Introduction

Probabilistic seismic hazard analysis (PSHA) is a statistical methodology employed to forecast the level of seismic hazard in a particular site by incorporating data on historical seismicity and tectonic characteristics of the region. Within the framework of PSHA, the integration of various model interpretations of geological data allows for the generation of valuable approximations of hazard levels in distinct sites, facilitating the assessment of probabilities associated with earthquake occurrences. PSHA consists of two main components, which are the definition of the earthquake catalogue and the analysis of active seismic sources for a site of interest (Cornell 1968).

The main goal of PSHA is to predict the mean frequency per unit time, namely the annual rate of any intensity measures (IMs) that are exceeded for a specific site of interest in a given time interval. The probabilistic approach includes the uncertainties in the problem, which enhances the accuracy of ground motion intensity calculations. Although this incorporation of uncertainties makes the procedure more complex, it significantly improves the reliability of the calculations for engineering decision-making aimed at risk reduction instead of neglecting the uncertainty of earthquakes (Baker et al. 2021). Accordingly, the findings in terms of probabilistic hazard maps and uniform hazard spectra (UHS) for various ground shaking parameters can be applied in the formulation of building codes, risk assessment and resilience studies, in the development of emergency plans, and in the implementation of precautionary measures for earthquake insurance. PSHA is commonly carried out when the region is prone to earthquakes in order to estimate the potential ground shaking intensity and the seismic hazard. There are several examples of regions, urban areas, or critical structures in which predominantly seismic hazard assessment was conducted in the literature (Altindal et al. 2021; Anbazhagan et al. 2009; Deniz et al. 2010; Ornthammarath et al. 2011; Ram and Wang 2013; Rebez et al. 2014; Santoyo and Sawires 2023; Tsapanos et al. 2004). Among them, more recently, the study of Altindal et al. (2021) conducted research to evaluate the seismic risk in a specific subdistrict of Beyoğlu, Istanbul, consisting of six neighbourhoods. This region, known for its cultural and commercial significance, is susceptible to frequent seismic activity. The study performed PSHA to evaluate the potential risk posed by densely populated and ageing buildings, as well as the proximity to active fault lines, highlighting the notable dangers faced by this urban centre.

Anbazhagan et al. (2009), which conducted PSHA in Bengaluru, encompassed the survey of the South India region, specifically within a 350-km radius of the city. This work was motivated by the occurrence of numerous recent destructive earthquakes, despite the region's previous characterisation as predominantly aseismic and geologically stable. The primary objective of the study was to conduct a realistic evaluation of the earthquake hazard in the area.

The study of Ornthammarath et al. (2011) concentrated on the collection of probabilistic maps indicating the likelihood of seismic hazards occurring in Thailand by employing methodologies similar to those utilised in the most recent US National Seismic Hazard Maps. Thailand is situated within the geologically stable Sunda Plate, characterised as an area with minimal seismic activity. Nevertheless, due to advancements in national seismographic stations, a notable occurrence of regular small- and medium-sized earthquakes has been detected, predominantly in northern Thailand. Furthermore, the continuous seismic activity serves as a critical indicator for the general population and authorities, prompting them to revise and enhance the national probabilistic seismic hazard maps, leading to potential updates in the country's seismic design code.

Ram and Wang (2013) evaluated seismic hazard for Nepal and its surroundings utilising PSHA framework. Again, in terms of location, Nepal is considered as one of the most seismically active countries in the world because it is situated within the approximately 800-km-long central segment of the Himalayan seismic belt. The hazard maps were presented using peak ground accelerations (PGAs), which offer fundamental and significant data for the government to formulate city development plans, as well as for civil engineers to design and assess the seismic behaviour of critical engineering structures (such as bridges, buildings, hospitals, schools, dams, pipelines, powerhouses, tunnels, etc.) within Nepal.

Another PSHA study is from Santoyo and Sawires (2023) for western Mexico, focussing on PGA and spectral acceleration (SA) distribution for different site classes in the National Earthquake Hazards Reduction Program (NEHRP) (Building Seismic Safety Council-Part 1 2003). The majority of the previous studies solely relied on instrumental earthquake data and neglected historical events, as well as site-specific conditions. Considering the limitations in existing seismic design regulations and previous assessments, along with the absence of detailed seismic hazard studies for western Mexico, a new seismic hazard assessment has been developed.

On the other hand, the study of Tsapanos et al. (2004) generated a new map that provides a spatial representation of seismic hazard that aligns well with the characteristic of shallow seismic activity in the analysed region in terms of PGA because the ground motion model (GMM) utilised was developed considering only these earthquakes.

The study of Deniz et al. (2010) establishes a comprehensive study of PSHA in Izmir/Turkey. The study faced difficulties because the previous studies inconsistently reported earthquakes using different magnitude scales, and complex and interconnected fault systems are present in the region. To resolve those issues, the authors conducted several statistical analyses to establish correspondence between magnitudes on different scales and established seismic source zones by clustering earthquake epicentres.

Finally, Rebez et al. (2014) conducted PSHA on carefully chosen hydroelectric dam sites deemed critical within the southern Italy region. The fundamental objective of the study was to ensure a precise evaluation of the highest expected ground acceleration. The selection of the specific dam sites stemmed from their recognised significance and importance. Heritage sites or structures were also recognised as at risk against ground shaking since most of the old structures were poorly designed or under severe damage states. Therefore, seismic-prone zones necessitate comprehensive PSHA studies to ascertain the level of hazard that the built environment may encounter from potential seismic events, thereby ensuring the preservation of structural integrity.

The 2016 Chauk earthquake in Myanmar (Mw = 6.8) produced significant damage in numerous ancient pagodas and temples in Bagan (Shiddiqi et al. 2018). Only a few studies have been conducted to assess the seismic hazard in this region. One research conducted by Pyi Soe Thein et al. (2018) focussed on seismic microzoning in Mandalay city. The authors evaluated the average shear wave velocity of specific locations using standard penetration test (SPT) measurements and developed a probabilistic framework to generate a PGA map. Their goal was to mitigate seismic hazard in the region and aid in environmental planning. Moreover, Hlaing et al. (2018), Somsa-Ard and Pailoplee (2013), and Yang et al. (2022) conducted a PSHA on Myanmar. Their research focussed on the mainland of Myanmar and involved conducting a comprehensive PSHA. In their study, they carefully examined the spatial distribution of earthquakes, specifically classifying them into shallow, intermediate, and deep earthquake classes. Additionally, they investigated the tectonic characteristics of seismic sources, considering factors such as the formation of subduction zones, active fault sources, and the presence of shallow areas. The aim was to gain insights into the tectonic regime of the region and assess its earthquake potential.

