Seismic hazard across Bulgaria and neighbouring areas: regional and site-specific maximum credible magnitudes and earthquake perceptibility

A probabilistic seismic hazard assessment is developed here using maximum credible earthquake magnitude statistics and earthquake perceptibility hazard. Earthquake perceptibility hazard is defined as the probability a site perceives ground shaking equal to or greater than a selected ground motion level X, resulting from an earthquake of magnitude M, and develops estimates for the most perceptible earthquake magnitude, M _P(max). Realistic and usable maximum magnitude statistics are obtained from both whole process and part process statistical recurrence models. These approaches are extended to develop relationships between perceptible earthquake magnitude hazard and maximum magnitude recurrence models that are governed by asymptotic and finite return period properties, respectively. Integrated perceptibility curves illustrating the probability of a specific level of perceptible ground motion due to all earthquakes over the magnitude range extending from ?∞ to a magnitude M _i are then developed from reviewing site-specific magnitude perceptibility. These lead on to achieving site-specific annual probability of exceedance hazard curves for the example cities of Sofia and Thessaloniki for both horizontal ground acceleration and ground velocity. Both the maximum credible earthquake magnitude M ₃ and the most perceptible earthquake magnitude M _P(max) are of importance to the earthquake engineer when approaching anti-seismic building design. Both forms of hazard are illustrated using contoured hazard maps for the region bounded by 39°–45°N, 19°–29°E. Patterns are observed for these magnitude hazard estimates—especially M _P(max) specific to horizontal ground acceleration and horizontal ground velocity—and compared to inferred patterns of crustal deformation across the region. The full geographic region considered is estimated to be subject to a maximum credible earthquake magnitude M ₃—estimated using cumulative seismic moment release statistics—of 7.53 M _w, calculated from the full content of the adopted earthquake catalogue, while Bulgaria’s capital, Sofia, is estimated a comparable value of 7.36 M _w. Sofia is also forecast most perceptible earthquake magnitudes for the lowest levels considered for horizontal ground acceleration of M _PA(50) = 7.20 M _w and horizontal ground velocity of M _PV(5) = 7.23 M _w for a specimen focal depth of 15 km.     

Probabilities for the occurrences of medium to large earthquakes in northeast India and adjoining region

The return periods and occurrence probabilities related to medium and large earthquakes (M _w 4.0–7.0) in four seismic zones in northeast India and adjoining region (20°–32°N and 87°–100°E) have been estimated with the help of well-known extreme value theory using three methods given by Gumbel (1958), Knopoff and Kagan (1977) and Bury (1999). In the present analysis, the return periods, the most probable maximum magnitude in a specified time period and probabilities of occurrences of earthquakes of magnitude M ≥ 4.0 have been computed using a homogeneous and complete earthquake catalogue prepared for the period between 1897 and 2007. The analysis indicates that the most probable largest annual earthquakes are close to 4.6, 5.1, 5.2, 5.5 and 5.8 in the four seismic zones, namely, the Shillong Plateau Zone, the Eastern Syntaxis Zone, the Himalayan Thrusts Zone, the Arakan-Yoma subduction zone and the whole region, respectively. The most probable largest earthquakes that may occur within different time periods have been also estimated and reported. The study reveals that the estimated mean return periods for the earthquake of magnitude M _w 6.5 are about 6–7 years, 9–10 years, 59–78 years, 72–115 years and 88–127 years in the whole region, the Arakan-Yoma subduction zone, the Himalayan Thrusts Zone, the Shillong Plateau Zone and the Eastern Syntaxis Zone, respectively. The study indicates that Arakan-Yoma subduction zone has the lowest mean return periods and high occurrence probability for the same earthquake magnitude in comparison to the other zones. The differences in the hazard parameters from zone to zone reveal the high crustal heterogeneity and seismotectonics complexity in northeast India and adjoining regions.     

