Unified earthquake catalogue and mapping of Gutenberg–Richter parameters for the East African Rift System

The initial phase of earthquake hazard assessment involves the consolidation of diverse magnitude scales, thereby requiring the homogenization of various magnitudes. Moment magnitude (Mw) emerges as the preferred descriptor for a range of magnitudes, encompassing local magnitude (ML), teleseismic magnitude (e.g., mb and MS), duration magnitudes (MD), and other magnitude proxies. Unlike alternative scales, Mw does not exhibit saturation at high magnitudes, enhancing its reliability. To achieve uniformity in magnitude representation, diverse regression techniques are employed, with the General Orthogonal Regression (GOR) method being widely regarded as the most dependable, accounting for uncertainty in both independent and dependent variables. This study utilized the International Seismological Centre (ISC) Catalogue (http://www.isc.ac.uk/) to compile an array of events related to the East Africa Rift System (EARS). Subsequently, the General Orthogonal Regression method was applied to merge and harmonize the collected data. Furthermore, the research computed Gutenberg-Richter b-values using the newly unified magnitude. Notably, the conversion relationships between magnitude proxies, including MS-mb, mb-Mw, MS-Mw, and ML-Mw, exhibited robust correlations, with coefficients of 0.86, 0.80, 0.88, and 0.94, respectively. In contrast, the relationship between ML and mb proxies revealed a notably weaker correlation, registering a coefficient of 0.54. Ultimately, the study identified a magnitude of completeness and a b-value of 3.8 and 0.71, respectively, for the EARS region, providing valuable insights for earthquake hazard assessment in this area. Generally, the homogeneous catalogue is a step forward in seismicity assessment and geodynamic activities in the EARS. Hence, developing the empirical equations for the area is essential for future studies on seismic hazards and engineering applications due to the peculiarity of EARS’s geological and tectonic characteristics. The empirical relations developed on the basis of the updated catalogue for the EARS are crucial and strong agreement with global studies for the earthquake hazard analysis in the region. The magnitude of completeness, Mc, for the EARS is significantly low as catalogues are continuously being updated. b-value obtained reveals that the EARS is experiencing active stress field with b-value significantly lower than 1. The empirical relations developed on the basis of the updated catalogue for the EARS are crucial and strong agreement with global studies for the earthquake hazard analysis in the region. The magnitude of completeness, Mc, for the EARS is significantly low as catalogues are continuously being updated. b-value obtained reveals that the EARS is experiencing active stress field with b-value significantly lower than 1.

Fig. 1 The EARS with major active faults (adapted from GEM Global Active Faults Database)

Introduction
The East African Rift System (EARS), a roughly 5000 km long continental rift that dates back to the Cenozoic period, extends from the Afar triple junction, which links the horn of Africa with the Middle East, up to western Mozambique.There are ongoing extensions from the Indian Ocean to Botswana and the Democratic Republic of the Congo.Geologists can learn more about how rifts in continents evolve over time into oceanic spreading and the NW-SE trending Tanganyika rift.(Fig. 1; Delvaux et al. 2012).The eastern branch is made up of a collection of rifts that aren't connected to one another, the majority of which have been impacted by magmatism.The eastern flank of EARS includes the northern Tanzania divergence, the Ethiopian Rift, the Kenya Rift, and the Davie Ridge, enumerated from north to south.Between the two EARS flanks is the Tanzanian craton, which contrasts with neighboring Paleoproterozoic to Neoproterozoic orogenic belts by appearing thicker, colder, and stronger (Delvaux 2001).
Generally speaking, one of the most active continental rift systems with many destructive tremors documented is the EARS in the African continent's most seismically active region, East Africa (Letamo et al. 2023).The Salima Earthquake of Malawi in the 1989 M w 6.3 (Williams et al. 2022), the 1990 earthquake of M S 7 and M S 7.1 of South Sudan (Kebede and Van Eck 1997), the 13 December 1910 M S 7.4 Rukwa (Tanzania) event (Ambraseys and Adams 1991), the M w 6.8 event of the Congo in 2005 are salient manifestations of earthquakes in the EARS.Numerous people have died as a result of these earthquakes, and the region's poorly built structures have sustained enormous property losses.
The unification of various magnitudes is the first step in the evaluation of earthquake risk.Magnitudes ought to be uniform.Thus, moment magnitude should be used to describe various heterogeneous magnitudes, including local and teleseismic magnitudes (such as m b and M S ).Moment magnitudes (M w ) do not saturate for big magnitudes, in contrast to local magnitudes (M L ) and teleseismic magnitudes (mb & MS) (Scordilis 2006).
Moment magnitude (M w ) is the standard magnitude measure used to categorize earthquakes according to size.Compared to other magnitude measures, it is more closely associated with the energy of an earthquake.
In general, regressions are normally executed using empirical relations with a Simple Orthogonal Regression (SOR) method (Ambraseys 1991) or the Ordinary Least Squares (OLS) method, which both presume the same level of ambiguity and the presumption that the independent variable is error-free (Gasperini & Ferrari 2000) in that order.Nonetheless, general orthogonal regression (GOR) techniques employ different degrees of biases for the two factors (Castellaro et al. 2006).In recent years, the GOR strategy has become more popular among researchers as the most consistent procedure for regressing magnitudes (Castellaro et al. 2006;Wason et al. 2012;Mobarki & Talbi 2022).Standard regression errors could even reach 0.3-0.4,according to Castellaro et al. (2006), considerably distorting estimates of the parameters used in seismic hazard analysis.
Since the region of study is seismically active, falling in the newly forming continent-wide rift system, it is prone to various stress causing forces.In the region forces responsible for the stress could be the boundary forces at the plates' sides and basal tractions at the base of the plate, and gravitational potential energy from density heterogeneities causing crustal stresses and deformations (Medvedev 2016;Rajaonarison et al. 2021).However, the latter is the most influencing factor that drives the seismicity of the EARS owing to the fact that the region is well known for its high elevations (e.g., East African plateaus and southern Africa plateaus; Stamps et al. 2014).Accordingly, all factors triggering the seismicity and the associated hazard occurrences need to be addressed and updated as new data emerge.
For this study, heterogeneous occurrences for the EARS were gathered from the ISC catalogue.After that, the data was combined using the General Orthogonal Regression technique.The conclusions are then made using comparisons from both local and international empirical relations.

