1 Introduction

Earthquakes are one of the natural hazards that have devastating effects on human life and property. Earthquakes have occurred across the globe, and the frequency of these earthquakes has been increasing annually, which causes a major impact on the economy of the nation. Notable major earthquakes across the world, such as the Iran earthquake of Richter magnitude 6.6 in 2003, caused fatalities of around 26,000 people. This is because of the northward movement of the Arabian plate against the Eurasian plate (Abolghasemi et al. 2006; Motamedi et al. 2012). The list of major earthquakes across the globe as well as Peninsular India (PI) have been illustrated in table 1.

Table 1 List of major earthquakes across the globe and Peninsular India (PI).
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PI has been considered a seismically stable shield region that can generate low seismicity (Bansal and Gupta 1998; Cisternas 2009). In the past decades, PI has experienced devastating earthquakes as listed in table 1 and caused many fatalities. According to the Bureau of Indian Standards IS 1893-I-(2016), these catastrophic events have changed the long-held perspective of Peninsular India’s (PI) low-order seismicity and changed the seismic zonation from low to moderate seismic prone areas. Due to these catastrophic events, it is important to assess the earthquakes either by deterministic or probabilistic approach. By considering a single magnitude and distance pair, the hazard has been estimated deterministically, but the uncertainty in the source, size, and distance has been accounted for by a probabilistic approach (Cornell 1968; Kramer 1996). The Monte Carlo simulation techniques account for the uncertainty in the earthquake magnitude and distance guides to a better result (Musson 2000). Pailoplee et al. (2009) evaluated the seismic hazard in terms of Peak Ground Acceleration (PGA) as 2–3 g for the Thailand region using both deterministic and probabilistic approaches. The maximum spectral acceleration \(\left({S}_{a}\right)\) at a 5 Hz frequency reaches up to 150 cm/s2 for the Switzerland region while evaluating the hazard in a probabilistic manner (Wiemer et al. 2009). The Design Basis Earthquake (DBE) for Yemen has been found in the range of 0.2–0.3 g and <0.05 g for Western and Eastern Yemen, respectively, corresponding to a 10% PoE in 50 yr (Mohindra et al. 2012). A new fault-based source of the PSHA approach leads to a better result rather than consideration of previous instrumental data and some areal sources PSHA approach in the Malawi region (Williams et al. 2023). Several PSHA works were carried out for the entire India and found that the PGA values were higher in the northern region, whereas it is lower in the southern region and PI (Basu and Nigam 1977; Jaiswal and Sinha 2007; Nath and Thingbaijam 2012; Ashish et al. 2016; Sreejaya et al. 2022). The contour maps of surface level Peak Horizontal Acceleration (PHA) have been drawn for PI using a slope map derived from Digital Elevation Model (DEM) data for 10 and 2% PoE (Sitharam et al. 2015). As an earthquake analyst, one should choose wisely both the Ground Motion Prediction Equations (GMPE’s) and the suitable weights used in the logic-tree approach to account for aleatory and temporal uncertainties (Basu and Nigam 1977; Kulkarni et al. 1984; Sabetta et al. 2005; Roshan and Basu 2010; Anbazhagan et al. 2019). Using the stochastic seismological model, Raghu Kanth and Iyengar (2007) generated a GMPE for PI and compared the analyzed results with strong earthquakes and it is widely used in recent studies. The probabilistic and deterministic approaches led to similar hazard results for the Bangalore region (Anbazhagan et al. 2009). A small increment in the PGA values w.r.t. codal provisions needs much more attention for the design of structures and preparation of hazard vulnerability maps for South India (Vipin et al. 2009). A more accurate ground motion model is essential for Tamil Nadu to evaluate the seismic hazard for various return periods (Menon et al. 2010). Panza et al. (2011) clearly distinguished the hazard and risk and carried out Seismic Hazard Analysis (SHA) in a scientific manner which is helpful for developing countries. Most of the western and north-western parts of Chennai were exposed to moderate hazards, and the remaining areas were exposed to low hazards using the weighted-average method in the GIS overlay (Ganapathy 2011). The seismic hazard for the Kakrapar nuclear power plant in Gujarat has shown a PGA value ranging from 0.05 to 0.2 g, which is slightly less when compared to the PGA values of the seismic zonation map (Mohanty and Verma 2013). Using sub-surface rupture phenomena, Anbazhagan et al. (2014) estimated the rock-level PGA for the Coimbatore region corresponds to different return periods and located the most probable locations of future earthquakes. Mohanty et al. (2015) addressed the hazard assessment using two first-order Markov models for northeast India. Singh et al. (2015) carried out PSHA for Warangal city using a single seismogenic source zone and determined that the spectral values were larger for longer periods. As a result of DSHA, Elayaraja et al. (2015) determined that the most potential sources for the Nilgiris are Moyar and Bhavani shears. For a maximum potential magnitude of \({m}_{\text{max}}\) of 6.80, the probable PGA at the bedrock level was found to be 0.156 g. A combined risk assessment of PSHA and Land-Use (LU) Hazard mapping has been evaluated for Mangalore, India (Ramkrishnan et al. 2019) which states that the city exposed to a PGA ranging from 0.0498 to 0.1087 g and 0.0466 to 0.0496 g for 2 and 10% PoE, respectively. The SHA has been evaluated for some parts of the Indo-Gangetic plains and obtained a PGA value of 0.062 and 0.1033 g for 475 and 2475-yr return periods, respectively (Keshri et al. 2020). A detailed seismicity estimation for Warangal in Peninsular India, Khan et al. (2020), shows a PGA value of 0.069 and 0.131 g for 475 and 2475-yr return periods, respectively. The seismic hazard has been evaluated for northeast India, and it shows that the Itanagar region has higher PGA values of 10 and 2% PoE than any other region in the vicinity of the study area (Borah and Kumar 2023).