A complete and homogeneous magnitude earthquake catalogue of Iraq

A complete and homogeneous magnitude earthquake catalogue spanning the period 1900 to 2010 was created. The catalogue covers the area 29° to 37.5° N and 39° to 48° E. Entries in the new earthquake catalogue were cross checked and additions made from various sources of earthquake records to ensure that repetitions are not included in this analysis. Events were considered duplicates if they had a time difference of 10 s or less and space origin difference of 0.5° or less. In a given set of duplicate events, an event, which had a magnitude and International Seismological Center source, was retained as the record of the event. The unified magnitude scale, the moment magnitude (M _w), was applied throughout the catalogue. The M _w for 18 events was reported. The M _w for other events was estimated using empirical relations between m _b, M _s, M _L, and M _w. Magnitude of completeness, M _c, was estimated using the maximum curvature. It was 4.3 M _w. Finally, a list of 213 events from 1900 to 2010 with M _w?≥?4.3 is presented. The list is considered complete for the period from 1962 to 2010.     

Tectonic structures across the East African Rift based on the source parameters of the 20 May 1990 M7.2 Sudan earthquake

Earthquakes in Kenya are common along the Kenya Rift Valley because of the slow divergent movement of the rift and hydrothermal processes in the geothermal fields. This implies slow but continuous radiation of seismic energy, which relieves stress in the subsurface rocks. On the contrary, the NW-SE trending rift/fault zones such as the Aswa-Nyangia fault zone and the Muglad-Anza-Lamu rift zone are the likely sites of major earthquakes in Kenya and the East African region. These rift/fault zones have been the sites of a number of strong earthquakes in the past such as the M _w = 7.2 southern Sudan earthquake of 20 May 1990 and aftershocks of M _w = 6.5 and 7.1 on 24 May 1990, the 1937 M _s = 6.1 earthquake north of Lake Turkana close to the Kenya-Ethiopian border, and the 1913 M _s = 6.0 Turkana earthquake, among others. Source parameters of the 20 May 1990 southern Sudan earthquake show that this earthquake consists of only one event on a fault having strike, dip, and rake of 315°, 84°, and ?3°. The fault plane is characterized by a left-lateral strike slip fault mechanism. The focal depth for this earthquake is 12.1 km, seismic moment M _o = 7.65 × 10¹⁹ Nm, and moment magnitude, M _w = 7.19 (?7.2). The fault rupture started 15 s earlier and lasted for 17 s along a fault plane having dimensions of ?60 km × 40 km. The average fault dislocation is 1.1 m, and the stress drop, ?σ, is 1.63 MPa. The distribution of historical earthquakes (M _w ≥ 5) from southern Sudan through central Kenya generally shows a NW-SE alignment of epicenters. On a local scale in Kenya, the NW–SE alignment of epicenters is characterized by earthquakes of local magnitude M _l ≤ 4.0, except the 1928 Subukia earthquake (M _s = 6.9) in central Kenya. This NW–SE alignment of epicenters is consistent with the trend of the Aswa-Nyangia Fault Zone, from southern Sudan through central Kenya and further southwards into the Indian Ocean. We therefore conclude that the NW–SE trending rift/fault zones are sites of strong earthquakes likely to pose the greatest earthquake hazard in Kenya and the East African region in general.     

Seismicity of Gujarat

Paper describes tectonics, earthquake monitoring, past and present seismicity, catalogue of earthquakes and estimated return periods of large earthquakes in Gujarat state, western India. The Gujarat region has three failed Mesozoic rifts of Kachchh, Cambay, and Narmada, with several active faults. Kachchh district of Gujarat is the only region outside Himalaya-Andaman belt that has high seismic hazard of magnitude 8 corresponding to zone V in the seismic zoning map of India. The other parts of Gujarat have seismic hazard of magnitude 6 or less. Kachchh region is considered seismically one of the most active intraplate regions of the World. It is known to have low seismicity but high hazard in view of occurrence of fewer smaller earthquakes of M????6 in a region having three devastating earthquakes that occurred during 1819 (M _w7.8), 1956 (M _w6.0) and 2001 (M _w7.7). The second in order of seismic status is Narmada rift zone that experienced a severely damaging 1970 Bharuch earthquake of M5.4 at its western end and M????6 earthquakes further east in 1927 (Son earthquake), 1938 (Satpura earthquake) and 1997 (Jabalpur earthquake). The Saurashtra Peninsula south of Kachchh has experienced seismicity of magnitude less than 6.     

