Calibration of an ML scale for South Africa using tectonic earthquake ...

Calibration of an M L scale for South Africa 

using tectonic earthquake data recorded by 

the South African National Seismograph 

Network: 2006 to 2009 

Ian Saunders, Lars Ottemöller, Martin 

B. C. Brandt & Christoffel J. S. Fourie 

Journal of Seismology 

ISSN 1383-4649 

J Seismol 

DOI 10.1007/s10950-012-9329-0 

1 23

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1 23

J Seismol 

DOI 10.1007/s10950-012-9329-0 

ORIGINAL ARTICLE 

Calibration of an M L scale for South Africa using tectonic 

earthquake data recorded by the South African National 

Seismograph Network: 2006 to 2009 

Ian Saunders & Lars Ottemöller & 

Martin B. C. Brandt & Christoffel J. S. Fourie 

Received: 18 April 2011 /Accepted: 21 August 2012 

# Springer Science+Business Media B.V. 2012 

Abstract A relation to determine local magnitude 

(ML) based on the original Richter definition is empirically 

derived from synthetic Wood–Anderson seismograms 

recorded by the South African National 

Seismograph Network. In total, 263 earthquakes in 

the distance range 10 to 1,000 km, representing 

1,681 trace amplitudes measured in nanometers from 

synthesized Wood–Anderson records on the vertical 

channel were considered to derive an attenuation relation 

appropriate for South Africa through multiple 

regression analysis. Additionally, station corrections 

were determined for 26 stations during the regression 

analysis resulting in values ranging between −0.31 and 

I. Saunders (*) : M. B. C. Brandt 

Council for Geoscience, 

Private Bag X112, Silverton, 

Pretoria, South Africa 0001 

e-mail: ians@geoscience.org.za 

M. B. C. Brandt 

email: martinb@geoscience.org.za 

L. Ottemöller 

Department of Earth Science, University of Bergen, 

Allegt 41, 5007, Norway 

e-mail: lars.ottmoller@geo.uib.no 

C. J. S. Fourie 

Environmental, Water and Earth Science Department, 

Faculty of Science, Tshwane University of Technology, 

Private Bag X460, 

Pretoria, South Africa 0001 

e-mail: fouriecjs@tut.ac.za 

Author's personal copy 

0.50. The most appropriate ML scale for South Africa 

from this study satisfies the equation: 

ML ¼ log 10ðAÞþ1:149 log 10ðRÞþ0:00063R þ 2:04 S 

The anelastic attenuation term derived from this 

study indicates that ground motion attenuation is significantly 

different from Southern California but comparable 

with stable continental regions. 

Keywords Local magnitude . South Africa . 

Attenuation relation . Stable continental region . 

Station corrections 

1 Introduction 

The use of earthquake magnitude scales to express the 

physical size or energy released by earthquakes is 

routine practice at seismological observatories and is 

based on quantities that are measured from waveform 

recordings. In general, magnitude scales are distancedependent 

and are only valid for a specific wave type 

recorded in a narrow frequency band and scale differently 

with seismic energy and moment. The most 

popular and widely used magnitude scale for expressing 

the size of an earthquake at local and regional 

distances remains the local magnitude (ML) scale, 

originally defined by Richter (1935). 

This Richter scale is of engineering interest, as emphasized 

by Bormann (2002), where the importance of a

calibrated M L scale in seismic hazard studies was 

highlighted since the frequency band of the Standard 

Wood–Anderson (SWA) seismograph (~0.8–10 Hz) is 

close to the resonant frequencies of many engineering 

structures. The attenuation curve derived from the ML 

scale can be used in the risk assessment of these 

structures. 

The practice of determining ML in South Africa 

during the period 1971 to 1997 is described by 

Fernández (1973, 1977, 1980, 1991, and 1993). 

Maximum peak-to-peak amplitudes in millimeters 

of the S-Lg wavecomplexrecordedonthevertical 

channel of short-period analogue seismograms 

were measured and then reduced to ML values 

using the magnitude–distance attenuation curves 

derived for Southern California (Richter 1935), 

modified for South African conditions, through 

the relation: 

ML ¼ log10ðAÞ log10ðA0ÞþS ð1Þ 

where A is the maximum amplitude, –log10A0 is 

the distance correction term, and S is a station 

correction term. 

The analogue instrumentation of the South African 

National Seismograph Network (SANSN) differed significantly 

from the SWA seismographs in California, 

specifically the gain factors at 1 Hz, viz. 1,300 for the 

SWA (Anderson and Wood 1925) and 50,000 for the 

SANSN instrumentation, respectively (Fernández 1993). 

Fernández argued that the conversion of the 

SANSN seismograms to simulate SWA torsion seismographs 

was impractical since the SANSN consisted 

mostly of vertical records as opposed to the horizontal 

channels of the SWA seismographs used to define the 

Richter magnitude. Hence, rather than simulating 

SWA seismograms, Fernández used the ratio of magnification 

of the SANSN seismographs to that of the 

SWA seismograph to modify the correction factor (A0) 

for South Africa. In practice, readings from all observing 

stations were averaged after adjustment with 

station-specific corrections (Fernández 1993) to obtain 

the ML value. 

The question of an equivalent ML relation for South 

Africa was considered by Brandt (1997) withthe 

introduction of the SEISAN earthquake analysis software 

(Havskov and Ottemöller 2005) during March 

1997 for routine data analysis. It was concluded that 

the relation of Hutton and Boore (1987) was the most 

relevant since it compared well with the modified 


J Seismol 

Richter (1935) relation introduced by Fernández 

(1993) to determine ML in South Africa. 

