Ground Motion Attenuation Research Articles

Comparison of the spatial distribution of ground motion between main shocks and strong aftershocks

Using the ground motion attenuation relation, we calculated and compared the effective peak acceleration (EPA) generated by main shocks and their strong aftershocks of 21 earthquake sequences with M S≥7 occurred in Chinese mainland and offing of China during 1966∼2002. The result shows that EPA of strong aftershocks usually exceed that of main shock for 76.2% earthquake sequences and EPA of more than 50% strong aftershocks are greatly larger than that of main shocks in large area, which suggests that it is necessary to take damage produced by strong aftershock into account in the probabilistic seismic hazard analysis and the seismic design.

The Persistence of Directivity in Small Earthquakes

Abstract We derive a simple inversion of peak ground acceleration (PGA) or peak ground velocity (PGV) for rupture direction and rupture velocity and then test this inversion on the peak motions obtained from seven 3.5≤ M ≤4.1 earthquakes that occurred in two clusters in November 2002 and February 2003 near San Ramon, California. These clusters were located on two orthogonal strike-slip faults so that the events share the same approximate focal mechanism but not the same fault plane. Three earthquakes exhibit strong directivity, but the other four earthquakes exhibit relatively weak directivity. We use the residual PGAs and PGVs from the other six events to determine station corrections for each earthquake. The inferred rupture directions unambiguously identify the fault plane for the three earthquakes with strong directivity and for three of the four earthquakes with weak directivity. The events with strong directivity have fast rupture velocities (0.63 β ≤ v ≤0.87 β ); the events with weak directivity either rupture more slowly (0.17 β ≤ v ≤0.35 β ) or bilaterally. The simple unilateral inversion cannot distinguish between slow and bilateral ruptures: adding a bilateral rupture component degrades the fit of the rupture directions to the fault planes. By comparing PGAs from the events with strong and weak directivity, we show how an up-dip rupture in small events can distort the attenuation of peak ground motion with distance. When we compare the rupture directions of the earthquakes to the location of aftershocks in the two clusters, we find than almost all the aftershocks of the three earthquakes with strong directivity occur within 70° of the direction of rupture.

Parameterization of a Composite Attenuation Relation for the Dead Sea Area Based on 3-D Modeling of Elastic Wave Propagation

3-D simulations of elastic wave propagation generated by earthquakes with magnitudes between 5.5 and 7.0 are used to parameterize strong ground motion attenuation relations for the Dead Sea Rift (DSR) graben structure. The results show that standard attenuation relations with an isotropic distance parameter are inadequate for a graben structure with a deep sedimentary trough. A new strategy is devised for the parameterization of attenuation relations in graben structures by looking at the statistical properties of 53 simulated earthquakes of variable magnitudes located at various sites along the western boundary fault of the DSR graben. An exemplary attenuation relation is designed from the synthetics for the 1 Hz spectral acceleration, modifying the Joyner-Boore-type parametrization by adding coefficients suited for three different source-to-sensor configurations: within the graben, beyond the graben and path unaffected by the graben structure.

時刻歴波形構築のための地震動エネルギースペクトルに関する距離減衰式の提案

This paper proposes a method for the evaluation of seismic wave, considering more effective representation of destructiveness of seismic wave. Specifically, a seismic wave energy spectrum is newly defined by decomposing the seismic wave energy into the frequency domain, and a ground motion attenuation law for the seismic wave energy spectrum is proposed. The wave form through this representation, which is considered as the best one for design and assessment of structures can be established along with the temporal characteristics which are beyond the scope of this study. The proposed attenuation law is considered to be utilized for a probabilistic seismic hazard analysis in which one aspect of the seismic ground motion such as PGA or PGV has been focused so far.

