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Empirical relationships of earthquake magnitude scales and estimation of Guttenberg–Richter parameters in gulf of Guinea region
Scientific African 6 (2019) e00161
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Scientific African journal homepage: www.elsevier.com/locate/sciaf
Empirical relationships of earthquake magnitude scales and estimation of Guttenberg–Richter parameters in gulf of Guinea region Ayodeji Adekunle Eluyemi a,b,c, Santanu Baruah b, Saurabh Baruah a,b,∗ a
Geosciences and Technology Division, CSIR, North-East Institute of Science and Technology, Jorhat 785006, Assam, India Academy of Scientific and Innovative Research (AcSIR), CSIR- North East Institute of Science and Technology (CSIR-NEIST) Campus, Jorhat 785006, Assam, India c Division of Environmental and Earth Sciences., Centre For Energy Research and Development (CERD), Obafemi Awolowo University (OAU), Ile-Ife, Nigeria b
a r t i c l e
i n f o
Article history: Received 15 January 2019 Revised 22 August 2019 Accepted 9 September 2019
Keywords: Magnitude scales Empirical relationships Gulf of Guinea West Africa
a b s t r a c t Attempts have been made to investigate the relationships between various earthquake magnitude scales for the region of the Gulf of Guinea, namely moment magnitude (Mw ), surface wave magnitude (Ms ), body wave magnitude (mb ) and local magnitude (ML ). The study involves a sum of 535 earthquake data from the period of 1918 to 2016. It was found that Ms − Mw ; Mw − ML and mb − Mw scales are in fairly good agreement while mb − Ms magnitude scale differs by a magnitude unit of 1.45. Since the region of study is seismically active and mainly under the ocean, comprising of the mid-Atlantic ridges and the plate boundary, the seismo-tectonics of the study region is inferred from the obtained Gutenberg-Richter (GR) recurrence parameters. The inferences made are the prime input to the seismic hazard assessment of the region. © 2019 Published by Elsevier B.V. on behalf of African Institute of Mathematical Sciences / Next Einstein Initiative. This is an open access article under the CC BY-NC-ND license. (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Introduction The Magnitude of an earthquake is one of the most vital aspects of earthquake source parameters which can be directly measured and quantified. Its various applications range from scientific studies to engineering investigations. The magnitude of an earthquake is used to study earthquake occurrence pattern. Therefore, the strength of an earthquake can be determined or identified from its magnitude [15,21]. ML Magnitude scale is defined as the logarithm of the maximum zero-to-peak (0–p) amplitude (A) that would be recorded at an epicentral distance of 100 km on a Standard Wood–Anderson (W–A) torsion seismograph [28,29]. This implies that the ML magnitude scale is often used for seismic events occurring nearer to the recording stations. However, the scale tends to develop a saturation problem at ML ≥ 6 [2,18]. Hence the need for other magnitude scales which arises mainly as a result of heterogeneous nature of the earth materials (geologic) upon which a seismic station is sited, advancement in seismological instrumentation, improved concepts and the use of teleseismic waves for quantifying the size of an ∗
Corresponding author at: Geosciences and Technology Division, CSIR, North-East Institute of Science and Technology, Jorhat 785006, Assam, India. E-mail address: [email protected] (S. Baruah).
https://doi.org/10.1016/j.sciaf.2019.e00161 2468-2276/© 2019 Published by Elsevier B.V. on behalf of African Institute of Mathematical Sciences / Next Einstein Initiative. This is an open access article under the CC BY-NC-ND license. (http://creativecommons.org/licenses/by-nc-nd/4.0/)
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Fig. 1. Map illustrating the epicentres of events in the gulf of Guinea and the adjoining continental crust of the countries of sub-Sahara west Africa. Data from year 1900 to 2015. Epicentre plots in red to green circles the red circles represent shallow earthquake events while the green circles represent deeper earthquake events and seismological stations of the International seismological centre (ISC) in blue triangles. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
earthquake event, altogether have led to the invention and development of several other magnitude scales that are being used nowadays. Mb and Ms are now being emphasized Gutenberg [14] and Gutenberg and Richter [16] both magnitude scales are derived from teleseismic waves. The relationship between Mb and Ms has been extensively investigated by Basham [3]; Marshall and Basham [25], purposely because of the usefulness of the relationship in discriminating between earthquakes and explosions. Gutenberg [14] gave a mathematical expression for Mb as follows: Mb = log10 (A/T ) + S(, h ), where S(, h) is an empirically determined term that account for source receivers distance and the focal depth h. The term S(, h) is usually referred to as calibration function and ratio A/T is the ground motion in nanometre per second. The surface wave magnitude Ms is mathematically defined as: Ms = log10 A() − log10 A0 () where:A0 is the amplitude associated with Ms = 0 earthquakes. Mb and Ms are used for quantification of large size earthquake magnitudes. While Mb is used specifically in differentiating an explosion from an earthquake, Mb tends to saturate at larger magnitude earthquake measurement while Ms is used in the determination of only large earthquake magnitudes (greater than Mb = 6) [14]. However, the scale is limited because of its application to earthquakes which generate measurable 20 s period surface waves, in other words, shallow earthquakes. The use of Ms scale is at advantage because there is a little lateral variation in the attenuation of 20 s period surface waves anywhere in the world [29]. The latest magnitude scale was introduced in the year 1977, [20], called moment magnitude (Mw ). Mw magnitude scale, unlike ML , Mb, and Ms does not saturate for large and larger earthquake magnitudes [2,14,17]. Mw magnitude scale, is therefore regarded as the best and the most stable magnitude scale [2,23]). All over the world, several studies have been carried out on a regional scale, to examine the relations between earthquake magnitude scales [21,30,33], and [2,9,11,35]), except for the seismically active zones of the Gulf of Guinea which is seismically connected to its adjoining sub-Sahara west African region (Fig. 1). Although, the adjoining region of the Gulf of Guinea (sub Sahara west African region) is regarded as aseismic, occurrences of devastating earthquakes have been reported on several occasions in Ghana (18th December, 1636 Ms = 5.7; 1862 ML ∼ 6.5 and Ms ≥ 6.5; 11th February 1907 and 22nd of June 1939 Ms ∼ 6.5 and mb ∼ 6.4). The 22 nd of June 1939 event claimed the lives of sixteen (16) people and one hundred and thirtythree (133) others were severely injured, while properties worth millions of pounds were also destroyed [1,4,19,38]. Later on, the event of 22nd December 1983 (Mw ∼ 6.3) in Guinea, claimed three hundred (300) lives, with loss of properties [27]. These earthquakes epicentres were both reported to have been located a few kilometers on the continent, away from the offshore and far out in the Gulf of Guinea (Atlantic ocean) The work of Blundell [4] shows several extensive fracture zones emanating from the mid Atlantic ridge traversing thousands of killometres into the African plate, namely: St Paul, Romanche, Chain, Chacotte and Ascension fracture lines (Fig. 1). These fracture lines cut across mega states / cities located both on the coastal boundaries and as well as the mainland of the west African sub region. Hence the seismicity along Akwapim fault (southern Ghana) up to Togo and Dahomey (Republic of Benin and South west Nigeria) are as a result of connection and interaction between the Akwapim fault and Romanche fracture zone, with the implication of active tectonism. Burke [6] and Blundell [4] concluded that coastal boundary fault and Akwapim fault systems are the continental extensions of Chain or Romanche fracture zones. In a similar way, other regional