A preliminary study with the MAG program of the 

SEISAN Earthquake Analysis Software (Havskov 

and Ottemöller 2005) to test coefficients for the 

ML scale in South Africa was undertaken during 

2008 (Saunders et al. 2008). The derived coefficients 

hinted that the geometrical spreading coefficient 

in South Africa is similar to other parts of 

the world while the anelastic attenuation value is 

significantly lower than that of the strongly attenuating 

crust of Southern California (Hutton and 

Boore 1987), indicating a high Q-value for the 

crystalline Archaean and Mesozoic crust in South 

Africa. The question of South Africa being located 

in a stable continental region (SCR) is debatable 

since the northeastern part of the country is in 

close proximity to the East African Rift System. 

However, for practical purposes, we followed the 

criteria of the Electric Power Research Institute 

(EPRI) Report (1994) for delineating SCRs since 

Africa is included in the nine major SCRs identified 

in the report. Thus, the authors tentatively 

accept that South Africa meets the norms of SCRs 

being older, with lower crustal temperatures and a 

low level of seismicity. 

Thus, since high Q values are expected in SCRs 

(Kvamme and Havskov 1989), we expected to have 

geometrical spreading and anelastic attenuation 

coefficients similar to other regions classified as 

being located in SCRs. Table 1 provides selected 

geometrical spreading and anelastic attenuation 

coefficients values determined for other regions 

of the world. 

The primary reason for continuing with the ML 

scale for quantifying earthquake sources in South 

Africa is to maintain continuity of the magnitude scale 

since the catalogue of instrumentally determined magnitudes 

dates back to 1971 based on maximumamplitude 

readings (Wright and Fernández 2003). 

Secondly, South Africa measures no more that 

2,000 km in either the north–south or east–west direction. 

This is within the distance limitations of the ML 

scale while the country is additionally considered to be 

located in a SCR (EPRI 1994) with a low level of 

seismic activity. 

On average, 11 earthquakes per annum are recorded 

in South Africa with M L≥4.0 (statistics based on the 

time period 1990 to 2009). It should be noted that this

J Seismol 

Table 1 Geometrical spreading 

and anelastic attenuation values 

determined for other regions 

(from Havskov and Ottemöller 

2010) 

Region Geometrical 

spreading 

number includes mining related tremors, which have 

decreased in recent years as production in the gold 

mining areas of South Africa had declined (see Fig. 1). 

The largest recorded tectonic earthquakes over the past 

century in southern Africa registered with magnitudes 

either equal or below the upper threshold of 7 on the 

M L scale. The last consideration is purely practical 

since the ML scale relies on relatively simple methodology 

in comparison to more computationally complicated 

magnitude scales, e.g., moment or energy 

magnitude scales. 

The aim of this study is to define coefficients for 

the M L scale in South Africa through simultaneous 

inversion on a dataset of earthquakes with a good 

regional distribution within the borders of South 

Africa and to determine stations corrections. 

Fig. 1 Earthquakes recorded 

in South Africa with M L≥4.0 

during the period 1990 to 

2009. It is evident that more 

mining-related earthquakes 

(solid bars) were recorded by 

the SANSN during the period 

1990 to 2009. The figure 

further shows a general decline 

in the number of 

mining-related earthquakes 

from 2001 (except for an 

anomalous number during 

2005) 


Anelastic 

attenuation 

Reference 

Albania 1.66 0.00080 Muco and Minga (1991) 

Central California 1.00 0.00310 Bakun and Joyner (1984) 

Ethiopia 1.20 0.00107 Keir et al. (2006) 

Northern Italy 1.00 0.00540 Bindi et al. (2005) 

Northwestern Turkey 1.00 0.00152 Baumbach et al. (2003) 

Norway 0.91 0.00087 Alsaker et al. (1991) 

South Africa 1.15 0.00063 This Study 

Southern Australia 1.10 0.00130 Greenhalgh and Singh (1986) 

Southern California 1.11 0.01890 Hutton and Boore (1987) 

Southwestern Germany 1.11 0.00095 Stange (2006) 

Tanzania 0.78 0.00090 Langston et al. 1998 

The Great Basin 1.00 0.00690 Chávez and Priestly (1985) 

Western USA 0.83 0.00260 Chávez and Priestly (1985) 

2 Major geological provinces and seismotectonic 

setting 

The basement geology in South Africa is of Archean 

to Mesozoic age hence attenuation of seismic waves 

with distance is expected to be similar to that of other 

SCRs (Bakun and McGarr 2002). 

The development of the basement geology of southern 

Africa (Fig. 2) spans a period of approximately 

2.9 Ga years, which commenced with the Kaapvaal 

craton becoming a stable 3.1 Ga assemblage (e.g., De 

Wit et al. 1992; McCourt and Wilson 1992). The Zimbabwe 

craton (Wilson et al. 1990) fused with the Kaapvaal 

craton during a collision 2.7 Ga ago (e.g., Light 

1982; Treloar et al. 1992) to form, what is collectively 

known as the Kalahari craton. Metamorphosed rocks of

Fig. 2 Simplified basement 

lithology of southern Africa 

the Limpopo Belt define the suture between the cratons 

(e.g., Watkeys 1983; Van Reenen et al. 1990; Barton and 

Van Reenen 1992). 

