Peak ground acceleration
(PGA) and study area (SA) distribution for the Patna district are presented
considering both the classical and zoneless approaches through a logic tree framework to capture the epistemic uncertainty. Seismicity parameters are
calculated by considering completed and mixed earthquake data. Maximum
magnitude is calculated using three methods, namely the incremental method, Kijko
method, and regional rupture characteristics approach. The best suitable ground motion prediction
equations (GMPEs)
are selected by carrying out an “efficacy test” using log likelihood. Uniform
hazard response spectra have been compared with Indian standard BIS 1893.
PGA varies from 0.38 to 0.30

Seismic hazard analysis is effective in presenting the potentially damaging
phenomenon associated with earthquake. Earthquake disaster is not only
associated with collapsing of structures due to ground shaking but also
triggers fire, liquefaction, and landslide. Thus, it is indispensable to
forecast the ground shaking level to serve the engineering needs in
mitigating the risk associated with earthquakes. In India, moderate
earthquakes (

There are two types of uncertainties associated with hazard analysis. One is
due to randomness of the nature of earthquake, wave propagation, and site
amplification, named “aleatory uncertainty”, while the other is due to incomplete
knowledge of earthquake process, named “epistemic uncertainty”. The former can
be easily reduced by integrating the distribution of ground motion about the
median (Bommer and Abrahamson, 2006) and the latter can be assessed using the logic
tree approach. Gullu and Iyisan (2016) selected the ground motion prediction
equations (GMPEs) for the logic
tree based on the weighting factors that were incorporated with a Venn
diagram of attenuation models regarding the experimenter's concern and expert's
knowledge. Epistemic uncertainty is due to improper knowledge about the
processes involved in earthquake events and algorithms used to model them.
Hence, in this study, the logic tree framework has been used to reduce the
epistemic uncertainty in the final hazard value calculation. In the absence
of the appropriate region-specific models of wave propagation, ground motion
prediction models are generally used to determine the hazard value. The
uncertainty in GMPEs can be reduced by incorporating a logic tree in the
hazard analysis study. Logic trees represent the various nodes that define
the alternative input choices and each branch is assigned a weight
factor that signifies the quantitative degree of likelihood assigned. To
quantify the epistemic uncertainty, different branches of logic tree need to
be considered, which is based on source models, regionalization of

In the present study, PSHA of Patna district (India) at the micro-level has been
prepared along with the response spectrum by reducing the epistemic
uncertainty. Patna lies at 250 km from the central seismic gap (Khattri,
1987) in the Himalayan region where huge devastation and destruction due
to the 1803, 1934 Bihar–Nepal and 2015 Nepal earthquakes were reported. Similar
to Bilham (2015), a large earthquake appears to be imminent in future due to rupturing of the main fault beneath the Himalayas because of the Nepal
2015 earthquake. Hence such studies need to be done for the cities that lie
within the vicinity of the Himalayan region and the Indo-Gangetic Basin.
Seismic sources and seismic events have been measured for a 500 km radius around
the district centre as per Anbazhagan et al. (2015a). The

Regional seismicity, geological, seismological, and seismotectonics
information of the seismic study area (SSA) have been assembled and evaluated
for a desirable radius for seismic hazard analysis. The present study area covers the longitude 84.6–85.65

Seismotectonic map of Patna SSA.

Patna district lies near the seismically active Himalayan belt and on the deep deposits of the Indo-Gangetic Basin (IGB). It is also surrounded by various active ridges such as the Monghyr–Saharsa Ridge Fault, many active tectonic features such as the Munger–Saharsa Ridge Fault, and active faults such as the East Patna Fault or West Patna Fault. These faults are acknowledged as transverse faults, and the occurrence of seismic events is due to stimulus of fluvial dynamics in the North Patna plains transverse faults (Valdiya, 1976; Dasgupta et al., 1987). According to Banghar (1991) the East Patna Fault is one of the active faults in the study area and its interaction with the Himalayan Frontal Thrust is characterized by a cluster of earthquakes. Dasgupta et al. (1993) state that all other faults between Motihari and Kishanganj cities have the same possibility of seismic hazard as they form part of a related fault system. Historic earthquakes such as 1833 Bihar, 1934 Bihar–Nepal, and 1988 Bihar–Nepal have affected Patna city as far as economic loss and loss of lives is concerned. Many other earthquakes that have occurred near the Bihar–Nepal border also prove to be devastating for Patna district. In addition, the north side of Patna is near the East and West Patna faults. The frequency of seismic events on these faults is high (Valdiya, 1976; Dasgupta et al., 1987). In addition SSA is also 250 km from the Himalayan plate boundary. These plate boundaries were the source of major historic earthquakes. Considering the above seismic aspects, Patna district can be acknowledged to be under a high seismic risk. Thus, in the present work, PSHA of Patna district has been carried out by considering all seismic sources and earthquake events by reducing epistemic uncertainty using the logic tree approach.