The present study presents the PSHA framework in the Bagan region of Myanmar, employing a comprehensive approach to enhance the accuracy of input parameters. In contrast with existing works in the literature, this research presents a novel study by develo** empirical relationships for magnitude conversion in different scales, which facilitates creating a homogenised earthquake catalogue with the same magnitude scale specific to the Myanmar region. Moreover, geological seismic source models are incorporated, encompassing both area and line (fault) sources within the region, considering their associated activity rates to control uncertainties. The most suitable GMMs are selected and utilised, while local soil information is integrated to enhance the accuracy of the study. Within the given framework, the primary objective of this study is to analyse 43 temples identified in the study conducted by Miura et al. (2019), particularly focussing on four prototypes. Two seismic source models are developed, one by referring to the study of Somsa-Ard and Pailoplee (2013) and the other adapted from the work of Wang et al. (2014) with minor modifications. Instrumental and historical records are gathered from both the literature and international earthquake databases. Meanwhile, catalogue completeness is performed by the methodology proposed by Stepp (1972). In order to evaluate the levels of seismic hazard, this study employs suitable GMMs that are representative of the geological characteristics and tectonic conditions in the region while effectively capturing the intensity of past seismic events. The study presents the outcomes in the form of hazard maps, which portray diverse IMs such as PGA and SA for the period of T = 0.2 s, considering return periods of 2475, 975, and 475 years. All map plots are prepared using ArcGIS Pro (ESRI 2011), while the plots of seismic hazard curves and site-specific response spectra (RS) are developed by MATLAB (The MathWorks Inc 2022). Furthermore, site-specific RS are obtained for four masonry temples, namely Myin Pya Gu, Tha Mu Ti Hpaya, Zya Zin Hpaya, and Zhan Thi selected as case studies by the Getty Conservation Institute in the context of the Bagan Conservation Project. Finally, the hazard maps are compared against the Myanmar National Building Code (2020).

Description of study area

Myanmar, which was previously known as Burma, is a region in Mainland Southeast Asia that is highly prone to seismic activity. It is surrounded by four major tectonic plates: the Eurasian, Indian, Sunda, and Burma plates. The collision of the India–Eurasia plates has caused numerous significant earthquakes in the area in the past century. These include the May Myo earthquake in 1912 \((M_{{\text{W}}} = 8.0)\), the Swa earthquake in 1929 \((M_{{\text{W}}} = 7.0)\), the Bago earthquake in 1930 \((M_{{\text{W}}} = 7.0)\), the Phyu earthquake in 1930 \(\left( {M_{{\text{W}}} = 7.3} \right)\), and the Sagaing earthquake in 1956 \((M_{{\text{W}}} = 7.0)\) (Aung 2017) (see Fig. 1). In addition, several high-magnitude earthquakes have occurred during the instrumental era, causing significant damage to ancient pagodas and temples, such as the Bagan earthquake in 1975 \((M_{{\text{W}}} = 6.8)\) and the Chauk earthquake in 2016 \((M_{{\text{W}}} = 6.8)\).

Fig. 1
figure 1

Major historical earthquakes that happened in Myanmar, adapted from Aung (2017). The red rectangle is the study area covering the specific temples

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The country is situated within the Alpide belt, a geologically intricate region with active faults that have produced devastating earthquakes throughout history. Given this context, there is a pressing need to explore the seismic hazard levels in this area in order to gain a better understanding of the dynamic behaviour of active fault systems and the potential earthquake regime. For this scope, a wide literature review is conducted to obtain information regarding the tectonic structure of the region. In general, the seismic sources are defined based on geological, geophysical, and seismological data, including seismicity maps which show the epicentres of past earthquakes. The study of Wang et al. (2014) investigated active fault sources to understand the geological settings and tectonic activity level within the country of Myanmar. Subsequently, Somsa-Ard and Pailoplee 2013 conducted a PSHA for Myanmar as a whole, specifying potential seismic sources within the region as it is presented in Fig. 2. Additionally, Myanmar National Building Code (2020) presents a tectonic map of the country and its surrounding prepared in 2007 (see Fig. 3).

Fig. 2
figure 2

a Myanmar and its neighbouring area, presenting the fault lines (Bender 1983; Pailoplee et al. 2009; Wang et al. 2014) responsible for earthquakes in grey, along with notable earthquakes since 1912 indicated by red dots and b seismic source zones in Myanmar and the nearby region, showcasing the distribution of mainshock earthquakes with a magnitude (Mw) greater than 4.0 after undergoing the earthquake de-clustering process, represented by blue dots, from Somsa-Ard and Pailoplee (2013) (The rectangular box shows the study area herein)

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Fig. 3
figure 3

Tectonic setting of Myanmar and its adjacent region given by Myanmar National Building Code (2020) (The rectangular box shows the study area herein)

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Finally, identifying the soil types in the region is crucial for site-specific hazard studies and assessing the likelihood of damage levels. To understand the soil behaviour and its site response in the study area, the average shear wave velocity (\(Vs_{30} )\) parameter plays a considerable role in PSHA. According to the literature review, after the Chauk earthquake in 2016, the Myanmar Earthquake Community (MEC) conducted a seismic refraction survey at 16 sites in the historical area of Bagan and revealed that 50 ancient temples were damaged critically (Miura et al. 2019). Estimated \({Vs}_{30}\) information at the selected 40 sites reveals that the region’s soil characteristic is defined by soil type B according to EN 1998-1 (2004).