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fracture/fault zones such as Kandi (Benin republic) and Ife-wara (Nigeria) regional fault lines can as well be described as the continental extension of either Romanche, Chain or Chacotte fracture lines. Annually, several earthquake events from moderate to large size are recorded and reported by International Seismological Centre (ISC) catalogue, emanating from the Gulf of Guinea and their epicentres are zone-wise categorised as either from Ascension island, north of Ascension island, mid Atlantic ridge, central mid Atlantic ridge and off south coast of northwest Africa respectively. From the foregoing, it is important to examine the empirical variations amongst the existing magnitude scales in the Gulf of Guinea region, as well as to assess the quality, consistency and homogeneity of the existing earthquake catalogues of the region through regression analytical method and a cut off magnitude which is directly related to the estimation of a and b values of the Gutenberg–Richter relationship. Since occurrence of earthquake events on the sub-Sahara west African region is directly linked to the Gulf of Guinea region, the above examination would have a significant impact on the present and future seismic hazard analysis (SHA) or evaluation of the sub-Sahara west African region. Tectonic settings Explanation of the tectonic activity in the sub-Sahara west Africa as it relates to the Gulf of Guinea in the last 90 m.y. was derived from the palaeocontinental location of Africa. Prior to 90 m.y., the palaeocontinental position of Africa remains constant, even during the development and extension of the west African rift system and separation of the Gondwanaland. However, in the last 90 m.y. Africa plate has slightly rotated in anticlockwise direction and also moved towards the north. “Since 90 m.y. to 40 m.y. tectonic activity in west Africa and the Gulf of Guinea was compressional and from 40 m.y. to present day tectonic activity has been extensional”. The northward movement and the anticlockwise rotation of African plate brought about changes from peripheral compression of the continental part of the African plate to peripheral extension, which simultaneously occurred as the effective mechanical centre of Africa crossed the equator [13]. Since the earth is an oblate spheroid and made up of rigid plates, membrane stresses are generated on a rigid plate moving from latitude to another due to peripheral tension and consequently fracturing. Thus a plate is subjected to peripheral compression when it approaches equator and peripheral extension as it moves away from the equator. Turcotte and Oxburgh [39] explained the tectonic activity observed in sub-Sahara west Africa and the Gulf of Guinea during the past 90 m.y. During the last 90 m.y. “Jebel Marra” has been moving northwards, away from the equator. This is the period of formation of rifts opening up in west Africa and the Gulf of Guinea, with major rift formation known as the Cameroun volcanic line (CVL) extending up to one thousand eight hundred kilometers (1800 Km), from the offshore up to the central African republic [34]. The Cameroun Volcanic Line (CVL) is further explained as a subset of the pan African belt formed by the collision of Sao Francisco, Congo and west African cratons during Neoproterozoic formation of Gondwana that lies within the Obanguides belt, with multiple shear zones, consisting of central African shear zones, in close association with Pernambuco lineament in Brazil [5]. CVL comprises of a chain of Tertiary to Recent alkaline volcanics, which split into two arms, running northward into the northeast of Nigeria, forming the Biu plateau. The other arm of CVL runs eastwards through Nagoundere plateau of eastern Cameroun [12] thereby forming a “Y” shaped volcanic feature. Magnitude conversion models The problems of the non-homogeneous distribution of magnitude amongst different magnitude scales in the Gulf of Guinea catalogue are better resolved by formulating the right empirical relationships. This facilitates a mathematical equation for conversion of various magnitude scales from one to another. In this study, we have employed the methods of standard least squares, inverted standard least squares and orthogonal regression. The peculiarities of each of the mentioned methods are as follows: The standard least-squares is a well known method, which would be applicable when the variable variances of X denoted by σx2 tends to zero (σx2 → 0 ) and when the variable variance of Y denoted by σy2 is greater than zero (σy2 0 ). This assumption suggests that the line of best interpolation in experimental points is located by minimizing the square of the vertical offsets to the best fit line but the squares of the horizontal offsets to the best fit line are minimized in inverted least-squares method [2,7,8]. Orthogonal regression method is one of the oldest known techniques of simple linear regression method which is sometimes referred to as the functional maximum likelihood estimator, under the constraint of known error variance ratio [22,24]. However, the squares of the perpendicular offset to the best fit line are minimized in orthogonal regression In most cases of magnitude scale relationships, the absolute variances of the data values are not usually known. Castellaro et al. [7] pointed out that the most widely used linear regression method is the standard least squares but the author also argued that the method has similar flaws on both the dependant and independent variables. As such, the author advocated for the use of orthogonal regression as the best method. From the foregoing, we hereby suggest computing all the three types of linear regression and comparing the out-put in terms of minimal error estimates on slope as well as on the intercept. In this study, we have computed and applied all the three types of linear regression methods. Out of one thousand and one hundred (1100) numbers of earthquake events reported for the Gulf of Guinea by ISC from 1918–2016. Only five hundred and thirty five (535) earthquake events have been recorded with more than one (4) of the existing magnitude scales (ML , Mb , Ms and Mw ) Table 1 presents the number of data set used in various regression methods for different magnitude pairs. The
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A.A. Eluyemi, S. Baruah and S. Baruah / Scientific African 6 (2019) e00161 Table 1 Illustrate number of events used for establishing the empirical relationships for magnitude conversion. Dependant variable
Independent variable
Number of data
Mb Mb Ms Mw
Ms Mw Mw ML
188 134 136 77
Fig. 2. Illustrates graphical representation of (a) mb − Ms (b) mb − Mw (c) Ms − Mw and (d) Mw − ML earthquake magnitude scales empirical relationships for the study region (gulf of Guinea), faint-dot lines represent inverted least squares, dash-lines represent orthogonal and continuous lines represent the standard least squares regression techniques respectively.
