1 Introduction

A reliable and homogenized earthquake catalogue is an important prerequisite for a probabilistic seismic hazard analysis (PSHA). Ideally, an earthquake catalogue should report all events that contribute to a seismic hazard. A single source is not enough to report all earthquakes, and therefore, catalogues are composites, i.e. having contributions from all available sources. Earthquakes occur frequently in and around Pakistan, and thus, a complete catalogue is essential for seismic hazard estimation. The objective of this research is to compile an updated, composite earthquake catalogue of Pakistan from the perspective of seismic hazard analysis. Moreover, processing of this earthquake catalogue, as well as the final outcomes, is presented as an input parameter to a PSHA.

Previous attempts have been made to compile an earthquake catalogue of Pakistan, which was included during the development of seismic provisions for the Building Code of Pakistan (BCP 2007) and, more recently, by Zare et al. (2014) and Waseem et al. (2018). Therefore, a fresh attempt is attempted to compile the catalogue in this study. The catalogue compiled for the study of the Building Code of Pakistan listed important historical and instrumental earthquakes in the region and was homogenized in moment magnitude up to 2007. However, this catalogue missed several important historical events. Similarly, the work of Zare et al. (2014) is complete only up to 2006 and that of Waseem et al. (2018) is limited to northern Pakistan.

The catalogue compiled in this study is bounded by the geographical limits 40–83° N to 20–40° E around Pakistan. For a reliable PSHA, the consideration of earthquakes from neighbouring countries is necessary. Therefore, during the compilation, earthquakes occurring at least 300 km from the point of interest (Pakistan) were included.

The catalogue was compiled in three phases: (1) prehistorical earthquakes from 25 AD to 1900, (2) historical earthquakes from 1901 to 1964 and (3) instrumental earthquakes from 1965 to 2016. The minimum threshold is set to a moment magnitude of 4.0.

To obtain a unified magnitude (i.e. MW), conversion relationships are developed between moment magnitude and other magnitude scales, which are reported in the available catalogues. The catalogue is processed for the removal of dependent events using a declustering algorithm from Gardner and Knopoff (1974), Uhrhammer (1986), Reasenberg (1985) and Gruenthal (per. comm.). Finally, seismicity parameters for the potential seismic sources in Pakistan are obtained.

2 Compilation of data

In the seismic hazard assessment of any area, the first step is to prepare a uniform catalogue that consists of historical and instrumental events.

The region under investigation in this study encompasses a quadrangle bounded by the geographical limits 40°–83° E and 20°–40° N. Prehistorical and historical earthquakes that have occurred in and around Pakistan are compiled from the published literature (e.g. Oldham 1883; Quittmeyer and Jacob 1979; Bilham 1999; Ambraseys 2000; Ambraseys and Bilham 2003a; Ambraseys and Douglas 2004; Bilham and Ambraseys 2005; Bilham et al. 2007; Heidarzadeh et al. 2008; Ambraseys and Bilham 2009; Martin and Szeliga 2010).

The instrumental databanks considered for compilation include the following: the International Seismological Centre (ISC), South Asian Catalog (SACAT), National Earthquake Information Center (NEIC), National Geophysical Data Center (NGDC), World Data Centre (WDCse), India Meteorological Department (IMD) and local networks such as the Pakistan Meteorological Department (PMD), Micro Seismic Studies Program (MSSP), seismic stations of Mangla and Tarbela dams and Water and Power Development Authority (WAPDA) (Fig. 1).

Fig. 1
figure 1

Pie chart of the sources contributing to the compilation of the earthquake catalogue (historical is the above figure and instrumental is the below figure)

The ISC catalogue contains 25,870 earthquake events in the study region and covers a period from 1918 to 2016. The ISC can be considered the most comprehensive catalogue based on the results of careful and systematic historical investigations. However, the ISC databank alone is not sufficient for a uniform catalogue, as some earthquake events in the region may have been missed in the databank.

Since several sources are used for the earthquake catalogue compilation, the presence of a single event multiple times is possible. Because of this, the priority of earthquake reporting source is set, which is shown in Fig. 2. Tables 1 and 2 list all sources used for data extraction.

Fig. 2
figure 2

Priority order of the historical (above) and instrumental (below) sources used for earthquake catalogue compilation

Table 1 List of sources for the historical and early instrumental catalogue (25 AD–1964)
Table 2 List of sources for the instrumental catalogue (1965–2016)

3 Homogenization

To prepare a uniform catalogue, earthquake events reported at different magnitude scales need to be homogenized to a single scale. In this study, the moment magnitude scale is selected as the representative scale of the catalogue. In this catalogue, earthquake events are reported in mb, MS, MW, ML, Modified Mercalli Intensity (MMI), MN and MD magnitude scales. A regression analysis is carried out between the available pairs of moment magnitude and other magnitude scales to develop relationships, as well as to be used for conversion to the moment magnitude scale.

