The study performs a temporal probabilistic analysis of earthquakes in a seismically active region like Bangladesh. Data from the USGS earthquake catalog, spanning from May 12, 1906, to August 24, 2022, within a 500km radius of Dhaka City, was analyzed to assess earthquake hazard and probability. It revealed that the country is located in an area with a high likelihood of earthquakes, and any moderate to major tremor might trigger an enormous human catastrophe. While 75% of the earthquakes were classified as the "light" category (4-4.9 Richter Scale), 64% occurred at shallow depths, and only 5% occurred within 200 kilometers of Dhaka. Since the 1990s, the earthquake frequency has increased significantly with an incidence rate of 1.556. The findings categorized the research area as having a relatively moderate risk of earthquake hazard, with depth, frequency, magnitude, and distance scores falling into various risk categories. Probability distributions of earthquake magnitudes were estimated using the graphical analysis and goodness-of-fit criteria. Cumulative probability distributions were also determined to predict earthquake occurrences of specific magnitudes in the coming years based on recurrence time. The study indicated a strong probability of major earthquakes in the future, which poses a severe threat to the country. Assessing the susceptibility of an area to earthquakes based on factors like geology, topography, population density, building quality, and coping mechanisms is crucial, and this earthquake catalog can support disaster preparedness, specific precautions in planning, and the development of a resilient nation.
Research Article
Recent Tremors in Bangladesh Might Hint at Bigger Quakes: A Probabilistic Approach for Earthquake Prediction
https://doi.org/10.21203/rs.3.rs-3103701/v1
This work is licensed under a CC BY 4.0 License
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Seismicity of Bangladesh
Earthquake Hazard
Probability of Occurrences
Bangladesh is highly susceptible to earthquakes and is regarded as one of the most earthquake-prone countries globally due to its proximity to the plate boundaries of the Indian and Eurasian plates. Several notable earthquakes have occurred in the vicinity of Bangladesh throughout history. Considering its high population density, unplanned infrastructure, and proximity to seismically active regions in India and Myanmar, resulting in increased seismic activity and extended vulnerability to seismic hazards (Karim 2004; Sattar et al. 2009; Islam et al. 2016). The seismic activity in Bangladesh is closely associated with the tectonic activities occurring within and around the country. These activities include the Himalayan Arc and Shillong plate in the northern region, the Burmese Arc, and the Arakan Yoma anticlinoria towards the east, as well as the intricate Naga Disang Jaflong thrust zones in the northeast. Additionally, the Dauki Fault systems are present in this area (Sattar et al. 2009). Bangladesh is situated such that five major fault lines are involved and several major rivers (e.g., Teesta-Lalmonirhat, Brahmaputra-Kurigram, Surma-Sylhet) flow into the country. Bangladesh's northern, western, and northeastern borders are directly linked to India's most earthquake-prone areas (Calcutta, Assam, and Tripura). According to its geological location, the Bogra fault zone, the Tripura fault zone, the Sub-Dauki fault zone, the Shillong plateau, and the Assam plateau are the five major faults that are active in Bangladesh (Hossain 1998; Roy 2014; Zaman and Monira 2017; Apu and Das 2020). For the presence of those predominant faults, Bangladesh is dealing with dreadful threats. There are earthquakes every second around the world, but they are all so small (ML≤3.0) that we are not vulnerable to them, whereas strong earthquakes (ML≥6.0) result in terrible situations. The earthquake catalog shows that no previous earthquake has affected Bangladesh as much as it did in the past few years or decades. Bangladesh experienced over 100 earthquakes of varying magnitudes during the 20th century. These seismic events ranged from small to medium in size. The actual number of earthquakes is thought to be much higher, as many are not recorded due to the lack of proper seismic equipment in the lone operational observatory in our country. Besides, most earthquakes are historical and instrumental, poorly documented, and not readily available for seismic hazard analysis. Since the majority of the stress that builds up within fault rupture zones is not released by recent repeated low to moderate-magnitude quakes, seismologists identify these tremors as constituents of large and potentially catastrophic earthquakes in the near future (Udías 2005; Yakovlev et al. 2006; Paul and Bhuiyan 2010).
According to USGS, there were 116 recognized evidences of earthquake from 1906-2022 in the Bangladesh territory (USGS 2022). Although, damages from several earthquakes were very severe in Sylhet, Chittagong, Dhaka, Rajshahi, Bogura, Rangpur and minor damage occurred practically throughout the country (Sarker et al. 2010; Apu and Das 2020; Alam and Haque 2020). Especially, Dhaka appeared to have one of the highest values of the Earthquake Disaster Risk Index (EDRI) in a study by Khan and Jahan (2021) on 20 cities around the globe. This was primarily because of the city's high population density, lack of earthquake-resistant building infrastructure, and inadequate emergency response and recovery capabilities. Such evidence justifies the need for earthquake assessment that can help concerned authorities to take action and help in the formulation of appropriate risk reduction policies.