Continental shelf deposits and sediments that accumulated 

along the western edge of the Kaapvaal and 

Zimbabwean cratons were subsequently folded and 

thrusted eastwards (Kheis and Magondi Belts) 

~1.8 Ga (e.g., Leyshon and Tennick 1988; Treloar 

and Kramers 1989), postulated as a collision between 

the Congo and Kalahari craton. An extensive platform 

of continental crust was created during the collision of 

the cratons (Congo and Kalahari) to form the Ubendian 

Belt (1.8 Ga). 

The assemblage of the palaeo-continent, Rodinia 

(1.1 Ga), through the amalgamation of Atlantica (parts 

of present-day West Africa and South America), Arctica 

(parts of present-day Canada, northern Siberia, 

and Greenland), and Ur (parts of present-day South 

Africa, Madagascar, India, and Australia), resulted in 

the formation of a global mountain range that has 

since been eroded to expose extensive metamorphic 

belts (Kibaren/Grenville Belt) (Thomas et al. 1993) 

known locally as the Namaqua-Natal Mobile Belt 

flanking the southern portion of the Kaapvaal craton. 

Sediments deposited in rifts that subsequently opened 

between the Congo and Kalahari craton during the 

fragmentation and break-up of Rodinia (700 Ma) were 

compressed, folded, and metamorphosed (500 to 

550 Ma) with the assemblage of the supercontinent, 

Pangaea, to form the Pan-African Belts, Damara Belts, 

and the Cape Granite Suite. 


J Seismol 

Around 500 Ma, the Supercontinent Gondwana 

consolidated from fragments of the Supercontinent 

Pangea (which had broken into the northern Supercontinent 

Laurasia and southern Supercontinent Gondwana). 

Gondwana was comprised mainly of the 

continents of the southern hemisphere known today 

as Africa, Antarctica, Australia, South America, 

Madagascar, and India (which today resides in the 

northern hemisphere). Thinning of the crust through 

rifting allowed the area presently known as the southern 

Cape to be inundated to form the Agulhas Sea. 

Sedimentary rocks of the Cape Supergroup and the 

Natal Group formed from sediments deposited in the 

Agulhas Sea (Johnson et al. 2006). 

Extensive folding of the Cape Supergroup (~310 Ma) 

created the Cape Mountains through compression of the 

interior of Gondwana from a subduction zone that had 

formed along the southern edge of Gondwana (e.g., 

Hälbich 1983; De Beer 1990). A basin developed along 

the northern margin of the Cape Mountains in which 

sedimentary rocks of the Karoo Supergroup were deposited. 

Massive quantities of flood basalt lavas erupted 

onto the surface, disrupting sedimentation in the Karoo. 

The extensive outpouring of lavas is postulated to be 

related to a mantle plume that had risen beneath, what is 

today known as southern Africa, and may have initiated 

the break-up of Gondwana at 182 Ma (e.g., Martin and 

Hartnady 1986; Watkeys and Sweeney 1988). 

By 140 Ma, oceanic crust formed between West 

Gondwana (Africa and South America) and East Gondwana 

(Antarctica, Australia, India, and Madagascar) to

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mark the beginning of the Indian Ocean. West 

Gondwana further fragmented around 120 Ma 

when oceanic crust, possibly resulting from a separate 

and distinct mantle plume, separated Africa 

from South America (proto-Atlantic Ocean). Simultaneously, 

continental crust of the Falkland 

Plateau detached along a major fracture (Agulhas 

Falkland Fracture Zone) and moved westwards 

with South America before completely separating from 

the Cape by 90 Ma (Von Veh and Anderson 1990). 

The faulting regime in South Africa changes from 

normal faulting in the northeast of the country, possibly 

related to the influence of the nearby East African 

Rift System to strike-slip along the southwestern part. 

The change to strike-slip faulting can be explained 

through the dominating stresses becoming horizontal 

through ridge push from the Mid-Atlantic Ridge 

against the African plate (Singh et al. 2009). 

3 Earthquake data 

Earthquake data used in our study were obtained from the 

South African National Seismograph Network (SANSN) 

Fig. 3 Distribution of mining-related earthquakes in the gold/ 

platinum mining areas (gray polygons), collieries, and iron/ 

manganese mines (black polygons) as well as smaller mining 

operations in the Western Cape aggregate mines (1), Lime Acres 

diamond mine (2) and the Zeerust mines (3) during the period 

2006 to 2009. A large number of recorded seismic disturbances 


operated by the Council for Geoscience (CGS) and three 

primary stations of the International Monitoring System. 

A total of 263 tectonic events were selected that 

were recorded by at least five stations during the 

period 2006 to 2009 within an area bounded by approximate 

coordinates 22° to 36° South and 15° to 35° 

East with amplitude readings in the distance range 10 

to 1,000 km and magnitudes ranging from 1.4 to 4.1. 

Stations with at least one clear phase reading and 

where the S and Lg phases were not truncated or 

clipped were used to measure the maximum amplitude. 

The displacement amplitudes were measured in 

nanometers on the vertical (Z) component by deconvolving 

the waveform with the instrument response, 

and the resulting ground displacement waveform convolved 

with the frequency response of the SWA instrument 

as given by Uhrhammer and Collins (1990) 

(T 000.8 s and damping factor H 000.7). 