The earthquake data are collected from various agencies such as the National
Earthquake Information Centre (NEIC), International Seismological Centre,
Indian Meteorological Department (IMD), United States Geological Survey
(USGS), Northern California Earthquake Data Centre (NCEDC), and GSI. The
events have been selected from all the mentioned agencies. Duplicate
events have been deleted, and the magnitude has been homogenized to
moment magnitude scale. A total of 2325 events have been compiled which are
on different magnitude scales such as local magnitude, surface wave magnitude,
and body wave magnitudes. To attain uniformity, all the reported events are
converted to moment magnitude (

The most widely known Gutenberg–Richter (G–R) relationship (Gutenberg and
Richter, 1956) is usually used for the determination of

Magnitude of completeness is defined as the lowest magnitude at which
100 % of the events in a space–time volume are detected (Rydelek and Sacks,
1989; Taylor et al., 1990; Wiemer and Wyss, 2000).

Variation in magnitude of completeness (

The maximum probable earthquake magnitude has been calculated using both
deterministic and probabilistic approaches. Three methods, viz. conventional
methods of increment of 0.5 in maximum observed magnitude (

GMPEs have been selected based on the efficacy test recommended by Scherbaum et al. (2009) and Delavaud et al. (2009). There are various GMPEs available for the active crustal region and basin. Out of various GMPEs, 27 GMPEs are applicable for the present SA. The details of the efficacy test have been given in Anbazhagan et al. (2015c). Details of these GMPEs are given in Anbazhagan et al. (2015a). Similar to Anbazhagan et al. (2015a), the hypocentral distance is divided into three length bins, viz. 0–100, 100–300, and 300–500 km. The applicable GMPEs with the abbreviation used in the present study are given as Table 2. The determined PGA values are used to estimate the log-likelihood (LLH) values. Further, the data support index (DSI) given by Delavuad et al. (2012) is used to rank the best suitable GMPEs. Positive DSI values have been identified for each segment and ranked based on high to low values. Positive DSI values for the Patna earthquake are marked as bold in Table 3. It can be seen from Table 3 that the three GMPEs ANBU-13, NDMA-10, and KANO-06 can be used for up to 100 km of hypocentral distance. For a 100–300 km distance, ANBU-13, NDMA-10, KANO-06, and BOAT-08 are used and for hypocentral distance greater than 300 km NDMA-10 will be used for further hazard analysis. NDMA-10 is used for a distance more than 300 km, as it is the only available equation for the larger distances. Seismic hazard values in terms of PGA and SA can be calculated considering these equations for each seismic source. The variation in PGA with distance for the selected GMPEs is given as Fig. S1. In addition, LLH-based weight as per Delavaud et al. (2012) for selected GMPEs was also calculated. Scherbaum and Kühn (2011) showed the importance of weight treatments through the logic tree approach as probabilities instead of generic quality measures of attenuation equations, which are subsequently normalized. They also indicated the risk of independently assigning grades by different quality criteria, which could result in an apparent insensitivity to the weights. In order to provide the consistency with a probabilistic framework, they proposed assigning the weight factors in a sequential manner, which is used in the present study. The weight factors of 0.72, 0.17, and 0.11 are calculated with ANBU-13, NDMA-10, and KANO-06 at up to 100 km of hypocentral distance according to Delavaud et al. (2012). For a 100–300 km distance, KANO-06, ANBU-13, NDMA-10, and BOAT-08 with weight factors of 0.32, 0.28, 0.26, and 0.14 are calculated, and for a hypocentral distance greater than 300 km a weight factor of 1 has been associated with NDMA-10. It can be noted here that only one GMPE is surfaced with positive DSI for a distance segment of 300 to 500 km and required additional GMPEs in this range, which is important for the far-field damage scenario in the region. These GMPEs with associated weight factors were further used in probabilistic seismic hazard analysis of Patna SSA. These weight factors would be further useful in forming the logic tree to reduce the epistemic uncertainty in final hazard value. Detailed analysis of determination of LLH and weight factor corresponding to each GMPE is given in Anbazhagan et al. (2015a).

Available GMPEs with their Abbreviations considered for the seismic study area.

Segmented ranking of GMPEs for the Patna region. Positive DSI values for the Patna earthquake are marked as bold.

NA: not available.

Various researchers have delineated the seismic source for various parts of
India. Considering tectonic features and past earthquake events,
Gupta (2006) delineated the seismic sources for India. Kiran et al. (2008)
and NDMA (2010) have done the same on the basis of the seismicity
parameters. Furthermore, Nath and Thingbaijam (2011) have delineated based
on focal mechanism data from the Global Centroid Moment Tensor database.
Kolathayar and Sitharam (2012) identified and delineated India into 104
seismic zones based on similar seismicity characteristics. Vipin and
Sitharam (2013) determined the seismic sources on the peninsula considering the
seismicity parameters. In the present study, delineation of the seismic
sources has been performed based on the seismicity parameters, viz.