In Bangladesh, however, several probabilistic earthquake studies have been conducted by various researchers (Al-Hussaini and Al Noman 2010; Roy 2014; Chakravorti et al. 2015; Al-Hussaini et al. 2015; Rahman et al. 2017; Siddique 2018; Ray et al. 2019; Rahman and Hossain 2019; Hossain and Hossain 2020; Haque et al. 2020; Fatema et al. 2021). Additionally, earthquake prediction relies on statistical analysis to ensure public safety, funding, and trust. A large number of prospect statistics, including the Laplacian or double exponential (Utsu 1972), Gamma (Utsu 1984), Log-normal (Nishenko and Buland 1987), and Weibull (Hagiwara 1974; Rikitake 1974) distributions, for computing conditional probabilities of future earthquakes distribution has been proposed. In addition, a reasonably good fit to a Weibull distribution for earthquake data was found by Yilmaz et al. (2004). The purpose of this paper is to review seismic zones according to the earthquake occurrences having greater magnitudes and to forecast earthquakes in the near future. It also analyzed the statistical tools for predicting earthquakes in Bangladesh to show the probability of occurrences, time span, and magnitude range of the earthquake.
The present study followed the quantitative approach where secondary data from the USGS earthquake catalog (1906-2022) was used (USGS 2022). Similarly, an index-based methodology was adopted for assessing earthquake hazards in the study area. A subjective weighting technique was also used to allocate values to classes of phenomena for each hazard indicator and formulate an index based on the following equation.
Where, WAI is the weighted average index, W1 to Wn are respective transformed values assigned to the weight value of the ith variable and n is the number of variables used for computing the individual weighted index. Ensuring the principle, Earthquake Hazard Index (HI) was calculated.
Table 1: Indicators used to develop earthquake Hazard Index
|
Sl. No. |
Earthquake hazard indicators |
Classes |
TV/ weight |
Explanation |
Empirical studies |
|
1 |
Frequency / Number of earthquakes per year |
Low (<2) |
0.33 |
Increased frequency posed higher earthquake hazard |
(Khan et al. 2019; Rahman et al. 2021) |
|
Moderate (2-5) |
0.66 |
||||
|
High (>5) |
1 |
||||
|
2 |
Magnitude in Richter scale |
≤4.0 |
0.2 |
High magnitude express enormous earthquake hazard |
(Paradise 2005; Paul and Bhuiyan 2010; Ainuddin et al. 2014) |
|
4.0 - 4.9 |
0.4 |
||||
|
5.0 -5.9 |
0.6 |
||||
|
6.0 – 6.9 |
0.8 |
||||
|
≥ 7.0 |
1 |
||||
|
3 |
Distance from study area |
<100 km |
1 |
Lower distance to the epicenter will tend to have severe earthquake disaster |
(Lo and Cheung 2015; Khan et al. 2019; Rahman et al. 2021) |
|
100-200 km |
0.8 |
||||
|
200-300 km |
0.6 |
||||
|
300-400 km |
0.4 |
||||
|
400-500 km |
0.2 |
||||
|
4 |
Depth of earthquake |
<70 km |
1 |
Shallow earthquakes produce more damage |
(Paradise 2005; Paul and Bhuiyan 2010; Ainuddin et al. 2014) |
|
70-300 km |
0.66 |
||||
|
>300 km |
0.33 |
Assessment of earthquake probability
The study made an attempt to conduct a probabilistic seismic hazard analysis for Bangladesh that addresses some of the existing shortcomings. Besides, the study also used Normal, Log-normal, Gamma, Logistic, Weibull, and Gumbel distributions to predict the statistical probability of earthquakes based on reviewed in-depth literature (Patel et al. 1976; Yakovlev et al. 2006; Roy 2014; Chakravorti et al. 2015; Ray et al. 2019; Rahman and Hossain 2019; Fatema et al. 2021). Statistical probability projections of these distributions were compared between them to allow more accurate prediction of future occurrence possibilities of Bangladeshi earthquakes.
Prediction of earthquake magnitude along with the probability of occurrences in upcoming years also analyzed based on the subjected distribution methods. The parameters for fitting the data are estimated, and the mean occurrence period is determined using the Maximum Likelihood Estimation technique. The cumulative distribution function provides valuable information on the probability of earthquake events surpassing a given timeframe, making it a useful tool for assessing recurrence times F(t).