An earthquake magnitude of 5.6 shook Indonesia in November 2022, causing a fatality of 268 people and injuring more than 100 people. This is because the focus of the earthquake is shallow, which is <10 km, and occurred in the vicinity of Jakarta, the capital of Indonesia, having densely occupied buildings that could not withstand this earthquake. In terms of magnitude scale, the city will be exposed to moderate damages, but the shallow focus of these earthquakes (<25 km) caused severe damage to the structures and led to more fatalities (Mandal et al. 2000; Dattatrayam and Suresh 2004; Elayaraja et al. 2015). It is notably important that Coimbatore city also more densely occupied and lacks earthquake-resistant structures. The city will be exposed to severe vulnerability if an earthquake happens in the future. In this present investigation, PSHA has been performed for Coimbatore city in order to develop hazard maps w.r.t. 10 and 2% PoE corresponding to 475 and 2475 yr return periods, respectively.

2 Framework of the study

This section describes the PSHA framework that has been carried out for the Coimbatore corporation area. The detailed steps are described in figure 1.

Figure 1
figure 1

The framework of PSHA.

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3 Study area and its tectonic setting

Coimbatore city municipal corporation area located in the western part of Tamil Nadu state, India, has been chosen as the study area for carrying out the PSHA framework. The headquarters of the Coimbatore district is the Coimbatore city with latitude 11.0168°N and longitude 76.9558°E. It is located at 411 m above Mean Sea Level (MSL). Coimbatore is the third-largest city in the state and is known as the ‘Manchester of South India’. According to the census of India 2021, the city population increased by about 15% as compared to the population in 2011. The city is famous for the manufacture of textiles which led to the textile boom in the early 1990s and has a mixture of more than 25,000 small, medium, and large size industries are present to manufacture different goods. The city is well-known for many educational institutions, and hi-tech software IT parks and is known to be an educational hub of South India. Perhaps most of the buildings within the boundary lack earthquake-resistant structures and need some attention to resist future earthquakes, if any. This study deals with the area that was exposed to more vulnerability and brings some attention to the design engineers and planners. Figure 2 depicts the study area of the present research work.

Figure 2
figure 2

Study area.

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According to the Indian Standard Code IS 1893-I-(2016), Coimbatore is located in Seismic Zone III. The Coimbatore earthquake, which occurred on February 8, 1900, had a maximum intensity scale of VII in the epicentral region and a focal depth of 70 km, with a magnitude of 6.0 assigned to it (SEISAT 2000). This event caused severe damage and destruction to buildings and houses (Basu 1964). Many tectonic faults and shear zones are present in and around the Coimbatore region with a radius of 500 km, which is the main focus of our study and evaluation of seismic hazards. There are 41 tectonic faults and four tectonic shear zones (https://bhukosh.gsi.gov.in) identified within the 500 km radius and which is shown in figure 3. In the vicinity of the study area, the Cauvery fault possesses a larger weak zone of about 348 km and has an epicentral distance of 8 km from Coimbatore city. It is considered a major source of the earthquake impact and similarly, the Periyar fault, Bhavani–Kanumudi fault, Tiruppur fault, and shear zones of Moyar and Bhavani shear zones are shown in figure 3.

Figure 3
figure 3

Tectonic faults and shear zones around the Coimbatore region.

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4 Earthquake catalogue

The earthquake catalogue was compiled from works of literature, primarily for South India by Sitharam and Kolathayar (2018). The earthquake catalogue has also been retrieved from various recognized agencies like the International Seismological Centre (ISC) (http://www.isc.ac.uk/isc-ehb/search/catalogue/), India Meteorological Department (IMD) (https://mausam.imd.gov.in/), National Earthquake Information Centre (NEIC) (https://seismo.gov.in/MIS/riseq/Earthquake/archive), SEISAT (https://data.gov.in/keywords/seisat), USGS (https://earthquake.usgs.gov/earthquakes/search/) and Gauribidanur Seismic Array (GSA). The earthquake catalogue has been prepared for a 500 km radius in and around Coimbatore city with latitude and longitude of 11.01680°N and 76.95580°E, respectively. A compiled earthquake catalogue of 457 events since 1806 AD is shown in figure 4(a), with various magnitude scales like \({m}_{b}\) and \({M}_{S}\) has been homogenized into a uniform magnitude scale of moment magnitude \({M}_{w}\) using the following equation (1) to equation (3) given by Scordilis (2006) and NDMA (2010).