Source parameters and scaling relations for small earthquakes in the Kachchh region of Gujarat,India

The scaling relationships for stress drop and corner frequency with respect to magnitude have been worked out using 159 accelerograms from 34 small earthquakes (M _w 3.3–4.9) in the Kachchh region of Gujarat. The 318 spectra of P and S waves have been analyzed for this purpose. The average ratio of P- to S-wave corner frequency is found to be 1.19 suggestive of higher corner frequency for P wave as compared to that for S wave. The seismic moments estimated from P waves, M ₀(P), range from 1.98 × 10¹⁴ N m to 1.60 × 10¹⁶ N m and those from S waves, M ₀(S), range from 1.02 × 10¹⁴ N m to 3.4 × 10¹⁶ N m with an average ratio, M ₀(P)/M ₀(S), of 1.11. The total seismic energy varies from 1.83 × 10¹⁰ J to 2.84 × 10¹³ J. The estimated stress drop values do not depend on earthquake size significantly and lie in the range 30–120 bars for most of the events. A linear regression analysis between the estimated seismic moment (M ₀) and corner frequency (f _c) gives the scaling relation M ₀ f _c ³  = 7.6 × 10¹⁶ N m/s³. The proposed scaling laws are found to be consistent with similar scaling relations obtained in other seismically active regions of the world. Such an investigation should prove useful in seismic hazard and risk-related studies of the region. The relations developed in this study may be useful for the seismic hazard studies in the region.     

Precursory seismicity rate changes prior to the large and major earthquakes along the Sagaing fault zone,Central Myanmar

In this study, the seismicity rate changes that can represent an earthquake precursor were investigated along the Sagaing Fault Zone (SFZ), Central Myanmar, using the Z value technique. After statistical improvement of the existing seismicity data (the instrumental earthquake records) by removal of the foreshocks and aftershocks and man-made seismicity changes and standardization of the reported magnitude scales, 3574 earthquake events with a M _w ≥ 4.2 reported during 1977–2015 were found to directly represent the seismotectonic activities of the SFZ. To find the characteristic parameters specifically suitable for the SFZ, seven known events of M _w ≥ 6.0 earthquakes were recognized and used for retrospective tests. As a result, utilizing the conditions of 25 fixed earthquake events considered (N) and a 2-year time window (T _w), a significantly high Z value was found to precede most of the M _w ≥ 6.0 earthquakes. Therefore, to evaluate the prospective areas of upcoming earthquakes, these conditions (N = 25 and T _w = 2) were applied with the most up-to-date seismicity data of 2010–2015. The results illustrate that the vicinity of Myitkyina and Naypyidaw (Z = 4.2–5.1) cities might be subject to strong or major earthquakes in the future.     

Spatial mapping of earthquake hazard parameters in the Hindukush–Pamir Himalaya and adjacent regions: Implication for future seismic hazard

The study deals spatial mapping of earthquake hazard parameters like annual and 100-years mode along with their 90% probability of not being exceeded (NBE) in the Hindukush–Pamir Himalaya and adjoining regions. For this purpose, we applied a straightforward and most robust method known as Gumbel’s third asymptotic distribution of extreme values (GIII). A homogeneous and complete earthquake catalogue during the period 1900–2010 with magnitude M_W ⩾ 4.0 is utilized to estimate these earthquake hazard parameters. An equal grid point mesh, of 1° longitude X 1° latitude, is chosen to produce detailed earthquake hazard maps. This performance allows analysis of the localized seismicity parameters and representation of their regional variations as contour maps. The estimated result of annual mode with 90% probability of NBE is expected to exceed the values of M_W 6.0 in the Sulaiman–Kirthar ranges of Pakistan and northwestern part of the Nepal and surroundings in the examined region. The 100-years mode with 90% probability of NBE is expected to exceed the value of M_W 8.0 in the Hindukush–Pamir Himalaya with Caucasus mountain belt, the Sulaiman–Kirthar ranges of Pakistan, northwestern part of the Nepal and surroundings, the Kangra–Himanchal Pradesh and Kashmir of India. The estimated high values of earthquake hazard parameters are mostly correlated with the main tectonic regimes of the examined region. The spatial variations of earthquake hazard parameters reveal that the examined region exhibits more complexity and has high crustal heterogeneity. The spatial maps provide a brief atlas of the earthquake hazard in the region.     