New seismic source zones identified for Patna based on seismicity
parameters (variation in

Seismic parameters for adopted source models (uncertainties with bootstrapping).

For spatial smoothening of the seismic source model, a grid size of

Probability of exceedance of a ground motion for a spectral period can be determined once the probability of its size, location, and level of ground shaking are identified cumulatively. Seismic hazard map for the Patna district has been developed by applying probabilistic methods, namely the classical method proposed by Cornell (1968), which was later improved by Algermissen et al. (1982), and smoothed–gridded seismicity models (Frankel, 1995).

A tool of 178 seismic sources (shown in Fig. 1 and given as Table ET1) have been used for determining the probability of occurrence of a specific magnitude, probability of hypocentral distance and probability of ground motion exceeding a specific value as per Cornell (1968). Probability of rupture to occur at different hypocentral distances has been determined as per Kiureghian and Ang (1977). The condition probability of exceedance for GMPEs was determined using a lognormal distribution as given by EM-1110 (1999). The ground motion at a site for a known probability of exceedance in a desired period has been calculated by amalgamating all the above probabilities. As a result of PSHA, the hazard curve is determined and shows the variation in PGA or SA with the frequency of exceedance of the different levels of seismic ground motion. A detailed explanation is given in Anbazhagan et al. (2015a). The deaggregation based on the principle of superposition proposed by Iyenger and Ghosh (2004) has been used. The probability of exceedance of ground motion for each seismic source has been computed by merging these uncertainties. Detailed discussion on the methodology of PSHA can be found in Anbazhagan et al. (2009).

It can be noted that in the SSA, the northwest and central parts of Patna are not
fully covered by well-identified seismic sources and many sources given in
the Fig. 1 are not well studied to prove its seismic activity. Moreover,
there are many places where the linear source has not been identified. Thus, to
overcome the limitation, a zoneless approach proposed by Frankel (1995) has
been used for developing the PSHA map for Patna SSA. This method accounts for
the spatial smoothing of historic seismicity to directly calculate the
probabilistic hazard. The annual rate of exceedance for a given ground
acceleration level is given by Eq. (2):

Four models used in the development of the PSHA map of Patna based on the zoneless approach.

Seismic hazard can be assessed more practically using a logic tree (Kulkarni
et al., 1984) as it includes the accounted for epistemic errors, components of
seismic models, and ground motion predictions (Fig. 5). For determining the
consistent model with different degrees of confidence, each branch of logic
tree is to be investigated for implementing the uncertainties in probability
models. Important consideration has been given to each branch of logic
tree by incorporating the weights for assessing the final hazard
of the Patna district. After declustering the catalogue and developing the
seismotectonic map, two models have been used with an equal weight of 50 %
for both the classical and zoneless approaches. The zoneless approach has been
further divided into the areal approach and Frankel approach of equal weight of
50 % each. For the Frankel approach, SSA has been considered for four models
(discussed above) with weight factors of 30 %, 30 %, 20 %, and 20 %
for model 1, model 2, model 3, and model 4 respectively. These weights have
been adopted based on the reliability of the source model. Larger weights
are assigned to model 1 and model 2 because they are based on more reliable
data and assumedly have better representation of seismicity of SSA. Model 3 deals
with the weak assumption that earthquakes with magnitude 3.0–7.0 are equally
probable everywhere in Patna SSA whereas there is a great uncertainty in the
data used for model 4. In addition,

Formulated logic tree used in PSHA of Patna SSA.

For determining the hazard value, a different weight has been considered with
respect to

Likewise, in classical approaches, epistemic uncertainty has been considered
and weight factors are considered as shown in Fig. 5. The PGA map of Patna
has been developed using the zoneless approach by dividing it into seven areal
zones based on seismicity parameters (Fig. 3), similar to Kolathayar and
Sitharam (2012) and Vipin and Sitharam (2013). For the development of the PSHA
map using a simplified areal zonal model, the seven zones along with the
seismic parameters (Fig. 3 and Table 4) are used. These seven areal
seismic sources are smoothed using the smoothed historic seismicity approach
recommended by Frankel (1995). For development of the seismic hazard map,
each zone is considered to be of seismic source with a constant seismicity value.
The activity rate was calculated for each zone and it was obtained by
counting the earthquakes having magnitude greater than or equal to

The hazard value for the Patna district has also been determined with the
four models proposed by Frankel (1995). Each of these four models (Fig. 4)
has a different spatial distribution of seismic activity. However, the present SSA
has five characteristic earthquakes (

