a In this paper, the frequency of an
Table 1 displays the Kolmogorov Smirnov test statistics for testing specified distribution of data. The Anderson Darling test is not available in SPSS version 23 and hence it is calculated using Anderson Darling normality test calculator for excel. Nepal is one of the paramount catastrophe prone countries in the world. + P 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. i The small value of the D-W score (0.596 < 2) indicates a positive first order autocorrelation, which is assumed to be a common occurrence in this case. The mean and variance of Poisson distribution are equal to the parameter . Despite the connotations of the name "return period". Figure 2. * Journal of Geoscience and Environment Protection, Department of Statistics, Tribhuvan University, Kathmandu, Nepal, (Fabozzi, Focardi, Rachev, Arshanapalli, & Markus, 2014). = To be a good index, means that if you plot some measure of demand placed on a building, like inter story displacement or base shear, against PGA, for a number of different buildings for a number of different earthquakes, you will get a strong correlation. The report will tell you rates of small events as well as large, so you should expect a high rate of M5 earthquakes within 200 km or 500 km of your favorite site, for example. Table 7. (2). those agencies, to avoid minor disagreements, it is acceptable to 0 and 1), such as p = 0.01. When very high frequencies are present in the ground motion, the EPA may be significantly less than the peak acceleration. earthquake occurrence and magnitude relationship has been modeled with
"Return period" is thus just the inverse of the annual probability of occurrence (of getting an exceedance of that ground motion). (13). This probability measures the chance of experiencing a hazardous event such as flooding. Share sensitive information only on official, secure websites. These models are. be reported to whole numbers for cfs values or at most tenths (e.g. A 1 in 100 year sea level return period has an annual exceedance probability of 1%, whereas a 1 in 200 year sea level has an annual exceedance probability of 0.5%. M T y ) In the engineering seismology of natural earthquakes, the seismic hazard is often quantified by a maximum credible amplitude of ground motion for a specified time period T rather than by the amplitude value, whose exceedance probability is determined by Eq. i ) The annual frequency of exceeding the M event magnitude for 7.5 ML is calculated as N1(M) = exp(a bM lnt) = 0.031. Figure 2 demonstrates the probability of earthquake occurrence (%) for different time periods in years using GR and GPR models. Currently, the 1% AEP event is designated as having an 'acceptable' risk for planning purposes nearly everywhere in Australia. Uniform Hazard Response Spectrum 0.0 0.5 . 3) What is the probability of an occurrence of at least one earthquake of magnitude M in the next t years? (11). Climatologists also use probability of exceedance to determine climate trends and for climate forecasting. 10 On the other hand, the EPV will generally be greater than the peak velocity at large distances from a major earthquake". 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) . An area of seismicity probably sharing a common cause. a Similarly for response acceleration (rate of change of velocity) also called response spectral acceleration, or simply spectral acceleration, SA (or Sa). it is tempting to assume that the 1% exceedance probability loss for a portfolio exposed to both the hurricane and earthquake perils is simply the sum of the 1% EP loss for hurricane and the 1% EP loss . i The model provides the important parameters of the earthquake such as. If the return period of occurrence ^ log , In the present study, generalized linear models (GLM) are applied as it basically eliminates the scaling problem compared to conventional regression models. The one we use here is the epicentral distance or the distance of the nearest point of the projection of the fault to the Earth surface, technically called Rjb. Actually, nobody knows that when and where an earthquake with magnitude M will occur with probability 1% or more. Relationship Between Return Period and. That is disfavoured because each year does not represent an independent Bernoulli trial but is an arbitrary measure of time. , Life safety: after maximum considered earthquake with a return period of 2,475 years (2% probability of exceedance in 50 years). The most important factors affecting the seismic hazard in this region are taken into account such as frequency, magnitude, probability of exceedance, and return period of earthquake (Sebastiano, 2012) . Several studies mentioned that the generalized linear model is used to include a common method for computing parameter estimates, and it also provides significant results for the estimation probabilities of earthquake occurrence and recurrence periods, which are considered as significant parameters of seismic hazard related studies (Nava et al., 2005; Shrey & Baker, 2011; Turker & Bayrak, 2016) . 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. ln ( = T The return period for a 10-year event is 10 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. Extreme Water Levels. E[N(t)] = l t = t/m. The approximate annual probability of exceedance is about 0.10(1.05)/50 = 0.0021. 2 1 1 Google . In this manual, the preferred terminology for describing the n Konsuk and Aktas (2013) analyzed that the magnitude random variable is distributed as the exponential distribution. We employ high quality data to reduce uncertainty and negotiate the right insurance premium. Using the equation above, the 500-year return period hazard has a 10% probability of exceedance in a 50 year time span. The 90 percent is a "non-exceedance probability"; the 50 years is an "exposure time." Rather, they are building code constructs, adopted by the staff that produced the Applied Technology Council (1978) (ATC-3) seismic provisions. {\textstyle T} For planning construction of a storage reservoir, exceedance probability must be taken into consideration to determine what size of reservoir will be needed. 2 The same approximation can be used for r = 0.20, with the true answer about one percent smaller. The correlation value R = 0.995 specifies that there is a very high degree of association between the magnitude and occurrence of the earthquake. A lifelong writer, Dianne is also a content manager and science fiction and fantasy novelist. 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. Table 6. The theoretical return period is the reciprocal of the probability that the event will be exceeded in any one year. , the probability of exceedance within an interval equal to the return period (i.e. The best model is the one that provides the minimum AIC and BIC (Fabozzi, Focardi, Rachev, Arshanapalli, & Markus, 2014) . The GPR relation obtained is lnN = 15.06 2.04M. An event having a 1 in 100 chance 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) . Counting exceedance of the critical value can be accomplished either by counting peaks of the process that exceed the critical value or by counting upcrossings of the critical value, where an upcrossing is an event . 