Table 2: PDF and CDF with parameters used in this study
Seismic zone of Bangladesh
The first map of the continent's seismic zones was made in 1935 by the Geological Survey of India. In 1972, The Bangladesh Meteorological Department subsequently adopted its seismic zone map. A group of experts was established by the Bangladeshi government in 1977 to examine the country's seismic problems and propose appropriate solutions (Islam et al. 2016). The Committee of Experts on Earthquake Hazard Minimization released the Bangladesh Geological Survey's first official seismic zone map in 1979 (Karim 2004; Sattar et al. 2009). It was then modified in 1993 while the Bangladesh National Building Code (BNBC) was being formed. According to Ali and Choudhury (1994), countries were divided into three zones, and coefficients were based on PGA values with a 200-year recurrence period. The revision of seismic zones from three to four is determined by analyzing the distribution of earthquake epicenters and the morphotectonic behavior of different tectonic blocks, with the Z value representing the maximum ground acceleration (Ansary and Sharfuddin 2002; Ahmed and Kabir 2021). It has been introduced in the new seismic zone map of the revised Building Code where the country has been divided into four zones having Z values of 0.12, 0.20, 0.28, and 0.36. Whereas, Zone-IV has been identified as the zone of high seismic risk followed by Zone-III, Zone-II, and Zone-I (Dipu 2017; Ahmed and Kabir 2021).
Bangladesh is near where the Indian, Eurasian, and Burma (Myanmar) plates converge. At the foot of the Himalayas, the Indian and Eurasian plates have been stuck in motion for a long time, building strain energy. When the lock is opened, the strain energy is released, triggering significant earthquakes in Bangladesh, northeast India, and Myanmar. Based on estimates, such faults could generate earthquakes with a maximum magnitude ranging from 8.2 to 9.0 (Steckler et al. 2016). Even though a magnitude 8 or greater earthquake might cause havoc anywhere in the world, this particular region may be especially vulnerable. According to the study, around 140 million people are living within 60 miles (100 km) of the active faults, including the 17 million residents of Bangladesh's densely populated metropolis of greater Dhaka who are particularly vulnerable to large earthquakes (Apu and Das 2020).
Table 3: Brief account of seismic zones of Bangladesh
|
Seismic Zones |
Location |
Seismic Intensity |
Seismic Zone Coefficient (Z) |
|
I |
Southwestern part including Barisal, Khulna, Jessore, Rajshahi |
Low |
0.12 |
|
II |
Lower Central and Northwestern part including Noakhali, Dhaka, Pabna, Dinajpur, as well as Southwestern corner including Sundarbans |
Moderate |
0.20 |
|
III |
Upper Central and Northwestern part including Brahmanbaria, Sirajganj, Rangpur |
Severe |
0.28 |
|
IV |
Northeastern part including Sylhet, Mymensingh, Kurigram |
Very Severe |
0.36 |
Source: (Dipu 2017; Ahmed and Kabir 2021)
3.1 Earthquake hazard in Bangladesh
The country is under high seismic risk, based on the historical seismicity and recent tremors in and around Bangladesh. To assess the earthquake hazard in the study area USGS data from 12 May 1906 to 24 August 2022 was analyzed and to measure the hazard index score 500 km radius from Shahid Noor Hossain Square, Dhaka Zero Point (lat. 23.728043°N, long. 90.410751°E) was considered.
It is observed that earthquake occurs in and around the study area every moment, all of these are not felt which are very minor (ML ≤3.0) and are not vulnerable for us but major earthquakes (ML ≥6.0) cause terrible situation. During 1906 to 2022, there were a total of 1889 earthquake occurrences among them 3 strong earthquakes, 36 major earthquakes (ML ≥6.0), 293 moderate earthquakes (ML 5.0 to 5.9), 1417 light earthquakes (ML 4.0 to 4.9), and another 140 minor earthquakes (ML ≤4.0) respectively (Table 4). It reveals that most of the earthquakes that occurred are of magnitude level 4.0 to 4.9; which is categorized as "light" earthquakes according to the Bangladesh Meteorological Department (BMD) considering the earthquake history in Bangladesh recorded from 1906 to 2022.
Table 4 reveals that earthquakes are recurrent in Bangladesh, although they are not as destructive as those with a magnitude of 6 and above. Nonetheless, the significant rise in earthquake occurrences over the past decade compared to the early 80s, as depicted in Fig. 6, suggests substantial changes in geographical structures and seismic patterns in the region.