The bulk of South African seismicity originates in 

the gold/platinum mines of the country with another 

significant number recorded from blasting activities in 

quarries (e.g., Saunders et al. 2010). The mining related 

events and quarry blasts in collieries, the iron/ 

manganese mines, and smaller quarries are identified 

by their spatial distribution relative to large-scale 

(gray triangles) can be attributed to explosions and suspected 

explosions while an equal number of earthquakes can spatially 

be related to mining operations (induced seismicity) in the gold/ 

platinum mines of South Africa. These seismic events were not 

included in the dataset used during the inversion (for more 

detail, see text)

mining operations (see Fig. 3) and are flagged in the 

database by fixing the depth to surface (explosions) or 

to 2-km depth (mining related earthquakes). Explosions 

are further identified by occurring in time between 

06:00 and 18:00 (local time) which is the time 

when blasting is allowed through South African Legislation. 

The depth of 2 km for mining-related earthquakes 

was chosen, since 2 km best represents the 

average depth of gold mines in South Africa. 

In South Africa, a simple one-dimensional velocity 

structure (Wright et al. 2002) is used for locating earthquakes 

with an average location error of less than 10 km. 

Furthermore, the routine practice at the CGS is to measure 

maximum amplitude on the vertical component as 

opposed to Richter (1935) who defined the ML scale 

from maximum amplitudes on the horizontal components. 

It is noted by Alsaker et al. (1991) thatthereis 

little difference between the maximum amplitudes measured 

on vertical and horizontal components in Norway. 

Additionally, amplification on horizontal channels is 

more pronounced at stations located on unconsolidated 

material whereas the vertical component is less affected. 

Using vertical component amplitudes thus leads to a 

more consistent M L estimation between stations located 

on different geological foundations (Havskov and 

Fig. 4 Ratio of amplitudes 

(1,681) measured on the 

vertical and horizontal components 

of earthquakes used 

in this study. The solid line 

delineates linear regression 

of data 


LogA (Vertical) 

4.5 

4 

3.5 

3 

2.5 

2 

1.5 

1 

0.5 

0 

Ottemöller 2010). This assumption was tested for 

South African conditions (Fig. 4) by comparing the 

ratio of 1,681 maximum amplitudes measured on the 

vertical channel (logA Vertical) to the arithmetic mean of 

the maximum amplitudes measured on the horizontal 

channels (logAHorizntal). The mean value of the vertical 

to horizontal ratio is 0.94 with a correlation coefficient 

of 0.96. 

Focal depths of earthquakes are not well constrained 

in South Africa due to the sparse station distribution of 

the SANSN. We therefore accepted that South Africa, 

tentatively located in a SCR, would have earthquake 

depths similar to other regions considered SCRs. Van 

Lanen and Mooney (2004) noted that the overall majority 

of earthquakes occurring in SCRs have hypocentral 

depths equal or less than 10 km with the maximum 

number occurring between 5–10 km. Thus, earthquakes 

resulting from tectonic activity in South Africa are restricted 

to depths of either 5 or 10 km depending on the 

best convergence calculated by the location software 

(Saunders et al. 2010). Brandt and Saunders (2011) 

determined the earthquake depths of three tectonic 

earthquakes in South Africa as shallow (between 9 and 

11 km) during a study to determine moment tensor 

solutions, however, further studies are needed to qualify 

-0.5 

-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 

LogA (Horizontal) 

J Seismol

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Fig. 5 Spatial distribution 

of earthquakes (solid 

circles) with paths (gray 

lines) indicated to stations 

(solid triangles) used in this 

study. The number indicated 

at the station relates to the 

number assigned in Table 2 

the shallow hypocentral depth hypothesis for tectonic 

earthquakes in South Africa. 

Figure 5 depicts the epicenters and station locations 

together with the resulting ray pattern. It shows that 

the majority of South Africa is covered spatially, traversing 

all the major crustal units. Details of the stations 

are listed in Table 2 with station corrections 

resulting from the inversion. 

4 Methodology 

The concept of local magnitude was introduced by 

Richter (1935) and is defined as the logarithm (log10A) 

of the peak average maximum displacement 

(millimeters) measured on the two horizontal components 

of a SWA (Anderson and Wood 1925) torsion 

seismometer (see Eq. 1). The scale was defined such 

that an earthquake of ML03 situated at 100-km distance 

from the recording stations resulted in 1 mm 

deflection on the seismogram. Hutton and Boore 

(1987) proposed a reference distance (Rref) of17km 

with a reference magnitude of 3 (resulting in a 10 mm 

deflection on a standard Wood–Anderson seismograph) 

in regions with dissimilar attenuation to Southern 

California, as is the case in South Africa. However, 

Alsaker et al. (1991) cautioned that sufficient observations 

are required within the chosen reference distance 

to justify deviating from the original reference 

distance of 100 km. The hypocentral distribution of data 

used in this study (Fig. 6) indicates that 90 % of the 


amplitude readings of our data occur in the distance 

range 100–800 km with only 3 % in the distance range 

0–100 km. We therefore used the same arbitrary constraint 

suggested by Richter (1935) during regression. 

The general form of the local magnitude scale can 

be expressed as: 

ML ¼ logðAÞþalogðRÞþb ðRÞþc þ Si ð4Þ 

where a relates to the geometrical spreading, b the 

attenuation factor, Si is a station correction term for 

station i, and c a source region correction term (see, 

e.g., Bormann (2002) and Havskov and Ottemöller 

(2010) for a more comprehensive discussion). 

We applied singular value decomposition (SVD) 

using the Numerical Recipe (Press et al. 2003) routines 

to invert our observations for a, b, and Si. 