Source parameters of earthquakes in the reservoir-triggered seismic (RTS) zone of Koyna–Warna, Western India

New empirical relations are derived for source parameters of the Koyna–Warna reservoir-triggered seismic zone in Western India using spectral analysis of 38 local earthquakes in the magnitude range M _L 3.5–5.2. The data come from a seismic network operated by the CSIR-National Geophysical Research Institute, India, during March 2005 to April 2012 in this region. The source parameters viz. seismic moment, source radius, corner frequency and stress drop for the various events lie in the range of 10¹³–10¹⁶ Nm, 0.1–0.4 km, 2.9–9.4 Hz and 3–26 MPa, respectively. Linear relationships are obtained among the seismic moment (M ₀), local magnitude (M _L), moment magnitude (M _w), corner frequency (fc) and stress drop (?σ). The stress drops in the Koyna–Warna region are found to increase with magnitude as well as focal depths of earthquakes. Interestingly, accurate depths derived from moment tensor inversion of earthquake waveforms show a strong correlation with the stress drops, seemingly characteristic of the Koyna–Warna region.     

Evaluating of the earthquake hazard parameters with Bayesian method for the different seismic source regions of the North Anatolian Fault Zone

The earthquake hazard parameters and earthquake occurrence probabilities are computed for the different regions of the North Anatolia Fault Zone (NAFZ) using Bayesian method. A homogenous earthquake catalog for M _S magnitude which is equal or larger than 4.0 is used for a time period between 1900 and 2015. Only two historical earthquakes (1766, M _S = 7. 3 and 1897, M _S = 7. 0) are included in Region 2 (Marmara Region) where a large earthquake is expected in the near future since no large earthquake has been observed for the instrumental period. In order to evaluate earthquake hazard parameters for next 5, 10, 20, 50, 100 years, M _max (maximum regional magnitude), β value, λ (seismic activity or density) are computed for the different regions of NAFZ. The computed M _max values are changed between 7.11 and 7.89. While the highest magnitude value is calculated in the Region 9 related to Tokat-Erzincan, the lowest value in the Region 10 including the eastern of Erzincan. The “quantiles” of “apparent” and “true” magnitudes of future time intervals of 5, 10, 20, 50, and 100 years are calculated for confidence limits of probability levels of 50, 70 and 90 % of the 10 different seismic source regions. The region between Tokat and Erzincan has earthquake hazard level according to the determined parameters. In this region the expected maximum earthquake size is 7.8 with 90 % occurrence probability in next 100 years. While the regional M _max value of Marmara Region is computed as 7.61, expected maximum earthquake size is 7.37 with 90 % occurrence probability in next 100 years.     

Damage risk assessment of breakwaters under tsunami attack

Turkey was struck by two major events on 17 August and 12 November 1999, named Izmit (M _w = 7.4) and Düzce (M _w = 7.2) earthquakes, respectively. Rubble mound breakwaters in Izmit Bay experienced little damage, as forecasted by the new risk assessment model in which tsunami occurrence risk was included in the damage estimations. In order to determine the occurrence probability of structural damage under design conditions, including the environmental loading parameters of tsunami and storm waves, tidal range and storm surge, the Conditional Expections Monte Carlo simulation was applied in the risk assessment model developed in this study for the Esenköy Fishery Harbour, Turkey. A tsunami was not the key design parameter when compared to storm waves for the main breakwater of the harbour, however, in places with great seismic activity, the tsunami risk should be important depending on the occurrence probability and magnitude of the tsunami.     

