Attenuation Equation Research Articles

Back-analysis of the source of the 1956 Eskisehir Earthquake using attenuation equation and damage data

The paper discusses the possible source fault which resulted in the Mw 6.4 Eskisehir earthquake on February 20, 1956, within the Anatolian complex. This is particularly important in view of the fact that Eskisehir, built mainly on alluvium, has a population of 500,000. The damage data were reviewed related to the number of people in the various villages affected. An empirical attenuation equation derived from Anatolian seismicity was applied to three suspected fault segments and the resultant ground motion rates were statistically compared with the damage data. A number of equally distributed suspected epicentres on each segment were considered. It is concluded that the earthquake was probably related to the Kavacik fault

Experimental and numerical study on the flight and penetration properties of explosively-formed projectile

The whole process of formation, flying and penetration of explosively-formed projectile (EFP) is simulated by a 3D coupled hydrocode of Ls_dyna. The caliber of the shaped charge is 60 mm and EFP is a kind of overturned shaped charge. The Arbitrary Lagrangian–Eulerian (ALE) method is adopted to consider the fluid–solid coupling problem. The velocity attenuation equation is fitted to forecast the flight distance of EFP. The penetration property of EFP to the armor plate is studied by similarity theory and numerical simulation. For validating the equation, a test is designed to study the residual velocity after penetrating a 25 mm thick steel plate from a distance of 48 m. Therefore, some important solutions are obtained from the comparison of the simulation and experiment. The solutions are optimized charge structure of EFP, the ideal shape of projectile, the attenuation rule of flight process and the penetration property after 48 m flight. The numerical solution fits the experimental data well and the study results provide important reference to the design of EFP in engineering.

2005년 Fukuoka 지진기록을 이용한 국내 및 일본의 지진동 감쇄 특성 평가

The characteristics of the ground motion attenuation in Korea and Japan were estimated using the earthquake ground motions recorded at the equal distance observation stations by KMA, K-NET and KiK-net of Korea and Japan. The ground motion attenuation equations proposed for Korea and Japan were evaluated by comparing the predicted value fer the Fukuoka earthquake with the observed records. The predicted value from the attenuation equations shows good agreement with the observed records and each other. It can be concluded from this study that the ground motion attenuation equations developed for Japan can be used usefully for the prediction of a ground motion from far field earthquake more than 200 km and for the evaluation of the far field ground motion attenuation equations proposed fer Korea.

Attenuation in Risk Estimates in Logistic and Cox Proportional-Hazards Models due to Group-Based Exposure Assessment Strategy

In occupational epidemiology, it is often possible to obtain repeated measurements of exposure from a sample of subjects (workers) who belong to exposure groups associated with different levels of exposure. Average exposures from a sample of workers can be assigned to all members of that group including those who are not sampled, leading to a group-based exposure assessment. We discuss how this group-based exposure assessment leads to approximate Berkson error model when the number of subjects with exposure measurements in each group is large, and how the error variance approximates the between-worker variability. Under the normality assumption of exposures and with moderately large number of workers in each group, there is attenuation in the estimate of the association parameter, the magnitude of which depends on the sizes of the between-worker variability and the true association parameter. Approximate equations for attenuation have been derived in logistic and Cox proportional-hazards models. These equations show that the attenuation in Cox proportional-hazards models is generally more severe than in logistic regression. Furthermore, when the between-worker variability is large, our simulation study found that the approximation by equation is poor for the Cox proportional-hazards model. If the number of subjects is small, the approximation does not hold for either model.

