probability of exceedance and return period earthquake

This suggests that, keeping the error in mind, useful numbers can be calculated. 2 M However, it is not clear how to relate velocity to force in order to design a taller building. Exceedance Probability = 1/(Loss Return Period) Figure 1. Maps for Aa and Av were derived by ATC project staff from a draft of the Algermissen and Perkins (1976) probabilistic peak acceleration map (and other maps) in order to provide for design ground motions for use in model building codes. y Model selection criterion for GLM. 2) Bayesian information criterion or Schwarz information (BIC): It is also a widespread model selection principle. An equivalent alternative title for the same map would be, "Ground motions having 10 percent probability of being exceeded in 50 years." 4.1. 4.2, EPA and EPV are replaced by dimensionless coefficients Aa and Av respectively. (2). ( We are performing research on aftershock-related damage, but how aftershocks should influence the hazard model is currently unresolved. as the SEL-475. 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. Official websites use .gov {\textstyle T} Critical damping is the least value of damping for which the damping prevents oscillation. PGA is a good index to hazard for short buildings, up to about 7 stories. Also, in the USA experience, aftershock damage has tended to be a small proportion of mainshock damage. Aa and Av have no clear physical definition, as such. earthquake occurrence and magnitude relationship has been modeled with and two functions 1) a link function that describes how the mean, E(Y) = i, depends on the linear predictor ^ y The spectrum estimated in Standard 2800 is based on 10 percent probability of exceedance within a 50-year period with a Return period of 475 years. For example an offshore plat-form maybe designed to withstanda windor waveloading with areturn periodof say 100 years, or an earthquake loading of say 10,000 years. Hence, the generalized Poisson regression model is considered as the suitable model to fit the data. 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. 2 . The primary reason for declustering is to get the best possible estimate for the rate of mainshocks. 0.0043 n C than the accuracy of the computational method. L ( M % This event has been the most powerful earthquake disaster to strike Nepal since the earthquake in 1934, tracked by many aftershocks, the largest being Mw = 7.3 magnitude on 12th May 2015. For example, for a two-year return period the exceedance probability in any given year is one divided by two = 0.5, or 50 percent. Time HorizonReturn period in years Time horizon must be between 0 and 10,000 years. 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. Therefore, let calculated r2 = 1.15. The industry also calls this the 100-year return period loss or 100-year probable maximum loss (PML). n the assumed model is a good one. 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. ln 0 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. 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. curve as illustrated in Figure 4-1. Table 5. the exposure period, the number of years that the site of interest (and the construction on it) will be exposed to the risk of earthquakes. ) i Exceedance probability is used as a flow-duration percentile and determines how often high flow or low flow is exceeded over time. Return period and/or exceedance probability are plotted on the x-axis. ". ) 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). Note also, that if one examines the ratio of the SA(0.2) value to the PGA value at individual locations in the new USGS national probabilistic hazard maps, the value of the ratio is generally less than 2.5. (MHHW) or mean lower low water (MLLW) datums established by CO-OPS. 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. Similarly for response acceleration (rate of change of velocity) also called response spectral acceleration, or simply spectral acceleration, SA (or Sa). In GPR model, the probability of the earthquake event of magnitude less than 5.5 is almost certainly in the next 5 years and more, with the return period 0.537 years (196 days). i . . This probability is called probability of exceedance and is related to return periods as 1/p where p is return period. {\displaystyle 1-\exp(-1)\approx 63.2\%} The residual sum of squares is the deviance for Normal distribution and is given by n Peak acceleration is a measure of the maximum force experienced by a small mass located at the surface of the ground during an earthquake. The following analysis assumes that the probability of the event occurring does not vary over time and is independent of past events. Aa was called "Effective Peak Acceleration.". t In addition, lnN also statistically fitted to the Poisson distribution, the p-values is not significant (0.629 > 0.05). Some researchers believed that the most analysis of seismic hazards is sensitive to inaccuracies in the earthquake catalogue. i ) 1-30 Seismic Rehabilitation Prestandard FEMA 356 Chapter 1: Rehabilitation Requirements where: and the mean return period, P R, at the desired exceedance probability shall be calculated from Equation (1-2): (1-2) where P EY is the probability of exceedance (expressed as a decimal) in time Y (years) for the desired earthquake hazard level. Hence, a rational probability model for count data is frequently the Poisson distribution. r T Whereas, flows for larger areas like streams may , the probability of exceedance within an interval equal to the return period (i.e. 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. In particular, A(x) is the probability that the sum of the events in a year exceeds x. The Durbin-Watson test is used to determine whether there is evidence of first order autocorrelation in the data and result presented in Table 3. 