Figure 4
figure 4

Moment magnitude catalogue (a) before declustering and (b) after declustering.

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$${M}_{w}=0.67{M}_{S}+2.07,\text{ for }\left(3.0\le {M}_{S}\le 6.1\right)$$
(1)
$${M}_{w}=0.99{M}_{S}+0.08,\text{ for }\left(6.2\le {M}_{S}\le 8.2\right)$$
(2)
$${M}_{w}=0.85{m}_{b}+1.03,\text{ for }\left(3.5\le {m}_{b}\le 6.2\right).$$
(3)

4.1 Declustering of earthquake catalogue

The earthquake events that were collected from NEIC, ISC, IRIS, etc., have a repetition of events, and they have been neglected with the help of comparing time, distance from the epicenter, and magnitude. For the design of structures, the earthquake events of \({M}_{w}\) < 3.0 have been considered minor events and neglected from the earthquake catalogue events (Ornthammarath et al. 2008). The earthquake catalogue comprising of foreshocks, aftershocks, and mainshocks events has been identified and declustered using the algorithm of Gardner and Knopoff (1974) and Uhrhammer (1991). The declustering process was done in Z-MAP Software (version 7.1) Wiemer (2001), which is in date, time, and magnitude format. Finally, the declustered earthquake catalogue of about 381 events has been digitalized in ArcGIS and shown in figure 4(b). After declustering, the faults map and magnitude catalogue map were combined to create a seismotectonic map of the research area within a 500 km radius. This map was digitalized in ArcGIS and is depicted in figure 5.

Figure 5
figure 5

Seismotectonic map of the Coimbatore region.

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4.2 Completeness analysis of earthquake catalogue

4.2.1 Visual Cumulative (CUVI) method

The smaller earthquake events occur frequently whereas the larger events occur rarely within the collected timespan. The Visual Cumulative method (CUVI), which was introduced by Tinti and Mulargia (1985), and Stepp’s method (Stepp 1974) have both been used for the completeness analysis. In the CUVI method, the collected earthquake events after declustering have been grouped incrementally with a common interval of 0.5 as 3.0–3.49, 3.5–3.99, 4.0–4.49, 4.5–4.99, 5.0–5.49, 5.5–5.99 and ≥6.0, respectively. A graph plot between the cumulative earthquake events was taken on the horizontal axis, while the time period was taken on the vertical axis. The corresponding year after which cumulative earthquake events should possess a linear relationship with the time has to be considered complete and has been used for further analysis. Therefore, smaller earthquake events should be complete for a finite period, whereas larger events like ≥5.0 should be considered complete for the entire period. The period of completeness by the CUVI method for the magnitude range 3.5–3.99 has been shown in figure 6 and for the remaining magnitude is shown in Supplementary figure S1.

Figure 6
figure 6

Completeness analysis using CUVI method for Mw = 3.5 to 3.99.

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4.2.2 Stepp’s method

In Stepp’s method (Stepp 1974), the number of events that occurred within the magnitude range has been taken into consideration for a magnitude bin size of 0.5, a subsequent time interval of 10 yr, and an annual rate of exceedance for the corresponding time-space has been calculated. A common time interval of 10 yr has been chosen as bin size from the latest year to the earliest year, such as 2008–2017, 1998–2007, 1988–1997, 1978–1987, and up to 1798–1807. Finally, a plot between the time and the standard deviation is shown in figure 7. The earthquake events follow Poisson’s distribution for estimating the variance (Khan and Kalyan Kumar 2018). When the slope of the linear line changes, the period is considered to be complete, which is commonly said to be over the last \(n\) years. Table 2 depicts the period of completeness analyzed by using CUVI and Stepp’s method for different magnitude ranges from 3.0 to 6.0.

Figure 7
figure 7

Analysis of completeness using Stepp’s method.

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Table 2 Period of completeness by Visual Cumulative (CUVI) and Stepp’s method.
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5 Evaluation of seismicity parameters

The most important phase in the evaluation of seismic hazards is the determination of seismicity parameters. It can be found with the help of the linear recurrence relationship given by Gutenberg and Richter (1956), which has been shown in equation (4), which assumes that the earthquake events were exponentially distributed.

$$\text{log}{\lambda }_{m}=a-bm,$$
(4)

where a represents the average annual number of earthquakes with a magnitude, m ≥ 0, b represents the relative likelihood of large and small earthquakes, and \({\lambda }_{m}\) represents the total number of earthquake events with a magnitude of m (Gutenberg and Richter 1956). The b parameter was more sensitive when evaluating the seismic hazard. Figure 8 illustrates the Guttenberg–Richter recurrence relationship for the areal source. Figure 8 shows that the values for a and b are 3.76 and 0.86, respectively. This indicates that relatively low seismicity is expected in the study region during the hazard (Tsapanos 1990). The b values have been compared with the various works of literature, which have been shown in table 3, and imply that the Coimbatore region was prone to smaller magnitude earthquakes rather than larger events (Bilim 2019).