Developing a Map of Geologically Defined Site-Condition Categories for California

Consideration of site conditions is a vital step in analyzing and predicting earthquake ground motion. The importance of amplification by soil conditions has long been recognized, but though many seismic-instrument sites have been characterized by their geologic conditions, there has been no consistent, simple classification applied to all sites. As classification of sites by shear-wave velocity has become more common, the need to go back and provide a simple uniform classification for all stations has become apparent. Within the Pacific Earthquake Engineering Research Center’s Next Generation Attenuation equation project, developers of attenuation equations recognized the need to consider site conditions and asked that the California Geological Survey provide site conditions information for all stations that have recorded earthquake ground motion in California. To provide these estimates, we sorted the available shear-wave velocity data by geologic unit, generalized the geologic units, and prepared a map so that we could use the extent of the map units to transfer the velocity characteristics from the sites where they were measured to sites on the same or similar materials. This new map is different from the California Geological Survey “preliminary site-conditions map of California” in that 19 geologically defined categories are used, rather than National Earthquake Hazards Reduction Program categories. Although this map does not yet cover all of California, when completed it may provide a basis for more precise consideration of site conditions in ground-motion calculations.

Volumetric fraction measurement in oil-water-gas multiphase flow with dual energy gamma-ray system

Volumetric fraction distribution measurement is a constituent part of process tomography system in oil-water-gas multiphase flow. With the technological development of nuclear radial inspection, dual-energy γ-ray techniques make it possible to investigate the concentration of the different components on the cross-section of oil-water-gas multiphase pipe-flow. The dual-energy gamma-ray technique is based on materials attenuation coefficients measurement comprised of two radioactive isotopes of241Am and241Cs which have emission energies at 59.5 keV and 662 keV in this project. Nuclear instruments and data acquisition system were designed to measure the material's attenuation dose rate and a number of static tests were conducted at the Multiphase Laboratory, Institute of Mechanics, Chinese Academy of Sciences. Three phases of oil-water-gas media were investigated for their possible use to simulate different media volumetric fraction distributions in experimental vessels. Attenuation intensities were measured, and the arithmetic of linear attenuation coefficients and the equations of volumetric fractions were studied. Investigation of an unexpected measurement error from attenuation equations revealed that a modified arithmetic was involved and finally the system achieved acceptable accuracy in experimental research.

The impact of epistemic uncertainty on an earthquake loss model

AbstractModels capable of estimating losses in future earthquakes are of fundamental importance for emergency planners, for the insurance and reinsurance industries, and for code drafters. Constructing a loss model for a city, region or country involves compiling databases of earthquake activity, ground conditions, attenuation equations, building stock and infrastructure exposure, and vulnerability characteristics of the exposed inventory, all of which have large associated uncertainties. Many of these uncertainties can be classified as epistemic, implying—at least in theory—that they can be reduced by acquiring additional data or improved understanding of the physical processes. The effort and cost involved in refining the definition of each component of a loss model can be very large, for which reason it is useful to identify the relative impact on the calculated losses due to variations in these components. A mechanically sound displacement‐based approach to loss estimation is applied to a test case of buildings along the northern side of the Sea of Marmara in Turkey. Systematic variations of the parameters defining the demand (ground motion) and the capacity (vulnerability) are used to identify the relative impacts on the resulting losses, from which it is found that the influence of the epistemic uncertainty in the capacity is larger than that of the demand for a single earthquake scenario. Thus, the importance of earthquake loss models which allow the capacity parameters to be customized to the study area under consideration is highlighted. Copyright © 2005 John Wiley & Sons, Ltd.

확률론적 지진재해도를 이용한 시나리오 지진의 결정기법에 관한 연구

The design earthquake used for the seismic analysis and design of NPP (Nuclear Power Plant) is determined by the deterministic or probabilistic methods. The probabilistic seismic hazard analysis(PSHA) for the nuclear power plant sites was performed for the probabilistic seismic risk assessment. The probabilistic seismic hazard analysis for the nuclear power plant site had been completed as a part of the probabilistic seismic risk assessment. The probabilistic method become a resonable method to determine the design earthquakes for NPPs. In this study, the defining method of the probability based scenario earthquake was established, and as a sample calculation, the probability based scenario earthquakes were estimated by the de-aggregation of the probabilistic seismic hazard. By using this method, it is possible to define the probability based scenario earthquakes for the seismic design and seismic safety evaluation of structures. It is necessary to develop the rational seismic source map and the attenuation equations for the development of reasonable scenario earthquakes.

