period t 0 k takes the form [

f M max ( m 0 k | υ β , m 0 , t 0 k ) = λ ¯ 0 t q λ f M ( m 0 k | υ β , m 0 ) F M max ( m 0 k | υ β , m 0 , t 0 k ) q λ + λ ¯ 0 t [ 1 − F M ( m 0 k | υ β , m 0 ) ] ,

with λ ¯ 0 = λ ¯ [ 1 − F M ( m 0 k | υ β , m 0 ) ] , the mean activity rate for earthquakes with magnitudes m 0 k ≥ m 0 and λ ¯ ≡ λ ¯ ( m min ) as the mean activity rate corresponding to the magnitude value m min . The functions F M ( m 0 k | υ β , m 0 ) and f M ( m 0 k | υ β , m 0 ) are respectively the CDF and PDF of earthquake magnitudes obtained in Equations (11) and (14). According to Equation (16), the likelihood function L C ( Θ ) based on all s complete subcatalogs is defined as [

L C ( Θ ) = ∏ i = 1 s L i ( λ ¯ | n i , t i ) L i ( β ¯ | m i k ) , with ( k = 1 , ⋯ , n i )

where

L i ( λ ¯ | n i , t i ) = ( λ ¯ ( i ) t i + q λ ) − q λ ( λ ¯ ( i ) t i λ ¯ ( i ) t i + q λ ) n i ,

and

L i ( β ¯ | m i k ) = [ C β β ¯ ] n i ∏ k = 1 n i [ 1 + β ¯ q β ( m i k − m min ( i ) ) ] − ( q β + 1 ) ,

L i ( λ ¯ | n i , t i ) and L i ( β ¯ | m i k ) are the likelihood functions of each complete subcatalog i ( i = 1 , ⋯ , s ) where λ ¯ ( i ) = λ ¯ [ 1 − F M ( m min ( i ) | υ β , m min ) ] is the mean earthquake activity rate, corresponding to the magnitude level of completeness m min ( i ) . F M ( m min ( i ) | υ β , m min ) is defined in Equation (11).

The maximum possible magnitude m max of earthquake occurring within a specified source is calculated using Bayesian formalism [

m ^ max = m max o b s + δ 1 / q exp [ n r q / ( 1 − r q ) ] β ¯ [ Γ ( − 1 / q , δ r q ) − Γ ( − 1 / q , δ ) ] . (17)

In Equation (17), Γ ( ⋅ , ⋅ ) denotes the complementary incomplete gamma function [

V a � ( m ^ max ) = σ M 2 + [ δ 1 / q exp [ n r q / ( 1 − r q ) ] β ¯ [ Γ ( − 1 / q , δ r q ) − Γ ( − 1 / q , δ ) ] ] 2 (18)

The procedure also accepts time gaps (periods during there is no seismic record) and takes into account the uncertainty in the magnitude of seismic events and treats them as random errors following a Gaussian distribution with zero mean and standard deviation σ [

The outlined technique was applied to West Africa to estimate the earthquake hazard parameters.

For each subcatalog, the level of completeness was determined using the maximum curvature technique [

Event | Date | Magnitude | Standard error of earthquake magnitude determination |
---|---|---|---|

1 | 1615 | 5.5 | 0.3 |

2 | 18 February 1618 | 5.2 | 0.3 |

3 | 18 December 1636 | 5.7 | 0.3 |

4 | 10 July 1682 | 6.5 | 0.3 |

5 | 1788 | 5.6 | 0.3 |

6 | 20 May 1795 | 5.2 | 0.3 |

Subcatalog | Start Date | End Date | Level of Completeness m min ( i ) | Number of events | Standard error of earthquake magnitude determination |
---|---|---|---|---|---|

1 | January 1818 | 31 December 1967 | 3.9 | 41 | 0.2 |

2 | 24 January 1968 | 10 October 1982 | 3.07 | 43 | 0.2 |

3 | 1 January 1983 | 6 March 1997 | 2.89 | 77 | 0.2 |

4 | 11 January 1999 | 3 February 2021 | 4.25 | 13 | 0.1 |

distribution (Equation (2)) from its linear trend.

It was assumed that earthquake magnitudes for the incomplete part of the catalog were determined with a standard error equal to 0.3 magnitude units and those of the complete part are assumed to have a magnitude standard error of 0.2 or 0.1 (

The obtained estimates of b value, mean activity rate occurrence λ , and area-characteristic maximum possible magnitude m max for West Africa, together with their standard deviations are given in

The seismic hazard curves are also plotted;

β (b value) | λ ( m min = 2.89 ) | m max ( m max o b s = 6.8 ± 0.2 ) |
---|---|---|

1.92 ± 0.18 (0.83 ± 0.08) | 3.425 ± 0.850 | 6.89 ± 0.22 |

exceedance of earthquake events for the next 25, 50 and 100 years. Each graph also provides the calculated level of confidence for the calculated values. The main results show that there is about 50% of probability that at least one event will exceed the magnitude M_{w} = 6.5 in the next 50 years and the return period of earthquake event with moment magnitude M_{w} ≥ 6.5 is at least one century.

Seismic hazard assessment in West Africa is rather difficult. The informations about the historical seismicity are very incomplete. Instrumental monitoring of seismicity in West Africa started from 1914 onwards [_{w}) recorded between 1615 and 1970. It was supplemented by the database built from Lamto seismic network of Ivory Coast. Bertil catalog is assumed to be the most complete of the region during 26 years. However, the location of earthquake events are not well constrained for epicentral distances greater than 600 km and the most of earthquake events with M_{w} ≤ 2.0 are near to the Lamto seismic network. The seismic events of M_{w} ≥ 3.0 have been detected in neighboring countries and GOG [

The seismicity parameters calculated give a b value (

The maximum observed magnitude (6.8) in the West Africa catalog fall into the southern part of Ghana. This magnitude had previously been used to assess magnitude of the largest possible earthquake for Ghana [

We are focused our study on the estimation of earthquake hazard parameters of West Africa. The sismotectonic analysis in the region showed the occurrence of strong earthquakes, some of which are associated with offshore faults closer to the coastline [

This work was carried out at the Institute for Geological and Mining Research, Cameroon. The authors sincerely thank Professor A. Kijko for giving us access to its seismic code software and we also thank the Department of Physics of the University of Yaounde I for their prompt collaboration.

The authors declare no conflicts of interest regarding the publication of this paper.

Mbossi, E.F., Ndibi, D.D.E., Nguet, P.W., Essi, J.M.A., Ntomb, E.O.B., Dili-Rake, J., Ateba, B. and Tabod, T.C. (2021) Preliminary Seismic Hazard Assessment in West Africa Based on Incomplete Seismic Catalogs. Open Journal of Earthquake Research, 10, 75-93. https://doi.org/10.4236/ojer.2021.102006