respective magnitude relation plots for each of the magnitude scales are illustrated in Fig. 2. Results of the linear regression analyses are summarized in Table 2. The quality of the results are good except for a very few cases, where the obtained error for the y-intercepts are a bit high. This could be as a result of the quality of data used and varying level of seismic noise with respect to time at different stations. The aforementioned may affect the amplitude picking during ML magnitude scale analysis, coupled with different levels of noise at different stations. Green’s functions are not perfect in every case of Mw magnitude scale, they could vary from perfect to good or worse, from event to event based on event’s location versus seismic station signal-to-noise ratio (SNR) and source depth, which may in turn introduce some errors to the set of data used [2,28]. The following empirical relationships mb − Ms , mb − Mw , Ms − Mw and Mw − ML for the region of study are illustrated in Fig. 2. The faint-dot lines represent inverted least squares; dashed-lines depict the orthogonal regression and continuous straight lines represent the standard least squares regression methods. However, our judgement of the best fit line was based on minimum error estimates on slope and intercept respectively. Therefore, we consider the standard least-squares as the best fit line with minimum errors in this regard compared to other regression methods used in this study. Generally, we observed that mb estimate is lower than Ms in the Gulf of Guinea (region of study) by a factor of 1.4539 ± 0.1649, mb
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Table 2 Illustrates regression parameters for various magnitude relations employ in this study. Regression used
Standard least squares
Inverted least squares
Orthogonal least squares
Mb − Ms
Slope y-intercept
0.7301 ± 0.0327 1.4539 ± 0.1649
1.1132 ± 0.1155 −0.6797 ± 0.6939
0.7917 ± 0.0650 1.1451 ± 0.3576
Mb − Mw
Slope y-intercept
0.8382 ± 0.0323 0.6577 ± 0.1764
1.0167 ± 0.1714 0.1354 ± −1.3880
0.9007 ± 0.0642 0.3175 ± 0.2055
Ms − Mw
Slope y-intercept
0.9703 ± 0.0213 −0.0369 ± 0.1162
0.9696 ± 0.1366 0.3578 ± 1.6068
1.0004 ± 0.0420 −0.2005 ± 22.3518
Mw − ML
Slope y-intercept
0.8880 ± 0.0256 0.7751 ± 0.1290
1.0301 ± 0.1476 −0.3719 ± 1.8247
0.9254 ± 0.0507 0.5882 ± 0.3994
Table 3 Illustrates results of Gutenberg-Richter parameters estimated for the gulf of Guinea region using Best combination (Mc95-Mc90 maximum curvature) (Wiemer, 2001) and Shi and Bolt [32] methods. Method
a-value
a-value (annual)
b-value
Magnitude of completeness (Mc)
Best combination (Mc95-Mc90-maximum curvature) Shi and Bolt [32]
6.39 ± 2.18 6.76 ± 2.31
4.4 ± 1.50 4.73 ± 1.62
0.81 ± 0.06 0.89 ± 0.01
4.5 ± 0.09 4.7 ± 0.02
estimate is lower than Mw by a factor of 0.6577 ± 0.1764, Ms estimate is lower than Mw by a factor of −0.0369 ± 0.1162 and ML estimate is lower than Mw by a factor of 0.7751 ± 0.1290 magnitude unit respectively. Estimation of Mc, a-value and b-value for the region of study Magnitude of completeness (Mc), known as threshold or cut-off magnitude, is theoretically defined as the lowest magnitude at which 100% of the earthquakes in a space-time volume are detected [26,31]. The importance of the correct Mc determination is that it has a direct impact on b-value evaluation, which in turn influences the evaluation of the a-value (overall seismicity rate). The Guttenberg Richter equation is the foundation for seismic hazard studies [10,26,37]. The Guttenberg Richter parameter is given as:
log10 N = a − bM The above parameters are responsible for earthquake forecasting and are also valuable tools in studying the physics of the earth crust [26,36]. In this study, estimates of Mc (magnitude of completeness), b-value and a-value, have been determined for the study region (Gulf of Guinea) using Best combination (Mc95-Mc90-maximum curvature) and Shi and Bolt [32] methods (Fig. 3). Majority of the earthquakes occurring in the Gulf of Guinea vary from moderate to large size earthquake magnitudes, as shown in (d) of Fig. 3. The result of the estimates is presented in Table 3. Magnitude of completeness Mc for the Gulf of guinea region using the afore-mentioned methods are 4.5 ± 0.09 and 4.7 ± 0.02; a-values for the entire data were estimated to 6.39 ± 2.18 and 6.76 ± 2.31; a-value on annual basis are 4.4 ± 1.50 and 4.73 ± 1.62 respectively. The b-value for the Gulf of Guinea using the above methods are: 0.81 ± 0.06 and 0.89 ± 0.01. Since the region of study is seismically complex, occurring mainly under the ocean and comprising of the mid-Atlantic ridges and the plate boundary, a better understanding of the seismo-tectonic of the study region is inferred from the estimated bvalue which therefore suggests that the most seismically active zone of the Gulf of Guinea region is along the plate boundary in between and around the African and south American plates. Discussion An earthquake catalogue is an important requirement for a seismologist and is by no means an easy-to-calibrate entity. An earthquake catalogue carries all the uncertainties that are intrinsic to the assumptions, during magnitude, location, depth and time estimation of an earthquake, altogether making the evaluation of an earthquake catalogue completeness quite challenging. In the scope of this study, efforts were geared towards deriving empirical relationships amongst the existing magnitude scales in the seismically active region of the Gulf of Guinea: Mb − Ms , Mb − Mw , Ms − Mw and Mw − ML and also estimating the Guttenberg–Richter parameters: Magnitude of completeness Mc, a-value, and b-value of the same region. Most of the seismic data recorded on the seismically active zone of the Gulf of Guinea region are found in International seismological centre (ISC) data catalogue. These were achieved mainly by means of teleseismic events and therefore, very few or no seismic data below magnitude of 2 were reported in the catalogue. Since the region in question is so seismically active, multiple of micro-seismic events occur on a daily basis, from the seismically active plate boundary in mid-Atlantic ocean and beyond the coastal boundaries of the west African sub-region. These however not been accessed with available equipment for proper documentation.
