probability of exceedance and return period earthquake

The probability of exceedance describes the 1 Nepal is one of the paramount catastrophe prone countries in the world. The latest earthquake experienced in Nepal was on 25th April 2015 at 11:56 am local time. For example, 1049 cfs for existing volume of water with specified duration) of a hydraulic structure Spectral acceleration is a measure of the maximum force experienced by a mass on top of a rod having a particular natural vibration period. Coles (2001, p.49) In common terminology, \(z_{p}\) is the return level associated with the return period \(1/p\) , since to a reasonable degree of accuracy, the level \(z_{p}\) is expected to be exceeded on average once every . Annual Exceedance Probability and Return Period. n against, or prevent, high stages; resulting from the design AEP On the average, these roughly correlate, with a factor that depends on period.While PGA may reflect what a person might feel standing on the ground in an earthquake, I don't believe it is correct to state that SA reflects what one might "feel" if one is in a building. Shrey and Baker (2011) fitted logistic regression model by maximum likelihood method using generalized linear model for predicting the probability of near fault earthquake ground motion pulses and their period. {\textstyle \mu =0.0043} M {\displaystyle \mu } t Hence, the generalized Poisson regression model is considered as the suitable model to fit the data. ) A lock () or https:// means youve safely connected to the .gov website. Furthermore, the generalized Poisson regression model is detected to be the best model to fit the data because 1) it was suitable for count data of earthquake occurrences, 2) model information criterion AIC and BIC are fewer, and 3 deviance and Pearson Chi square statistics are less than one. n = , The fatality figures were the highest for any recorded earthquake in the history of Nepal (MoHA & DP Net, 2015; MoUD, 2016) . M In the existence of over dispersion, the generalized negative binomial regression model (GNBR) offers an alternative to the generalized Poisson regression model (GPR). 1 The available data are tabulated for the frequency distribution of magnitude 4 M 7.6 and the number of earthquakes for t years. If stage is primarily dependent on flow rate, as is the case , This question is mainly academic as the results obtained will be similar under both the Poisson and binomial interpretations. , Table 6. x of occurring in any single year will be described in this manual as ! Mean or expected value of N(t) is. The probability function of a Poisson distribution is given by, f t A typical seismic hazard map may have the title, "Ground motions having 90 percent probability of not being exceeded in 50 years." . = , [ i 1 Table 1 displays the Kolmogorov Smirnov test statistics for testing specified distribution of data. Small ground motions are relatively likely, large ground motions are very unlikely.Beginning with the largest ground motions and proceeding to smaller, we add up probabilities until we arrive at a total probability corresponding to a given probability, P, in a particular period of time, T. The probability P comes from ground motions larger than the ground motion at which we stopped adding. [ ( a) PGA exceedance area of the design action with 50 years return period, in terms of km 2 and of fraction of the Italian territory, as a function of event magnitude; ( b) logistic . . GLM allows choosing the suitable model fit on the basis of dispersion parameters and model fit criteria. The value of exceedance probability of each return period Return period (years) Exceedance probability 500 0.0952 2500 0.0198 10000 0.0050 The result of PSHA analysis is in the form of seismic hazard curves from the Kedung Ombo Dam as presented in Fig. In order to check the distribution of the transformed variable, first of all Kolmogorov Smirnov test is applied. M 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. [Irw16] 1.2.4 AEP The Aggregate Exceedance Probability(AEP) curve A(x) describes the distribution of the sum of the events in a year. "100-Year Floods" When hydrologists refer to "100-year floods," they do not mean a flood occurs once every 100 years. That distinction is significant because there are few observations of rare events: for instance if observations go back 400 years, the most extreme event (a 400-year event by the statistical definition) may later be classed, on longer observation, as a 200-year event (if a comparable event immediately occurs) or a 500-year event (if no comparable event occurs for a further 100 years). D For example, the Los Angeles Ordinance Retrofit program [11] requires the retrofitting component to be designed for 75% of the 500-year (more precisely 475-year) return period earthquake hazard. . Steps for calculating the total annual probability of exceedance for a PGA of 0.97% from all three faults, (a) Annual probability of exceedance (0.000086) for PGA of 0.97% from the earthquake on fault A is equal to the annual rate (0.01) times the probability (0.0086, solid area) that PGA would exceed 0.97%. y 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. .For purposes of computing the lateral force coefficient in Sec. log scale. , 2 of hydrology to determine flows and volumes corresponding to the This concept is obsolete. Less than 10% of earthquakes happen within seismic plates, but remaining 90% are commonly found in the plate periphery (Lamb & Jones, 2012) . is 234 years ( 2 Table 2-3 Target Performance Goal - Annual Probability, Probability of Exceedance, and . more significant digits to show minimal change may be preferred. The null hypothesis is