Methodology

The estimation of seismic hazard levels may be performed through two alternative approaches. The first approach is deterministic seismic hazard analysis (DSHA), which involves estimating the strong-motion parameters for the most severe earthquake that is deemed possible to occur at the nearest feasible distance from the site of interest. This estimation is done without incorporating the probability of the earthquake happening within a specified exposure period. The second approach is according to a probabilistic framework, in which all potential earthquake scenarios are considered along with their likelihood of occurrence (Cornell 1968; Cornell et al. 1971). Deterministic methods are often perceived as simpler and more conservative. However, this conservatism is contingent on decisions regarding factors such as the chosen scenario rupture magnitude and GM intensity measure. As Baker et al. (2021) highlighted, this sensitivity can result in non-robust outputs from the analysis. On the other hand, probabilistic methods have more complex statistical formulations and take uncertainties into account in the magnitude of an earthquake, as well as in its location and time of occurrence.

Performing PSHA allows for the estimation of ground shaking levels, expressed in specified ground motion IMs and different return periods, by determining the expected seismic hazard through a pre-established probability of exceedance. The probabilistic framework incorporates the effects of all seismic sources and potential earthquake occurrences with their randomness and uncertainties regarding earthquake magnitude, location, and source-to-site distance for a specified return period. Developed by Cornell et al. (1971), the objective of PSHA is to express the probability of exceedance of certain GM levels in each period at a selected site of interest. The main steps of PSHA are as follows: (1) forming a homogenous earthquake catalogue; (2) defining seismic sources in the study area; (3) characterising seismicity of the study area by an appropriate magnitude recurrence relationship; (4) defining local soil information on the study area; (5) estimating GM parameter by using GMMs; (6) constructing seismic hazard curves for different IMs in a site-specific interest, after selecting suitable models; (7) obtaining seismic hazard maps for different return periods in the region; and (8) develo** UHS at different sites for a specified return period. Thus, the step-by-step computation of probabilities is performed based on the regional seismic activity, seismic sources, local soil models, and suitable GMMs. The framework employed in such a study, including the fundamental steps of PSHA, is displayed in Fig. 4 and is described in detail in the following sections.

Fig. 4
figure 4

Framework of PSHA in this study

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Definition of seismicity

This section consists of three subsections that focus on different aspects related to earthquake catalogues. The first part deals with the homogenisation process, which aims to establish uniformity and consistency in earthquake catalogues. The second part discusses the methodology used for removing fore/aftershocks, known as de-clustering. This process helps in distinguishing mainshocks from fore/aftershocks. Lastly, the third section covers the completeness test (Stepp 1972), which assesses the degree to which the earthquake catalogue includes all relevant events within a given magnitude range.

Homogenisation of earthquake catalogue

As proposed by Gupta (2002), the seismicity is identified within a radius of about 300 km around Bagan, involving most of the old pagodas and temples. For this purpose, all earthquakes of historical and instrumental periods are compiled from available open sources, including Global CMT, ISC, and USGS (GCMT, n.d.; ISC, n.d.; USGS, n.d.), avoiding overlaps and removing duplicates. According to Somsa-Ard and Pailoplee (2013), based on the surveyed data, international catalogues have captured earthquake events in and around Myanmar since 1967. Therefore, a homogenous earthquake catalogue covering all earthquakes during the instrumental period between 1967 and 2022 in the study area is formed. The minimum magnitude \(M_{{\text{W}}}\) is assumed to be 4.5, as the threshold for a destructive magnitude (Bommer and Crowley 2017).

Earthquake catalogues provide different scales of magnitude for the past events. Since the reported magnitudes according to different magnitude scales can show discrepancies, a set of rules is applied to select the representative magnitude for each event. The final compiled catalogue consists of earthquakes with different magnitude scales: body wave magnitude (\(M_{{\text{b}}}\)), surface wave magnitude (\(M_{{\text{s}}}\)), and moment wave magnitude (\(M_{{\text{W}}}\)). While considering the constraints of seismic networks, \(M_{{\text{W}}}\) is selected as a reference magnitude scale for all events. In this study, to convert different magnitude scales to \(M_{{\text{W}}}\) based on the information provided by the earthquake catalogues, empirical relationships in terms of \(M_{{\text{s}}} - M_{{\text{W}}}\) and \(M_{{\text{b}}} - M_{{\text{W}}}\) are developed as follows, using the least squares method:

$$M_{{\text{W}}} = 0.04M_{{\text{s}}}^{2} + 0.02M_{{\text{s}}} + 3.30,$$
(1)
$$M_{{\text{W}}} = 0.47M_{{\text{b}}}^{2} - 4.22M_{{\text{b}}} + 14.53.$$
(2)

The distribution of the real earthquake dataset in terms of \(M_{{\text{s}}}\) and \(M_{{\text{b}}}\) with respect to \(M_{{\text{W}}}\) is shown in Fig. 5. The derived equations are also plotted with red dashed lines in the same figure. For the proposed magnitude scale models, Table 1 presents the correlation coefficient (r), and the root-mean-square error (RMSE) obtained, which indicate an acceptable fit.

Fig. 5
figure 5

Distribution of the real earthquake dataset and proposed empirical models between a Ms − Mw and b Mb − Mw. The red dashed lines show the derived empirical equations

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Table 1 Information on the r and RMSE of the proposed empirical models between different magnitude scales
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After using the derived empirical equations, the homogenised earthquake catalogue is obtained. Figure 6a shows the spatial distribution of all earthquakes in the region. In addition, the percentage of earthquakes in different magnitude classes in the region is illustrated in Fig. 6b, which indicates a gradual decrease in frequency as magnitudes increase. This distribution implies that smaller earthquakes are more prevalent while larger ones occur less frequently.

Fig. 6
figure 6

a Instrumental seismicity, starting from 1967 to 2022 in the region and b distribution of earthquakes with respect to Mw

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Earthquake de-clustering

Next, the earthquake catalogue is processed in two steps. The first step is pre-processing, which includes de-clustering analysis, i.e. the elimination of fore/aftershocks. The results of de-clustering include only the mainshocks. Within the scope of this study, the secondary event identification procedure for the seismicity data is performed based on the time and space windows of earthquake magnitudes for which the earthquakes are not independent (Deniz 2006). This method utilises space and time windows derived from the previous studies, and the dimensions of the time windows are determined by averaging values from Gardner and Knopoff (1974) and Savage and Rupp (2000) for various magnitude levels. Additionally, all earthquakes with magnitudes larger than 6.0 are treated as mainshocks. To identify foreshocks, magnitude-dependent filtering is employed using the same spatial–temporal thresholds as for aftershocks. However, it should be noted that distinguishing between fore/aftershocks is subject to some degree of uncertainty.

