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

The return period has been erroneously equated to the average recurrence interval () of earthquakes and used to calculate seismic risk (Frankel and The normality and constant variance properties are not a compulsion for the error component. i The inverse of the annual probability of exceedance is known as the "return period," which is the average number of years it takes to get an exceedance. Make use of the formula: Recurrence Interval equals that number on record divided by the amount of occasions. Return period as the reciprocal of expected frequency. 8 Approximate Return Period. This concept is obsolete. Photo by Jean-Daniel Calame on Unsplash. years. design engineer should consider a reasonable number of significant ^ The peak discharges determined by analytical methods are approximations. . ( ( Figure 4 provides an overview of the estimated EEWS-related reduction in injury and fatality exceedance by return period for each of 11 large Swiss municipalities . Extreme Water Levels. An important characteristic of GLM is that it assumes the observations are independent. Vol.1 No.1 EARTHQUAKE ENGINEERING AND ENGINEERING VIBRATION June 2002 Article ID: 1671-3664(2002) 01-0010-10 Highway bridge seismic design: summary of FHWA/MCEER project on . = 2 + Consequently, the probability of exceedance (i.e. 1 ) A building natural period indicates what spectral part of an earthquake ground-motion time history has the capacity to put energy into the building. For r2* = 0.50, the error is less than 1 percent.For r2* = 0.70, the error is about 4 percent.For r2* = 1.00, the error is about 10 percent. = The 1-p is 0.99, and .9930 is 0.74. We are going to solve this by equating two approximations: r1*/T1 = r2*/T2. Here I will dive deeper into this task. = Given the spectrum, a design value at a given spectral period other than the map periods can be obtained. The Durbin Watson test is used to measure the autocorrelation in residuals from regression analysis. 1 In this manual, the preferred terminology for describing the X2 and G2 are both measure how closely the model fits the observed data. Probability of exceedance (%) and return period using GPR Model. In order to check the distribution of the transformed variable, first of all Kolmogorov Smirnov test is applied. ^ difference than expected. The latter, in turn, are more vulnerable to distant large-magnitude events than are short, stiff buildings. What is annual exceedance rate? x Compare the results of the above table with those shown below, all for the same exposure time, with differing exceedance probabilities. y The earthquake data are obtained from the National Seismological Centre, Department of Mines and Geology, Kathmandu, Nepal, which covers earthquakes from 25th June 1994 through 29th April 2019. Nevertheless, this statement may not be true and occasionally over dispersion or under dispersion conditions can be observed. y The Durbin Watson test statistics is calculated using, D 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. 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. Table 6 displays the estimated parameters in the generalized Poisson regression model and is given by lnN = 15.06 2.04M, where, lnN is the response variable. Thus, a map of a probabilistic spectral value at a particular period thus becomes an index to the relative damage hazard to buildings of that period as a function of geographic location. . The relation between magnitude and frequency is characterized using the Gutenberg Richter function. Thus, in this case, effective peak acceleration in this period range is nearly numerically equal to actual peak acceleration. being exceeded in a given year. Predictors: (Constant), M. Dependent Variable: logN. where, N Flow will always be more or less in actual practice, merely passing Note that for any event with return period value, to be used for screening purposes only to determine if a . Probability of Exceedance for Different. The other side of the coin is that these secondary events arent going to occur without the mainshock. One can now select a map and look at the relative hazard from one part of the country to another. PGA is a natural simple design parameter since it can be related to a force and for simple design one can design a building to resist a certain horizontal force.PGV, peak ground velocity, is a good index to hazard to taller buildings. (4). Figure 1. The ground motion parameters are proportional to the hazard faced by a particular kind of building. The same approximation can be used for r = 0.20, with the true answer about one percent smaller. 1 i acceptable levels of protection against severe low-probability earthquakes. for expressing probability of exceedance, there are instances in 63.2 , Fig. Definition. So, let's say your aggregate EP curve shows that your 1% EP is USD 100 million. Choose a ground motion parameter according to the above principles. + 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. e The GPR relation obtai ned is ln Examples of equivalent expressions for The model selection information criteria that are based on likelihood functions and applications to the parametric model based problems are 1) Akaike information criterion (AIC): AIC procedure is generally considered to select the model that minimizes AIC = 2LL + 2d, where LL is the maximized log likelihood of the model given n observation, d is the dimension of a model. Example: "The New Madrid Seismic Zone.". is 234 years ( Over the past 20 years, frequency and severity of costly catastrophic events have increased with major consequences for businesses and the communities in which they operate. One does not actually know that a certain or greater magnitude happens with 1% probability, only that it has been observed exactly once in 100 years. 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. M Find the probability of exceedance for earthquake return period ) els for the set of earthquake data of Nepal. The Gutenberg Richter relation is, log corresponding to the design AEP. ) a The probability of exceedance of magnitude 6 or lower is 100% in the next 10 years. 1 After selecting the model, the unknown parameters are estimated. T Also, the estimated return period below is a statistic: it is computed from a set of data (the observations), as distinct from the theoretical value in an idealized distribution. This is not so for peak ground parameters, and this fact argues that SA ought to be significantly better as an index to demand/design than peak ground motion parameters. There is a statistical statement that on an average, a 10 years event will appear once every ten years and the same process may be true for 100 year event. Peak acceleration is a measure of the maximum force experienced by a small mass located at the surface of the ground during an earthquake. y For many purposes, peak acceleration is a suitable and understandable parameter.Choose a probability value according to the chance you want to take. 1 . 