Figure 8
figure 8

Guttenberg–Richter recurrence relationship for the areal source.

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Table 3 Comparison of b-values with various works of literature.
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The exponential distribution of the G–R relationship has been modified and accounts for maximum magnitude and hence, bounded Guttenberg–Richter relationship law (Mcguire and Arabasz 1985) enters into equation (4) as given by equation (5).

$${\lambda }_{m}=\mu \frac{{\text{exp}}\left(-\beta \left(m-{m}_{\text{min}}\right)\right)-{\text{exp}}\left(-\beta \left({m}_{\text{max}}-{m}_{\text{min}}\right)\right)}{1-{\text{exp}}\left(-\beta \left({m}_{\text{max}}-{m}_{\text{min}}\right)\right)}$$
(5)

where µ = exp(α – β*mmin), α = 2.303 × a; β = 2.303 × b, mmin = minimum magnitude and mmax = maximum magnitude, respectively.

5.1 Evaluation of potential maximum magnitude \(\left({m}_{u}\right)\)

The determination of the maximum magnitude \(\left({m}_{\text{max}}\right)\) is more important in evaluating the safe design of structures. The evaluation of maximum magnitude \(\left({m}_{\text{max}}\right)\) will be of immense use to seismologists, disaster management agencies, etc. In this method, the maximum magnitude observed in the earthquake catalogue in the vicinity of the study area has been given in equation (6) as

$${m}_{u}=\text{max}\left\{\begin{aligned}& {\text{Maximum\, observed\, magnitude}},\, \left({m}_{\text{obs}}^{\text{max}}\right)\\ & {\text{Maximum\, observed\, magnitude}}\,+0.5, \left({m}_{\text{obs}}^{\text{max}}+0.5\right) \\ & {\text{Considering\, rupture\, characteristics \,by \,Anbazhagan}} \,et\, al.\, \left(2015\right).\end{aligned}\right.$$
(6)

The evaluation of the potential maximum magnitude \(\left({m}_{u}\right)\), determined by Anbazhagan et al. (2015) which, accounts for the regional rupture characteristics of the region. This method has less standard error when compared to other methods of maximum magnitude estimation. The tectonic faults in the study region have been divided into three different bins based on each fault length (km) to estimate the worst-case percentage fault rupture (PFR) which is shown in table 4. The ratio of PFR for the worst-case scenario (WS) to the maximum PFR of each bin is greater than unity for all the three cases. The ratio of PFR to the total fault length (TFL) is unique for the particular region, which represents the regional rupture characteristics of the particular region and the corresponding study area (Huded and Dash 2022). Table 5 represents the worst-case RLD for each fault and estimated \({m}_{u}\) varies from 6.1 to 6.7. Figure 9 shows the plot between the PFR and the TFL for the study area.

Table 4 Regional rupture characteristics of three different bins of various fault lengths.
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Table 5 Estimated \({{m}}_{{u}}\) and worst-case RLD for each fault of the study area.
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Figure 9
figure 9

Plot between the PFR and the TFL for the study area.

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5.2 Fault level recurrence

The recurrence relationship for the seismic areal source zone has been estimated using equation (4), and it is also important to study the fault-level recurrence of all 45 faults, which is used in this study (NDMA 2010). The Geological Survey of India (GSI) has compiled linear seismic sources from the web (https://bhukosh.gsi.gov.in) in the vicinity of the study region for the entire India. It is critical to distinguish between the activity rates of several seismic source zones. The crucial step is to plot a frequency–magnitude relationship for each unique source. It is extremely difficult to predict the seismicity characteristics for particular faults using equation (4) due to a lack of sufficient earthquake data (Jaiswal and Sinha 2006). An alternative method is to determine the b-value by measuring the slip rate of the fault (Thaker et al. 2012). No slip values have been available for those considered areas. It is difficult to evaluate the recurrence relationship for individual faults due to a lack of information on fault characteristics. Furthermore, earthquakes in PI are associated with poor surface expressions of faults, making reliable estimation of slip rates difficult (Rajendran and Rajendran 2003; Raghu Kanth and Iyengar 2006). Hence, an approach suggested by Raghu Kanth and Iyengar (2006) based on a heuristic basis invoking the principle of conservation of seismic activity is adopted in this study. Vipin et al. (2009) and Anbazhagan et al. (2009) used this approach for the corresponding regions of PI and Bangalore. According to the theory of conservation of seismic activity by Raghu Kanth and Iyengar (2006), the seismicity rate of individual faults must be equal to the overall seismicity of that region (i.e., \({N}_{\left({m}_{0}\right)}\) = \(\sum {N}_{i\left({m}_{0}\right)}\)), where \({N}_{i}\) stands for the annual frequency of earthquakes (\({M}_{w}\) ≥ 3.0) on the \({i}{\text{th}}\) source in the region (\(i=\rm{1, 2, 3,} \dots .).\)

Based on the distribution of seismic events associated with each specific fault, a weighting factor \({\eta }_{i}\) is used, which is shown in equation (7).