Attenuation characteristics between dissimilar 

regions vary resulting in different trace amplitudes 

measured for identical magnitude earthquakes observed 

at identical distances. However, as mentioned 

previously, Richter (1935) defined the M L scale that 

the maximum trace amplitude on a SWA should measure 

1 mm from an earthquake registering 3 on the 

Richter scale, originating at a distance of 100 km from 

an observation station in Southern California. In order 

to compensate for the difference in attenuation along 

the path to source to obtain an equivalent M L in South 

Africa, we set c such that 1 mm amplitude at 100 km 

on a SWA seismograph would also compute ML03. 

Since a least-squares inversion procedure was followed 

for solving Eq. 4, errors can be expected during

Table 2 Details of stations used in the study with station corrections 

Number Station Code Sensor Period of 

operation 

the inversion should the data not be normally distributed 

(Stange 2006). Therefore, the dependency on a 

specific station was applied to test whether the parameters 

determined during the SVD inversion was mutually 

free. The procedure was to create secondary 

datasets, omitting stations in succession, then 


Site Lithology Station 

correction 

1 Belfast BFT CMG-40T 03/2006–present Vault Gabbro 0.06 

2 Boshof a 

BOSA KS-54000 08/1999–present Borehole Granite 0.50 

3 Buffelsbos BUFB L4C-3D 09/2008–present Vault Sandstone 0.22 

4 Ceres CER KS-2000 03/2002–present Vault Quartzite 0.15 

5 Calvinia CVNA KS-2000 04/2004–present Vault Dolerite −0.21 

6 East Rand 

propriety mines 

ERPM L4C-3D 05/2006–present Vault Quartzite 0.26 

7 Elim ELIM L4-3D 10/1996–03/2007 Vault Quartzitic −0.05 

CMG-40T 03/2007–present 

sandstone 

8 Grahamstown GRM KS-2000 10/2002–present Vault Quartzite −0.08 

9 Gariep Dam HVD CMG-40T 02/2004–present Vault Dolerite −0.08 

10 Kloof KLOF L4-3D 08/2006–present Ground floor Dolomite −0.23 

11 Komaggas KOMG L4C-3D 06/2003–05/2007 Vault Gneiss −0.08 


12 Kokstad KSD CMG-40T 07/2005–03/2007 Vault Dolerite 0.03 

KS-2000 03/2007–present 

13 Koster KSR S-13 04/2002–05/2006 Vault Sandstone −0.25 


14 Lobatse a 

LBTB KS-54000 04/1993–present Borehole Granite 0.37 

15 Mopani MOPA CMG-40T 04/2004–present Vault Granite 0.02 

16 Mussina MSNA CMG-40T 03/2003–11/2006 Vault Quartzite −0.11 

KS-2000 11/2006–present 

17 Observatory OBSV L4C-3D 10/2009–12/2009 Ground floor Quartzite 0.20 

18 Parys PRYS S-13 11/2004–09/2006 Vault Granite −0.07 


19 Prieska PKA CMG-40T 04/2004–present Vault Alluvium, 

calcrete 

0 

20 Pongola POGA KS-2000 03/2005–present Vault Sandstone −0.12 

21 Senekal SEK CMG-40T 12/2003–present Vault on hill Sandstone −0.30 

22 Somerset East SOE L4C-3D 03/2005–09/2008 Vault Mudstone, 0 


sandstone 

23 Sutherland b 

SUR STS-2 10/1990–present Vault Dolerite 0.20 

24 Schweizer-Reneke SWZ CMG-40T 04/2006–present Vault Sandstone −0.11 

25 Upington UPI CMG-40T 06/2005–05/2007 Vault Calcrete −0.03 

KS-2000 05/2007–present 

26 Western deep 

levels mine 

WDLM L4C-3D 12/2009–present Vault Quartzite −0.31 

a Station of the Global Telemetered Seismological Network (GTSN) 

b Station of the Incorporated Research Institutions for Seismology (IRIS) 

J Seismol 

executing the SVD inversion on each subset and comparing 

the results. The deviation of the different solutions 

provides an indication of the error introduced 

during the inversion. Figure 7 indicates negligible 

deviation from the original results using the entire 

dataset and subsets.

J Seismol 

Fig. 6 Distance/magnitude 

distribution of events used 

in this study. The magnitudes 

shown were determined 

with the Hutton and 

Boore (1987) relation (original 

dataset) 

5 Station corrections 

Station corrections were determined during the inversion 

for 26 stations used during the study, and the 

results are presented in Table 2 and Fig. 8. 

The IMS stations at Boshof and Lobatse have 

large corrections, viz. 0.50 and 0.37, respectively. 

This observation indicates that the amplitude readings 

at these stations are lower than expected which 

Distance Corrrection (M L ) 

5 

4 

3 

2 

1 

101 102 103 0 

Hypocentral distance (km) 

Fig. 7 Graphical representation of Eq. 4 shown as a broken 

black line with the gray shaded area representing the standard 

deviation determined during the study to establish whether there 

is a dependency on any particular station 


may be related to the free surface effect (e.g., Lay 

and Wallace 1995) since the sensors at both these 

stations are located in boreholes, as opposed to 

vaults located at the surface, as is the case for the 

other stations considered during this study. Furthermore, 

the stations at BUFB, CVNA, ERPM, KLOF, 

KSR, OBSV, SEK, SUR, and WDLM have large 

station corrections (>±0.2) that are explained 

through poor seismic coupling for stations ERPM, 

KLOF, OBSV, and WDLM since the sensors at 

these station are not located in ideal seismic vaults, 

while stations SEK and CVNA are located on hillocks 

where wave interactions may lead to complex 

interference. The larger-than-expected station residuals 

for stations BUFB, KSR, and SUR are unclear 

but may be related to unknown geological structures 

at these sites or could be a result of poor 

seismic coupling. Figure 9a, b shows the magnitude 

residuals computed without station corrections using 

the original dataset (Hutton and Boore 1987) 

and with station corrections (this study). The average 

residuals with station corrections considered are 

close to zero (0.05) with a standard deviation of 

0.28 and variance σ 2 of 0.079 while residuals without 

station corrections have a standard deviation of 

0.38 with a variance σ 2 of 0.144. Therefore, the 

variance is reduced by 45.1 % when adopting the 

station corrections.