Before the instrumental era of earthquake monitoring, the epicenter, previously believed to be the area of maximum damage, is now understood to be the point directly above the hypocenter or focus, with the fault rupture potentially extending along a considerable length and causing damage across the entire rupture zone (Yeats et al. 1997). Hence, strong earthquakes having greater magnitude and depth can affect and feel from several distances to the epicenter. In accordance with such an assumption, a 500 km ring buffer was drawn and every 100km distance in and around Dhaka City earthquake occurrences was analyzed using GIS technique. The closest earthquake epicenter was 9.28 km away from Dhaka Zero point of the Dhaka earthquake in 2001 followed by 18.64 km of the 2012 earthquake (13 km North-east of Dohar, Dhaka), 43.91 km of the 2010 earthquake (27 km of Sonargaon, Dhaka), 45.56 km of 2019 earthquake (20 km east of Mirzapur, Dhaka) and another 16 earthquakes that occurred within 100 km radius from Dhaka Zero Point respectively. Accordingly, 58 earthquake epicenter was within 100-200 km of Dhaka City followed by 183 (200-300km), 335 (300-400 km), and the rest of 1293 earthquakes (400-500km) respectively (Table 4).
The depth of an earthquake may vary from 0-700 km and is divided into three zones shallow (0-70 km), intermediate (70-300 km), and deep (300-700 km) according to USGS. As the mechanism behind deep earthquakes remains partially unknown, the study focuses only shallow earthquakes for their prevalence, greater destruction, and better-understood mechanism. However, the deep focus earthquake was about 200km in 1997 (52km North-east of Mawlaik, Myanmar) majority of the earthquake occurrences in the study area from 1906-2022 were in the level shallow depth category except 672 earthquakes in the level intermediate category. The shallowest earthquake was 3.3km depth in 2008 (45km North-west of Gyalshing, India) and another 126 earthquakes were within 10km depth that occurred in India and Myanmar outside the Bangladesh border. Inside the boundary of Bangladesh, the shallowest earthquake was 9.8km depth in 2003 (13km east of Raojan, Chittagong) and another 29 shallow earthquakes were found within 10km depth (Table 4).
Table 4: Statistics of earthquake hazard indicators for the period of 1906-2022
|
Hazard indicators |
Descriptor |
Estimates & occurrences |
|
|
Summary of statistics |
Mean |
4.550238 |
|
|
Standard Error |
0.012123 |
||
|
Median |
4.50 |
||
|
Mode |
4.30 |
||
|
Standard Deviation |
0.526902 |
||
|
Sample Variance |
0.277626 |
||
|
Kurtosis |
2.457271 |
||
|
Skewness |
1.207316 |
||
|
Range |
3.98 |
||
|
Minimum |
3.20 |
||
|
Maximum |
7.18 |
||
|
Count |
1889 |
||
|
Confidence Level (95.0%) |
0.023776 |
||
|
Magnitude Level (ML) in Richter Scale |
< 4.0 |
Minor |
140 |
|
4.0 - 4.9 |
Light |
1417 |
|
|
5.0 - 5.9 |
Moderate |
293 |
|
|
6.0 – 6.9 |
Major |
36 |
|
|
≥ 7.0 |
Strong |
3 |
|
|
Distance in km |
<100 |
Closest |
20 |
|
100-200 |
Nearest |
58 |
|
|
200-300 |
Moderate |
183 |
|
|
300-400 |
Far |
335 |
|
|
400-500 |
Farthest |
1293 |
|
|
Depth in km |
<70 |
Shallow |
1217 |
|
70-300 |
Intermediate |
672 |
|
|
300+ |
Deep |
- |
|
Fig. 7 and Tables 4 & 5 revealed that the overall earthquake hazard index score of about 0.595270 was calculated, indicating relatively moderate earthquake hazard (0.4-0.6). In the case of frequency, the index score was determined as 0.787474 which denotes the high risk of hazard (>0.6). There were tremors almost every year based on the USGS Earthquake Catalog, with the exception of 21 years, and there were a total of 1889 events from 1906 to 2022. Among them, an excessive number of tremors were observed in the year 2021 (75 times) followed by 2014 (70 times), 2008 (70 times), 2020 (70 times), 1996 (61 times), and 2006 (57 times) respectively (Fig. 5). The earthquake decadal trend showed a sharp uptick in recent times, especially after the 1970-1980 decade. From 1980 to 1990, there were more than twice as many events, and the trend has continued with an incidence rate of 1.556 (Fig. 6).
The magnitude index score was found 0.413023, signifying the moderate risk of earthquake hazard (0.40-0.60). 75.01% (1417 times) of the tremor’s arrays in the light category (4.0-4.9 Richter Scale) followed by 15.51% (293 times) in the moderate category (5.0-5.9 Richter Scale), 1.91% (36 times) in the major category (6.0-6.9 Richter Scale) and only 0.16% (3 times) were found in the strong category (≥ 7.0 Richter Scale) as shown in Table 4.