Seismicity assessment in and around Syria based on instrumental data: application of Gumbel distributions and Gutenberg-Richter relationship

An instrumental earthquake catalog covering the time span between 1903 and 2007 and for the area bounded by 32°N–38°N and 35°E–43°E has been compiled in this research. The catalog has a magnitude of completeness (M _c ) with 3.5. Least squares and statistical probability Gumbel’s techniques with different approaches have been applied on the instrumental events in order to assess the average recurrence time periods for different earthquake magnitudes. The constants a and b of Gutenberg-Richter and the average recurrence times have been computed firstly for the study area and secondly for the central and northern parts of Dead Sea fault system. The different statistical computations using Knopoff and Kagan formalism are generally in agreement and suggest an average recurrence time of 203 years for an earthquake of magnitude 7 for the region. The occurrence of large well-documented historical earthquakes in Lebanon and western Syria, the existence of active fault segments, the absence of large earthquakes during the study period, the increasing number of the low-magnitude earthquakes, and the continued accumulation of the strain since 1900 indicate therefore the probability of an earthquake occurrence of a large magnitude. This should be permanently taken into consideration in seismic hazard assessment on the local and regional scales.     

Seismic hazard and probability assessment of Kashmir valley,northwest Himalaya,India

Seismic hazard analysis of the northwest Himalayan belt was carried out by using extreme value theory (EVT). The rate of seismicity (a value) and recurrence intervals with the given earthquake magnitude (b value) was calculated from the observed data using Gutenberg–Richter Law. The statistical evaluation of 12,125 events from 1902 to 2017 shows the increasing trend in their inter-arrival times. The frequency–magnitude relation exhibits a linear downslope trend with negative slope of 0.8277 and positive intercept of 4.6977. The empirical results showed that the annual risk probability of high magnitude earthquake M?≥?7.7 in 50 years is 88% with recurrence period of 47 years, probability of M?≤?7.5 in 50 years is 97% with recurrence period of 27 years, and probability of M?≤?6.5 in 50 years is 100% with recurrence period of 4 years. Kashmir valley, located in the NW Himalaya, encompasses a peculiar tectonic and structural setup. The patterns of the present and historical seismicity records of the valley suggest a long-term strain accumulation along NNW and SSE extensions with the decline in the seismic gap, posing a potential threat of earthquakes in the future. The Kashmir valley is characterized by the typical lithological, tectono-geomorphic, geotechnical, hydrogeological and socioeconomic settings that augment the earthquake vulnerability associated with the seismicity of the region. The cumulative impact of the various influencing parameters therefore exacerbates the seismic hazard risk of the valley to future earthquake events.     

A new procedure to best-fit earthquake magnitude probability distributions: including an example for Taiwan

Since the year 1973, more than 54,000 M _w ≥ 3.0 earthquakes have occurred around Taiwan, and their magnitude–frequency relationship was found following with the Gutenberg–Richter recurrence law with b value equal to 0.923 from the least-square calculation. However, using this b value with the McGuire–Arabasz algorithm results in some disagreement between observations and expectations in magnitude probability. This study introduces a simple approach to optimize the b value for better modeling of the magnitude probability, and its effectiveness is demonstrated in this paper. The result shows that the optimal b value can better model the observed magnitude distribution, compared with two customary methods. For example, given magnitude threshold = 5.0 and maximum magnitude = 8.0, the optimal b value of 0.835 is better than 0.923 from the least-square calculation and 0.913 from maximum likelihood estimation for simulating the earthquake’s magnitude probability distribution around Taiwan.     