Sources
As a result of its suitability and completeness nature of worldwide data, our study data were collected from ISC catalogue in the latitude ( 25 • S − 20 • N ) and longitude ( 25 • E − 52 • E ) for the time extent of 1900-2022.A total of 27,000 events with magnitudes ranging from 2.5 to 7.5 with various magnitude scales and depths between 0 and 700 km were recorded in the specified period.After a completeness check, a total of 21,333 events were selected for regression analysis (see Fig. 2).Nevertheless, only 2,568 events, with sufficient numbers of pairs (refer Table 1) were selected to make the relationships between the magnitude proxies of Mw.Sometimes the connection can be implicitly inferred from another proxy magnitude when data is lacking.

Magnitude conversion
Unbiased and homogenous earthquake magnitude measure is required in order to evaluate seismic risks caused by different earthquake magnitudes.Most earthquake data is not recorded in moment magnitude (M w ) scale, which is directly derived from the seismic moment (M 0 ) and represents the amount of energy released.In addition, because the moment magnitude scale is not susceptible to saturation at higher magnitudes, it has additional benefits over many other earthquake measuring scales (Das et al. 2013).The majority of events are typically quantified in scales of M L , M S , m b etc.There are, of course, very few M w events that are directly determined from data.In order to accurately identify the earthquake hazard parameters (e.g., M min , b, and M max ), conversion from other scales must be established.Table 2 provides a review of worldwide and local relations for the Fig. 2 The seismic events for the EARS from 1900 to 2022: with blue dots showing earthquake events and black lines represent Plate boundaries and borders

Dependent variable
Independent variable Number of data conversion of various magnitudes to M w .In our study, regression analysis was performed using Statgraphics 19 Centurion (https:// www.statg raphi cs.com/).This study employed the General Orthogonal Regression (GOR) approach due to its superiority in terms of overall performance.We utilized error ratios between λ = 0.2 and λ = 7, as suggested by Castellaro et al. (2006), which falls within the range of λ = 1.25 and λ = 7.