The distance index score of 0.301535 depicted a low risk of earthquake hazard (0.21-0.40). Table 4 suggests that 68.45% (1293 times) of the quakes occurred in the farthest distance (400-500km), followed by 17.73% (335 times) in the far distance (300-400km), 9.69% (183 times) in the moderate distance category (200-300km), 3.07% (58 times) in the nearest (100-200km), and the remaining 1.06% (20 times) in the closest distance from Dhaka (<100km).
With a depth index score of 0.879047, the study area posed a very high risk of hazards (>0.80) since more than 64% (1217 times) of the tremors were found in the shallow depth (70km) and the remaining 35.57% (672 times) found in the intermediate depth category (70-300km).
Nevertheless, a highly moderate risk of earthquake was found in the study area, followed by a very high-risk category for the depth index score, a high-risk category for the frequency index, a moderate risk category for the magnitude index, and a low-risk category for the distance index (Fig. 7).
Table 5: Criteria of assessment
|
Very low |
Low |
Moderate |
High |
Very high |
|
< 0.20 |
0.20 – 0.40 |
0.40 – 0.60 |
0.60 – 0.80 |
> 0.80 |
Based on the USGS record of earthquake data from 1906-2022 e.g., magnitude, depth, distance, and the total number of earthquake occurrences overall seismic risk map was prepared and finalized using the ArcGIS tool. Specifically, the Kriging Interpolation technique was employed to assess the seismic zoning map (Fig. 8). It revealed that the country was within the moderate seismic risk zone. Such findings of the result initiated as very much similar to the findings of the average hazard index score.
The normal distribution with parameters mean and standard deviation, the log-normal distribution with parameters log mean and log standard deviation, the gamma distribution with parameters shape and rate, the logistic distribution with parameters location and scale, the Weibull distribution with parameters shape and scale, and the Gumbel distribution with parameters location and scale are used to fit the probability distributions to determine the earthquake magnitudes (in Richter scale) in Bangladesh. While the parameters of the distributions are estimated through the iterative maximum likelihood method and the findings are presented in Figs. 9 & 10 to see the fitting in terms of cumulative distribution functions plots, and probability density plots.
The Box-and-Whisker plot and histogram (Figs. 3 & 4) used to illustrate the empirical distributional pattern of earthquake magnitudes show that the distribution is positively skewed, and the value of the kurtosis in Table 4 explains that the distribution pattern is leptokurtic. The average magnitude of an earthquake is 4.55 and the average distance between magnitudes is calculated as 0.53. In the study period, the maximum and minimum earthquake magnitude levels are 3.20 and 7.18 separately, and the median and mode earthquake magnitude is 4.50 and 4.30 correspondingly.
The distribution of earthquake magnitude levels (on the Richter scale) follows a leptokurtic pattern, as shown in Fig. 4, and the value of Kurtosis is in Table 4. The mean earthquake magnitude levels include standard errors of 0.012 and 95% confidence intervals of 0.024. The earthquakes take place within the study period with an interval of 3.98 which contains a total of 1889 earthquakes.
Table 6: Estimated parameters of different PDFs and tests for normality of different earthquake probability distributions
|
Distribution types |
Parameters |
Estimate |
Goodness-of-fit statistics |
|||
|
Kolmogorov -Smirnov Statistic |
Shapiro-Wilk Statistic |
df |
sig. |
|||
|
Normal |
Mean (μ) |
4.550238 |
0.109939 |
0.950349 |
1889 |
0.000 |
|
Standard Deviation (σ) |
0.526902 |
|||||
|
Log-normal |
Log Mean (μ) |
1.508906 |
0.105909 |
0.956588 |
0.000 |
|
|
Log Standard Dev. (σ) |
0.110458 |
|||||
|
Gamma |
Shape (k) |
79.862410 |
0.107431 |
0.954863 |
0.000 |
|
|
Rate (θ) |
0.056976 |
|||||
|
Logistic |
Location (μ) |
4.550238 |
0.121583 |
0.941846 |
0.000 |
|
|
Scale (α) |
0.290496 |
|||||
|
Weibull |
Shape (β) |
4.773073 |
0.137707 |
0.920272 |
0.000 |
|
|
Scale (α) |
10.591380 |
|||||
|
Gumbel |
Location (μ) |
4.787376 |
0.221292 |
0.793912 |
0.000 |
|
|
Scale (β) |
0.410824 |
|||||
The estimated parameter of the normal distribution, mean and standard deviation are found to be 4.550238 and 0.526902 correspondingly. The parameters of log-normal distribution - Log Mean and Log Standard Deviation are 1.508906 and 0.110458 respectively. The shape and rate parameters of the Gamma distribution are 79.862410 and 0.056976 and the shape and scale parameters of the Weibull distribution are 4.773073 and 10.591380 accordingly. The location and scale parameters of Logistic distribution and Gumbel distribution are 4.550238 and 0.290496, 4.787376 and 0.410824 respectively (Table 6).