$${\eta }_{i}=\frac{\text{Number of earthquake events associated with that source}}{\text{Total number of earthquake events in the region}}$$
(7)

and where µi is a different weighting factor shown in equation (8), which represents the proportion of each fault’s length (\({L}_{i}\)) to the overall length of all the faults (∑Li).

$${\mu }_{i}=\frac{{L}_{i}}{\sum {L}_{i}}.$$
(8)

The estimated recurrence relation for the corresponding ith fault is then estimated as the average of two weighting factors, which is depicted in equation (9).

$${N}_{{i(m}_{0})}=0.5\left({\eta }_{i}+{\mu }_{i}\right){N}_{\left({m}_{0}\right)}.$$
(9)

For the seismic hazard estimation, \({m}_{0}\) has been fixed as 3.0 for all the seismic sources, because less than a magnitude of 3.0, cannot cause significant damage to the structures. The notation \({L}_{i}\) represents the length of the respective \({i}{\text{th}}\) fault, whereas the \(\sum {L}_{i}\) represents the summation of the length of all faults present in that particular zone. The value of \({N}_{{i(m}_{0})}\) represents the a-value of a particular \({i}{\text{th}}\) fault, and the b-value has been fixed as constant, which is equal to the regional b-values estimated from the recurrence relationship (equation 4). Detailed weightage factors for the corresponding 45 linear/fault sources are shown in table 6. The fault level recurrence for the linear and areal seismic sources using the bounded Guttenberg–Richter relationship is depicted in figure 10(a and b). From figure 10, it is inferred that the annual probability of exceedance will be in the range of 0.008 to 0.009 for the areal sources as well as linear (fault) sources.

Table 6 Weightage factors for the linear/fault sources in fault level recurrence.
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Figure 10
figure 10

Magnitude–frequency relationship (a) linear (fault) sources and (b) areal sources.

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6 Ground motions prediction equation (GMPE)

The GMPE depends on various factors like source-to-site distance, types of fault, magnitude, propagation path, source characteristics, etc. (Dujardin et al. 2016). The GMPE, which has been chosen for the appropriate location, relates to the moment magnitude \(\left({M}_{w}\right)\), epicentral distances, and fault type to the estimated values of PGA and spectral acceleration \(\left({S}_{a}\right)\) (Douglas 2003). The first and most important step is to select the appropriate GMPE for the relevant study region because the chosen GMPE has a significant influence on the outcomes of the seismic hazard analysis. There is no ground motion predictive equation/attenuation models developed for the Coimbatore region (Anbazhagan et al. 2014). Anbazhagan et al. (2014) evaluated the best suitable GMPE equations for the Coimbatore region by efficacy test (log-likelihood (LLH)) analysis and identified NDMA (2010) as one of the best-suited GMPE equation for the Coimbatore region. Anbazhagan et al. (2009, 2014) and Menon et al. (2010) have carried out PSHA and evaluated the ground motion parameters for the region of Bangalore, Coimbatore, and entire Southern India, respectively, using the GMPE available for PI. The description of GMPEs is depicted in table 7 and the corresponding equations are shown in table 8. These GMPEs have been used by Vipin et al. (2009) and Menon et al. (2010) for the hazard estimation of the entire South India. In this study, the seismic hazard analysis was conducted using three GMPEs, namely, Raghu Kanth and Iyengar (2007), NDMA (2010), and Anbazhagan et al. (2013). Raghu Kanth and Iyengar (2007) and NDMA (2010) GMPEs have addressed the attenuation characteristics of Southern Peninsular India, and so the study area, which is located in that specified region, has adopted these equations. Anbazhagan et al. (2013) GMPE has been applied to any region-specific but more suitable to the Himalayan region and, therefore, adopted a lower weightage of 0.2 in the logic-tree approach. The NDMA (2010) GMPE is applicable for India and accounts for uncertainty by considering 32 areal sources in which the coefficients for the PI have been adopted for the study area with more weightage than the other two GMPEs. To compute the seismic hazard analysis, a hybrid GMPE (Sulastri et al. 2021) composed of three attenuation equations like Raghu Kanth and Iyengar (2007), NDMA (2010), and Anbazhagan et al. (2013) having a weightage of 0.3, 0.5, and 0.2, respectively, has been used. Instead of a single GMPE, the mean or median curve of a hybrid GMPE shows a better representation of the hazard (Sulastri et al. 2021).

Table 7 Description of GMPE.
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Table 8 Equations of GMPE.
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6.1 Logic tree approach