rejected if the values of X2 and G2 are large enough. Yes, basically. to occur at least once within the time period of interest) is. , = + where, N is a number of earthquakes having magnitude larger than M during a time period t, logN is a logarithm of the number of earthquakes with magnitude M, a is a constant that measures the total number of earthquakes at the given source or measure of seismic activity, and b is a slope of regression line or measure of the small versus large events. It is an open access data available on the website http://seismonepal.gov.np/earthquakes. (Gutenberg & Richter, 1954, 1956) . Includes a couple of helpful examples as well. log "Thus the EPA and EPV for a motion may be either greater or smaller than the peak acceleration and velocity, although generally the EPA will be smaller than peak acceleration while the EPV will be larger than the peak velocity. Recurrence interval = , i Return period as the reciprocal of expected frequency. ) A seismic zone could be one of three things: Building code maps using numbered zones, 0, 1, 2, 3, 4, are practically obsolete. y viii Solve for exceedance probability. Using our example, this would give us 5 / (9 + 1) = 5 / 10 = 0.50. For illustration, when M = 7.5 and t = 50 years, P(t) = 1 e(0.030305*50) = 78%, which is the probability of exceedance in 50 years. (as percent), AEP The lower amount corresponds to the 25%ile (75% probability of exceedance) of the forecast distribution, and the upper amount is the amount that corresponds to the 75%ile (25% probability of exceedance) of the forecast distribution. Parameter estimation for Gutenberg Richter model. The GPR relation obtai ned is ln M The USGS 1976 probabilistic ground motion map was considered. . Frequencies of such sources are included in the map if they are within 50 km epicentral distance. probability of an earthquake incident of magnitude less than 6 is almost certainly in the next 10 years and more, with the return period 1.54 years. ( Here, F is the cumulative distribution function of the specified distribution and n is the sample size. The Weibull equation is used for estimating the annual frequency, the return period or recurrence interval, the percentage probability for each event, and the annual exceedance probability. The probability of exceedance in a time period t, described by a Poisson distribution, is given by the relationship: to 1000 cfs and 1100 cfs respectively, which would then imply more The probability of occurrence of at least one earthquake of magnitude M in the next t years, is obtained by the relation, But EPA is only defined for periods longer than 0.1 sec. = 10.29. x {\displaystyle n\rightarrow \infty ,\mu \rightarrow 0} The 90 percent is a "non-exceedance probability"; the 50 years is an "exposure time." n On 16th January 1934 AD, an earthquake called Nepal Bihar Earthquake, hit Nepal and its surrounding regions with Mw = 8.4 magnitude. ( i exceedance probability for a range of AEPs are provided in Table So, let's say your aggregate EP curve shows that your 1% EP is USD 100 million. i Actually, nobody knows that when and where an earthquake with magnitude M will occur with probability 1% or more. Aftershocks and other dependent-event issues are not really addressable at this web site given our modeling assumptions, with one exception. Photo by Jean-Daniel Calame on Unsplash. 0 ) probability of exceedance is annual exceedance probability (AEP). model has been selected as a suitable model for the study. y This does not mean that a 100-year flood will happen regularly every 100 years, or only once in 100 years. (design earthquake) (McGuire, 1995) . Relationship Between Return Period and. the designer will seek to estimate the flow volume and duration If the observed variability is significantly smaller than the predicted variance or under dispersion, Gamma models are more appropriate. The other side of the coin is that these secondary events arent going to occur without the mainshock. The return periods commonly used are 72-year, 475-year, and 975-year periods. + The Anderson Darling test statistics is defined by, A Also, in the USA experience, aftershock damage has tended to be a small proportion of mainshock damage. For instance, a frequent event hazard level having a very low return period (i.e., 43 years or probability of exceedance 50 % in 30 years, or 2.3 % annual probability of exceedance) or a very rare event hazard level having an intermediate return period (i.e., 970 years, or probability of exceedance 10 % in 100 years, or 0.1 % annual probability . on accumulated volume, as is the case with a storage facility, then ( being exceeded in a given year. The previous calculations suggest the equation,r2calc = r2*/(1 + 0.5r2*)Find r2*.r2* = 1.15/(1 - 0.5x1.15) = 1.15/0.425 = 2.7. {\textstyle T} The map is statewide, largely based on surface geology, and can be seen at the web site of the CDMG. y Probability of Exceedance for Different. Taking logarithm on both sides, logN1(M) = logN(M) logt = logN(M) log25 = 6.532 0.887M 1.398 = 5.134 0.887*M. For magnitude 7.5, logN1(M 7.5) = 5.134 0.887*7.5 = 1.5185. This is precisely what effective peak acceleration is designed to do. The purpose of most structures will be to provide protection engineer should not overemphasize the accuracy of the computed discharges. ( Rather, they are building code constructs, adopted by the staff that produced the Applied Technology Council (1978) (ATC-3) seismic provisions. A region on a map for which a common areal rate of seismicity is assumed for the purpose of calculating probabilistic ground motions. Look for papers with author/coauthor J.C. Tinsley. n difference than expected. It is an index to hazard for short stiff structures. 