The Kolmogorov-Smirnov and Shapiro-Wilk goodness of fit statistics are computed by using SPSS for the fitted probability distribution for the earthquake magnitude levels in Bangladesh.
The value of Kolmogorov-Smirnov Statistic for the Normal, Log-normal, Gamma, Logistic, Weibull, and Gumbel distributions are 0.109939, 0.105909, 0.107431, 0.121583, 0.137707and 0.221292 respectively. The values of the goodness of fit statistic -Shapiro-Wilk statistic for the Normal, Log-normal, Gamma, Logistic, Weibull, and Gumbel distribution are 0.950349, 0.956588, 0.954863, 0.941846, 0.920272 and 0.793912 respectively.
Based on the graphical analysis and goodness-of-fit statistics, the multiple predicted probability distributions of the earthquake magnitude levels in Bangladesh are fitted, and it is discovered that the data best matches the Log-normal distribution (Fig. 10 & Table 6). Moreover, the pdf of log-normal distribution conveyed that there is an 80.18% of chance to occur an earthquake having a magnitude of about 4.5 on the Richter Scale. The results are also consistent with the findings reported by Rahman and Hossain (2019). The outcomes of all other distributions showed almost similar findings according to CDF except the Gumbel distribution (65.46%) (Fig. 9).
Table 7: Probability of occurrences based on the distributions for the different time frame of the earthquake magnitude levels in Bangladesh
|
Magnitude in Richter Scale |
Distribution types |
Year wise CDF statistics |
|||||||
|
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
||
|
<4
|
Normal |
0.0000 |
0.9458 |
1.0000 |
|
|
|
|
|
|
Log-normal |
0.0000 |
0.9382 |
1.0000 |
|
|
|
|
|
|
|
Gamma |
0.0000 |
0.9415 |
1.0000 |
|
|
|
|
|
|
|
Logistic |
0.0000 |
0.9484 |
1.0000 |
|
|
|
|
|
|
|
Weibull |
0.0005 |
0.9645 |
1.0000 |
|
|
|
|
|
|
|
Gumbel |
0.0000 |
0.7968 |
1.0000 |
|
|
|
|
||
|
4 – 4.9
|
Normal |
0.0000 |
0.0459 |
0.9903 |
1.0000 |
|
|
|
|
|
Log-normal |
0.0000 |
0.0407 |
0.9869 |
1.0000 |
|
|
|
|
|
|
Gamma |
0.0000 |
0.0423 |
0.9882 |
1.0000 |
|
|
|
|
|
|
Logistic |
0.0000 |
0.0449 |
0.9858 |
1.0000 |
|
|
|
|
|
|
Weibull |
0.0002 |
0.0742 |
0.9994 |
1.0000 |
|
|
|
|
|
|
Gumbel |
0.0000 |
0.0000 |
0.9150 |
0.9995 |
1.0000 |
|
|
||
|
5 – 5.9
|
Normal |
0.0000 |
0.0000 |
0.1264 |
0.9933 |
1.0000 |
|
|
|
|
Log-normal |
0.0000 |
0.0000 |
0.1210 |
0.9914 |
1.0000 |
|
|
|
|
|
Gamma |
0.0000 |
0.0000 |
0.1251 |
0.9916 |
1.0000 |
|
|
|
|
|
Logistic |
0.0000 |
0.0002 |
0.1116 |
0.9888 |
1.0000 |
|
|
||
|
Weibull |
0.0000 |
0.0019 |
0.1624 |
0.9992 |
1.0000 |
|
|
|
|
|
Gumbel |
0.0000 |
0.0000 |
0.0004 |
0.9278 |
0.9993 |
1.0000 |
|
|
|
|
≥ 6
|
Normal |
0.0000 |
0.0000 |
0.0001 |
0.1637 |
0.9666 |
1.0000 |
|
|
|
Log-normal |
0.0000 |
0.0000 |
0.0000 |
0.1570 |
0.9655 |
1.0000 |
|
|
|
|
Gamma |
0.0000 |
0.0000 |
0.0000 |
0.1638 |
0.9635 |
1.0000 |
|
|
|
|
Logistic |
0.0000 |
0.0000 |
0.0010 |
0.1448 |
0.9653 |
0.9998 |
1.0000 |
||
|
Weibull |
0.0000 |
0.0001 |
0.0073 |
0.1904 |
0.9734 |
1.0000 |
|
|
|
|
Gumbel |
0.0000 |
0.0000 |
0.0000 |
0.0019 |
0.8439 |
0.9954 |
0.9999 |
1.0000 |
|
After examining the statistics of time of earthquake occurrences, the cumulative probability distribution (CDF) of an earthquake having a certain magnitude in this region in t years later was also exercised using the similar models discussed earlier.