Fig. 8 Station corrections determined during the SVD shown in 

relation to the simplified surface geology of South Africa, 

Lesotho, and Swaziland. Positive station corrections are 

Fig. 9 Magnitude residuals 

versus distance. a Magnitude 

residuals computed 

with A 0(R) (Hutton and 

Boore 1987) without station 

corrections. The standard 

deviation is 0.38, and the 

variance is 0.144. b Magnitude 

residuals computed 

with A 0(R) (this study) with 

station corrections considered. 

The standard deviation 

is 0.28, and the variance is 

0.079. A variance reduction 

of 45.1 % is achieved 

through applying station 

corrections 


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indicated through triangles while inverted triangles indicate a 

negative station correction. The number indicated at the station 

relates to the number assigned in Table 2

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Fig. 10 Comparison of attenuation 

curves for Southern 

California. The original 

relation (Richter 1935) is 

indicated as open squares, 

Hutton and Boore (1987) as 

filled circles, Norway 

(Alsaker et al. 1991) asa 

solid line, and South Africa 

(this study) as crosses 

6 Results and discussion 

The distance correction term (−logA 0) determined during 

this study, using 100-km distance normalization, is 

given by: 

logðA0Þ ¼ 1:149 logðRÞþ0:00063ðRÞþ2:04 ð5Þ 

Fig. 11 Magnitude determined 

during this study 

plotted against the magnitude 

determined with the 

Hutton and Boore (1987) 

relation. The broken line 

indicates linear regression of 

data. An overestimation of 

magnitude using the Hutton 

and Boore (1987) relation in 

South Africa is implied 


ML (This study) 

5 

4.5 

4 

3.5 

3 

2.5 

2 

1.5 

The overall magnitude standard deviation obtained 

during the inversion (10–1,000 km) was 0.27 considering 

station residuals. 

A comparison of the attenuation curves obtained 

for Southern California (Richter 1935; Hutton and 

Boore 1987) and South Africa (this study) indicates 

lower attenuation in South Africa with distance 

1 

1 1.5 2 2.5 3 3.5 4 4.5 5 

ML (Hutton and Boore (1987)

Fig. 12 Comparison of 

magnitudes calculated at 

ten stations located at varying 

distances (>100 to 

J Seismol 

of importance, since a modified Richter (1935) attenuation 

relation developed by Fernández (1993) and 

that of Hutton and Boore (1987) had been used to 

determine local magnitude in South Africa from the 

inception of the SANSN to present. A comparison 

with the attenuation relation obtained for Norway 

(Alsaker et al. 1991) indicates that the attenuation 

relation obtained during this study is similar to Norway 

which is located in a SCR, which cautiously 

suggests that South Africa displays attenuation characteristics 

like those of other SCRs. Thus, a 

frequency-dependent attenuation relation for South 

Africa would assist in supporting results obtained 

during our study. 

Figure 12 indicates that the attenuation curve derived 

during our study more consistently estimates 

magnitude over different hypocentral distances in 

comparison to previous M L scales used in South 

Africa which appear to have had a tendency to overestimate 

magnitude (Fernández 1993; Hutton and 

Boore 1987). 

The mean magnitude residuals obtained by subtracting 

ML, independently calculated for each recording 

station, from the arithmetic mean of M L 

determined from all stations per earthquake is shown 

in Fig. 13. The mean values, averaged at 50-km distance 

intervals, follow the zero baseline closely. This 

trend indicates that the relationship between attenuation 

and hypocentral distance in the region is accurately 

modeled with our attenuation curve. 

A calibrated local magnitude scale is a useful tool 

as a relative scale for general seismic studies but is not 

practical for studies of the seismic source. To this end, 

we plan to develop a moment magnitude scale for 

South Africa and develop a relationship between the 

local and moment magnitude scales. 

7 Conclusion 

A local magnitude scale, based on the Richter (1935) 

definition, was developed for South Africa from 1,943 

maximum amplitude observations measured on vertical 

component synthetic Wood–Anderson seismograms 

in the distance range 10 to 1,000 km. Results 

from the inversion for event magnitudes resulted in a 

ML scale for South Africa expressed as Eq. 5. 

It was shown that the average difference between 

local magnitude calculated from the horizontal 


components and vertical components is 0.1 magnitude 

units. This confirms that the practice of computing 

local magnitude on the vertical channel is valid for 

South Africa. 

The attenuation curve up to 150 km is similar to 

Southern California but deviates at distances beyond 

150 km, indicating that ground motion attenuation is 

lower in South Africa in comparison to Southern California. 

It is, however, consistent with observations 

from other regions located in SCRs. 

It was shown that the attenuation relation determined 

during this study provides a more consistent 

estimation of ML over a range of hypocentral distances 

when compared with previous ML relations used in 

South Africa. 