The uncertainties involved in PSHA computations were broadly classified as aleatory uncertainty and epistemic uncertainty. The epistemic uncertainty arises due to various parameters like insufficient knowledge about the earthquake events, whereas the aleatory uncertainty arises due to randomness in earthquake occurrence, size of the earthquake, and the magnitude of earthquake events (Ordaz and Arroyo 2016). To minimize the epistemic uncertainty, additional data, and suitable weightage will be assigned to the different input models. The uncertainties involved in the recurrence models and maximum magnitude have to be incorporated into the PSHA computations for better results. The epistemic uncertainty can be minimized using the logic tree approach by assigning appropriate weightage factors to the corresponding attenuation models (Kulkarni et al. 1984; Roshan and Basu 2010; Vipin and Sitharam 2013). Several nodes and branches constitute a logic tree. Each branch of the logic tree represents an individual recurrence model, each with a unique attenuation relation and a predetermined weightage. The sum of all probabilities at the branch end must be equal to unity. In this study, a logic tree composed of linear/fault and areal sources having equal weightage of 0.5 with three potential maximum magnitudes such as the maximum observed magnitude \(\left({m}_{\text{max}}^{\text{obs}}\right)\), maximum observed magnitude +0.5\(\left({m}_{\text{max}}^{\text{obs}}+0.5\right)\), and maximum magnitude estimation by considering regional rupture characteristics (Anbazhagan et al. 2015) with weightage of 0.2, 0.3, and 0.5, respectively. The potential maximum magnitude estimation \(\left({m}_{u}\right)\) by Anbazhagan et al. (2015) has assigned more weightage because it has less standard deviation than the other two methods of maximum magnitude estimation. A hybrid GMPE (Sulastri et al. 2021) composed of Raghu Kanth and Iyengar (2007), NDMA (2010), and Anbazhagan et al. (2013) attenuation relations with weightage of 0.3, 0.5 and 0.2, respectively. The NDMA (2010) attenuation equation was developed for India which accounts for source uncertainty and so the study area has adopted more weightage when compared to the other two attenuation equations. A total of 18 branches with various weightage for the logic tree approach which was shown in figure 11 and the corresponding weights were shown in the parentheses.

Figure 11
figure 11

Logic tree approach.

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7 Probabilistic seismic hazard analysis (PSHA)

The uncertainties due to hypocentral distance and moment magnitude \(\left({M}_{w}\right)\) have to be addressed while evaluating the seismic hazards. The overall hazard curve for a particular site \(s\) has to be obtained by equation (10). It is noted that the overall hazard curve for the entire region is the total of all the hazard curves based on all the sources within that specific location obtained by equation (11) (Kramer 1996; Surve et al. 2021). 

$${\lambda }_{i,s}={N}_{i}\sum_{{m}_{i}=3}^{{m}_{\text{max}}}\sum_{{r}_{j}={r}_{0}}^{{r}_{\text{max}}}P\left(Y>{y}^{*}|{m}_{i},{r}_{j}\right)\times{\left[{PDF}_{ms}\right]}_{m={m}_{i}}\times{\left[{PDF}_{rs}\right]}_{r={r}_{j}}$$
(10)
$${\lambda }_{s}=\sum_{i=1}^{i}{N}_{i}\sum_{{m}_{i}=3}^{{m}_{\text{max}}}\sum_{{r}_{j}={r}_{0}}^{{r}_{\text{max}}}P\left(Y>{y}^{*}|{m}_{i},{r}_{j}\right)\times[{{PDF}_{ms}]}_{m={m}_{i}}\times[{{PDF}_{rs}]}_{r={r}_{j}}.$$
(11)

7.1 Magnitude uncertainty [PDF]ms

The maximum probable magnitude \(\left({m}_{\text{max}}\right)\) for every fault has been estimated as given in section 5.1. There is a possibility that the different sizes of earthquake events have been generated by a single seismic source. A source can generate more earthquake events of smaller sizes rather than larger sizes of earthquake events (Kramer 1996). There is no possibility that a seismic source can generate an earthquake having a size of more than the maximum probable magnitude \(\left({m}_{\text{max}}\right)\) (Joshi and Sharma 2008). In general, a particular fault can generate an earthquake event having a size ranging from \(\left({m}_{\text{min}}\right)\) to \(\left({m}_{\text{max}}\right)\). For a particular fault, the variation of frequency of seismic events corresponds to the magnitude evaluated by the probability density function of magnitude uncertainty \({\left[PDF\right]}_{\text{ms}}\). In this research, the truncated exponential recurrence model (Kramer 1996; Iyengar and Ghosh 2004) has been used. The recurrence model is given by the following equation (12) as,

$${PDF}_{\text{ms}}=\frac{\beta {e}^{-\beta (m-{m}_{\text{min}})}}{1-{e}^{-\beta ({m}_{\text{max}}-{m}_{\text{min}})}},$$
(12)

where β = 2.303 × b and mmin ≤ m ≤ mmax.

This equation has been used to calculate the probability density function of magnitude uncertainty \({\left[PDF\right]}_{\text{ms}}\) for all faults in that area. Figure 12 depicts the \({\left[PDF\right]}_{\text{ms}}\) of the Cauvery fault having a moment magnitude ranging from 3.0 to 6.8.

Figure 12
figure 12

PDFms of magnitude uncertainty for the Cauvery fault.

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7.2 Hypocentral distance uncertainty [PDF]rs

The estimate of seismic risks for the specific site of interest mainly depends on the source-to-site distance. It was considered that the seismic occurrences had an equal chance of happening everywhere inside the specific source zone. Then, hypocentral distance is said to be a random variable that corresponds to the rupture point. Thus, the resulting probability density function for the hypocentral uncertainty has been given by the following equation (13) (Charles Scawthorn 1977; Kramer 1996).

$${PDF}_{\text{rs}}=\frac{r}{{L}_{i}\sqrt{{r}^{2}-{r}_{\text{min}}^{2}}},$$
(13)

where rmin is the minimum hypocentral distance from the source of interest.