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Fig. 3. Plots of cumulative numbers of events with magnitude higher than corresponding magnitude (a) best combination (Mc95-Mc90-maximum curvature) (b) Shi and Bolt [32] methods (c) Guttenberg-Richter relation and (d) number of events vs magnitude histogram.
In the course of this investigation, we observed that mb is equal to ms by 1.45; mb is equal to Mw by 0.6577; Ms is equal to Mw by −0.0369 and Mw is equal to ML by 0.7751 magnitude unit respectively. Thus suggests that mb − Mw ; Ms − Mw and Mw − ML magnitude scales are significantly consistent and in fair agreement but mb − Ms magnitude scale is significantly different and this could be explained based on varying approaches (issues) employed for calculating mb and Ms magnitude estimates for the region, which incidentally depends on the analyst. Adequate knowledge of small magnitude earthquake events is very important in most seismological related works such as stress tensor inversion; coulomb stress determination and seismic hazard assessment. All of the aforementioned add up to give better characterization and understanding of the potential of a seismogenic zone/zones during related research. Following the recent re-installation and rehabilitation of seismic monitoring stations in some of the countries of the sub-Sahara west African region which are directly connected to the Gulf of Guinea (Ghana, Nigeria and Cameroun). Cameroun seismic monitoring network in 20 0 0, Ghana digital seismic network in 2005 and the Nigerian new seismic network of stations in 2008, more and more micro seismic events from 1.5 up to 3.5 are expected to be recorded, with respect to a specific magnitude scale, which could differ from one station to another, depending on the analyst. However, during seismic hazard related works, there is always need to utilize all available sizes of earthquake magnitudes, hence the necessity for the provision of mathematical expression amongst different earthquake magnitude scales. Most seismicity studies and soft- wares, nowadays require the use of Mw scale and this scale is specifically designed for the measurement of large earthquakes.
Conclusion Empirical relationships between Mb − Ms , Mb − Mw , Ms − Mw and Mw − ML magnitude scales have been examined for the seismically active zone of the Gulf of Guinea region, (535) in which earthquake dataset, from the time period of 1918 to 2016 have been utilized. The following empirical relationships hold for earthquake magnitude scales in the Gulf of Guinea region: Mb = (0.7301 ± 0.0327) Ms + (1.4539 ± 0.1649); Mb = (0.8382 ± 0.0323) Mw + (0.6577 ± 0.1764); Ms = (0.9703 ± 0.0213) Mw − (0.0369 ± 0.1162) and Mw = (0.8880 ± 0.0256) ML + (0.7751 ± 0.1290) respectively.
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Magnitude of completeness (Mc), a-value and b-value otherwise known as Guttenberg Richter relation parameters were also determined using Shi and Bolt [32] and Best combination techniques (Mc95-Mc90-maximum curvature). Since b-value is a tectonic parameter that varies from 1.8–1.0 (oceanic), 1.0–0.7 (Interplate) and 0.7–0.4 (Intraplate), the study therefore concluded that the seismically active zone of the Gulf of Guinea is located mainly between the inter-plate boundary of the African and the south American plates. Hopefully, derived relationships amongst the magnitude scales will remain significant for several seismological related works in and around the Gulf of Guinea (west Africa sub region) such as strain build up, tectonic stress investigations through change in moment release rate with time and seismic hazard analysis (SHA). Data and resources The International Seismological Centre catalogue was searched using http://www.isc.ac.uk/iscbulletin/search/catalogue/ (Accessed on October, 2nd, 2016) Declaration of Competing interest There are no conflicts of interest to be declared amongst the co authors. Acknowledgements Eluyemi A.A. pays gratitude and appreciation to The World Academy for Sciences (TWAS) Italy and Council for Scientific and Industrial Research (CSIR) India, for a CSIR-TWAS sub UNESCO Ph.D fellowship. The Academy of Scientific and Innovative Research (AcSIR) India is acknowledged by EAA for availing the opportunity to carry-out Ph.D and The Centre for Energy Research and Development, Obafemi Awolowo University Nigeria for granting me a study leave with pay for the period of study in India. The Authors also acknowledge the International Seismological Centre, On-line Bulletin, http://www.isc.ac.uk Internatl. Seismol. Cent., Thatcham, United Kingdom, 2014 for enabling us access to recent and historic seismic data. Authors hereby acknowledge the criticisms and loopholes identified and presented by the anonymous reviewer in contribution to the quality of this manuscript. Those comments have sincerely improved the quality of this manuscript. Much profound appreciation is hereby extended. Funding This work was fully supported by The Council of Scientific and Industrial Research (CSIR) India and The World Academy For Sciences (TWAS), Italy [CSIR-TWAS, FR number: 3240275042]. References [1] M. Bacon, A.O. Quaah, Earthquake activity in Southeastern Ghana (1977-1980), Bull. Seismol. Soc. Am. 71 (3) (1981) 771–785. [2] S. Baruah, S. Baruah, P.K. Bora, R. Duarah, A Kalita, R. Biswas, N. Gogoi, J.R. Kayal, Moment magnitude (Mw ) and local magnitude (ML ) relationship for earthquakes in Northeast India, Pure Appl. Geophys. (2012), doi:10.10 07/s0 0 024- 012- 0465- 9. [3] P.W. 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[26] A. Mignan, J. Woessner, Estimating the magnitude of completeness for earthquake catalogues, Commun. Online Resour. Stat. Seismicity Anal. (2012) Available athttp://www.corssa.org, doi:10.5078/corssa-00180805. [27] M. Ramdani, B. Tadili, D.B. Sari, A strong earthquake strikes Guinea (22nd December 1983), Bull. Seismol. Soc. Am. 74 (5) (1984) 2045–2047. [28] C.F. Richter, An instrumental earthquake magnitude scale, Bull Seismol. Soc. Am. 25 (1) (1935) 1–32. [29] C.F. Richter, in: Elementary seismology., W.H. Freeman, San Francisco, Calif, 1958, p. 768. [30] J. Ristau, G.C. Rogers, J.F. Cassidy, Moment magnitude, local magnitude calibration for earthquakes off Canada’s West Coast, Bull. Seismol. Soc. Am. 93 (20 03) 2296–230 0. [31] P.A. Rydelek, I.S. Sacks, Testing the completeness of earthquake catalogues and the hypothesis of self-similarity, Nature 337 (1989) 251–253. [32] Y. Shi, A.B. Bolt, The standard error of magnitude frequency-b value, Bull. Seismol. Soc. Am. 72 (5) (1982) 1677–1687. [33] A.M. Suteau, J.H. Whitcomb, A local earthquake coda magnitude and its relation to duration moment, Mo and local Richter magnitude Ml , Bull. Seismol. Soc. Am. 59 (April (2)) (1979) 353–368. [34] K.A.P. Tokam, C.T. Tabod, A.A. Nyblade, J. Julia, D.A. Wiens, M.E. Pasyanos, Structure of the crust beneath Cameroon, West Africa, from the joint inversion of Rayleigh wave group velocities and receiver functions, Geophys. J. Int. 183 (2) (2010) 106–1076 https://doi.org/10.1111/j.1365-246X.2010. 04776.x. [35] H.R. Wason, R. Das, M.L Sharma, Magnitude conversion problem using general orthogonal regression, Geophys. J. Int. 190 (2012) 1091–1096. [36] S. Wiemer, D. Schorlemmer, ALM: an asperity-based likelihood model for California, Seismol. Res. Lett. 78 (2007) 134–140, doi:10.1785/gssr1.78.1.134. [37] S. Wiemer, D. Giardini, D. Fah, N. Deichmann, S. Sellami, Probabilistic seismic hazard assessment of Switzerland best estimates and uncertainties, J. Seismol. 13 (2009) 449–478. [38] D.R. Yarwood, D.I. Doser, Deflection of oceanic transform motion at a continental margin as deduced from waveform inversion of the 1939 Accra, Ghana earthquake, Tectonophysics 172 (1989) 341–349. [39] D.L. Turcotte, E.R. Oxburgh, Intra-plate volcanism and discussion, Philos.Trans. R. Soc. London. Ser. A: Math. Phys. Sci. 288 (1978) 561–579.