Table 2 presents the time and space windows of the secondary event analysis proposed by Deniz (2006). As a result of the elimination of foreshocks, a total of 689 events are specified as mainshocks from the 1771 earthquake events. Figure 7 presents all mainshocks in the study area. Then, the derived catalogue will be used in the calculation of the earthquake parameters which are necessary for PSHA.

Table 2 Dimension of space and time windows for secondary event analysis (adapted from Deniz (2006))
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Fig. 7
figure 7

Mainshocks in the study area

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Catalogue completeness

Finally, a catalogue completeness analysis is performed, as proposed in Stepp (1972). This approach either defines the completeness of a certain magnitude level above which the catalogue can be considered as complete or defines a time interval for which there is a full set of data for a predefined magnitude range. This is done by counting the number of records in the earthquake catalogue within a specified magnitude level, starting from the latest events and moving back in time. The reason for this procedure is that most of the small magnitude earthquakes were recorded recently due to a larger array of sensors.

In order to apply this approach, all events are grouped into six magnitude intervals (4.5–4.9; 5.0–5.4; 5.5–5.9; 6.0–6.4; 6.5–6.9; and larger than 7.0) as a function of time intervals. Table 3 shows the rate of earthquake occurrence in different time intervals for all earthquakes. The column \(N\) shows the total number of earthquakes within each time interval, and the column \(\lambda\) shows the number of earthquakes per year (or mean rate of occurrence). It is necessary to determine the standard deviation of the estimate of mean, \(\sigma_{\lambda }\). This allows to gain specific information regarding the occurrence rates of earthquakes and their variance. To compute \(\sigma_{\lambda }\) of each magnitude interval, the following equation is employed:

$$\sigma_{\lambda } = \sqrt {\frac{\lambda }{Time}},$$
(3)

where Time is the number of years.

Table 3 Rate of occurrence and time interval based upon all earthquakes
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The results of completeness analysis for all earthquakes are given in Table 3. The findings reveal that the events between \(M_{{\text{W}}}\) of 4.5–4.9 were complete during the past 20 years, and events between \(M_{{\text{W}}}\) of 5.0–5.4 and \(M_{{\text{W}}}\) of 5.5–5.9 were complete for the past 50 years. Events equal to or larger than \(M_{{\text{W}}}\) of 6.0 are complete data samples in the full period.

Identification of seismic sources

In general, the geographical locations of seismic sources are defined based on geological, geophysical, and seismological data. In addition, seismicity maps which show the epicentres of past earthquakes may be employed. Thus, two alternative seismic source models are proposed in the site of interest to account for the uncertainty in terms of the seismic source model. Model 1 involves area sources, while model 2 accounts for combined source models of line and potential area sources.

Overall, the primary seismic sources are categorised into their geological formation, such as subduction zones. The mainland of Myanmar includes two types of subduction zones which are the Sumatra–Andaman Interplate and Sumatra–Andaman Intraslab. Additionally, one of the major active fault settings is lying in Sagaing Fault Zone, namely Sagaing Fault, which generated various destructive earthquakes in the past. Finally, Hsenwi-Nanting Fault Zone is investigated in the literature (Pailoplee and Choowong 2013; Somsa-Ard and Pailoplee 2013). The principal subduction zones in this area are the Sumatra–Andaman Interplate, which is governed by shallow-focus earthquakes along the trench, and the Sumatra–Andaman Intraslab, which is responsible for intermediate- to deep-focus earthquakes under Myanmar's western fold belt. The remaining seismic sources, Sagaing Fault Zone and Hsenwi-Nanting Fault Zone, are characterised by a right-lateral strike-slip fault mechanism.

The area sources identified in this study are consistent with the findings of Somsa-Ard and Pailoplee (2013), with the exception of source 3 from their study. In this research, a slight adjustment to the source model proposed by Somsa-Ard and Pailoplee (2013) is suggested. This adjustment entails dividing area source 3 from their study into two distinct source zones (referred to the source 2 and source 3 in this study), as depicted in Fig. 8a. As a result, for model 1, a total of five area sources are categorised into three classifications of shallow-background area, interface, and intraplate subduction sources. These sources include sources 1 and 3: Sumatra–Andaman Interplate; source 2: Sumatra–Andaman Intraslab; source 4: Sagaing Fault Zone; and source 5: Hsenwi-Nanting Fault Zone (Pailoplee and Choowong 2013; Somsa-Ard and Pailoplee 2013).

Fig. 8
figure 8

Active tectonism in Myanmar: a Potential area sources of model 1 and b major fault lines with potential area sources of model 2 (The combined active faults are: KWf: KabaW fault; MBf: MinBya fault; LMf: LayMyo fault; YCKf: Yenangyat Chauk fault; SGf: SaGaing fault; TCf: Thahtay Chaung fault; KMf: KyaukMe fault; KYf: KyaukkYan fault; and NTf: NanTing fault)

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On the contrary, model 2 incorporates active faults suggested by Wang et al. (2014), along with potential area sources that represent designated polygons within a region where seismic activity occurs without explicitly identified seismic sources. A few modifications are made in the faults as well, including the inclusion of active faults and the removal of inactive faults segments. These modifications are in line with the tectonic setting map specified in the Myanmar National Building Code. As a result, model 2 consists of a total of fourteen-line sources and three potential area sources (see Fig. 8b).