For all seismic sources, this equation has been utilized to assess the probability density function of hypocentral uncertainty \({\left[PDF\right]}_{\text{rs}}\). The Cauvery fault’s \({\left[PDF\right]}_{\text{rs}}\) are depicted in figure 13 with hypocentral distances ranging from 0 to 500 km. The estimation of hazards using the open-source software R-CRISIS 2015 version 20.3 (http://www.r-crisis.com) (Singh et al. 2015; Khan et al. 2020) has been carried out.

Figure 13
figure 13

PDFrs of hypocentral distance uncertainty for the Cauvery fault.

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The Classical Cornell technique (Cornell 1968) was used to carry out the complete PSHA in this study. The study area was consistently divided into grids that were 0.0005° × 0.0005° in size, covering the whole of Coimbatore city within the suggested grid points. The seismic parameter has been assessed at the center of each grid point that covers the full study region for the bed-rock condition (Vs > 1500 m/s). A hybrid GMPE (Sulastri et al. 2021) composed of Raghu Kanth and Iyengar (2007), Anbazhagan et al. (2013), and NDMA (2010) equation has been used to evaluate the hazard analysis. The hazard has been evaluated using all branches of the logic tree approach with appropriate pre-defined weightage for each grid point. As a result, the hazard curves corresponding to 72, 224, 475, 975, and 2475 yr return periods, respectively, have been obtained using RCRISIS 2015 software version 20.3. The output will be in the form of the PoE of a particular intensity, which has been incorporated in ArcGIS 10.5 Desktop to prepare the hazard contour maps in terms of gravity (g) for the various return periods. The return period corresponds to a 475-yr return period known to be a Design Basis Earthquake (DBE) and similarly, a 2475-yr return period is said to be a Maximum Credible Earthquake (MCE) considered for the design of structures (Eurocode 2005).

8 Results and discussions

8.1 Seismic hazard maps

The entire PSHA computations for Coimbatore city have been evaluated by incorporating the uncertainties with equal weightage using the classical Cornell approach (Cornell 1968) and the logic tree approach. By using these approaches, hazard maps were created as contour maps with the help of ArcGIS 10.5 Desktop, which are illustrated in figures 14, 15, 16, 17. These hazard contour maps were expressed as the spatial variation of PGA and PSA in terms of ‘g’ with structural periods of T = 0.1, 0.5, and 1.0 sec for 10 and 2% PoE which corresponds to 475 and 2475 yr return period, respectively. From figures 14–17, it was inferred that the northern part of the study region was exposed to more bed-rock acceleration, whereas the southern part of the study region was exposed to low bed-rock acceleration. The obtained results of PGA and PSA with structural periods of T = 0.1, 0.5, and 1.00 sec, which have been compared with the results of Menon et al. (2010) hold good and match well with the results of the present study. Results are compared with Menon et al. (2010) depicted in table 9 for a 10 and 2% PoE, which correspond to 475 and 2475 yr of the return period, respectively. The PGA values from this research study slightly exceed the values presented by Menon et al. (2010) and IS 1893-I-(2016), implying that there is a need for consideration of the seismic forces to be incorporated for the careful design of structures.

Figure 14
figure 14

Spatial variation of hazard maps using Cornell approach for 10% probability of exceedance, which corresponds to 475 yr return period (a) PGA contours, (b) PSA, T = 0.10 sec, (c) PSA, T = 0.50 sec and (d) PSA, T = 1.00 sec.

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Figure 15
figure 15

Spatial variation of hazard maps using Cornell approach for 2% probability of exceedance which corresponds to 2475 yr return period (a) PGA contours, (b) PSA, T = 0.10 sec, (c) PSA, T = 0.50 sec and (d) PSA, T =1.00 sec.

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Figure 16
figure 16

Spatial variation of hazard maps using logic tree approach for 10% probability of exceedance, which corresponds to 475 yr return period (a) PGA contours, (b) PSA, T = 0.10 sec, (c) PSA, T = 0.50 sec and (d) PSA, T = 1.00 sec.

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Figure 17
figure 17

Spatial variation of hazard maps using logic tree approach for 2% probability of exceedance, which corresponds to 2475 yr return period (a) PGA contours, (b) PSA, T = 0.10 sec, (c) PSA, T = 0.50 sec and (d) PSA, T = 1.00 sec.