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Scientific African journal homepage: www.elsevier.com/locate/sciaf
Empirical relationships of earthquake magnitude scales and estimation of Guttenberg–Richter parameters in gulf of Guinea region Ayodeji Adekunle Eluyemi a,b,c, Santanu Baruah b, Saurabh Baruah a,b,∗ a
Geosciences and Technology Division, CSIR, North-East Institute of Science and Technology, Jorhat 785006, Assam, India Academy of Scientific and Innovative Research (AcSIR), CSIR- North East Institute of Science and Technology (CSIR-NEIST) Campus, Jorhat 785006, Assam, India c Division of Environmental and Earth Sciences., Centre For Energy Research and Development (CERD), Obafemi Awolowo University (OAU), Ile-Ife, Nigeria b
a r t i c l e
i n f o
Article history: Received 15 January 2019 Revised 22 August 2019 Accepted 9 September 2019
Keywords: Magnitude scales Empirical relationships Gulf of Guinea West Africa
a b s t r a c t Attempts have been made to investigate the relationships between various earthquake magnitude scales for the region of the Gulf of Guinea, namely moment magnitude (Mw ), surface wave magnitude (Ms ), body wave magnitude (mb ) and local magnitude (ML ). The study involves a sum of 535 earthquake data from the period of 1918 to 2016. It was found that Ms − Mw ; Mw − ML and mb − Mw scales are in fairly good agreement while mb − Ms magnitude scale differs by a magnitude unit of 1.45. Since the region of study is seismically active and mainly under the ocean, comprising of the mid-Atlantic ridges and the plate boundary, the seismo-tectonics of the study region is inferred from the obtained Gutenberg-Richter (GR) recurrence parameters. The inferences made are the prime input to the seismic hazard assessment of the region. © 2019 Published by Elsevier B.V. on behalf of African Institute of Mathematical Sciences / Next Einstein Initiative. This is an open access article under the CC BY-NC-ND license. (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Introduction The Magnitude of an earthquake is one of the most vital aspects of earthquake source parameters which can be directly measured and quantified. Its various applications range from scientific studies to engineering investigations. The magnitude of an earthquake is used to study earthquake occurrence pattern. Therefore, the strength of an earthquake can be determined or identified from its magnitude [15,21]. ML Magnitude scale is defined as the logarithm of the maximum zero-to-peak (0–p) amplitude (A) that would be recorded at an epicentral distance of 100 km on a Standard Wood–Anderson (W–A) torsion seismograph [28,29]. This implies that the ML magnitude scale is often used for seismic events occurring nearer to the recording stations. However, the scale tends to develop a saturation problem at ML ≥ 6 [2,18]. Hence the need for other magnitude scales which arises mainly as a result of heterogeneous nature of the earth materials (geologic) upon which a seismic station is sited, advancement in seismological instrumentation, improved concepts and the use of teleseismic waves for quantifying the size of an ∗
Corresponding author at: Geosciences and Technology Division, CSIR, North-East Institute of Science and Technology, Jorhat 785006, Assam, India. E-mail address: [email protected] (S. Baruah).