An analysis of the mean magnitude residuals 

obtained with the attenuation curve from our study 

does not show pronounced complexities in the crustal 

structure of South Africa. The station corrections 

obtained during the study show that 13 of the 26 

stations considered during the study have correction 

factors equal or less than ±0.1. This indicates that local 

site amplification does not have a significant influence 

on magnitude estimates at these stations. However, it 

was postulated that, in some instances, less than ideal 

vault conditions, topography, and local site effects 

may lead to erroneous magnitude calculations. 

Acknowledgments This work was funded by the National 

Research Foundation under Grant Number TP2010061400012. 

We are grateful to the editors and four anonymous reviewers for 

their thoughtful suggestions and positive criticism to improve 

the manuscript and a special word of gratitude to Prof. Bormann 

for contributing to the manuscript through invaluable support 

and insightful ideas. The authors further wish to express their 

gratitude to the copy editor, Sonja van Eck, for her meticulous 

and careful review of the manuscript and to Magda Roos for her 

assistance with the figures for the manuscript. 

References 

Alsaker A, Kvamme LB, Hansen RA, Dahle A (1991) The M L 

scale in Norway. Bull Seismol Soc Am 81(2):379–398 

Anderson JA, Wood HO (1925) Description and theory of the 

torsion seismometer. Bull Seismol Soc Am 15(1):1–72 

Bakun WH, Joyner WB (1984) The M L scale in Central California. 

Bull Seismol Soc Am 74:1827–1843 

Bakun WH, McGarr A (2002) Differences in attenuation between 

the stable continental regions. Geophys Res Lett 29 

(23):36–1–36–4 

Barton JM, Van Reenen DD (1992) When was the Limpopo 

Orogeny? Precambrian Res 5:7–16

Baumbach M, Bindi D, Grosser H, Milkereit C, Paralai S, Wang 

R, Karakisa S, Zünbül S, Zschau J (2003) Calibration of a 

M L scale in Northwestern Turkey from 1999 Izmit aftershocks. 

Bull Seismol Soc Am 93:2289–2295 

Bindi D, Spallarossa D, Evan C, Cattaneo M (2005) Local and 

duration magnitudes in Northwestern Italy, and seismic 

moment versus magnitude relationships. Bull Seismol 

Soc Am 95:592–604 

Bormann P (ed) (2002) Magnitude of seismic events, in IASPEI 

New Manual of Seismological Observatory Practice. Geo- 

ForschungsZentrum, Potsdam, vol. 1, chapter 3, 16–50 

Brandt MBC (1997) Implementation of SEISAN earthquake 

software for the SUN to analyze the data obtained through 

the South African National Seismograph Network. Report 

no. 1970–0263, Council for Geoscience, 48 pp 

Brandt MBC, Saunders I (2011) New regional moment tensors 

in South Africa. Seismol Res Lett 82(1):69–80 

Chávez DE, Priestly KF (1985) M L observations in the Great 

Basin and M 0 versus M L relationship for the 1980 Mammoth 

Lakes, California, earthquake sequence. Bull Seismol 

Soc Am 75:1583–1598 

De Beer CH (1990) Simultaneous folding in the western and 

southern branches of the Cape Fold Belt. South Afr J Geol 

93:583–591 

De Wit MJ, Roering C, Hart RJ, Armstrong RA, De Ronde CEJ, 

Green RWE, Tredoux M, Peberdy E, Hart RA (1992) 

Formation of an Archaean continent. Nature 357:553–562 

Electric Power Research Institute (EPRI) (1994) The earthquakes 

of stable continental regions, EPRI vol. 1. In: 

Schneider JF. EPRI, California, pp 1-1–6-21 

Fernández LM (1973) Program to evaluate epicentral distance, 

origin time and local magnitude of regional tremors. Report 

no. Gh 1968, Geological Survey of South Africa, 11 pp 

Fernández LM (1977) Evaluation of epicentral distances, origin 

times and local magnitudes of local seismic events. A 

computer program for the HP-9830. Report no. Gh 2256, 

Geological Survey of South Africa, 12 pp 

Fernández LM (1980) Adaptation of the Richter seismic local 

magnitude scale to South Africa. Report no. 1980-0175, 

Geological Survey of South Africa, 22 pp 

Fernández LM (1991) A UNIX operating software package to 

process the data obtained by the South African National 

digital Seismograph System. Report no. 1991-0009, Geological 

Survey of South Africa, 25 pp 

Fernández LM (1993) The practice of evaluating local Richter 

magnitude in South Africa. Report no. 1993–0038, Council 

for Geoscience, 16 pp 

Greenhalgh SA, Singh R (1986) A revised magnitude scale for 

South Australian earthquakes. Bull Seismol Soc Am 76 

(3):757–769 

Hälbich IW (1983) Intraformational folding in the Cape Fold 

Belt. Spec Publ Geol Soc South Afr 12:125–130 

Havskov J, Ottemöller L (2005) SEISAN Earthquake Analysis 

Software for the Windows, Solaris, Linux and MACOSX. 

University of Bergen, Bergen 

Havskov J, Ottemöller L (2010) Routine earthquake analysis 

in earthquake seismology: with sample data, exercise 

and software. Chapter 6. Springer, ISBN 978-90- 

481-8696-9 

Hutton LK, Boore DM (1987) The M L scale in Southern California. 

