probability of exceedance and return period earthquake probability of exceedance and return period earthquake

The Anderson Darling test is not available in SPSS version 23 and hence it is calculated using Anderson Darling normality test calculator for excel. People worldwide desire to know the likelihood of earthquakes but neither physical nor statistical models are adequate for predictions and other analysis of seismic pattern (Konsuk & Aktas, 2013; Vere-Jones, Ben-Zion, & Zuniga, 2005) . log n The model provides the important parameters of the earthquake such as. experienced due to a 475-year return period earthquake. As would be expected the curve indicates that flow increases is the estimated variance function for the distribution concerned. A return period, also known as a recurrence interval or repeat interval, is an average time or an estimated average time between events such as earthquakes, floods, landslides, or . A final map was drawn based upon those smoothing's. ( Exceedance probability is used as a flow-duration percentile and determines how often high flow or low flow is exceeded over time. On 16th January 1934 AD, an earthquake called Nepal Bihar Earthquake, hit Nepal and its surrounding regions with Mw = 8.4 magnitude. regression model and compared with the Gutenberg-Richter model. The higher value. The available data are tabulated for the frequency distribution of magnitude 4 M 7.6 and the number of earthquakes for t years. All the parameters required to describe the seismic hazard are not considered in this study. This probability measures the chance of experiencing a hazardous event such as flooding. , Figure 2. M (9). duration) being exceeded in a given year. It is observed that the most of the values are less than 26; hence, the average value cannot be deliberated as the true representation of the data. ( Earthquake Parameters. Annual recurrence interval (ARI), or return period, is also used by designers to express probability of exceedance. is the expected value under the assumption that null hypothesis is true, i.e. . be reported to whole numbers for cfs values or at most tenths (e.g. Konsuk and Aktas (2013) analyzed that the magnitude random variable is distributed as the exponential distribution. We don't know any site that has a map of site conditions by National Earthquake Hazard Reduction Program (NEHRP) Building Code category. 2 m n n i log ^ Table 6. This is older work and may not necessarily be more accurate than the CDMG state map for estimating geologic site response. On the other hand, the ATC-3 report map limits EPA to 0.4 g even where probabilistic peak accelerations may go to 1.0 g, or larger. The probability of at least one event that exceeds design limits during the expected life of the structure is the complement of the probability that no events occur which exceed design limits. If stage is primarily dependent , 1 2 Choose a ground motion parameter according to the above principles. d Hence, the spectral accelerations given in the seismic hazard maps are also 5 percent of critical damping. The EPA is proportional to spectral ordinates for periods in the range of 0.1 to 0.5 seconds, while the EPV is proportional to spectral ordinates at a period of about 1 second . i If we take the derivative (rate of change) of the displacement record with respect to time we can get the velocity record. These models are. i ) , = x N be the independent response observations with mean 1 For instance, one such map may show the probability of a ground motion exceeding 0.20 g in 50 years. model has been selected as a suitable model for the study. It is assumed that the long-term earthquake catalogue is not homogeneous and the regular earthquakes, which might include foreshocks and aftershocks of characteristic events, follow Gutenberg-Richter frequency magnitude relationship (Wyss, Shimazaki, & Ito, 1999; Kagan, 1993) . S187-S208.In general, someone using the code is expected either to get the geologic site condition from the local county officials or to have a geotechnical engineer visit the site. ] Whether you need help solving quadratic equations, inspiration for the upcoming science fair or the latest update on a major storm, Sciencing is here to help. ( The approximate annual probability of exceedance is about 0.10(1.05)/50 = 0.0021. max i The estimated values depict that the probability of exceedance increases when the time period increases. n If the return period of occurrence ) The Anderson Darling test statistics is defined by, A ) (11.3.1). 2 The relationship between the return period Tr, the lifetime of the structure, TL, and the probability of exceedance of earthquakes with a magnitude m greater than M, P[m > M, TL], is plotted in Fig. It selects the model that minimizes where, ei are residuals from ordinary least squares regression (Gerald, 2012) . The earthquake catalogue has 25 years of data so the predicted values of return period and the probability of exceedance in 50 years and 100 years cannot be accepted with reasonable confidence. t this manual where other terms, such as those in Table 4-1, are used. In these cases, reporting Table 2-2 this table shows the differences between the current and previous annual probability of exceedance values from the BCA [11]. Now, N1(M 7.5) = 10(1.5185) = 0.030305. The (n) represents the total number of events or data points on record. Q10=14 cfs or 8.3 cfs rather than 14.39 cfs The designer will determine the required level of protection The parameters a and b values for GR and GPR models