Some historical earthquake events reported in MMI are converted to MS using Eq. (1) of Ambraseys and Melville (1982).

$$ {M}_{\mathrm{S}}=0.77\times {I}_{\mathrm{O}}-0.07 $$
(1)

Surface wave magnitudes are mostly reported by the NEIC and ISC databanks. Globally, a bilinear trend was observed by Scordilis (2006) between the MW and MS magnitude scales, which differentiated low- and high-level magnitudes of 6.2 > MS ≥ 6.2.

In this study, deviation of MS corresponding to MW is observed at an MS value of 6.0 (Fig. 3). Bilinear relationships [Eqs. (2) and (3)] are established and used to convert MS to MW. The relationships are derived from 762 paired events of MS and MW present in the catalogue.

$$ {\displaystyle \begin{array}{l}{M}_{\mathrm{W}}=0.58\times {M}_{\mathrm{S}}+2.46\\ {}\mathrm{for}\kern1em 3.5\le {M}_{\mathrm{S}}\le 6.0\end{array}} $$
(2)
$$ {\displaystyle \begin{array}{l}{M}_{\mathrm{W}}=0.94\times {M}_{\mathrm{S}}+0.36\\ {}\mathrm{for}\kern1em 6.1<{M}_{\mathrm{S}}\le 8.2\end{array}} $$
(3)
Fig. 3
figure 3

Relationships developed between mb → MW and MS → MW

Earthquake events reported in body wave magnitude scales are converted to moment magnitude using Eq. (4), which is derived from 286 paired events reported in both mb and MW

$$ {\displaystyle \begin{array}{l}{M}_{\mathrm{W}}=0.93\times {m}_{\mathrm{b}}+0.45\\ {}\mathrm{for}\;4.0\le {m}_{\mathrm{b}}\le 6.2\end{array}} $$
(4)

Figure 3 shows the linear distribution of mb and MW up to an mb value of 6.2. The trend lines of relationships of surface and body waves are compared (Table 3, Fig. 3) to those of Scordilis (2006), Zare et al. (2014) and Rafi et al. (2012).

Table 3 Comparison of magnitude error with Zare et al. (2014) and Scordilis (2006) and conversions from mb to MW and from MS to MW

For ML-type magnitudes, due to a lack of a relationship between paired events, a relation could not be developed between ML and MW. Therefore, Eq. (5) from Zare et al. (2014) between 2271 paired records of MW and ML is used to convert the ML scale events.

$$ {\displaystyle \begin{array}{l}{M}_{\mathrm{W}}=1.01\times {M}_{\mathrm{L}}-0.05\\ {}\mathrm{for}\;4.0\le {M}_{\mathrm{L}}\le 8.3\end{array}} $$
(5)

The relationship for duration magnitude (MD) and local magnitude (MN) (Nuttli 1973; Rezapour 2005) was also not able to be developed due to absence of paired events. There are 22 events reported in MD and 355 in MN. The relations [Eqs (6) and (7)] of Kaviris et al. (2008) are adopted in this study to convert MD to MW, and Eq. (8) of Karimiparidari et al. (2013) is used for MN conversion to MW.

$$ {\displaystyle \begin{array}{l}{M}_{\mathrm{W}}=0.5\times {M}_{\mathrm{D}}\\ {}\mathrm{for}\;{M}_{\mathrm{D}}<3.0\end{array}} $$
(6)
$$ {\displaystyle \begin{array}{l}{M}_{\mathrm{W}}=0.6+{M}_{\mathrm{D}}\\ {}\mathrm{for}\;3.0\le {M}_{\mathrm{D}}\end{array}} $$
(7)
$$ {\displaystyle \begin{array}{l}{M}_{\mathrm{W}}=0.739\times {M}_{\mathrm{N}}+1.409\\ {}\mathrm{for}\;3.5\le {M}_{\mathrm{N}}\le 6.3.\end{array}} $$
(8)

4 Data processing

To construct the catalogue, the magnitude is entered in a priority order of MW, mb, MS, ML, IO, MN and MD. The major data reporting eras are shown in Figs. 2 and 4 with the reporting events. Events with zero magnitudes are excluded from the catalogue. Additionally, duplicate events occurring on the same date, hour and minute within an epicentral distance of 30 km are manually removed.

Fig. 4
figure 4

Temporal distributions of the earthquakes in the catalogue

After the homogenization, the catalogue consists of 36,563 events (Fig. 5). This catalogue contains events in moment magnitude (4.0–8.3) from the year 25 AD to 2016.