In the case of less than 4 Richter Scale earthquakes (140 times), the values of normal distribution parameters μ (mean) and α (standard deviation) originated as 3.774286 and 0.140590 respectively. Whereas, Log-normal distribution’s parameters are calculated as 1.327500 (log mean) and 0.038173 (log standard deviation) followed by the Gamma distribution’s parameters 702.89343 (shape) and 0.005370 (rate), the Logistic distribution’s parameters 3.774286 (location) 0.077512 (scale), Weibull distribution’s parameters 3.844387 (shape) and 30.387723 (scale), and Gumbel distribution’s parameters 3.837560 (location) and 0.109618 (scale) compatibly. By using those distribution’s CDF, the risk of another earthquake after the preceding one in 4 years is designated in Normal distribution as 94.58% followed by Log-normal distribution (93.82%), Gamma distribution (94.15%), Logistic distribution (94.84%), Weibull distribution (96.45%) and Gumbel distribution (79.68%) accordingly.
The mean and standard deviation of a normal distribution are 4.418984 and 0.248526 in the case of 4.0-4.9 Richter Scale earthquakes (1417 times), followed by the log-normal distribution's parameters 1.484329 (log mean) and 0.056265 (log standard deviation), Gamma distribution’s parameters 316.43099 (shape) and 0.013965 (rate), Logistic distribution’s parameters 4.418984 (location) and 0.137019 (scale), Weibull distribution’s parameters 4.532264 (shape) and 20.514160 (scale), and Gumbel distribution’s parameters 4.530835 (location) and 0.193775 (scale) in an aligned manner. The likelihood of another earthquake with a magnitude of 4.0 to 4.9 Richter Scale occurring after a 5-year period (2027) is calculated as follows: Normal distribution: 99.03%; Log-normal distribution: 98.69%; Gamma distribution: 98.82%; Logistic distribution: 98.58%; Weibull distribution: 99.94%; and Gumbel distribution: 91.50%.
In the case of 5-5.9 Richter Scale earthquakes (293 times), the normal distribution's parameters (mean) and (standard deviation) are 5.316451 and 0.276667, respectively, followed by Log-normal distribution's parameters 1.669481 (log mean) and 0.051329 (log standard deviation), Gamma distribution’s parameters 369.25580 (shape) and 0.014398 (rate), Logistic distribution’s parameters 5.316451 (location) and 0.152535 (scale), Weibull distribution’s parameters 5.445997 (shape) and 20.254131 (scale), and Gumbel distribution’s parameters 5.440967 (location) and 0.215717 (scale). The likelihood of another earthquake occurring within 6 years of the previous one is denoted as 99.33% in the Normal distribution, 99.14% in the Log-normal distribution, 99.16% in the Gamma distribution, 98.88% in the Logistic distribution, 99.92% in the Weibull distribution, and 92.78% in the Gumbel distribution.
The values of the normal distribution's parameters (mean) and (standard deviation) are derived as 6.3482 and 0.35556 in the case of 6+ Richter Scale earthquakes (39 times), followed by the log-normal distribution's parameters 1.846696 (log mean) and 0.054558 (log standard deviation), Gamma distribution’s parameters 318.7754 (shape) and 0.019914 (rate), Logistic distribution’s parameters 6.348205 (location) and 0.196029 (scale), Weibull distribution’s parameters 6.527750 (shape) and 18.446442 (scale), and Gumbel distribution’s parameters 6.508227 (location) and 0.277226 (scale) respectively. The probability of an earthquake occurring seven years after the last one is denoted by the Normal distribution as 96.66%, followed by the Log-normal distribution (96.55%), Gamma distribution (96.35%), Logistic distribution (96.33%), Weibull distribution (97.34%), and Gumbel distribution (84.39%).
This indicates that the coming years are highly risky for the upcoming major earthquakes. These earthquake recurrences of a certain magnitude are very dangerous for the country and their impact will be demonstrated in the near future. Besides, the recently repeated shocks around this region indicate the possibilities of the potential threat of even much higher intensity than projected. With the frequency of earthquakes increasing, it is natural for people to be concerned, since experts believe they are a forewarning of what is to come. Besides, they predict that a significant tremor will happen any day as the frequency of tremors in this area is rising.