are (a = 6.532, b = 0.887) and (a =15.06, b = 2.04) respectively. M i It can also be noticed that the return period of the earthquake is larger for the higher magnitudes. ( Uniform Hazard Response Spectrum 0.0 0.5 . and 8.34 cfs). Don't try to refine this result. Return Period Loss: Return periods are another way to express potential for loss and are the inverse of the exceedance probability, usually expressed in years (1% probability = 100 years). This study suggests that the probability of earthquake occurrence produced by both the models is close to each other. An area of seismicity probably sharing a common cause. criterion and Bayesian information criterion, generalized Poisson regression 0 1969 was the last year such a map was put out by this staff. ) The theoretical return period between occurrences is the inverse of the average frequency of occurrence. ln Note that, in practice, the Aa and Av maps were obtained from a PGA map and NOT by applying the 2.5 factors to response spectra. i See acceleration in the Earthquake Glossary. as AEP decreases. Evidently, r2* is the number of times the reference ground motion is expected to be exceeded in T2 years. The deviance residual is considered for the generalized measure of discrepancy. The ground motion parameters are proportional to the hazard faced by a particular kind of building. software, and text and tables where readability was improved as The approximate annual probability of exceedance is about 0.10(1.05)/50 = 0.0021. In most loadings codes for earthquake areas, the design earthquakes are given as uniform hazard spectra with an assessed return period. . The return periods from GPR model are moderately smaller than that of GR model. The return period of earthquake is a statistical measurement representing the average recurrence interval over an extensive period of time and is calculated using the relation In a real system, the rod has stiffness which not only contributes to the natural period (the stiffer the rod, the shorter the period of oscillation), but also dissipates energy as it bends. to 1000 cfs and 1100 cfs respectively, which would then imply more The generalized linear model is made up of a linear predictor, 2 acceptable levels of protection against severe low-probability earthquakes. A building natural period indicates what spectral part of an earthquake ground-motion time history has the capacity to put energy into the building. Nepal situated in the center of the Himalayan range, lies in between 804' to 8812' east longitude and 2622' to 3027' north latitude (MoHA & DP Net, 2015) . i The probability of exceedance (%) for t years using GR and GPR models. In GR model, the. 1 {\displaystyle n\rightarrow \infty ,\mu \rightarrow 0} n (This report can be downloaded from the web-site.) Hence, it can be concluded that the observations are linearly independent. 10 + One can now select a map and look at the relative hazard from one part of the country to another. . A 10-year event has a probability of 0.1 or 10% of being equaled or exceeded in any one year (exceedance probability = 1/return period = 1/100). 1 = The earthquake of magnitude 7.8 Mw, called Gorkha Earthquake, hit at Barpark located 82 kilometers northwest of Nepals capital of Kathmandu affecting millions of citizens (USGS, 2016) . 2 ) 0 T = i ^ periods from the generalized Poisson regression model are comparatively smaller It is also intended to estimate the probability of an earthquake occurrence and its return periods of occurring earthquakes in the future t years using GR relationship and compared with the Poisson model. Here are some excerpts from that document: Now, examination of the tripartite diagram of the response spectrum for the 1940 El Centro earthquake (p. 274, Newmark and Rosenblueth, Fundamentals of Earthquake Engineering) verifies that taking response acceleration at .05 percent damping, at periods between 0.1 and 0.5 sec, and dividing by a number between 2 and 3 would approximate peak acceleration for that earthquake. the probability of an event "stronger" than the event with return period . Nevertheless, the outcome of this study will be helpful for the preparedness planning to reduce the loss of life and property that may happen due to earthquakes because Nepal lies in the high seismic region. Predictors: (Constant), M. Dependent Variable: logN. Thus, the contrast in hazard for short buildings from one part of the country to another will be different from the contrast in hazard for tall buildings. log The recorded earthquake in the history of Nepal was on 7th June 1255 AD with magnitude Mw = 7.7. Generally, over the past two decades, building codes have replaced maps having numbered zones with maps showing contours of design ground motion. GLM allows choosing the suitable model fit on the basis of dispersion parameters and model fit criteria. Whereas, flows for larger areas like streams may i Other site conditions may increase or decrease the hazard. The latest earthquake experienced in Nepal was on 25th April 2015 at 11:56 am local time. Most of these small events would not be felt. Relationship Between Return Period and. ( of hydrology to determine flows and volumes corresponding to the , i ) n Mean or expected value of N(t) is. n=30 and we see from the table, p=0.01 . For planning construction of a storage reservoir, exceedance probability must be taken into consideration to determine what size of reservoir will be needed. THUS EPA IN THE ATC-3 REPORT MAP may be a factor of 2.5 less than than probabilistic peak acceleration for locations where the probabilistic peak acceleration is around 1.0 g. The following paragraphs describe how the Aa, and Av maps in the ATC code were constructed. 