Attenuation relations for horizontal peak ground acceleration and response spectrum in northeastern Tibetan Plateau region

The seismic intensity attenuation relations in northeastern Tibetan Plateau region are established by a regression analysis on isoseismal data. Then the attenuation relations for horizontal peak ground acceleration and short-period response spectrum for western North America are derived based on the database of HUO Jun-rong and strong motion data from recent earthquakes. The attenuation relations of long-period response spectrum for western North American are developed by analyzing the broadband digital seismic recordings of southern California. By integrating the short-period and long-period attenuation relationships, the attenuation relations for horizontal acceleration response spectrum in the period range of 0.04–6 s for western North America are established. The attenuation equation that accounts for the magnitude saturation and near-field saturation of high frequency ground motion is used. Finally the attenuation relations for horizontal peak ground acceleration and response spectrum for the region of northeastern Tibetan Plateau are developed by using the transforming method.

Probabilistic seismic hazard analysis for Sumatra, Indonesia and across the Southern Malaysian Peninsula

The ground motion hazard for Sumatra and the Malaysian peninsula is calculated in a probabilistic framework, using procedures developed for the US National Seismic Hazard Maps. We constructed regional earthquake source models and used standard published and modified attenuation equations to calculate peak ground acceleration at 2% and 10% probability of exceedance in 50 years for rock site conditions. We developed or modified earthquake catalogs and declustered these catalogs to include only independent earthquakes. The resulting catalogs were used to define four source zones that characterize earthquakes in four tectonic environments: subduction zone interface earthquakes, subduction zone deep intraslab earthquakes, strike-slip transform earthquakes, and intraplate earthquakes. The recurrence rates and sizes of historical earthquakes on known faults and across zones were also determined from this modified catalog. In addition to the source zones, our seismic source model considers two major faults that are known historically to generate large earthquakes: the Sumatran subduction zone and the Sumatran transform fault. Several published studies were used to describe earthquakes along these faults during historical and pre-historical time, as well as to identify segmentation models of faults. Peak horizontal ground accelerations were calculated using ground motion prediction relations that were developed from seismic data obtained from the crustal interplate environment, crustal intraplate environment, along the subduction zone interface, and from deep intraslab earthquakes. Most of these relations, however, have not been developed for large distances that are needed for calculating the hazard across the Malaysian peninsula, and none were developed for earthquake ground motions generated in an interplate tectonic environment that are propagated into an intraplate tectonic environment. For the interplate and intraplate crustal earthquakes, we have applied ground-motion prediction relations that are consistent with California (interplate) and India (intraplate) strong motion data that we collected for distances beyond 200 km. For the subduction zone equations, we recognized that the published relationships at large distances were not consistent with global earthquake data that we collected and modified the relations to be compatible with the global subduction zone ground motions. In this analysis, we have used alternative source and attenuation models and weighted them to account for our uncertainty in which model is most appropriate for Sumatra or for the Malaysian peninsula. The resulting peak horizontal ground accelerations for 2% probability of exceedance in 50 years range from over 100% g to about 10% g across Sumatra and generally less than 20% g across most of the Malaysian peninsula. The ground motions at 10% probability of exceedance in 50 years are typically about 60% of the ground motions derived for a hazard level at 2% probability of exceedance in 50 years. The largest contributors to hazard are from the Sumatran faults.

A Potential Attenuation Equation for Design and Analysis of Pipeline Cathodic Protection Systems with Displaced Anodes

Abstract A recently proposed potential attenuation equation for pipelines and risers with multiple, equally spaced, identical superimposed (bracelet) galvanic anodes that incorporates all relevant ...