Figure 9a presents the area sources of model 1 with the associated seismicity. The seismicity occupies not only the subduction zones but also shallow-background area sources. However, according to the earthquake catalogues, sources 4 and 5 experience shallow earthquakes and have rare seismicity within the region. The seismic sources of model 2, along with the associated seismicity (all earthquakes), are presented in Fig. 9b. Similarly, Fig. 10 shows the area sources of model 1 and line sources with the predicted potential area sources of model 2 with their associated seismicity (only mainshocks). The spatial distribution of earthquakes in the region reveals that the faults known as Kabaw, Fault 1, and Fault 2 exhibit a concentration of earthquakes falling within the magnitude range of 5.0–5.9. This pattern indicates that these faults currently experience continuous activity enabling a better understanding of their potential to generate future earthquakes.

Fig. 9
figure 9

Tectonic setting of Myanmar: a model 1 with all earthquakes and b model 2 with all earthquakes in the study area

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Fig. 10
figure 10

Tectonic setting of Myanmar: a model 1 with only mainshocks and b model 2 with only mainshocks in the study area

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Once the seismic sources with the corresponding earthquake catalogue are determined, the next step is to assess the maximum expected magnitude of each seismic source. For area sources, the maximum expected magnitude is the maximum of the historical and instrumental magnitude corresponding to that source (see Table 4). However, for line sources of model 2, the maximum expected magnitude is the maximum of the historical, instrumental records and the value coming from the relationship of Wells and Coppersmith (1994), as presented in Table 5 with the associated fault mechanism. The largest recorded seismic event \((M_{{\text{W}}} = 8.8){ }\) took place in the Sumatra–Andaman Plate, which is where area source 1 is located. Also, it is highly likely that this event was generated by the Arakan Megathrust.

Table 4 Maximum magnitude information on the seismic sources of model 1
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Table 5 Information on the seismic sources of model 2 (R: reverse; RLSS: right-lateral strike-slip; and LLSS: right-lateral strike-slip), PAS: potential area source
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Earthquake parameters

The next step is to build a magnitude-frequency relationship for each seismic source in the region. The classical PSHA applies the Gutenberg and Richter (1944) and assumes that earthquake magnitudes are exponentially distributed with respect to the total number of earthquakes in any given region and time of at least that magnitude. In the logarithmic scale, a linear relationship follows:

$$log10N\left( m \right) = a - bm,$$
(4)

where \(N\left( m \right)\) is the number of earthquakes with a magnitude larger or equal to \(m\), \(b\) is a scaling parameter, and \(a\) is a constant. Values \(a\) and \(b\) are representative seismicity parameters.

In PSHA, the lowest value of magnitude \(m_{0}\) is the level of expected intensity that may cause damage. In this study, as stated, \(m_{0}\) is assumed to be equal to 4.5. In addition, an upper limit of \(m_{1}\) is the estimation of the largest earthquake likely to occur in the region of interest. This upper limit can either be obtained from catalogues of the historical activity or estimated from empirical relationships between rupture dimensions and magnitude, particularly in the case of line sources. Due to the truncations at both lower and upper magnitude limits, the probability density function of earthquake magnitudes can be expressed as follows (Yücemen 1982):

$$f_{M} \left( m \right) = { }k\beta e^{{ - \beta \left( {m - m_{0} } \right)}} { }k = \left[ {1 - e^{{ - \beta \left( {m_{1} - m_{0} } \right)}} } \right]^{ - 1},$$
(5)

where \(\beta\) is a seismotectonic parameter that describes the frequency of large earthquakes compared to smaller ones. The parameter \(k\) is a normalising constant which adjusts the cumulative distribution function to unity at \(m = m_{1}\).

In this study, to minimise the uncertainty, instead of using the estimated value for the seismicity parameter \(\lambda\), which represents the average annual number of earthquakes with equal or higher magnitude than \(m_{0}\), the observed value is considered. On the other hand, the \(\beta\) values of each seismic source zone are evaluated from two alternative algorithms: least square regression (LSR) and maximum likelihood (MLH) approaches. The LSR approach minimises the sum of squares of the difference between the observed and estimated values, whereas the MLH method maximises the likelihood of fit of the estimated function to the observed data. In LSR approach, for the incomplete catalogue, the following formula is used for calculation of \(\beta\) value:

$$\beta = b{\text{*ln}}\left( {10} \right),$$
(6)

where b may be obtained from Eq. (4). In MLH approach, the \(\beta\) value, of the incomplete catalogue, is assessed based on the approach of Aki (1965) as follows:

$$\beta = \frac{1}{{\overline{m} - m_{{{\text{min}}}} }},$$
(7)

where \(\overline{m}\) is the average magnitude, and \(m_{\min }\) corresponds to the minimum magnitude of incomplete catalogue. Tables 6 and 7 present the results in terms of activity rates for seismic sources of models 1 and 2 for the incomplete catalogue, respectively. In the tables, the results of two alternative algorithms are shown (LSR and MLH), for all earthquakes and only mainshocks. The results reveal that the activity rate of the seismic sources is significantly affected by their associated seismicity.

Table 6 Seismicity parameters of model 1 based on LSR and MLH approaches (not corrected for complete catalogue)
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Table 7 Seismicity parameters of line sources for model 2 based on LSR and MLH approaches (not corrected for complete catalogue)
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The \(\beta\) values corresponding to the artificially completed earthquake catalogues are also calculated using the LSR and MLH methods. The main difference between the complete and incomplete catalogues is the time interval, which can be explained by the difference in the observed mean activity rate \(\lambda\). For the calculation of \(\beta\) value of the complete catalogue based on the LSR approach, Eq. (6) is employed. On the other hand, for the calculation of seismicity parameters based on MLH corresponding to the complete catalogue, the study by Kijko and Smit (2012) proposed an algorithm to account for this difference. In this case, the \(\hat{\beta }\) estimator is found by dividing an incomplete catalogue into completed sub-catalogues with different magnitude classes, since each magnitude interval has a different completeness level, as follows:

$$\hat{\beta } = \left( {\frac{{r_{1} }}{{\hat{\beta }_{1} }} + \frac{{r_{2} }}{{\hat{\beta }_{2} }} + \cdots + \frac{{r_{3} }}{{\hat{\beta }_{3} }}} \right)^{ - 1},$$
(8)

where\({ }\hat{\beta }_{i}\) is the Aki–Utsu estimator (Aki 1965). The term \(r_{i} = n_{i} /\mathop \sum \nolimits_{s}^{i} n_{i}\) where \(n\) corresponds to total number of events with magnitude equal to or greater than the level of completeness.