Bangladesh is at a high seismic risk as evinced by recent tremors that occurred in and around the country. It is observed that 75% of the earthquakes which occurred in the previous 117 years were "light" earthquakes (4-4.9 Richter Scale). Nearly 5% of the earthquakes occurred within 200 km of Dhaka, and 64% were deemed to be shallow in depth. The regular occurrence of medium and light earthquakes may significantly alter the geographical pattern of fault zones in Bangladesh as the frequency of earthquakes has highly increased since the 1990s. The WAI results indicated a highly moderate risk of earthquake, following a very high-risk for the depth index score, a high-risk for the frequency index, a moderate risk for the magnitude index, and a low-risk for the distance index.
The earthquake magnitudes ranged from 3.20 to 7.18 in Richter Scale; similarly, the mean, median, and mode of earthquake magnitude values are initiated as 4.55, 4.50, and 4.30, respectively throughout the study period (12 May 1906 to 24 August 2022). The distribution of earthquake magnitudes exhibits a shape that is positively skewed, leptokurtic, and characterized by a high concentration of values around the center, with relatively few extreme values occurring as outliers. The Normal, Log-Normal, Gamma, Logistic, Weibull, and Gumbel expected distributions' parameters are estimated using the maximum likelihood technique. Based on the graphical analysis and the goodness-of-fit criterion, the various predicted probability distributions of the earthquake magnitude levels in Bangladesh are well-suited.
Besides, six distributions show the recurrence probability of an earthquake having magnitude ML> 4.00 after 4 years from 2022 (2026) in this region, which is 94.58%, 93.82%, 94.15%, 94.84%, 96.45% and 79.68% for Normal, Log-normal, Gamma, Logistic, Weibull, and Gumbel distribution respectively. The risk of another earthquake having a magnitude 4.0-4.9 Richter Scale after the preceding one in 5 years is designated as 99.03%, 98.69%, 98.82%, 98.58%, 99.94%, and 91.50% accordingly. Probability of another earthquake of magnitude 5.0 to 5.9 after the previous one in 6 years from 2022 (2028) is consistent with the Normal, Log-normal, Gamma, Logistic, Weibull, and Gumbel distribution as 99.33% 99.14%, 99.16%, 98.88%, 99.92%, and 92.78% successively. When the Richter Scale is 6 or higher, the Normal distribution has intended the probability of 96.66%, followed by the Log-normal distribution (96.55%), Gamma distribution (96.35%), Logistic distribution (96.33%), Weibull distribution (97.34%), and Gumbel distribution (84.39%) in that order. This suggests that the area around the five major faults (Bogra fault zone, Sub-Dauki fault zone, Shillong plateau, Tripura fault zone, and Assam plateau) will be at very high risk in the upcoming years. Additionally, the potential of fatalities and considerable property damage in Bangladesh will also be high in the event of a big earthquake and greater seismic probability. The country's severe most risk zones are assumed to be the northern parts of Dinajpur, Rangpur, Mymensingh, Sylhet, Tangail, and the northern parts of Dhaka, Khulna, Jessor, Kushtia, and Chittagong. The loss of life and property damage can be reduced, however, by making accurate earthquake predictions and issuing warnings. Concerning both pre-preparedness and post-earthquake disaster management, emphasis is placed on the requirement of generating public awareness campaigns through the physical planning of human settlements, adherence to building codes, and implementation of settlement management strategies.
I the undersigned declare that this manuscript is original, has not been published before and is not currently being considered for publication elsewhere.
Availability of data and materials: I declare that the collected data are original and all the data are collected by the authors.
Conflicts of interest: The authors declare that there is no competing interest associated with this publication.
Funding: I declare that this research is not supported or funded by any organization or individual. Authors bear all the expanses of this study by themselves. So, this research is self-funded research of the authors.
Author’s contribution: All authors contributed to the study conception and design. The manuscript has been read and approved by all named authors and there are no other persons who satisfied the criteria for authorship but are not listed. The individual contribution of the authors is given herewith. Introduction, literature review and methodology: [Md. Rayhan Ali and Nafia Muntakim]; data collection: [Nahid Hasan]; data analysis: [Hasan Mahmud]; Mapping: [Md. Abdul Aziz]; findings, writing, reviewing and editing: [Zihad Ahmed]; critically revised the works: [Dr. Md. Mizanoor Rahman].
Ethics approval: I also confirmed that due considerations have been given to the protection of intellectual property associated with this work. I further confirm that ethical considerations of all relevant bodies have been covered in this manuscript.
Consent to participate: Verbal informed consent was obtained from all individual respondents as well as key informants in the study prior to the interview.
Consent for publication: All participants have given their consent regarding publishing their statement and data.
Acknowledgement: N/A
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