Bull Seismol Soc Am 77(6):2074–2094 


J Seismol 

Johnson MR, Anhaeusser CR, Thomas RJ (2006) The geology 

of South Africa. Geological SocietyofSouthAfrica, 

Johannesburg/Council for Geoscience, Pretoria 

Keir D, Stuart GW, Jackson A, Ayele A (2006) Local magnitude 

scale and seismicity rate for the Ethiopian Rift. Bull Seismol 

Soc Am 96:2221–2230 

Kvamme LB, Havskov J (1989) Q in Southern Norway. Bull 

Seismol Soc Am 79(5):1575–1599 

Langston CA, Brazier R, Nyblade AA, Owens TJ (1998) Local 

magnitude scale and seismicity rate for Tanzania, East 

Africa. Bull Seismol Soc Am 88(3):712–721 

Lay T, Wallace TC (1995) Modern global seismology. Academic, 

San Diego, ISBN: 978-0-12-732870-6 

Leyshon PR, Tennick FP (1988) The Proterozoic Magondi 

Mobile Belt in Zimbabwe—a review. South Afr J Geol 

91(1):114–131 

Light MPR (1982) The Limpopo Belt: a result of continental 

collision. Tectonics 1:325–342 

Martin AK, Hartnady CJH (1986) Plate tectonic development 

of the southwest Indian Ocean: a revised reconstruction 

of East Antarctica and Africa. J Geophys Res 

91:4767–4786 

McCourt S, Wilson JF (1992) Late Archaean and Early Proterozoic 

tectonics of the Limpopo and Zimbabwean provinces, 

southern Africa. In: Glover JE, Ho SE (eds) The 

Archaean: terrains, processes and metallogeny pp 237–246 

Muco B, Minga P (1991) Magnitude determination of near 

earthquakes for the Albanian network. Bolletinno di Geofisica 

Teorico ed Applicata 33(129):17–24 

Press WH, Tuekolsky SA, Vetterling WT, Flanerry BP (2003) 

Numerical recipes in Fortran 77, 2nd edn. Cambridge 

University Press, Cambridge 

Richter CF (1935) An instrumental earthquake scale. Bull Seismol 

Soc Am 25(1):1–32 

Saunders I, Brandt MBC, Roblin DL (2008) Determination of a 

local magnitude scale for South Africa. Report No. 2008- 

0111, Council for Geoscience, 18 pp 

Saunders I, Brandt MBC, Molea TT, Akromah L, Sutherland 

BE (2010) Seismicity of southern Africa during 2006 with 

special reference to the MW 7 Machaze earthquake. South 

African Journal of Geology 113(4):369–380 

Singh M, Kijko A, Durfheim R (2009) Seismotectonic models 

for South Africa: synthesis of geoscientific information, 

problems, and the way forward. Seismol Res Lett 80 

(1):71–80 

Stange S (2006) M L determinations for local and regional events 

using a sparse network in southwestern Germany. J Seismol 

10:247–257 

Thomas RJ, von Veh MW, McCourt S (1993) The tectonic 

evolution of southern Africa: an overview. J Afr Earth Sci 

16:5–24 

Treloar PJ, Kramers JD (1989) Metamorphism and geochronology 

of granulites and migmatitic granulites from the 

Magondi Mobile Belt, Zimbabwe. Precambrian Res 

46:277–289 

Treloar PJ, Coward MP, Harris NBW (1992) Himalayan–Tibetan 

analogies for the evolution of the Zimbabwe craton and 

Limpopo Belt. Precambrian Res 55:571–587 

Uhrhammer RA, Collins ER (1990) Synthesis of Wood–Anderson 

seismograms from broadband digital records. Bull 

Seismol Soc Am 89(8):702–716

J Seismol 

Van Lanen X, Mooney WD (2004) Integrated geologic and 

geophysical studies of North American intraplate seismicity. 

In: Stein S, Mazotti S (eds) Continental intraplate 

earthquakes: science, hazard and policy issues. Geological 

Society of America Special Paper, p 425, doi: 10.1130/ 

2007.2425(19) 

Van Reenen DD, Roering C, Brandl G, Smit CA, Barton 

JM (1990) The granulite facies rocks of the Limpopo 

belt in southern Africa. In: Vielzeuf D, Vidal P (eds) 

Granulites and crustal evolution. Kluwer, Dordrecht, pp 

257–289 

Von Veh MW, Anderson NJB (1990) Normal-slip faulting in the 

coastal areas of northern Natal and Zululand, South Africa. 

South Afr J Geol 93(4):574–582 

Watkeys MK (1983) Brief explanatory notes on the provisional 

geological map of the Limpopo Belt and environs. Spec 

Publ Geol Soc South Afr 8:5–8 


Watkeys MK, Sweeney RJ (1988) Tuli-Lebombo volcanism and 

Gondwana rifting. Extended abstracts, Geocongres 1988, 

Geological Society of South Africa, Durban, pp 725–228 

Wilson JF, Baglow N, Orpen JL, and Tsomondo JM (1990) A 

reassessment of some regional correlations of greenstonebelt 

rocks in Zimbabwe and their significance in the development 

of the Archaean craton. In: Glover JE and Ho SE 

(Comps) Third International Archaean Symposium, extended 

volume, pp 43–44 

Wright C, Fernández LM (2003) International handbook of 

earthquake and engineering seismology (Hung Kan Lee 

W) chapter 79. Elsevier, ISBN 0124406580 

Wright C, Kwadiba MTO, Kgaswane EM, Simon RE (2002) 

The structure of the crust and upper mantle to depths of 320 

km beneath the Kaapvaal craton, from P-arrivals generated 

by regional earthquakes and mining-induced tremors. J Afr 

Earth Sci 35(4):477–488

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