https://doi.org/10.1016/j.sciaf.2019.e00161 2468-2276/© 2019 Published by Elsevier B.V. on behalf of African Institute of Mathematical Sciences / Next Einstein Initiative. This is an open access article under the CC BY-NC-ND license. (http://creativecommons.org/licenses/by-nc-nd/4.0/)
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Fig. 1. Map illustrating the epicentres of events in the gulf of Guinea and the adjoining continental crust of the countries of sub-Sahara west Africa. Data from year 1900 to 2015. Epicentre plots in red to green circles the red circles represent shallow earthquake events while the green circles represent deeper earthquake events and seismological stations of the International seismological centre (ISC) in blue triangles. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
earthquake event, altogether have led to the invention and development of several other magnitude scales that are being used nowadays. Mb and Ms are now being emphasized Gutenberg [14] and Gutenberg and Richter [16] both magnitude scales are derived from teleseismic waves. The relationship between Mb and Ms has been extensively investigated by Basham [3]; Marshall and Basham [25], purposely because of the usefulness of the relationship in discriminating between earthquakes and explosions. Gutenberg [14] gave a mathematical expression for Mb as follows: Mb = log10 (A/T ) + S(, h ), where S(, h) is an empirically determined term that account for source receivers distance and the focal depth h. The term S(, h) is usually referred to as calibration function and ratio A/T is the ground motion in nanometre per second. The surface wave magnitude Ms is mathematically defined as: Ms = log10 A() − log10 A0 () where:A0 is the amplitude associated with Ms = 0 earthquakes. Mb and Ms are used for quantification of large size earthquake magnitudes. While Mb is used specifically in differentiating an explosion from an earthquake, Mb tends to saturate at larger magnitude earthquake measurement while Ms is used in the determination of only large earthquake magnitudes (greater than Mb = 6) [14]. However, the scale is limited because of its application to earthquakes which generate measurable 20 s period surface waves, in other words, shallow earthquakes. The use of Ms scale is at advantage because there is a little lateral variation in the attenuation of 20 s period surface waves anywhere in the world [29]. The latest magnitude scale was introduced in the year 1977, [20], called moment magnitude (Mw ). Mw magnitude scale, unlike ML , Mb, and Ms does not saturate for large and larger earthquake magnitudes [2,14,17]. Mw magnitude scale, is therefore regarded as the best and the most stable magnitude scale [2,23]). All over the world, several studies have been carried out on a regional scale, to examine the relations between earthquake magnitude scales [21,30,33], and [2,9,11,35]), except for the seismically active zones of the Gulf of Guinea which is seismically connected to its adjoining sub-Sahara west African region (Fig. 1). Although, the adjoining region of the Gulf of Guinea (sub Sahara west African region) is regarded as aseismic, occurrences of devastating earthquakes have been reported on several occasions in Ghana (18th December, 1636 Ms = 5.7; 1862 ML ∼ 6.5 and Ms ≥ 6.5; 11th February 1907 and 22nd of June 1939 Ms ∼ 6.5 and mb ∼ 6.4). The 22 nd of June 1939 event claimed the lives of sixteen (16) people and one hundred and thirtythree (133) others were severely injured, while properties worth millions of pounds were also destroyed [1,4,19,38]. Later on, the event of 22nd December 1983 (Mw ∼ 6.3) in Guinea, claimed three hundred (300) lives, with loss of properties [27]. These earthquakes epicentres were both reported to have been located a few kilometers on the continent, away from the offshore and far out in the Gulf of Guinea (Atlantic ocean) The work of Blundell [4] shows several extensive fracture zones emanating from the mid Atlantic ridge traversing thousands of killometres into the African plate, namely: St Paul, Romanche, Chain, Chacotte and Ascension fracture lines (Fig. 1). These fracture lines cut across mega states / cities located both on the coastal boundaries and as well as the mainland of the west African sub region. Hence the seismicity along Akwapim fault (southern Ghana) up to Togo and Dahomey (Republic of Benin and South west Nigeria) are as a result of connection and interaction between the Akwapim fault and Romanche fracture zone, with the implication of active tectonism. Burke [6] and Blundell [4] concluded that coastal boundary fault and Akwapim fault systems are the continental extensions of Chain or Romanche fracture zones. In a similar way, other regional
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fracture/fault zones such as Kandi (Benin republic) and Ife-wara (Nigeria) regional fault lines can as well be described as the continental extension of either Romanche, Chain or Chacotte fracture lines. Annually, several earthquake events from moderate to large size are recorded and reported by International Seismological Centre (ISC) catalogue, emanating from the Gulf of Guinea and their epicentres are zone-wise categorised as either from Ascension island, north of Ascension island, mid Atlantic ridge, central mid Atlantic ridge and off south coast of northwest Africa respectively. From the foregoing, it is important to examine the empirical variations amongst the existing magnitude scales in the Gulf of Guinea region, as well as to assess the quality, consistency and homogeneity of the existing earthquake catalogues of the region through regression analytical method and a cut off magnitude which is directly related to the estimation of a and b values of the Gutenberg–Richter relationship. Since occurrence of earthquake events on the sub-Sahara west African region is directly linked to the Gulf of Guinea region, the above examination would have a significant impact on the present and future seismic hazard analysis (SHA) or evaluation of the sub-Sahara west African region. Tectonic settings Explanation of the tectonic activity in the sub-Sahara west Africa as it relates to the Gulf of Guinea in the last 90 m.y. was derived from the palaeocontinental location of Africa. Prior to 90 m.y., the palaeocontinental position of Africa remains constant, even during the development and extension of the west African rift system and separation of the Gondwanaland. However, in the last 90 m.y. Africa plate has slightly rotated in anticlockwise direction and also moved towards the north. “Since 90 m.y. to 40 m.y. tectonic activity in west Africa and the Gulf of Guinea was compressional and from 40 m.y. to present day tectonic activity has been extensional”. The northward movement and the anticlockwise rotation of African plate brought about changes from peripheral compression of the continental part of the African plate to peripheral extension, which simultaneously occurred as the effective mechanical centre of Africa crossed the equator [13]. Since the earth is an oblate spheroid and made up of rigid plates, membrane stresses are generated on a rigid plate moving from latitude to another due to peripheral tension and consequently fracturing. Thus a plate is subjected to peripheral compression when it approaches equator and peripheral extension as it moves away from the equator. Turcotte and Oxburgh [39] explained the tectonic activity observed in sub-Sahara west Africa and the Gulf of Guinea during the past 90 m.y. During the last 90 m.y. “Jebel Marra” has been moving northwards, away from the equator. This is the period of formation of rifts opening up in west Africa and the Gulf of Guinea, with major rift formation known as the Cameroun volcanic line (CVL) extending up to one thousand eight hundred kilometers (1800 Km), from the offshore up to the central African republic [34]. The Cameroun Volcanic Line (CVL) is further explained as a subset of the pan African belt formed by the collision of Sao Francisco, Congo and west African cratons during Neoproterozoic formation of Gondwana that lies within the Obanguides belt, with multiple shear zones, consisting of central African shear zones, in close association with Pernambuco lineament in Brazil [5]. CVL comprises of a chain of Tertiary to Recent alkaline volcanics, which split into two arms, running northward into the northeast of Nigeria, forming the Biu plateau. The other arm of CVL runs eastwards through Nagoundere plateau of eastern Cameroun [12] thereby forming a “Y” shaped volcanic feature. Magnitude conversion models The problems of the non-homogeneous distribution of magnitude amongst different magnitude scales in the Gulf of Guinea catalogue are better resolved by formulating the right empirical relationships. This facilitates a mathematical equation for conversion of various magnitude scales from one to another. In this study, we have employed the methods of standard least squares, inverted standard least squares and orthogonal regression. The peculiarities of each of the mentioned methods are as follows: The standard least-squares is a well known method, which would be applicable when the variable variances of X denoted by σx2 tends to zero (σx2 → 0 ) and when the variable variance of Y denoted by σy2 is greater than zero (σy2 0 ). This assumption suggests that the line of best interpolation in experimental points is located by minimizing the square of the vertical offsets to the best fit line but the squares of the horizontal offsets to the best fit line are minimized in inverted least-squares method [2,7,8]. Orthogonal regression method is one of the oldest known techniques of simple linear regression method which is sometimes referred to as the functional maximum likelihood estimator, under the constraint of known error variance ratio [22,24]. However, the squares of the perpendicular offset to the best fit line are minimized in orthogonal regression In most cases of magnitude scale relationships, the absolute variances of the data values are not usually known. Castellaro et al. [7] pointed out that the most widely used linear regression method is the standard least squares but the author also argued that the method has similar flaws on both the dependant and independent variables. As such, the author advocated for the use of orthogonal regression as the best method. From the foregoing, we hereby suggest computing all the three types of linear regression and comparing the out-put in terms of minimal error estimates on slope as well as on the intercept. In this study, we have computed and applied all the three types of linear regression methods. Out of one thousand and one hundred (1100) numbers of earthquake events reported for the Gulf of Guinea by ISC from 1918–2016. Only five hundred and thirty five (535) earthquake events have been recorded with more than one (4) of the existing magnitude scales (ML , Mb , Ms and Mw ) Table 1 presents the number of data set used in various regression methods for different magnitude pairs. The
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A.A. Eluyemi, S. Baruah and S. Baruah / Scientific African 6 (2019) e00161 Table 1 Illustrate number of events used for establishing the empirical relationships for magnitude conversion. Dependant variable
Independent variable
Number of data
Mb Mb Ms Mw
Ms Mw Mw ML
188 134 136 77
Fig. 2. Illustrates graphical representation of (a) mb − Ms (b) mb − Mw (c) Ms − Mw and (d) Mw − ML earthquake magnitude scales empirical relationships for the study region (gulf of Guinea), faint-dot lines represent inverted least squares, dash-lines represent orthogonal and continuous lines represent the standard least squares regression techniques respectively.