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Table 9 Comparison of PGA and PSA values T = 0.1, 0.5, and 1 sec with Menon et al. (2010) for the Coimbatore region.
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8.2 Uniform hazard response spectra (UHRS)

The response spectra for the structures match the design PGA level over the full frequency range. The response spectra are used to evaluate the structures when they are subjected to dynamic loading. For the examination of structures, design response spectra have been extracted from seismic hazard curves for the same probability of exceedance across the full frequency range (Raghu Kanth and Iyengar 2006). Such response spectra were said to be Uniform Hazard Response Spectra (UHRS). For rock stratum or stiff soil, UHRS has been evaluated for a particular site within the Coimbatore city with latitude and longitude of 11.089°N and 76.941°E, respectively, for the 10 and 2% PoE, which corresponds to 475 and 2475 yr return period, respectively. The plot of UHRS with structural periods ranging from 0 to 2 sec has been shown in figure 18. The obtained spectral acceleration \(\left({S}_{a}\right)\) values were slightly higher than the IS seismic code values IS 1893-I-(2016). The comparison of results with IS 1893-I-(2016) for the structural periods, T = 0.1, 0.5, and 1.00 sec have been reported in table 10. From table 10, it is inferred that at low periods the PGA values of the research area surpassed the IS 1893-I-(2016) codal values while the opposite trend has been observed for longer periods.

Figure 18
figure 18

Uniform Hazard Response Spectra (UHRS) for 10 and 2% probability of exceedance (PoE), which corresponds to 475 and 2475 yr return period.

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Table 10 Comparison of spectral acceleration (Sa) values with IS 1893-I-(2016).
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8.3 Deaggregation analysis

The deaggregation analysis has been carried out to identify the predominant hazard at a particular distance for a particular moment magnitude (Peláez Montilla et al. 2002). It describes ‘where the hazard comes from’ (Kramer 1996; Peláez Montilla et al. 2002). Due to consideration of areal sources and the uncertainties involved in the distance and magnitude, the deaggregation analysis helps us to identify the particular moment magnitude and epicentral distance that contributes to the hazard. The deaggregation analysis has been depicted in the 3D chart, in which the x-axis represents the moment magnitude \(\left({M}_{w}\right)\), the y-axis represents the epicentral distance (km), and the z-axis represents the exceedance probability. The deaggregation analysis was examined in the present study for a 10 and 2% PoE, corresponding to 475 and 2475 yr return periods, respectively, as depicted in figure 19. It was inferred that the predominant hazard would be at an epicentral distance of about 25 km, having a moment magnitude \(\left({M}_{w}\right)\) of 5.24 for the 10% PoE, which corresponds to 475 yr return period. Similarly, for the 2% PoE which corresponds to the 2475-yr return period, the predominant hazard would be at an epicentral distance of about 25 km for a moment magnitude \(\left({M}_{w}\right)\) of 6.07. From the analysis, it has been clear that the contribution of hazard has been at a shorter distance, which is less than about 100 km in both cases, and hazards with minimum PoE exist for longer distances. These findings imply that the seismic waves impact the structures in the vicinity of a 100 km radius, and after, the seismic waves will attenuate for a larger distance.

Figure 19
figure 19

Deaggregation analysis (a) for 10% probability of exceedance corresponds to a 475-yr return period and (b) for 2% probability of exceedance corresponds to a 2475-yr return period.

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9 Conclusions

The following conclusions have been drawn from the current study:

  1. 1.

    Using Gardner and Knopoff (1974) and later modified by Uhrhammer (1991) declustering algorithm, an earthquake catalogue of 381 independent events has been evaluated for completeness analysis using the Visual Cumulative (Tinti and Mulargia 1985) and Stepp’s (Stepp 1974) method.

  2. 2.

    The seismicity parameter (b-value) has been evaluated as 0.86 for the present study using the Guttenberg and Richter recurrence relationship.

  3. 3.

    A hybrid GMPE (Sulastri et al. 2021) composed of Raghu Kanth and Iyengar (2007), Anbazhagan et al. (2013), and NDMA (2010) attenuation relationship has been employed to evaluate the Peak Ground Acceleration (PGA) for the bed-rock condition. To account for the epistemic uncertainty, the logic tree approach has been incorporated into this present study.

  4. 4.

    Using the Cornell approach (Cornell 1968), the PGA values were obtained as 0.107 and 0.2258 g, whereas, using the logic tree approach, the obtained PGA values as 0.108 and 0.226 g, which correspond to 475 and 2475 yr return periods, respectively. It was concluded from the seismic hazard maps that the southern part of the study region was subjected to low bed-rock acceleration while the northern part of the study region was exposed to more bed-rock acceleration.

  5. 5.

    From the Uniform Hazard Response Spectra (UHRS), the spectral acceleration (Sa/g) values have been evaluated, and they are slightly higher than the IS 1893-I-(2016) values. The hazard maps have been disaggregated to find out the predominant hazard. As a result, the hazard within a 100 km radius has been a controlling scenario from the analysis.

The goal of the current study is to assess the ground motion parameters and create hazard vulnerability maps, which will be useful for planners and design engineers in learning about the seismicity of the region. This study guides and promotes the design of earthquake-resistant structures in the earthquake susceptibility region. The obtained PGA corresponds to the bedrock condition and the effect of local soil conditions is not incorporated in this study. The PGA values at the ground/foundation level may vary slightly depending upon the amplification/de-amplification effects of the local site. Based on the analysis of a few bore-log data collected, the Southern region of Coimbatore city has a low Standard Penetration Test (SPT) N-values which implies a slight amplification of ground motions is possible. It is recommended to update the seismicity information periodically to perform the hazard analysis.