Empirical Attenuation Equations for Vertical Ground Motion in Turkey

In the aftermath of two destructive urban earthquakes in 1999 in Turkey, empirical models of strong motion attenuation relationships that have been previously developed for North American and European earthquakes have been utilized in a number of national seismic hazard studies. However, comparison of empirical evidence and estimates present significant differences. For that reason, a data set created from a suite of 100 vertical strong ground motion records from 47 national earthquakes that occurred between 1976 and 2002 has been used to develop attenuation relationships for strong ground motion in Turkey. A consistent set of empirical attenuation relationships was derived for predicting vertical peak and pseudo-absolute vertical acceleration spectral ordinates in terms of magnitude, source-to-site distance, and local geological conditions. The study manifests the strong dependence of vertical to horizontal (V/H) acceleration ratio on spectral periods and relatively weaker dependence on site geology, magnitude, and distance. The V/H ratio is found to be particularly significant at the higher frequency end of the spectrum, reaching values as high as 0.9 at short distances on soil sites. The largest long-period spectral ratios are observed to occur on rock sites where they can reach values in excess of 0.5. These results raise misgivings concerning the practice of assigning the V/H ratio a standard value of two-thirds. Hence, nonconservatism of this value at short periods and its conservatism at long periods underline the need for its revision, at least for practice in Turkey.

An attenuation relationship based on Turkish strong motion data and iso-acceleration map of Turkey

This paper presents an attenuation relationship of peak ground acceleration (PGA) derived from Turkish strong motion data for rock, soil and soft soil sites and an iso-acceleration map of Turkey based on this relationship. For the purpose, among all the three-component accessible records, 221 records from 122 earthquakes that occurred in Turkey between 1976 and November 2003 were selected. The database was compiled for earthquakes with moment magnitudes ( M w) and PGA values ranging between 4.1 and 7.5, and 20 and 806 gal, and distances to epicenter considered in the database were between 5 and 100 km. From the regression analysis of the data, an attenuation equation of PGA considering rock, soil and soft soil conditions was developed. The PGA values predicted from the equation suggested in this study and those both from a few domestic equations and some imported equations were compared. In addition, an iso-acceleration map of Turkey was constructed using the suggested attenuation equation and considering both known active faults and epicenter locations of the earthquakes that have occurred in Turkey.

Comparisons of Ground Motions from Five Aftershocks of the 1999 Chi-Chi, Taiwan, Earthquake with Empirical Predictions Largely Based on Data from California

The observed ground motions from five large aftershocks of the 1999 Chi-Chi, Taiwan, earthquake are compared with predictions from four equations based primarily on data from California. The four equations for active tectonic re- gions are those developed by Abrahamson and Silva (1997), Boore et al. (1997), Campbell (1997, 2001), and Sadigh et al. (1997). Comparisons are made for horizontal-component peak ground accelerations and 5%-damped pseudoaccelera- tion response spectra at periods between 0.02 sec and 5 sec. The observed motions are in reasonable agreement with the predictions, particularly for distances from 10 to 30 km. This is in marked contrast to the motions from the Chi-Chi mainshock, which are much lower than the predicted motions for periods less than about 1 sec. The results indicate that the low motions in the mainshock are not due to unusual, localized absorption of seismic energy, because waves from the mainshock and the aftershocks generally traverse the same section of the crust and are recorded at the same stations. The aftershock motions at distances of 30-60 km are somewhat lower than the predictions (but not nearly by as small a factor as those for the mainshock), suggesting that the ground motion attenuates more rapidly in this region of Taiwan than it does in the areas we compare with it. We provide equations for the regional attenuation of response spectra, which show increasing decay of motion with distance for decreasing oscillator periods. This observational study also demonstrates that ground motions have large earthquake-location-dependent variability for a specific site. This variability reduces the accuracy with which an earthquake-specific predic- tion of site response can be predicted. Online Material: PGAs and PSAs from the 1999 Chi-Chi earthquake and five aftershocks.