Fig. 5
figure 5

Distribution of focal depths of events in the catalogue

Based on the focal depths of earthquakes, the catalogue is divided into deep and shallow earthquakes (Figs. 6 and 7). Figure 8 shows historical and instrumental earthquakes of magnitude > 6.5, which are described in the Appendix.

Fig. 6
figure 6

Earthquake (focal depth ≤ 50 km) spatial distribution

Fig. 7
figure 7

Earthquake (focal depth > 50 km) spatial distribution

Fig. 8
figure 8

Earthquake (6.5) spatial distribution

5 Declustering

Earthquake seismicity (space-time correlation) is generally exhibited by foreshock and aftershock events; therefore, statistical modelling is necessary to identify the independent occurrence of the main shocks. Space-time windowing techniques are normally used for this purpose (e.g. Uhrhammer 1986; Knopoff et al. 1982; Gardner and Knopoff 1974; Reasenberg 1985).

In this work, earthquake events are declustered using four algorithms from Gardner and Knopoff (1974), Gruenthal (pers. comm.), Uhrhammer (1986) and Reasenberg (1985) in Z-Map (Wiemer 2001). Each algorithm considers different time and distance ranges for declustering. An approximation of window sizes according to Gardner and Knopoff (1974), Gruenthal (pers. comm.) and Uhrhammer (1986) is shown in Table 4. The default standard parameter values of Reasenberg’s algorithm are given in Table 5.

Table 4 An approximation of the window sizes according to Gardner and Knopoff (1974), Gruenthal (pers. comm.) and Uhrhammer (1986)
Table 5 Default standard parameters of Reasenberg’s algorithm

The declustered catalogue using the Gardner and Knopoff (1974), Gruenthal (pers. comm.), Uhrhammer (1986) and Reasenberg (1985) algorithms contains 8579, 5344, 18,754 and 31,856 events, respectively (Table 6). The declustered catalogue using the Gardner and Knopoff (1974) algorithm is selected for computation of hazard value parameters.

Table 6 Clustered and declustered event results from the four algorithms

6 Magnitude uncertainties and data completeness

In the study region, prehistorical records (prior to 1900) are somewhat insignificant. The NGDC database has listed prehistorical earthquakes but suffers from data inconsistencies (Dunbar et al. 1992). Quittmeyer and Jacob (1979) and Martin and Szeliga (2010) presented a catalogue based on the data of macroseismic intensity for events occurring as early as 1636 in Pakistan and surrounding regions. The data is completed for larger magnitudes (> 8.0) and for larger periods (1800) (Szeliga et al. 2010). In their study, higher uncertainty associated with the magnitude and location of an earthquake is estimated using macroseismic intensity data. The historical events (1900–1964) are compiled by consulting several relevant online publications that report earthquakes in magnitude scales of mb, MS and MW (Tables 1 and 2), e.g. Lee et al. (1976), Chandra (1977), Bapat et al. (1983), Dunbar et al. (1992), Bilham (1995, 1999), Rao (2000), Ambraseys (2000), Rajendran and Rajendran (2001), Ambraseys and Jackson (2003), Ambraseys and Bilham (2003b), Ambraseys and Douglas (2004), Jaiswal and Sinha (2004), Bilham et al. (2005), Bilham and Ambraseys (2005), Okal and Synolakis (2008) and Amateur Seismic Centre (2009).

In the Afghanistan region, Ambraseys and Bilham (2003a) have also projected MS values for the historical record, which is based on an apparent intensity of destruction.

The occurrence of some historical earthquakes does not have adequate evidence (e.g. Szeliga et al. 2010; Bapat et al. 1983; Heidarzadeh et al. 2008). In the Makran region, unknown (magnitude/intensity) historical earthquakes are reported by Heidarzadeh et al. (2008) during 326 BC, 1008, 1483, 1668, 1765 and 1851.

For the compilation of main shocks in the instrumental data (1964–2016), the distribution of prominent errors indicates 0.18 units for mb entries and 0.07 units for MS (Table 3). The homogenous earthquake catalogue of Pakistan in the MW scale and the description of the sources are attached to this manuscript as supplementary material.

7 Magnitude of completeness

Determination of the magnitude of completeness (MC) is an important parameter for studying seismic hazards. The MC values reported for Pakistan along with potential seismic sources are shown in Fig. 9. Minimum and maximum magnitudes of completeness observed in the region are MC 4.0 for source 4 and MC 5.3 for source 5 (Table 7). The completion magnitude in Hindu Kush, Islamabad, Peshawar, western Makran and south of the Karachi region is observed to be MC 4.4 and MC 5.5 in the Punjab Plain, Gwadar and Quetta regions (Fig. 9). The completion magnitude over time from 1975 to 2016 for Pakistan is shown in Fig. 10.