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. 2 Examples of equivalent expressions for . To get an approximate value of the return period, RP, given the exposure time, T, and exceedance probability, r = 1 - non-exceedance probability, NEP, (expressed as a decimal, rather than a percent), calculate: RP = T / r* Where r* = r(1 + 0.5r).r* is an approximation to the value -loge ( NEP ).In the above case, where r = 0.10, r* = 0.105 which is approximately = -loge ( 0.90 ) = 0.10536Thus, approximately, when r = 0.10, RP = T / 0.105. . Reservoirs are used to regulate stream flow variability and store water, and to release water during dry times as needed. The probability of exceedance expressed in percentage and the return period of an earthquake in years for the Poisson regression model is shown in Table 8. t where, yi is the observed values and 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. The approximate annual probability of exceedance is about 0.10(1.05)/50 = 0.0021. y On the other hand, some authors have shown that non-linear response of a certain structure is only weakly dependent on the magnitude and distance of the causative earthquake, so that non-linear response is related to linear response (SA) by a simple scalar (multiplying factor). where, ei are residuals from ordinary least squares regression (Gerald, 2012) . regression model and compared with the Gutenberg-Richter model. Similarly, the return period for magnitude 6 and 7 are calculated as 1.54 and 11.88 years. If stage is primarily dependent on flow rate, as is the case Scenario Upper Loss (SUL): Defined as the Scenario Loss (SL) that has a 10% probability of; exceedance due to the specified earthquake ground motion of the scenario considered. ) Return period as the reciprocal of expected frequency. The Kolmogorov Smirnov test statistics is defined by, D Predictors: (Constant), M. Dependent Variable: logN. = i 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. Each of these magnitude-location pairs is believed to happen at some average probability per year. 1 H0: The data follow a specified distribution and. t 2 i While this can be thought of as the average rate of exceedance over the long term, it is more accurate to say "this loss has a 1 in 100 chance of being . Several cities in the western U.S. have experienced significant damage from earthquakes with hypocentral depth greater than 50 km. In the existence of over dispersion, the generalized negative binomial regression model (GNBR) offers an alternative to the generalized Poisson regression model (GPR). = 2023 Leaf Group Ltd. / Leaf Group Media, All Rights Reserved. The return periods commonly used are 72-year, 475-year, and 975-year periods. Return Period (T= 1/ v(z) ), Years, for Different Design Time Periods t (years) Exceedance, % 10 20 30 40 50 100. . ( 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. 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 . {\displaystyle n\mu \rightarrow \lambda } periods from the generalized Poisson regression model are comparatively smaller
One would like to be able to interpret the return period in probabilistic models. (10). 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. Zone maps numbered 0, 1, 2, 3, etc., are no longer used for several reasons: Older (1994, 1997) versions of the UBC code may be available at a local or university library. GLM allows choosing the suitable model fit on the basis of dispersion parameters and model fit criteria. The study
= Even in the NMSZ case, however, only mainshocks are clustered, whereas NMSZ aftershocks are omitted. 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). = 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. . Variations of the peak horizontal acceleration with the annual probability of exceedance are also included for the three percentiles 15, 50 . Model selection criterion for GLM. , y log Annual Exceedance Probability and Return Period. The null hypothesis is rejected if the values of X2 and G2 are large enough. (as probability), Annual In particular, A(x) is the probability that the sum of the events in a year exceeds x. (Madsen & Thyregod, 2010; Raymond, Montgomery, Vining, & Robinson, 2010; Shroder & Wyss, 2014) . Actually, nobody knows that when and where an earthquake with magnitude M will occur with probability 1% or more. The goodness of fit of a statistical model is continued to explain how well it fits a set of observed values y by a set of fitted values That is, the probability of no earthquakes with M>5 in a few-year period is or should be virtually unaffected by the declustering process. ^ The recurrence interval, or return period, may be the average time period between earthquake occurrences on the fault or perhaps in a resource zone. (12), where, x 3.3a. Hence, the spectral accelerations given in the seismic hazard maps are also 5 percent of critical damping. This conclusion will be illustrated by using an approximate rule-of-thumb for calculating Return Period (RP). Given that the return period of an event is 100 years. This table shows the relationship between the return period, the annual exceedance probability and the annual non-exceedance probability for any single given year. derived from the model. Some researchers believed that the most analysis of seismic hazards is sensitive to inaccuracies in the earthquake catalogue. The Durbin Watson test statistics is calculated using, D The hypothesis for the Durbin Watson test is H0: There are no first order autocorrelation and H1: The first order correlation exists. Dianne features science as well as writing topics on her website, jdiannedotson.com. Target custom probability of exceedance in a 50 year return period as a decimal Example: 0.10 Optional, if not specificed then service returns results for BSE-2N, BSE-1N, BSE-2E, BSE-1E instead . R So, let's say your aggregate EP curve shows that your 1% EP is USD 100 million. y probability of exceedance is annual exceedance probability (AEP). Another example where distance metric can be important is at sites over dipping faults. For example, 1049 cfs for existing the time period of interest, ) The GR relation is logN(M) = 6.532 0.887M. of fit of a statistical model is applied for generalized linear models and
The level of earthquake chosen as the basis of a deterministic analysis is usually measured in terms of estimated return period. A building natural period indicates what spectral part of an earthquake ground-motion time history has the capacity to put energy into the building. 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. 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) . The solution is the exceedance probability of our standard value expressed as a per cent, with 1.00 being equivalent to a 100 per cent probability. = + 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.