Estimation of maximum magnitude (M max ): Impending large earthquakes in northeast region,India

In the present study, the cumulative seismic energy released by earthquakes (M _w ≥ 5) for a period of 1897 to 2009 is analyzed for northeast (NE) India. For this purpose, a homogenized earthquake catalogue in moment magnitude (M _w ) has been prepared. Based on the geology, tectonics and seismicity, the study region is divided into three source zones namely, 1: Arakan-Yoma Zone (AYZ), 2: Himalayan Zone (HZ) and 3: Shillong Plateau Zone (SPZ). The maximum magnitude (M _max ) for each source zone is estimated using Tsuboi’s energy blocked model. As per the energy blocked model, the supply of energy for potential earthquakes in an area is remarkably uniform with respect to time and the difference between the supply energy and cumulative energy released for a span of time, is a good indicator of energy blocked and can be utilized for the estimation of maximum magnitude (M _max ) earthquakes. The proposed process provides a more consistent model of gradual accumulation of strain and non-uniform release through large earthquakes can be applied in the assessment of seismic hazard. Energy blocked for source zone 1, zone 2 and zone 3 regions is 1.35×10¹⁷ Joules, 4.25×10¹⁷ Joules and 7.25×10¹⁷ Joules respectively and will act as a supply for potential earthquakes in due course of time. The estimated M _max for each source zone AYZ, HZ, and SPZ are 8.2, 8.6, and 8.7 respectively. M _max obtained from this model is well comparable with the results of previous workers from NE region.     

Long-term earthquake prediction in western Anatolia with the time- and magnitude-predictable model

Instrumental and historical data on mainshocks for 13 seismogenic sources in western Anatolia have been used to apply a regional time- and magnitude-predictable model. Considering the interevent time between successive mainshocks, the following two predictive relations were computed: log T _t = 0.13 M _min + 0.21 M _p ? 0.15 log M ₀ + 2.93 and M _f = 0.87 M _min ? 0.06 M _p + 0.33 log M ₀ ? 6.54. Multiple correlation coefficient and standard deviation have been computed as 0.50 and 0.29, respectively, for the first relation, and 0.65 and 0.47, respectively, for the second relation. The positive dependence of T _t on M _p and the negative dependence of M _f on M _p indicate the validity of time- and magnitude-predictable model on the area considered in this study. On the basis of these relations and using the occurrence time and magnitude of the last main shocks in each seismogenic source, the probabilities of occurrence P(Δt) of the next main shocks during the next 50 years with decade interval as well as the magnitude of the expected main shocks were determined. The highest probabilities P ₁₀ = 80 % (M _f = 6.8 and T _t = 13 years) and P ₁₀ = 32 % (M _f = 7.6 and T _t = 29 years) were estimated for the seismogenic source 11 (Golhisar-Dalaman-Rhodes) for the occurrence of a strong and a large earthquake during the future decade, respectively.     

Source mechanism and parameters of the 19 October 2012 earthquake,northern Egyptian continental margin

The 19 October 2012 earthquake (M _L = 5.1) occurred in the northern continental margin of Egypt within the Nile Cone at latitude 32.35° N and longitude 31.27° E. The quake was felt over a wide area in north Egypt and East Mediterranean countries, but no casualties have been reported. This area had experienced the large earthquake (Ms = 6.7) of 12 September 1955. The fault plane solution of the 19 October 2012 earthquake is here presented based on the digital seismograms recorded by the Egyptian National Seismological Network (ENSN) and other regional seismic stations. The analysis is carried out using the well-known techniques of first motion polarities of P-wave and the amplitude ratios of P-, SH-, and SV-waves with lower hemisphere projection. The fault plane solution based on the first P-wave onset demonstrates a left lateral strike-slip faulting mechanism, while the solution based on both P-wave polarities and amplitude ratios of P-, SH-, and SV-waves reveals a reverse fault with strike-slip component trending NW–SE to NE–SW, in conformity with the N–S compression along the Hellenic Arc convergence zone. Following the Brune’s model, the source dynamic parameters for the 19 October 2012 earthquake are estimated as corner frequency = 1.47 Hz, fault radius = 0.7 km, stress drop = 22.1 MPa, seismic moment = 2.80E + 16 Nm, and moment magnitude M _w = 4.9. These parameters may provide important quantitative information for the seismic hazard assessment studies.     