respective magnitude relation plots for each of the magnitude scales are illustrated in Fig. 2. Results of the linear regression analyses are summarized in Table 2. The quality of the results are good except for a very few cases, where the obtained error for the y-intercepts are a bit high. This could be as a result of the quality of data used and varying level of seismic noise with respect to time at different stations. The aforementioned may affect the amplitude picking during ML magnitude scale analysis, coupled with different levels of noise at different stations. Green’s functions are not perfect in every case of Mw magnitude scale, they could vary from perfect to good or worse, from event to event based on event’s location versus seismic station signal-to-noise ratio (SNR) and source depth, which may in turn introduce some errors to the set of data used [2,28]. The following empirical relationships mb − Ms , mb − Mw , Ms − Mw and Mw − ML for the region of study are illustrated in Fig. 2. The faint-dot lines represent inverted least squares; dashed-lines depict the orthogonal regression and continuous straight lines represent the standard least squares regression methods. However, our judgement of the best fit line was based on minimum error estimates on slope and intercept respectively. Therefore, we consider the standard least-squares as the best fit line with minimum errors in this regard compared to other regression methods used in this study. Generally, we observed that mb estimate is lower than Ms in the Gulf of Guinea (region of study) by a factor of 1.4539 ± 0.1649, mb
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Table 2 Illustrates regression parameters for various magnitude relations employ in this study. Regression used
Standard least squares
Inverted least squares
Orthogonal least squares
Mb − Ms
Slope y-intercept
0.7301 ± 0.0327 1.4539 ± 0.1649
1.1132 ± 0.1155 −0.6797 ± 0.6939
0.7917 ± 0.0650 1.1451 ± 0.3576
Mb − Mw
Slope y-intercept
0.8382 ± 0.0323 0.6577 ± 0.1764
1.0167 ± 0.1714 0.1354 ± −1.3880
0.9007 ± 0.0642 0.3175 ± 0.2055
Ms − Mw
Slope y-intercept
0.9703 ± 0.0213 −0.0369 ± 0.1162
0.9696 ± 0.1366 0.3578 ± 1.6068
1.0004 ± 0.0420 −0.2005 ± 22.3518
Mw − ML
Slope y-intercept
0.8880 ± 0.0256 0.7751 ± 0.1290
1.0301 ± 0.1476 −0.3719 ± 1.8247
0.9254 ± 0.0507 0.5882 ± 0.3994
Table 3 Illustrates results of Gutenberg-Richter parameters estimated for the gulf of Guinea region using Best combination (Mc95-Mc90 maximum curvature) (Wiemer, 2001) and Shi and Bolt [32] methods. Method
a-value
a-value (annual)
b-value
Magnitude of completeness (Mc)
Best combination (Mc95-Mc90-maximum curvature) Shi and Bolt [32]
6.39 ± 2.18 6.76 ± 2.31
4.4 ± 1.50 4.73 ± 1.62
0.81 ± 0.06 0.89 ± 0.01
4.5 ± 0.09 4.7 ± 0.02
estimate is lower than Mw by a factor of 0.6577 ± 0.1764, Ms estimate is lower than Mw by a factor of −0.0369 ± 0.1162 and ML estimate is lower than Mw by a factor of 0.7751 ± 0.1290 magnitude unit respectively. Estimation of Mc, a-value and b-value for the region of study Magnitude of completeness (Mc), known as threshold or cut-off magnitude, is theoretically defined as the lowest magnitude at which 100% of the earthquakes in a space-time volume are detected [26,31]. The importance of the correct Mc determination is that it has a direct impact on b-value evaluation, which in turn influences the evaluation of the a-value (overall seismicity rate). The Guttenberg Richter equation is the foundation for seismic hazard studies [10,26,37]. The Guttenberg Richter parameter is given as:
log10 N = a − bM The above parameters are responsible for earthquake forecasting and are also valuable tools in studying the physics of the earth crust [26,36]. In this study, estimates of Mc (magnitude of completeness), b-value and a-value, have been determined for the study region (Gulf of Guinea) using Best combination (Mc95-Mc90-maximum curvature) and Shi and Bolt [32] methods (Fig. 3). Majority of the earthquakes occurring in the Gulf of Guinea vary from moderate to large size earthquake magnitudes, as shown in (d) of Fig. 3. The result of the estimates is presented in Table 3. Magnitude of completeness Mc for the Gulf of guinea region using the afore-mentioned methods are 4.5 ± 0.09 and 4.7 ± 0.02; a-values for the entire data were estimated to 6.39 ± 2.18 and 6.76 ± 2.31; a-value on annual basis are 4.4 ± 1.50 and 4.73 ± 1.62 respectively. The b-value for the Gulf of Guinea using the above methods are: 0.81 ± 0.06 and 0.89 ± 0.01. Since the region of study is seismically complex, occurring mainly under the ocean and comprising of the mid-Atlantic ridges and the plate boundary, a better understanding of the seismo-tectonic of the study region is inferred from the estimated bvalue which therefore suggests that the most seismically active zone of the Gulf of Guinea region is along the plate boundary in between and around the African and south American plates. Discussion An earthquake catalogue is an important requirement for a seismologist and is by no means an easy-to-calibrate entity. An earthquake catalogue carries all the uncertainties that are intrinsic to the assumptions, during magnitude, location, depth and time estimation of an earthquake, altogether making the evaluation of an earthquake catalogue completeness quite challenging. In the scope of this study, efforts were geared towards deriving empirical relationships amongst the existing magnitude scales in the seismically active region of the Gulf of Guinea: Mb − Ms , Mb − Mw , Ms − Mw and Mw − ML and also estimating the Guttenberg–Richter parameters: Magnitude of completeness Mc, a-value, and b-value of the same region. Most of the seismic data recorded on the seismically active zone of the Gulf of Guinea region are found in International seismological centre (ISC) data catalogue. These were achieved mainly by means of teleseismic events and therefore, very few or no seismic data below magnitude of 2 were reported in the catalogue. Since the region in question is so seismically active, multiple of micro-seismic events occur on a daily basis, from the seismically active plate boundary in mid-Atlantic ocean and beyond the coastal boundaries of the west African sub-region. These however not been accessed with available equipment for proper documentation.