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. For example, for an Ultimate Limit State = return period of 450 years, approximately 10% probability of exceedance in a design life of 50 years. "To best understand the meaning of EPA and EPV, they should be considered as normalizing factors for construction of smoothed elastic response spectra for ground motions of normal duration. y = 10.29. The aim of the earthquake prediction is to aware people about the possible devastating earthquakes timely enough to allow suitable reaction to the calamity and reduce the loss of life and damage from the earthquake occurrence (Vere-Jones et al., 2005; Nava et al., 2005) . ( Q10), plot axes generated by statistical This would only be true if one continued to divide response accelerations by 2.5 for periods much shorter than 0.1 sec. The cumulative frequency of earthquake (N) is divided by the time period (t) and used as a response variable in generalized linear models to select a suitable model. is the fitted value. PGA, PGV, or SA are only approximately related to building demand/design because the building is not a simple oscillator, but has overtones of vibration, each of which imparts maximum demand to different parts of the structure, each part of which may have its own weaknesses. Annual recurrence interval (ARI), or return period, is also used by designers to express probability of exceedance. = . y + ^ 63.2 instances include equation subscripts based on return period (e.g. For more accurate statistics, hydrologists rely on historical data, with more years data rather than fewer giving greater confidence for analysis. This is Weibull's Formula. The relation is generally fitted to the data that are available for any region of the globe. Solving for r2*, and letting T1=50 and T2=500,r2* = r1*(500/50) = .0021(500) = 1.05.Take half this value = 0.525. r2 = 1.05/(1.525) = 0.69.Stop now. ( i 1 Any particular damping value we can express as a percentage of the critical damping value.Because spectral accelerations are used to represent the effect of earthquake ground motions on buildings, the damping used in the calculation of spectral acceleration should correspond to the damping typically experienced in buildings for which earthquake design is used. The systematic component: covariates y If the return period of occurrence The most logical interpretation for this is to take the return period as the counting rate in a Poisson distribution since it is the expectation value of the rate of occurrences. The annual frequency of exceeding the M event magnitude is N1(M) = N(M)/t = N(M)/25. of hydrology to determine flows and volumes corresponding to the H0: The data follow a specified distribution and. y 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. The objective of = {\displaystyle \mu } 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) . ( , (equivalent to 2500-years return period earthquake) and 1% exceeded in 100 years . 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. Decimal probability of exceedance in 50 years for target ground motion. or . digits for each result based on the level of detail of each analysis. . The selection of measurement scale is a significant feature of model selection; for example, in this study, transformed scale, such as logN and lnN are assumed to be better for additivity of systematic effects (McCullagh & Nelder, 1989) . The corresponding ground motion (peak acceleration) is said to have a P probability of exceedance (PE) in T years.The map contours the ground motions corresponding to this probability at all the sites in a grid covering the U.S. 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. Comparison of annual probability of exceedance computed from the event loss table for four exposure models: E1 (black solid), E2 (pink dashed), E3 (light blue dashed dot) and E4 (brown dotted). [4]:12[5][failed verification]. The theoretical return period is the reciprocal of the probability that the event will be exceeded in any one year. This probability also helps determine the loading parameter for potential failure (whether static, seismic or hydrologic) in risk analysis. The statistical analysis has been accomplished using IBM SPSS 23.0 for Mac OS. If we take the derivative (rate of change) of the displacement record with respect to time we can get the velocity record. is also used by designers to express probability of exceedance. What is annual exceedance rate? respectively. n The TxDOT preferred In this study, the magnitude values, measured in local magnitude (ML), 4.0 or greater are used for earthquake data. n = (10). 12201 Sunrise Valley Drive Reston, VA 20192, Region 2: South Atlantic-Gulf (Includes Puerto Rico and the U.S. Virgin Islands), Region 12: Pacific Islands (American Samoa, Hawaii, Guam, Commonwealth of the Northern Mariana Islands), See acceleration in the Earthquake Glossary, USGS spectral response maps and their relationship with seismic design forces in building codes, p. 297. 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. i 2 The probability of no-occurrence can be obtained simply considering the case for After selecting the model, the unknown parameters have to be estimated. The important seismic parameters (a and b values) of Gutenberg Richter (GR) relationship and generalized linear models are examined by studying the past earthquake data. Care should be taken to not allow rounding Using the equation above, the 500-year return period hazard has a 10% probability of exceedance in a 50 year time span. When the damping is large enough, there is no oscillation and the mass-rod system takes a long time to return to vertical. Given that the return period of an event is 100 years. 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) . . Corresponding ground motions should differ by 2% or less in the EUS and 1 percent or less in the WUS, based upon typical relations between ground motion and return period. Example:Suppose a particular ground motion has a 10 percent probability of being exceeded in 50 years. ^ For example, if a river reaches a flood stage of several feet one time in 100 years, there is a 1 percent chance of such a flood in any given year. t F For instance, one such map may show the probability of a ground motion exceeding 0.20 g in 50 years. S 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 Answer:No. 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).