The 1905 Chamonix earthquakes: active tectonics in the Mont Blanc and Aiguilles Rouges massifs

Linking earthquakes of moderate size to known tectonic sources is a challenge for seismic hazard studies in northwestern Europe because of overall low strain rates. Here we present a combined study of macroseismic information, tectonic observations, and seismic waveform modelling to document the largest instrumentally known event in the French northern Alps, the April 29, 1905, Chamonix earthquake. The moment magnitude of this event is estimated at M_w 5.3 ± 0.3 from records in Göttingen (Germany) and Uppsala (Sweden). The event of April 29 was followed by several afterschocks and in particular a second broadly felt earthquake on August 13, 1905. Macroseismic investigations allow us to favour a location of the epicentres 5–10 km N–NE of Chamonix. Tectonic analysis shows that potentially one amongst several faults might have been activated in 1905. Among them the right lateral strike-slip fault responsible for the recent 2005 M_w = 4.4 Vallorcine earthquake and a quasi-normal fault northeast of the Aiguilles Rouges massif are the most likely candidates. Discussion of tectonic, macroseismic, and instrumental data favour the normal fault hypothesis for the 1905 Chamonix earthquake sequence.     

Bayesian probabilities of earthquake occurrences in Shanxi rift system (China)

China has a long history of earthquake records. The Shanxi rift system (SRS) is situated along the axial zone of the domal uplift of the Shanxi Highlands and is the boundary between the Ordos block and the North China Plain block. Strong earthquakes in the SRS have been recorded since the thirteenth century. In our work, we applied the Bayesian probability method using extreme value distribution of earthquake occurrences to estimate the seismic hazard in the SRS. The seismic moment, slip rate, earthquake recurrence rate, and magnitude were considered as the basic parameters for computing the Bayesian prior estimates of the seismicity. These estimates were then updated in terms of Bayes’ theorem and historical estimates of seismicity in the SRS. The probability of occurrence of $M_{\text{s}} = 5.0$ for Z1, Z2, and Z3 is less than 0.3, 0.1, and 0.6, respectively (T = 5 years). The probability of the occurrence of M  $\ge$  8.0 is small for the whole SRS. The selection of upper bound magnitude probably influences the result, and the upper bound magnitude of Z1, Z2, and Z3 may be 7.5, 7.0, and 8.5, respectively. We obtained the values of the magnitude of completeness M _c (3.2) and the Gutenberg–Richter b value before applying the Bayesian extreme value distribution of earthquake occurrences method.     

Probabilistic seismic hazard of Pakistan, Azad-Jammu and Kashmir

The seismic hazard study for Pakistan and Azad Jammu and Kashmir has been conducted by using probabilistic approach in terms of peak ground acceleration (PGA) in m/s² and also seismic hazard response spectra for different cities. A new version of Ambraseys et al. (Bull Earthq Eng 3:1–53, 2005) ground acceleration model is used, and parameterization is based on most recent updated earthquake catalogs that consisted of 14,000 events. The threshold magnitude was fixed at M _w 4.8, but seismic zones like northern Pakistan–Tajikistan, Hindukush and northern Afghanistan–Tajikistan border had M _w 5.2. The average normalized ‘a’ and ‘b’ values for all zones are 6.15 and 0.95, respectively. Seismicity of study area was modeled, and ground motion was computed for eight frequencies (0.025, 0.1, 0.2, 0.5, 1.0, 1.5, 2.0, 2.5 s) for different annual exceedance rates of 0.02, 0.01, 0.005, 0.002 and 0.001 (return periods 50, 100, 200, 500 and 1,000 years) for stiff rocks at the gridding of 0.1° × 0.1°. Seismic hazard maps based on computed PGA for 0.02, 0.01 and 0.002 annual exceedance are prepared. These maps indicate the earthquake hazard of Pakistan and surrounding areas in the form of acceleration contour lines, which are in agreement with geological and seismotectonic characteristics of the study area. The maximum seismic hazard values are found at Muzaffarabad, Gilgit and Quetta areas.