The study by Vermeulen and Kijko (2018) proposed a new optimisation algorithm for the formula of Aki (1965) to reduce the bias and coefficient of variance (COV) of the estimators. The iteration process of Vermeulen and Kijko (2018) is applied herein for calculation of \(\hat{\beta }\) in order to improve the results. The results for the complete catalogues for the two models corresponding to each seismic source are summarised in Tables 8 and 9.

Table 8 Seismicity parameters of the area sources of model 1 (corrected for completeness)
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Table 9 Seismicity parameters of the line sources with assumed potential area sources of model 2 (corrected for completeness)
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Local soil information

This section discusses the \(Vs_{30}\) values at the sites where the temples are located, referring to different studies in the literature. The literature proposes two alternative soil models for different sets of temples in the region. The Report on Seismic Hazard and Vulnerability Assessment for Bagan/Nyaung U Area (2019) used the topographical information along with horizontal-to-vertical spectral amplitudes to estimate the \(Vs_{30}\) of the temples in the Bagan region. In another study by Miura et al. (2019), the \(Vs_{30}\) values were estimated by inversion analysis of the microtremor horizontal-to-vertical spectral ratios through the diffuse field assumption employing the results of existing seismic refraction surveys at the site of interest.

Based on the available information in the region, \(Vs_{30}\) maps are developed using the natural neighbourhood interpolation approach. The developed \(Vs_{30}\) maps from alternative sources are plotted in Fig. 11. It is observed that Report on Seismic Hazard and Vulnerability Assessment for Bagan/Nyaung U Area (2019) describes the central and southern parts of the region mostly with softer soil conditions when compared to the study of Miura et al. (2019). According to the findings of Miura et al. (2019), the riverbanks have a softer soil condition, which is usually the case. For the sake of validation, the Vs30 map is also developed using the information provided by (Methods for Repair and Strengthening the National Monuments in Pagan, Burma, Vol.II, Geophysical and Geotechnical Investigations in Pagan Region and Determination of the Influence of Local Geotechnical Conditions on Ground Motion Modification, 1983) for 16 temples. Overall, the results from the provided reference are closer to the findings of Miura et al. (2019). For this reason, in this study, PSHA is conducted by considering the study of Miura et al. (2019) for the selected sites.

Fig. 11
figure 11

Spatial distribution of Vs30 in the site of interest according to a Report on Seismic Hazard and Vulnerability Assessment for Bagan/Nyaung U Area (2019), b Miura et al. (2019), and c Methods for Repair and Strengthening the National Monuments in Pagan, Burma, Vol.II, Geophysical and Geotechnical Investigations in Pagan Region and Determination of the Influence of Local Geotechnical Conditions on Ground Motion Modification (1983)

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Attenuation models

To perform reliable PSHA, besides knowledge of seismicity, the selection of suitable GMM is essential. The GMMs express the amplitudes of GM parameters, namely PGA, peak ground acceleration (PGV), and SA, at different periods, as a function of seismological parameters such as earthquake magnitude, soil properties, and site-to-source distance. Several region-specific or global models have been developed in the literature (Keshri and Mohanty 2023; Mohammadi et al. 2023; Yaghmaei-Sabegh et al. 2022). Among the developed models, the selection criteria depend mostly on their potential applicability to the study area where the PSHA is being conducted. Here, a literature review is performed to find the most proper GMMs for the seismic sources of the study area.

The properties of the tectonic plates in the region are crucial selection factors for GMMs. For this reason, the seismic sources of this study are classified into two seismic zones, namely Sumatra–Andaman subduction zones and shallow active zones, by considering the features of the tectonic plates in the site of interest. According to the Global Mosaic of Hazard Models from Global Earthquake Model (GEM) (Chan et al. 2017; Ornthammarath et al. 2020), GMMs by ZO06 (Zhao et al. 2006) and AB03 (Atkinson et al. 2003) are recommended for the Southeast Asia region, which includes subduction zone subdivisions. Additionally, Aung et al. (2019) study investigated the trend of different GMMs in capturing the behaviour of real events in the region. The study provided evidence that ZO06 (Zhao et al. 2006) and AB03 (Atkinson et al. 2003) are suitable for subduction zones, especially considering that ZO06 aligns more closely with the 2016 Chauk event and other earthquakes in the Myanmar region. In another study by Somsa-Ard and Pailoplee (2013), the BJF97 (Boore et al. 1997) model was used to perform PSHA in the region. This study incorporates uncertainties in the PSHA of the region by utilising three GMMs: BJF97 (Boore et al. 1997), AB03 (Atkinson et al. 2003), and ZO06 (Zhao et al. 2006), based on the referenced information.

PSHA results

Epistemic uncertainty due to the assumption of different models, including earthquake catalogues, seismic sources, seismicity parameters, and GMMs, as described in the previous sections, is captured through a logic tree framework by assigning equal weights to each model. It should be noted that weights play a crucial role in determining the most likely outcomes. This study made an equal weight assumption to control the uncertainties and furthermore simplify the analysis, as there are no available data or information to suggest that one branch is more likely than another. Therefore, the limitations and uncertainties associated with this assumption must be noted, and further investigation on a sound GMM is recommended. Figure 12 presents the logic tree algorithm. Next, PSHA is performed using the weights given in the logic tree framework.

Fig. 12
figure 12

Logic tree framework used. Red and blue values in the last branch correspond to the weights of GMMs adopted for the subduction zones and the shallow crustal earthquake zones, respectively

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Seismic hazard curves and intensity levels

This section presents hazard curves in terms of various ground motion parameters, such as PGA and SA at T = 0.2 s. The selection of these IMs is based on the fact that the seismic response of masonry structures shows a stronger correlation with PGA and a short period SA (i.e. at a period of 0.2 s). The results are plotted for selected prototypes, including ZZH, MPG, TMTH, and ZT in Fig. 13. These prototypes showcase diverse configuration structures according to the presence or absence of vertical continuity and plan symmetry that effectively captures the wide range of temples in the area. The estimated levels of ground shaking that may occur at particular sites are due to earthquake activity by considering various factors such as the location, frequency, and magnitude of the earthquake in the region. The results reveal that the annual probability of exceedance for both IMs at Temples ZZH and MPG follows a similar trend, while Temple ZT exhibits a resemblance with Temple TMTH. This observation can be attributed to their similar soil characteristics among the selected sites.