1 Photo by Jean-Daniel Calame on Unsplash. National Weather Service Climate Prediction Center: Understanding the "Probability of Exceedance" Forecast Graphs for Temperature and Precipitation, U.S. Geological Survey: Floods: Recurrence Intervals and 100-Year Floods (USGS), U.S. Geological Survey: Calculating Flow-Duration and Low-Flow Frequency Statistics at Streamflow-Gaging Stations, Oregon State University: Analysis Techniques: Flow Duration Analysis Tutorial, USGS The USGS Water Science School: The 100-Year Flood It's All About Chance, California Extreme Precipitation Symposium: Historical Floods. . Exceedance probability can be calculated with this equation: If you need to express (P) as a percent, you can use: In this equation, (P) represents the percent (%) probability that a given flow will be equaled or exceeded; (m) represents the rank of the inflow value, with 1 being the largest possible value. Suppose someone tells you that a particular event has a 95 percent probability of occurring in time T. For r2 = 0.95, one would expect the calculated r2 to be about 20% too high. Currently, the 1% AEP event is designated as having an 'acceptable' risk for planning purposes nearly everywhere in Australia. These parameters are called the Effective Peak Acceleration (EPA), Aa, and the Effective Peak Velocity (EPV), Av. Frequencies of such sources are included in the map if they are within 50 km epicentral distance. M The 90 percent is a "non-exceedance probability"; the 50 years is an "exposure time." This implies that for the probability statement to be true, the event ought to happen on the average 2.5 to 3.0 times over a time duration = T. If history does not support this conclusion, the probability statement may not be credible. Exceedance probability is used in planning for potential hazards such as river and stream flooding, hurricane storm surges and droughts, planning for reservoir storage levels and providing homeowners and community members with risk assessment. "Probability analysis of return period of daily maximum rainfall in annual data set of Ludhiana, Punjab", https://en.wikipedia.org/w/index.php?title=Return_period&oldid=1138514488, Articles with failed verification from February 2023, Creative Commons Attribution-ShareAlike License 3.0, This page was last edited on 10 February 2023, at 02:44. The level of protection Often that is a close approximation, in which case the probabilities yielded by this formula hold approximately. Make use of the formula: Recurrence Interval equals that number on record divided by the amount of occasions. probability of an earthquake occurrence and its return period using a Poisson The constant of proportionality (for a 5 percent damping spectrum) is set at a standard value of 2.5 in both cases. . Nepal has a long history of numerous earthquakes and has experienced great earthquakes in the past two centuries with moment magnitudes Mw = 7 and greater. Time HorizonReturn period in years Time horizon must be between 0 and 10,000 years. y then. log ) If m is fixed and t , then P{N(t) 1} 1. S Decimal probability of exceedance in 50 years for target ground motion. Magnitude (ML)-frequency relation using GR and GPR models. The true answer is about ten percent smaller, 0.63.For r2* less than 1.0 the approximation gets much better quickly. t M For this ideal model, if the mass is very briefly set into motion, the system will remain in oscillation indefinitely. "The EPA and EPV thus obtained are related to peak ground acceleration and peak ground velocity but are not necessarily the same as or even proportional to peak acceleration and velocity. the time period of interest, curve as illustrated in Figure 4-1. An alternative interpretation is to take it as the probability for a yearly Bernoulli trial in the binomial distribution. I n = It is an open access data available on the website http://seismonepal.gov.np/earthquakes. That is disfavoured because each year does not represent an independent Bernoulli trial but is an arbitrary measure of time. In the present study, generalized linear models (GLM) are applied as it basically eliminates the scaling problem compared to conventional regression models. Nevertheless, this statement may not be true and occasionally over dispersion or under dispersion conditions can be observed. The probability of exceedance in a time period t, described by a Poisson distribution, is given by the relationship: The theoretical return period is the reciprocal of the probability that the event will be exceeded in any one year. digits for each result based on the level of detail of each analysis. Return period or Recurrence interval is the average interval of time within which a flood of specified magnitude is expected to be equaled or exceeded at least once. e y x Copyright 2006-2023 Scientific Research Publishing Inc. All Rights Reserved. Look for papers with author/coauthor J.C. Tinsley. For sites in the Los Angeles area, there are at least three papers in the following publication that will give you either generalized geologic site condition or estimated shear wave velocity for sites in the San Fernando Valley, and other areas in Los Angeles. Table 4. But we want to know how to calculate the exceedance probability for a period of years, not just one given year. Deterministic (Scenario) Maps. If Another example where distance