4-1. Below are publications associated with this project. Short buildings, say, less than 7 stories, have short natural periods, say, 0.2-0.6 sec. Mean or expected value of N(t) is. Table 1 displays the Kolmogorov Smirnov test statistics for testing specified distribution of data. You can't find that information at our site. Factors needed in its calculation include inflow value and the total number of events on record. In seismology, the Gutenberg-Richter relation is mainly used to find the association between the frequency and magnitude of the earthquake occurrence because the distributions of earthquakes in any areas of the planet characteristically satisfy this relation (Gutenberg & Richter, 1954; Gutenberg & Richter, 1956) . 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) . i + is the return period and The GR relation is logN(M) = 6.532 0.887M. As an example, a building might be designed to withstand ground motions imparted by earthquakes with a return period of 2,500 years as mandated by relevant design codes.2-For a ground motion with an associated average return period, the annual probability of exceedance is simply the inverse of the average return period. years containing one or more events exceeding the specified AEP. n L exceedance probability for a range of AEPs are provided in Table 1 A flood with a 1% AEP has a one in a hundred chance of being exceeded in any year. i Figure 2 demonstrates the probability of earthquake occurrence (%) for different time periods in years using GR and GPR models. 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. The GPR relation obtained is lnN = 15.06 2.04M. . e 1 The frequency of exceedance is the number of times a stochastic process exceeds some critical value, usually a critical value far from the process' mean, per unit time. 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. (as probability), Annual the assumed model is a good one. Is it (500/50)10 = 100 percent? I e the designer will seek to estimate the flow volume and duration n 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. The be reported by rounding off values produced in models (e.g. 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. ^ F The chance of a flood event can be described using a variety of terms, but the preferred method is the Annual Exceedance Probability (AEP). d But EPA is only defined for periods longer than 0.1 sec. The entire region of Nepal is likely to experience devastating earthquakes as it lies between two seismically energetic Indian and Eurasian tectonic plates (MoUD, 2016) . PML losses for the 100-year return period for wind and for the 250-year return period for earthquake. 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. i e The earlier research papers have applied the generalized linear models (GLM), which included Poisson regression, negative-binomial, and gamma regression models, for an earthquake hazard analysis. Earthquake Parameters. For example, a 10-year flood has a 1/10 = 0.1 or 10% chance of being exceeded in any one year and a 50-year flood has a 0.02 or 2% chance of being exceeded in any one year. C (MHHW) or mean lower low water (MLLW) datums established by CO-OPS. Yes, basically. Similarly, the return period for magnitude 6 and 7 are calculated as 1.54 and 11.88 years. probability of an earthquake occurrence and its return period using a Poisson i The maps can be used to determine (a) the relative probability of a given critical level of earthquake ground motion from one part of the country to another; (b) the relative demand on structures from one part of the country to another, at a given probability level. The probability of exceedance ex pressed in percentage and the return period of an earthquake in ye ars for the Poisson re gression model is sho wn in T able 8 . 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. N N Examples include deciding whether a project should be allowed to go forward in a zone of a certain risk or designing structures to withstand events with a certain return period. The annual frequency of exceeding the M event magnitude for 7.5 ML is calculated as N1(M) = exp(a bM lnt) = 0.031. Despite the connotations of the name "return period". + n Calculating exceedance probability also provides important risk information to governments, hydrologists, planners, homeowners, insurers and communities. / Anchor: #i1080498 Table 4-1: Three Ways to Describe Probability of . When the observed variance is greater than the variance of a theoretical model, over dispersion happens. 2 = 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). It is a statistical measurement typically based on historic data over an extended period, and is used usually for risk analysis. A earthquake strong motion record is made up of varying amounts of energy at different periods. x 0 and 1), such as p = 0.01. more significant digits to show minimal change may be preferred. The probability of exceedance (%) for t years using GR and GPR models. design engineer should consider a reasonable number of significant The probability of no-occurrence can be obtained simply considering the case for viii An equivalent alternative title for the same map would be, "Ground motions having 10 percent probability of being exceeded in 50 years." N i The Kolmogorov Smirnov test statistics is defined by, D than the accuracy of the computational method. ) duration) being exceeded in a given year. Loss Exceedance Probability (Return Period) Simulation Year Company Aggregate Loss (USD) 36: 0.36% (277 years) 7059: 161,869,892: 37: . ! Relationship Between Return Period and. 1 Algermissen, S.T., and Perkins, David M., 1976, A probabilistic estimate of maximum acceleration in rock in the contiguous United States, U.S. Geological Survey Open-File Report OF 76-416, 45 p. Applied Technology Council, 1978, Tentative provisions for the development of seismic regulations for buildings, ATC-3-06 (NBS SP-510) U.S Government Printing Office, Washington, 505 p. Ziony, J.I., ed, 1985, Evaluating earthquake hazards in the Los Angeles region--an earth-science perspective, U.S. Geological Survey Professional Paper 1360, US Gov't Printing Office, Washington, 505 p. C. J. Wills, et al:, A Site-Conditions Map for California Based on Geology and Shear-Wave Velocity, BSSA, Bulletin Seismological Society of America,December 2000, Vol.