Technical Note:A Modified Potential Attenuation Equation for Cathodically Polarized Marine Pipelines and Risers

Abstract A previously developed first-principles-based equation for potential attenuation along marine pipelines and risers with multiple, equally spaced, identical galvanic anodes was modified to accommodate an error in its derivation. Both the original and modified equations account for the electrolyte (anode), coating, polarization, and metallic path resistances and, as such, represent improvements over previously available representations. Coordinate mapping-based finite difference method (CoMB-FDM) solutions are presented; and to the extent possible, accuracy of the proposed modified equation is verified.

Equations of laser‐induced plasma shock wave motion in air

AbstractSimple equations of laser‐induced plasma shock wave motion in air are studied, based on the point blast theory. The theoretical models of the shock wave front evolution characterize two stages of shock wave propagation: the initial formation stage and the free attenuation stage. Due considerations of the boundary conditions, the validity range of the attenuation equation is larger than the one of the t2/5 law of the self‐similar solution. Furthermore, the theoretical results are in good agreement with the experimental data and nuclear explosion results. © 2003 Wiley Periodicals, Inc. Microwave Opt Technol Lett 38: 75–79, 2003

An empirical formula for the prediction of rain attenuation in frequency range 0.6 - 100 GHz

An empirical formula for calculating the extinction cross section (ECS) by raindrops over a broad frequency range is first derived based on extensive calculations made on a widely varying in mean radius of modified Pruppacher and Pitter (MPP) raindrop models ranging from 0.25 to 3.5 mm. The expansion coefficients in the empirical formula are determined by least-squares curve fitting of numerical data obtained by the volume integral equation formulation (VIEF). The formula satisfies the frequency and raindrop size dependence. Numerical results obtained from the empirical formula for calculating the ECS are generally in good agreement with those calculated by the VIEF for raindrops with mean radius varying from 0.25 to 3.5 mm in the frequency range from 0.6 to 100 GHz. The average error in the ECS is less than 10%. The formula thus provides a simple and inexpensive method for calculating the ECS of raindrops, which otherwise requires complicated and expensive methods of calculation. By implementing this empirical formula of ECS into the rain attenuation equation, a new numerically empirical formula for calculating the specific rain attenuation is also proposed. The validity of the empirical formula for calculating the specific rain attenuation is also checked by comparing the obtained results of specific rain attenuation with those obtained from Li et al.'s (1995) solution, Yeo et al.'s (1993) measurement, and Olsen et al.'s (1978) power-law equation.

Sistema probabilístico de información geográfica de Amenaza sísmica de Colombia

Computation of seismic hazard at rock or firm sites has been a well established technique for many years. Hazard is generally expressed in terms of exceedance rates (ER), defined as the mean annual number of times in which a given value of intensity is exceeded. The inverse of the ER of some intensity is called its mean return period. Usually, the practice was to compute seismic hazard in terms of ER of peak motion values, such as peak ground acceleration, velocity and displacement,. More recently, uniform-hazard response spectra (UHS) have been constructed in a more direct and precise way, by means of attenuation equations that relate, typically, magnitude and distance with response spectral values for a range of periods. By performing a conventional hazard analysis on a period by period basis, it is possible to construct response spectra whose ordinates are, all, associated to the same return period, thus constituting a UHS. In order to compute approximate uniform-hazard response spectra at places affected by local soil amplifications, several approaches have been adopted in the past to overcome analytical difficulties. We present a coherent approach to construct UHS of different intensities at soft soil sites by means of interactive Internet-software named Zp, which will be illustrated with deterministic validations on Armenia city during the 25 January Armenia Earthquake and probabilistic examples for Bogota city.