metric can be important is at sites over dipping faults. , R The following analysis assumes that the probability of the event occurring does not vary over time and is independent of past events. n The p-value is not significant (0.147 > 0.05) and failed to accept H1 for logN, which displayed that normality, exists in the data. So, let's say your aggregate EP curve shows that your 1% EP is USD 100 million. For reference, the 50% exceedance in 100 years (144 year return period) is a common basis for certain load combos for heavy civil structures. ) ) log exp The software companies that provide the modeling . Secure .gov websites use HTTPS . (These values are mapped for a given geologic site condition. , Figure 1. Damage from the earthquake has to be repaired, regardless of how the earthquake is labeled. What does it mean when people talk about a 1-in-100 year flood? = The other side of the coin is that these secondary events arent going to occur without the mainshock. of coefficient of determination (R2 = 0.991) portrayed, the magnitude of earthquake explained 99.1% of the variation in occurrence of earthquake while 0.9% were due to other variables that were not included in the model. Then, through the years, the UBC has allowed revision of zone boundaries by petition from various western states, e.g., elimination of zone 2 in central California, removal of zone 1 in eastern Washington and Oregon, addition of a zone 3 in western Washington and Oregon, addition of a zone 2 in southern Arizona, and trimming of a zone in central Idaho. 2 A seismic zone could be one of three things: Building code maps using numbered zones, 0, 1, 2, 3, 4, are practically obsolete. Sample extrapolation of 0.0021 p.a. 2% in 50 years(2,475 years) . [ Is it (500/50)10 = 100 percent? ( M The peak discharges determined by analytical methods are approximations. This probability also helps determine the loading parameter for potential failure (whether static, seismic or hydrologic) in risk analysis. The designer will apply principles Many aspects of that ATC-3 report have been adopted by the current (in use in 1997) national model building codes, except for the new NEHRP provisions. It states that the logarithm of the frequency is linearly dependent on the magnitude of the earthquake. 1 FEMA or other agencies may require reporting more significant digits i els for the set of earthquake data of Nepal. While AEP, expressed as a percent, is the preferred method The current National Seismic Hazard model (and this web site) explicitly deals with clustered events in the New Madrid Seismic Zone and gives this clustered-model branch 50% weight in the logic-tree. For many purposes, peak acceleration is a suitable and understandable parameter.Choose a probability value according to the chance you want to take. M , The probability of exceedance in 10 years with magnitude 7.6 for GR and GPR models is 22% and 23% and the return periods are 40.47 years and 38.99 years respectively. on accumulated volume, as is the case with a storage facility, then e The significant measures of discrepancy for the Poisson regression model is deviance residual (value/df = 0.170) and generalized Pearson Chi square statistics (value/df = 0.110). + L , y Effective peak acceleration could be some factor lower than peak acceleration for those earthquakes for which the peak accelerations occur as short-period spikes. {\displaystyle T} Because of these zone boundary changes, the zones do not have a deeper seismological meaning and render the maps meaningless for applications other than building codes. This table shows the relationship between the return period, the annual exceedance probability and the annual non-exceedance probability for any single given year. {\displaystyle r} n 1 Caution is urged for values of r2* larger than 1.0, but it is interesting to note that for r2* = 2.44, the estimate is only about 17 percent too large. Reservoirs are used to regulate stream flow variability and store water, and to release water during dry times as needed. This means the same as saying that these ground motions have an annual probability of occurrence of 1/475 per year. Immediate occupancy: after a rare earthquake with a return period of 475 years (10% probability of exceedance in 50 years). {\displaystyle \mu =1/T} The correlation value R = 0.995 specifies that there is a very high degree of association between the magnitude and occurrence of the earthquake. is the fitted value. The distance reported at this web site is Rjb =0, whereas another analysis might use another distance metric which produces a value of R=10 km, for example, for the same site and fault. The calculated return period is 476 years, with the true answer less than half a percent smaller. , Solve for exceedance probability. Note that the smaller the m, the larger . viii Let , n , The normality and constant variance properties are not a compulsion for the error component. The best model is the one that provides the minimum AIC and BIC (Fabozzi, Focardi, Rachev, Arshanapalli, & Markus, 2014) . = In many cases, it was noted that n ( Q50=3,200 (2). Annual Exceedance Probability and Return Period. F N If one wants to estimate the probabilistic value of spectral acceleration for a period between the periods listed, one could use the method reported in the Open File Report 95-596, USGS Spectral Response Maps and Their Use in Seismic Design Forces in Building Codes. t However, some limitations, as defined in this report, are needed to achieve the goals of public safety and .