It can be seen from the mean deaggregation plot that the motion for 6.0

Final seismic hazard map of Patna SSA for

The final hazard value has been developed by assigning the weight factor of
0.5 to both PGA values calculated with the classical and zoneless
approaches. In the present study the average of the hazard values from both
the methods have been considered. Hazard integration has been performed as the
SSA seismic sources are not identified fully (e.g. northwest and central
parts of Patna); hence, to overcome the limitation, the zoneless approach has
also been used for developing the PSHA map. It is necessary here to note
that the experimenters performing for the seismic hazard assessment using a
weighting factor may lead to complication in the calculations with the
inclusion of different branches. To prevent this trouble, Bommer et al. (2005) suggested avoiding using the branches having slight differences
between the options that it carries, in cases when those options result in
very similar nodes. Therefore, when selecting the weighting factors in the
logic tree in this study, the cases contrasting (or different) with each
other as much as possible have been taken into consideration. In the zoneless
approach, 0.5 weight factors were given to both PGA maps developed using areal
and Frankel (1995) approaches as explained earlier. Thus, both the hazard maps
were compiled and finally a 0.5 weight factor is given to the zoneless approach.
The final PGA variation corresponds to 2 % and 10 % probability of
exceedance in 50 years, was shown in Fig. 11a and b. In addition, SA at 0.2 and 1 s considering epistemic uncertainty has
been given as Fig. 12a, b, c, and d for 2 % and 10 % probability
of exceedance in 50 years. PGA varies from 0.37

In addition, a uniform hazard response spectrum (UHRS) has been developed considering all three approaches and compared with IS 1893 (2002). For developing UHRS, seismic hazard curves of spectral accelerations at a different spectral period for the same probability of exceedance have been developed. The UHRS at 2 % and 10 % probability of exceedance for 50 years at the centre of the district using classical and zoneless approaches, viz. Frankel and areal approaches, has been drawn and given as Fig. 13a (marked as star in Fig. 11a). Similarly, the UHRS has been developed at the northeastern part of Patna considering 2 % and 10 % probability of exceedance, shown as Fig. 13b (marked as plus in Fig. 11a). It can be seen from Fig. 13 that the hazard value at 2 % probability is more for the same return period when compared to 10 % probability of exceedance in 50 years. It has also been observed that spectral acceleration at the zero period, i.e. PGA, is less in the case of the Cornell approach when compared to the Frankel and areal approaches at the centre of the district where as it is more when compared to the northeastern part of SSA. The developed UHRS has been compared with IS 1893 (2002) and it has been observed that the SA predicted is lower at the centre of the district at 2 % and 10 % probability of exceedance in 50 years except for Frankel's approach. However, in the case of the northeastern parts of SSA, the predicted SA values are more compared to IS 1893 (2002) (Fig. 13b). Hence, UHRS should be developed based on the regional characteristics so that it could be effectively used in infrastructural development of a district.

A new seismic hazard map for the Patna district was developed considering the
earthquake events and seismic sources through the logic tree approach. Based on
past earthquake damage distribution, the seismic study area of 500 km was
arrived at and the seismotectonic map was generated. The maximum magnitude has
been estimated by considering three weighted-mean methods, i.e. incremental
method, Kijko method and regional rupture-based characteristics. From 28
applicable GMPEs, GMPEs ANBU-13, NDMA-10, and KANO-06 were selected up to 100 km epicentral distance; however ANBU-13, NDMA-10, BOAT-10, and KANO-06 were selected up to
300 km and NDMA-10 for more than 300 km. These GMPEs were ranked and weights
were found based on the log-likelihood method. A new hazard map for the Patna
district has been developed using both classical and zoneless approaches
considering different weight factor corresponding to

The earthquake data are collected from National Earthquake Information
Centre, International Seismological Centre, Indian Meteorological
Department, United State Geological Survey, and Geological Survey of India.
A software package developed by Stefan Wiemer named ZMAP has been used for
analysing the seismicity of the study area (

The supplement related to this article is available online at:

PA and KB analysed the data and developed the in-hand MATLAB code for developing the hazard map. KM, SSRM, and NSNA helped in developing the maps and writing the paper.

The authors declare that they have no conflict of interest.

The authors thank the Science and Engineering Research Board (SERB) of the Department of Science and Technology (DST), India, for funding.

Funding has been provided by the Science and Engineering Research Board (SERB) of the Department of Science and Technology (DST), India, for the project titled “Measurement of shear wave velocity at deep soil sites and site response studies”, Ref: SERB/F/162/2015-2016. This research has been also supported by the International Scientific Partnership Program (ISPP), King Saud University (grant no. ISPP#040).

This paper was edited by Maria Ana Baptista and reviewed by Hamza Gullu, Sreevalsa Kolathayar, and two anonymous referees.