Deterministic seismic hazard parameters and engineering risk implications for the Hong Kong region

The paper reviews and compares recent regional studies evaluating the seismic hazard parameters required to assess the seismic risk to engineering construction in the Coastal Region of South China (CRSC) including Hong Kong (HK). The review establishes that the CRSC, and in particular the offshore seismic belt, has mean earthquake magnitude recurrence intervals (MRIs) or return periods that are 2–3 times shorter than those in the eastern United States (EUS), with which the HK region has been compared. An ensemble of realistic design-level earthquake events suitable for defining the regional seismic hazard and for undertaking engineering risk assessment is then formulated, in the form of deterministic magnitude–distance pairs associated with earthquake magnitudes having a range of MRIs, and the significance of the maximum credible earthquake (MCE) magnitude is highlighted. Next, the scenario earthquake events have been used to predict the expected levels of peak design ground motions (for bedrock) in the HK region. The approximate method proposed here indicates that peak (effective) ground accelerations may reasonably be estimated to be around 10% g for 500-year earthquake events and 15–20% g for 1000-year events. However, the predicted ground motions arising from design-level earthquake events indicate large uncertainties arising from the attenuation equations. The uncertainties arise from both epistemic (event-to-event) and aleatory (site-to-site) considerations. These uncertainties represent the greatest source of errors in defining the seismic hazard for engineering design purposes. Further research is required to define the attenuation characteristics of ground motions for the CRSC, across a range of parameters including ground displacement and velocity as well as acceleration. It is further found that the Chinese earthquake building code gives a reasonably conservative estimate of seismic demand for the region, and is quite consistent with results from both probabilistic and pseudo-probabilistic seismic hazard analysis carried out herein, and by other researchers over the past 7 years. Finally, a discussion is presented of some key issues related to earthquake-resistant design and performance in Hong Kong, including the necessity to consider a range of design-level events with different MRIs when implementing acceptable structural design for earthquake effects.

Modeling underwater light climate in relation to sedimentation, resuspension, water quality and autotrophic growth

The underwater light climate ultimately determines the depth distribution, abundance and primary production of autotrophs suspended within and rooted beneath the water column. This paper addresses the underwater light climate, with reference to effects of suspended solids and growth responses of autotrophs with emphasis on phytoplankton. Effects of the most important factors contributing to the absorption and scattering of light in surface waters were described. A comparison between spectral and scalar approaches to underwater light climate modeling was made and examples of linear approximations to light attenuation equations were presented. It was demonstrated that spectral and scalar photosynthesis models may converge to similar values in spectral-flat, high photon flux environments, but that scalar PAR models may overestimate biomass-specific production by 70%. Such differences can lead to serious overestimates of habitat suitability for the growth and survival of submersed macrophytes, particularly in relatively turbid, coastal waters. Relationships between physical and optical properties of suspended sediments were described theoretically, and illustrated with modeling examples and measurements. It was found that the slowly settling particulate fraction contributed substantially to the suspended solids concentration, and greatly to light attenuation within the water column. It was concluded that distinguishing particles by fall velocity and concomitant light attenuation properties in the modeling of underwater light conditions allowed the establishment of useful, although not simply linear, relationships. In eutrophic, shallow lakes, the largest contribution to light attenuation often originates from phytoplankton on a seasonal basis (months–years), but from suspended solids behavior on a shorter time scale (days–weeks), particularly when water bodies are wind-exposed. Temporal and spatial variabilities in wave height, suspended solids concentrations, and light attenuation within the water column, and their importance for autotrophic growth were described, and illustrated with a case study pertaining to Markermeer, The Netherlands. The influence of underwater light conditions on phytoplankton succession was briefly discussed and illustrated with a case study pertaining to Lake Veluwe, The Netherlands. It was concluded that modeling the underwater light climate in a water body on a few sites only can indicate how important various components are for the attenuation of light, but based on the current state of the art, it can not be expected that this will provide accurate predictions of the underwater light climate, and of phytoplankton and submersed macrophyte growth.