Seismicity parameters
In order to assess earthquake hazards, dependent events must first be removed from the catalogue.In order to accomplish this, a window that is defined in both the space and time dimensions must be created, and dependent events (foreshocks and aftershocks) must be eliminated from the updated catalogue.The Gardner and Knopoff 's (1974) method is one of the techniques used to window catalogues in space-time window in (Eq.1): In order to accurately predict seismic hazard, the Gutenberg-Richter (G-R) b-value is a vital variable.The local cut-off point, M c , must be selected in this way to optimize the G-R relation's reliability.The M c value is also influenced by additional factors, including the number and caliber of the sensors, their geometrical layout, and the level of background noise.The accuracy of the b-value calculation determines the effectiveness of the technique.The Maximum Curvature technique (MAXC), developed by Wiemer and Wyss (2000), was used in this manuscript to assess the completeness check in the frequency magnitude distribution.
Once the independent events with complete catalogue is defined, the determination of b-values is most crucial and determined by Gutenberg and Richter (1944) relation: (1) d[km] = 10. 0.1238 * M w +0.983 ; t[days] = 10. 0.032 * M w +2.7389 , M w ≥ 6.5 10. 0.5409 * M w −0.547 , M w < 6.5 , The frequency-magnitude distribution is described by the constants a and b, and n is the size of population of earthquakes with a magnitude exceeding m.The productivity of earthquakes is described by parameter a, and the relative size distribution of events are described by parameter b.
The magnitude of b is typically 1 or very close to 1 for seismicity of tectonic origin (Muller & Jokat 2000), and a value of b less than 1 denotes the dominance of larger earthquakes in relation to smaller events.Reduction in the frequency of low-magnitudes earthquakes, particularly in seismically active areas, indicate the build-up of stress, while high seismicity in the area may be explained by high b-values in the volcanic chambers (Sanchez et al. 1995).Low b values suggest that the earth's crust is under significant differential stress, which points to the completion of the Seismic Cycle (Schorlemmer et al. 2005).The Seismic Cycle can be referred as the sequence of repeated stresses, strains, and energy releases in the Earth's crust that cause earthquakes.
The maximum likelihood technique and the least square fit method are used to compute b values, but the assumption that every data point has the same weight and residuals are Gaussian-distributed makes the least square method biased.Aki (1965) proposed the maximum likelihood technique (MLE) to circumvent these inconveniences.
In this study, ZMAP (Weimer, 2001) was used to determine GR parameters, such as b-values, a-values and Mc, using an MLE method in log scale.

Magnitude conversion
From Eqs. ( 2)-( 7) provide the regression relations developed for different magnitude proxies while Fig. 3 displays the GOR findings of this study against various regression models.
We deploy the General Orthogonal Regression relation to compute m b − M w pairs (Eq.2): We relate M S to m b using relation in Eq. ( 3): m b is related to M L in GOR analysis (Eq.4): Conversion from M S to M w in GOR takes the form in Eq. ( 5): (2) Moreover, Eq. 6 is used to convert from local magnitude to moment magnitude.

Comparisons with different studies
We compare our findings with relations from various studies at global scale (e.g., Scordilis 2006;Akkar et al. 2010;Weatherill et al. 2016) and studies around the EARS (Lamessa et al. 2019;Ibrahim et al. 2015).The comparisons are presented for m b -M w and M S -Mw pairs in Fig. 4.

G-R parameters
Generally the seismicity of the EARS is moderate type with some stronger events (see Fig. 5).The temporal variation of events (Fig. 6) and Cumulative Moment release of the EARS (Fig. 7) both demonstrate a sharp rise in graph depicting that the recording facilities of the region have only improved late 1990s.
Magnitude of completeness M c for EARS in regional level using the MLE method was found to be 3.8 for the entire range of study    3. Most notably, one can deduce that the seismicity of the EARS is active with few exceptions such as areas under stable Tanzanian Craton, and some southern Africa parts (e.g., southern Mozambique) exhibit less   (Dipok et al., 2018).On the contrary, the area between the eastern flank and the western flank of the EARS is less seismic with b-value of 1.29.This is the area with underlying thicker and stable Tanzanian Craton.Far towards south is also the stable and less seismic block in the southern Mozambique with b-value of 1.37 (see Table 3; Fig. 9).

Fig. 4
Fig. 4 Comparisons of various global and local empirical relations: a m b -M w , b Ms-Mw as shown in Fig. 8.However, the G-R parameters varied from place to place and temporally.The b-values, M c and a-values of typical parts of the EARS such as Afar, northern Main Ethiopian Rift (NMER), central Main Ethiopian (CMER), Sothern Main Ethiopian Rift (SMER), Tanzanian Craton, and Mozambique are presented in Table

Fig. 5 Fig. 6 Fig. 7
Fig. 5 Number of Events versus magnitude size in a bin size of 0.1

Fig. 9
Fig. 9 Spatial distribution of b-values in the EARS ranging from Afar, the triple junction of the EARS, to Mozambique, in the southern extreme of the rift.Here, grid size of 1.15° × 1.15° was used.Moreover, the minimum number of events used per node were 50

Table 2
Review of various regression models for different scales