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. n There is a little evidence of failure of earthquake prediction, but this does not deny the need to look forward and decrease the hazard and loss of life (Nava, Herrera, Frez, & Glowacka, 2005) . Example: "The New Madrid Seismic Zone.". The Durbin Watson test is used to measure the autocorrelation in residuals from regression analysis. ( Why do we use return periods? The primary reason for declustering is to get the best possible estimate for the rate of mainshocks. In a previous post I briefly described 6 problems that arise with time series data, including exceedance probability forecasting. (Public domain.) a than the accuracy of the computational method. These parameters are called the Effective Peak Acceleration (EPA), Aa, and the Effective Peak Velocity (EPV), Av. In addition, lnN also statistically fitted to the Poisson distribution, the p-values is not significant (0.629 > 0.05). These return periods correspond to 50, 10, and 5 percent probability of exceedance for a 50-year period (which is the expected design life . In particular, A(x) is the probability that the sum of the events in a year exceeds x. F This is consistent with the observation that chopping off the spectrum computed from that motion, except at periods much shorter than those of interest in ordinary building practice has very little effect upon the response spectrum computed from that motion, except at periods much shorter than those of interest in ordinary building practice. Now, N1(M 7.5) = 10(1.5185) = 0.030305. Journal of Geoscience and Environment Protection, Department of Statistics, Tribhuvan University, Kathmandu, Nepal, (Fabozzi, Focardi, Rachev, Arshanapalli, & Markus, 2014). The GR relationship of the earthquakes that had occurred in time period t = 25 years is expressed as logN = 6.532 0.887M, where, N is the number of earthquakes M, logN is the dependent variable, M is the predictor. FEMA or other agencies may require reporting more significant digits 1 The result is displayed in Table 2. Exceedance Probability = 1/(Loss Return Period) Figure 1. , The 1-p is 0.99, and .9930 is 0.74. / Even if the earthquake source is very deep, more than 50 km deep, it could still have a small epicentral distance, like 5 km. ) is independent from the return period and it is equal to ( If the variable of interest is expressed as exceedence over a threshold (also known as POT analysis in hydrology) the return period T can be ex-pressed as a function of the probability distri-bution function F X and of the average waiting The residual sum of squares is the deviance for Normal distribution and is given by In these cases, reporting There is no advice on how to convert the theme into particular NEHRP site categories. y Gutenberg and Richter (1954) have suggested an expression for the magnitude and frequency of earthquake events larger than magnitude (M). A lifelong writer, Dianne is also a content manager and science fiction and fantasy novelist. y = = Raymond, Montgomery, Vining, & Robinson, 2010; Creative Commons Attribution 4.0 International License. ) as the SEL-475. If the return period of occurrence 0 = The software companies that provide the modeling . 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. earthquake occurrence and magnitude relationship has been modeled with A .gov website belongs to an official government organization in the United States. i {\displaystyle r} 0.4% Probability of Exceeding (250-Year Loss) The loss amount that has a 0.4 percent probability of being equaled or exceeded in any given year. According to the results, it is observed that logN and lnN can be considered as dependent variables for Gutenberg-Richter model and generalized Poisson regression model or negative binomial regression model respectively. We employ high quality data to reduce uncertainty and negotiate the right insurance premium. Aa was called "Effective Peak Acceleration.". There are several ways to express AEP. It can also be perceived that the data is positively skewed and lacks symmetry; and thus the normality assumption has been severely violated. ( 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). The devastating earthquake included about 9000 fatalities, 23,000 injuries, more than 500,000 destroyed houses, and 270,000 damaged houses (Lamb & Jones, 2012; NPC, 2015) . cfs rather than 3,217 cfs). T = In GR model, the. = Another example where distance metric can be important is at sites over dipping faults. a result. ] Time Periods. . The AEP scale ranges from 100% to 0% (shown in Figure 4-1 An attenuation function for peak velocity was "draped" over the Aa map in order to produce a spatial broadening of the lower values of Aa. {\displaystyle ={n+1 \over m}}, For floods, the event may be measured in terms of m3/s or height; for storm surges, in terms of the height of the surge, and similarly for other events. Deterministic (Scenario) Maps. PGA is a good index to hazard for short buildings, up to about 7 stories. 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. The study The data studied in this paper is the earthquake data from the National Seismological Centre, Department of Mines and Geology, Kathmandu, Nepal, which covers earthquakes from 25th June 1994 through 29th April 2019. Input Data. M 2 (12), where, The GPR relation obtained is lnN = 15.06 2.04M. P Flow will always be more or less in actual practice, merely passing In addition, building codes use one or more of these maps to determine the resistance required by buildings to resist damaging levels of ground motion.

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