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Fig. 3. Plots of cumulative numbers of events with magnitude higher than corresponding magnitude (a) best combination (Mc95-Mc90-maximum curvature) (b) Shi and Bolt [32] methods (c) Guttenberg-Richter relation and (d) number of events vs magnitude histogram.
In the course of this investigation, we observed that mb is equal to ms by 1.45; mb is equal to Mw by 0.6577; Ms is equal to Mw by −0.0369 and Mw is equal to ML by 0.7751 magnitude unit respectively. Thus suggests that mb − Mw ; Ms − Mw and Mw − ML magnitude scales are significantly consistent and in fair agreement but mb − Ms magnitude scale is significantly different and this could be explained based on varying approaches (issues) employed for calculating mb and Ms magnitude estimates for the region, which incidentally depends on the analyst. Adequate knowledge of small magnitude earthquake events is very important in most seismological related works such as stress tensor inversion; coulomb stress determination and seismic hazard assessment. All of the aforementioned add up to give better characterization and understanding of the potential of a seismogenic zone/zones during related research. Following the recent re-installation and rehabilitation of seismic monitoring stations in some of the countries of the sub-Sahara west African region which are directly connected to the Gulf of Guinea (Ghana, Nigeria and Cameroun). Cameroun seismic monitoring network in 20 0 0, Ghana digital seismic network in 2005 and the Nigerian new seismic network of stations in 2008, more and more micro seismic events from 1.5 up to 3.5 are expected to be recorded, with respect to a specific magnitude scale, which could differ from one station to another, depending on the analyst. However, during seismic hazard related works, there is always need to utilize all available sizes of earthquake magnitudes, hence the necessity for the provision of mathematical expression amongst different earthquake magnitude scales. Most seismicity studies and soft- wares, nowadays require the use of Mw scale and this scale is specifically designed for the measurement of large earthquakes.
Conclusion Empirical relationships between Mb − Ms , Mb − Mw , Ms − Mw and Mw − ML magnitude scales have been examined for the seismically active zone of the Gulf of Guinea region, (535) in which earthquake dataset, from the time period of 1918 to 2016 have been utilized. The following empirical relationships hold for earthquake magnitude scales in the Gulf of Guinea region: Mb = (0.7301 ± 0.0327) Ms + (1.4539 ± 0.1649); Mb = (0.8382 ± 0.0323) Mw + (0.6577 ± 0.1764); Ms = (0.9703 ± 0.0213) Mw − (0.0369 ± 0.1162) and Mw = (0.8880 ± 0.0256) ML + (0.7751 ± 0.1290) respectively.
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Magnitude of completeness (Mc), a-value and b-value otherwise known as Guttenberg Richter relation parameters were also determined using Shi and Bolt [32] and Best combination techniques (Mc95-Mc90-maximum curvature). Since b-value is a tectonic parameter that varies from 1.8–1.0 (oceanic), 1.0–0.7 (Interplate) and 0.7–0.4 (Intraplate), the study therefore concluded that the seismically active zone of the Gulf of Guinea is located mainly between the inter-plate boundary of the African and the south American plates. Hopefully, derived relationships amongst the magnitude scales will remain significant for several seismological related works in and around the Gulf of Guinea (west Africa sub region) such as strain build up, tectonic stress investigations through change in moment release rate with time and seismic hazard analysis (SHA). Data and resources The International Seismological Centre catalogue was searched using http://www.isc.ac.uk/iscbulletin/search/catalogue/ (Accessed on October, 2nd, 2016) Declaration of Competing interest There are no conflicts of interest to be declared amongst the co authors. Acknowledgements Eluyemi A.A. pays gratitude and appreciation to The World Academy for Sciences (TWAS) Italy and Council for Scientific and Industrial Research (CSIR) India, for a CSIR-TWAS sub UNESCO Ph.D fellowship. The Academy of Scientific and Innovative Research (AcSIR) India is acknowledged by EAA for availing the opportunity to carry-out Ph.D and The Centre for Energy Research and Development, Obafemi Awolowo University Nigeria for granting me a study leave with pay for the period of study in India. The Authors also acknowledge the International Seismological Centre, On-line Bulletin, http://www.isc.ac.uk Internatl. Seismol. Cent., Thatcham, United Kingdom, 2014 for enabling us access to recent and historic seismic data. Authors hereby acknowledge the criticisms and loopholes identified and presented by the anonymous reviewer in contribution to the quality of this manuscript. Those comments have sincerely improved the quality of this manuscript. Much profound appreciation is hereby extended. Funding This work was fully supported by The Council of Scientific and Industrial Research (CSIR) India and The World Academy For Sciences (TWAS), Italy [CSIR-TWAS, FR number: 3240275042]. References [1] M. Bacon, A.O. Quaah, Earthquake activity in Southeastern Ghana (1977-1980), Bull. Seismol. Soc. Am. 71 (3) (1981) 771–785. [2] S. Baruah, S. Baruah, P.K. Bora, R. Duarah, A Kalita, R. Biswas, N. Gogoi, J.R. Kayal, Moment magnitude (Mw ) and local magnitude (ML ) relationship for earthquakes in Northeast India, Pure Appl. Geophys. (2012), doi:10.10 07/s0 0 024- 012- 0465- 9. [3] P.W. 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