Fig. 13
figure 13

Seismic hazard curves in terms of a PGA and b SA at T = 0.2 s

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Site-specific response spectra

Subsequently, by computing the mean value of the spectral ordinates acquired from seismic source model 1 and model 2, the final form of RS for the selected temples for the return period of 475 years is obtained and shown in Fig. 14. According to the soil information at this specific site, Temple ZZH has the lowest \(Vs_{30}\) value among the temples, and therefore, the RS of this temple has higher spectral ordinates than the other prototypes.

Fig. 14
figure 14

Site-specific RS at selected prototypes for a return period of 475 years

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Seismic hazard maps

The site-specific PSHA results are combined to create a unified map representing seismic hazard for different return periods. These maps are developed for IMs, including PGA and SA at T = 0.2 s, to determine the level of hazard at a particular site for a given return period. The findings are illustrated separately for seismic source model 1, which is an area source model, and model 2, a line source model for all return periods, including 475, 975, and 2475 years. Additionally, the average results for both models are presented. The results are plotted in Figs. 15, 16, 17, 18, 19, and 20, which demonstrate the potential seismicity of the region. It is also observed that the area source model generally overestimates the hazard level in the region compared to the line source model. Overall, the overestimation of hazard in the PSHA by the area source model compared to the line source model can be attributed to the broader coverage and assumptions regarding seismic activity distribution and the specific fault-related considerations incorporated in each model. This finding has also been observed in a former study by Woessner et al. (2015), in which three seismic source models were examined for the project “Seismic Hazard Harmonization in Europe”. These models included an area source model, a kernel-smoothed, zonation-free stochastic earthquake rate model, and a fault source and background model. The findings of that study revealed that the area source model estimated a higher level of PGA compared to the other two seismic source models.

Fig. 15
figure 15

PGA spatial distribution within the city Bagan for the return period of 2475 years based on a area source model, b line source model, and c mean model

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Fig. 16
figure 16

PGA spatial distribution within the city Bagan for the return period of 975 years based on a area source model, b line source model, and c mean model

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Fig. 17
figure 17

PGA spatial distribution within the city Bagan for the return period of 475 years based on a area source model, b line source model, and c mean model

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Fig. 18
figure 18

SA (T = 0.2 s) spatial distribution within the city Bagan for the return period of 2475 years based on a area source model, (b) line source model, and c mean model

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Fig. 19
figure 19

SA (T = 0.2 s) spatial distribution within the city Bagan for the return period of 975 years based on a area source model, (b) line source model, and c mean model

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Fig. 20
figure 20

SA (T = 0.2 s) spatial distribution within the city Bagan for the return period of 475 years based on a area source model, b line source model, and c mean model

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Finally, upon examining the impact of soil effects in PSHA, a clear observation emerges that regions characterised by softer soil conditions experience a substantial influence on the hazard level. Overall, the entire region has a high seismic hazard level due to its proximity to the active fault, namely Yenangyat Chauk, which passes through the area where most of the temples and pagodas are located. In addition, this region falls into the Sumatra–Andaman subduction zone that can generate earthquakes with an \(M_{{\text{W}}}\) of 7.0–7.5.

Discussion of results and validation

A few studies have been carried out to assess seismic hazard level in Myanmar, as documented in the existing literature (Hlaing et al. 2018; Somsa-Ard and Pailoplee 2013; Yang et al. 2022). One of the PSHA studies conducted by Somsa-Ard and Pailoplee (2013) involved the development of PGA maps for different return periods, including 2475 and 475 years, with corresponding PGA ranges of 0.10–0.40 g and 0.05–0.20 g, respectively, for the mainland of Myanmar, see Fig. 21 for PGA results of the study by Somsa-Ard and Pailoplee (2013). After evaluating the outcomes of that study in the Bagan city centre, the estimated values of PGA for the return period of 2475 and 475 years are approximately 0.35 g and 0.18 g, respectively. It should be emphasised that the study of Somsa-Ard and Pailoplee (2013) was conducted in a bedrock without taking into account the effects of soil, and the PSHA results of our study are 0.25–0.36 g and 0.18–0.24 g, respectively, for the return period of 2475 years and 475 years considering the mean results for the two modes. Our study reveals a finer resolution in estimating hazard levels by considering soil effects, demonstrating larger values compared to the study of Somsa-Ard and Pailoplee (2013). Furthermore, it is worth mentioning that the results of model 2, specifically for the 475-year return period, accurately depict the hazard level of the region, ranging between 0.16 and 0.22 g in terms of PGA. This finding closely aligns with the reference study, highlighting the consistency achieved by employing similar source models in both studies.

Fig. 21
figure 21

Distribution of PGA according to PSHA results of Somsa-Ard and Pailoplee (2013) for the return periods of a 2475 years and b 475 years (The blue pin shows Bagan historical centre)

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On the other hand, the Global Seismic Hazard Assessment Program (Global Seismic Hazard Assessment Program 1992) conducted a seismic hazard analysis for the Southeast Asia region and developed the spatial distribution of PGA with a 10% probability of being exceeded in 50 years (475 years of return period) for the specified rock conditions \((Vs_{30} = 600 - 800\;{\text{m/s}})\), and a map was generated by gathering national and regional probabilistic seismic hazard models from projects, intuitions, and GEM foundation (Chan et al. 2017), and scientists (see Fig. 22). They describe the mainland of Myanmar region having a PGA range of 0.05–0.35 g, while 0.13–0.20 g for the study area of this research (Bagan centre) for the return period 475 years. In line with the previous observation, this study yields larger results, in addition to indicating higher consistency when model 2 is utilised.