Fig. 9
figure 9

The MC values reported for Pakistan along with the potential seismic sources

Table 7 Seismicity parameters for 20 seismic sources obtained using the maximum likelihood method of Aki (1965)
Fig. 10
figure 10

Complete magnitudes over time for Pakistan

8 Seismicity parameters

The study region (Pakistan) is divided into 20 major seismic sources (shallow and deep) based on seismicity data and regional tectonics (Figs. 11 and 12). The deep source delineation is taken from Waseem et al. (2018). For these seismic sources, the b value is estimated using the maximum likelihood method proposed by Aki (1965). This method is based on a theoretical consideration that gives an estimate of b value (Eq. (9)) with a modified (Shi and Bolt 1982) standard deviation error δb (Eq. (10)).

$$ b=\frac{\log_{10}e}{M-{M}_0} $$
(9)
$$ \delta b=2.3{b}^2\sqrt{\frac{\sum \left({M}_i-M\right)}{n\left(n-1\right)}} $$
(10)

where M0 is the threshold; M i and M are the magnitude of the ith event and the average magnitude, respectively; and n is the earthquake number in the set.

Fig. 11
figure 11

Shallow seismic sources divided based on seismicity data for Pakistan

Fig. 12
figure 12

Deep seismic sources divided based on seismicity data for Pakistan

The computations are completed in Z-Map (Wiemer 2001). The estimated Gutenberg and Richter (1944) parameters a and b are shown in Table 7 for shallow and deep seismic sources (Fig. 13 and 14). The b value varies from 0.536 to 1.380 for all seismic sources. The maximum activity rate is observed in source 15 (i.e. 35.809) with a b value of 0.969 and a maximum magnitude (MW) of 7.5.

Fig. 13
figure 13figure 13

Cumulative curve with complete magnitudes for shallow seismic sources. Seismicity parameters, i.e. b values, are estimated using the maximum likelihood method of Aki (1965). Blank circles represent cumulative data, and triangles show non-cumulative data

Fig. 14
figure 14

Cumulative curve with complete magnitudes for deep seismic sources. Seismicity parameters, i.e. b values, are estimated using the maximum likelihood method of Aki (1965). Blank circles represent cumulative data, and triangles show non-cumulative data

9 Discussion and conclusions

A homogenized earthquake catalogue is compiled and presented for Pakistan, which is a very useful tool for carrying out seismic hazard assessment studies. To compile the earthquake catalogue, all available sources including international online data reporting agencies, local reporting networks and individual catalogues have been consulted. The compiled catalogue is homogenized in terms of moment magnitude and reports 36,563 events with a magnitude range (MW) of 4.0 to 8.3, which is bounded by the geographical limits 40–83° N and 20–40° E. Indigenous relationships are developed between mb, MS and MW and used for the homogenization. The catalogue is processed for completeness and removal of dependent events for regional seismic hazard assessment studies. The declustering (i.e. removal of dependent events) is performed following Gardner and Knopoff (1974), Uhrhammer (1986), Reasenberg (1985) and Gruenthal (per. comm.) algorithms from Z-Map (Wiemer 2001). These declustering algorithms confirms the existance of epistemic uncertainty to be considered in seismic hazard analysis for Pakistan. The declustered catalogue based on these algorithms is further processed to compute parameters of the Gutenberg and Richter (1944) relationship for 20 potential seismic sources (deep and shallow) in Pakistan. The minimum completion magnitude (Fig. 9) (MC) of 4.4 is observed in the western Makran and Hindu Kush regions.

For shallow seismic sources, the activity rate varies from 0.376 to 35.809 in comparison to deep seismic sources that vary from 2.032 to 16.569. Shallow source 4 is interpreted as the least active seismic region with an activity rate of 0.376 compared to the other seismic sources. In this source, 15 earthquakes (maximum magnitude (MW) is 6.4) are reported.

The capital of Pakistan, Islamabad, lies within shallow source 18 (Fig. 12) and deep source 8 (Fig. 12). In source 18, the maximum magnitude (MW) of 6.5 is observed with an activity rate of 2.409 and a b value of 0.797. In source 8, the maximum magnitude (MW) of 7.4 is observed with an activity rate of 6.886 and a b value of 0.733. This leads to the conclusion that in the Islamabad region, shallow earthquakes contribute more compared to deep earthquakes. Conversely, in the Hindu Kush region, deep earthquakes (source 16 of Fig. 12) added more to the activity rate compared to shallow earthquakes (source 1 of Fig. 11) and contributed more to the seismic hazard.

In the Gwadar and western Makran regions, a deep earthquake of MW 7.5 is observed in source 20 (Fig. 12), but the activity rate is still 7.8% higher due to shallow earthquakes.