Fig. 22
figure 22

Seismic hazard map in terms of PGA for the return period of 475 years of Myanmar proposed by GEM Global Mosaic of Hazard Level (Chan et al. 2017) (The blue pin shows Bagan historical centre)

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Moreover, Fig. 23 shows a seismic zone map of Myanmar prepared for a return period of 2475 years for the whole country taken from Myanmar National Building Code (2020). According to PSHA results, the PGA range within the region is 0.25–0.36 g for the return period of 2475 years (see Fig. 15c), whereas the Myanmar National Building Code describes the region that includes most of the temples in Bagan with a range of 0.20–0.30 g. As an additional comment, findings from the area source model are much closer to the hazard map of Myanmar than the results of the line source model. Figure 24 also presents the results in terms of SA (T = 0.2 s) in the Myanmar region. According to the Myanmar National Building Code, Bagan city may experience a hazard level with a range of 0.60–1.20 g. However, our study reveals a narrower range of 0.62–0.88 g for the same hazard level (see Fig. 18c). As an additional comment, the line source model in Fig. 18b displays a much closer distribution with Myanmar National Building Code (2020).

Fig. 23
figure 23

Hazard level distribution for the return period of 2475 years within the mainland of Myanmar taken by Myanmar National Building Code (2020) (The blue pin shows Bagan historical centre)

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Fig. 24
figure 24

SA (T = 0.2 s) spatial distribution for the return period of 2475 years within the mainland of Myanmar taken by Myanmar National Building Code (2020) (The rectangle detail shows Bagan historical centre)

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Noteworthily, it is crucial to acknowledge that the choice of GMM significantly influences PSHA results, leading to variations in hazard levels. Differences among the results of different PSHA studies can arise due to various factors, including the selection of GMM, definition of seismicity and seismic sources, or more generally the application of logic tree algorithms. The findings of various PSHA investigations are now extended with the present investigation, which considers the most up to date information and models.

Conclusions

The present study conducted a probabilistic seismic hazard analysis (PSHA) to develop seismic hazard maps for different return periods within the study area, specifically, the region where the Bagan/Myanmar temples are located. The seismicity between 1969 and 2022 was analysed by collecting earthquake data from available catalogues. Additionally, the development of empirical relationships to convert different magnitude scales to \(M_{{\text{W}}}\) contributed to address the discrepancies arising from various magnitude scales reported in earthquake catalogues, enhancing the accuracy of the seismic hazard assessment. Subsequently, de-clustering and secondary event identification were processed to ensure accurate PSHA calculations. The last step of the homogenisation of the earthquake catalogue was to conduct a completeness analysis proposed by Stepp (1972). Next, seismic sources were defined based on evaluating previous studies. Two seismic source models, an area source model and a line source model, were proposed for the region, enabling more robust and reliable assessments for seismic hazard analysis. As a result, the uncertainty associated with various input parameters in PSHA was managed using a logic tree algorithm.

To introduce local soil information for the related sites, two soil models (Miura et al. 2019; Seismic Hazard and Vulnerability Assesment for Bagan/Nyaung U Area 2019) from the literature were compared. Based on the developed soil maps within the study area, it is concluded that the soil dataset provided by Miura et al. (2019) offers a higher level of reliability and reflects more recent investigations in the study area. Therefore, the effects of soil conditions in PSHA were considered by utilising a soil model proposed by Miura et al. (2019).

Particular emphasis in PSHA was placed on the historical centre of Bagan, which houses a significant number of temples and pagodas. The results include seismic hazard curves, site-specific response spectra (RS), and seismic hazard maps for peak ground acceleration (PGA) and spectral acceleration (SA) at T = 0.2 s at the selected four prototype temples, namely ZZH, MPG, TMTH, and ZT. Due to the region's proximity to active faults and significant seismicity, hazard levels were estimated as 0.25–0.36 g, 0.22–0.32 g, and 0.18–0.24 g in terms of PGA for the return periods of 2475, 975, and 475 years, respectively. In addition to PGA, the hazard levels were expressed in terms of SA at the period T = 0.2 s, which were obtained as 0.62–0.88 g, 0.48–0.76 g, and 0.34-0.054 g for the return periods of 2475, 975, and 475 years, respectively. It was observed that the area source model (model 1) generally yielded higher hazard level estimates compared to the line source model (model 2). The influence of soil effects on PSHA was highlighted, particularly with respect to the significant impact of softer soil regions on hazard levels. In this study, different from the other studies, a more accurate estimation of hazard levels in the region is achieved by considering soil effects and incorporating them into the seismic hazard assessment. Furthermore, site-specific RS were presented at the selected temples for the return period of 475 years. It was observed that Temple ZZH experiences comparatively higher RS when compared to the other prototypes, which can be related to its lower \(Vs_{30}\) value.

The consistency between our study and other studies, such as the Global Seismic Hazard Assessment Program and the Myanmar National Building Code (Chan et al. 2017; Myanmar National Building Code 2020), validates the accuracy of our findings. While this study contributes to the existing literature on seismic hazard assessment in Myanmar by considering soil effects, there are inherent uncertainties involved in PSHA analyses, including the use of GMMs instead of region-specific models. It is worth noting that the PSHA herein is conducted based on the recently developed GMMs, which are more suitable for the attenuation of the regional earthquakes in the study area. Yet, it is important to perform additional research, particularly on develo** region-specific GMMs and further microtremor studies in the area.

Overall, the findings of this research, including seismic hazard curves, site-specific RS, and seismic hazard maps, have practical implications for risk mitigation studies and conservation efforts. The outcomes that were developed in this study can serve as valuable tools for assessing and managing seismic risks in the study area. By understanding the hazard levels and potential areas of vulnerability, appropriate measures can be taken to mitigate the risks posed to historic structures and ensure their preservation. Furthermore, this study contributes to enhancing our understanding of local seismicity, which is crucial for develo** effective strategies to mitigate the impacts of earthquakes in the region. This knowledge can inform decision-making processes related to urban planning, building codes, and infrastructure development, promoting safer and more resilient communities. However, it is important to acknowledge the study's limitations, particularly the need for further investigation and improvement in the light of the scarcity of research in the Bagan/Myanmar region, the utilisation of equal weights in the logic tree method due to a lack of information about model superiority, and the suggestion to create region-specific GMM to minimise errors in seismic hazard assessment caused by uncertainties.