Inverse-Form Modelling for Initial Seismic Retrofit Design

The concept of performance-based seismic design (PBSD) has been explored by researchers for over a decade and the implementation stage is at the cusp of beginning. One important aspect of this early implementation stage is to examine existing analysis and design concepts that can serve as linkages to help improve and speed up implementation by integrating directly into the PBSD philosophy. To date, structural reliability has served as the cornerstone for load and resistance factor design (LRFD) code calibration and to some extent it could provide for some level of PBSD code calibration. This paper presents a summary of the results of a numerical study to examine the application of the inverse first order reliability method (I-FORM) for preliminary design of a base isolation system within the context of PBSD. In other words, it is given that a target structural reliability level is required for a particular structure, how does one select the properties (i.e., design) of the base isolation system to ensure the desired reliability level to all possible earthquakes? This is accomplished herein by decoupling the earthquake demand from the structural concept using a method known as the environmental contour procedure which is essentially I-FORM. The earthquake is described in terms of magnitude, site-to-source distance, and an uncertainty parameter that lumps both aleatory and epistemic uncertainties using readily available earthquake data. A ground motion attenuation function provides the link between the earthquake demand description and the structural concept in the form of spectral acceleration as a function of natural period. An illustrative example for a hypothetical building located in Los Angeles, CA having a fundamental period of vibration of 0.4s prior to retrofit is presented. In this example, the stiffness of a laminated rubber bearing isolation system is the design variable of interest.

Ground motion environment of the Los Angeles region

AbstractThis paper reviews aspects of fault geometry and geological structure that cause spatial variations in the level of ground motions expected from large‐scenario earthquakes. These conditions include style of faulting, differences between surface faulting and buried faulting earthquakes, rupture directivity effects, basin effects and basin edge effects. These effects are illustrated in large‐scale ground motion simulations of scenario earthquakes on the Puente Hills Blind Thrust and the Southern San Andreas fault. The impact of these effects on probabilistic seismic hazard is also explored by means of CyberShake calculations in which the ground motions at a given site from a very large number of earthquake scenarios are represented by simulated time histories in place of conventional ground motion attenuation equations used in probabilistic seismic hazard analysis. We find that the seismic hazard estimates are quite similar in some locations, such as downtown Los Angeles, but quite different at others, such as Whittier. These differences are attributable to the coupling of rupture directivity and basin effects that are present in the CyberShake and TeraShake calculations but not in the conventional attenuation relations. Copyright © 2006 John Wiley & Sons. Ltd.

Local Earthquake Magnitude Scale and Seismicity Rate for the Ethiopian Rift

A calibrated local earthquake magnitude scale is essential for quantitative analyses of seismicity. In Ethiopia, effective monitoring of earthquakes and resulting assessment of seismic hazard are especially important as regions with seismic and volcanic activity coincide with regions of economic significance and population growth. We have developed a local magnitude ( M L) scale for the northern Main Ethiopian rift (mer) using earthquake data collected during 2001–2003 on 122 three-component broadband seismic stations. Waveform data from 2139 local earthquakes were corrected for instrument response and convolved with the nominal Wood–Anderson torsion seismograph response appropriate for the original definition of local magnitude. The hypocentral distances considered are 5 to 800 km, with the best represented range from 5 to 150 km. A total of 30,908 maximum zero-to-peak amplitudes ( AWA ) were incorporated into a direct linear inversion for individual earthquake local magnitudes ( M L), 244 station factors ( C ), and 2 linear distance-dependent factors ( n, K ) in the distance correction term, log ( A o), of the equation for local magnitude: M L = log( AWA ) − log( A o) + C . The resulting distance correction is given by −log( A o) = 1.196997log( r /17) + 0.001066( r − 17) + 2, which implies that ground-motion attenuation is relatively high, consistent with ongoing magma intrusion and the presence of shallow magma reservoirs beneath the mer. Station corrections significantly reduce M L residuals and range between ±0.42 M L units. The catalog of earthquakes is complete above M L ∼2.1 and the annual cumulative seismicity rate follows the relation log N = 4.5 − 1.13 M L. Our results are critical for accurate routine quantitative analysis of past, current and, future seismicity in Ethiopia.

Probabilistic Seismic-Hazard Assessment of the Canary Islands

This article presents the first probabilistic seismic hazard assessment of the Canary Islands. The Canary Islands form a volcanic archipelago located on the passive margin of the African plate, 100 km off West Africa. Active volcanism has taken place on the islands in historical times, commonly together with the occurrence of volcanic-related seismic sequences, some of them felt as high as I msk = X. In 1989 a notorious seismic sequence ( m bLg 5.2) took place along a submarine fault located between the islands of Gran Canaria and Tenerife, clearly representing the occurrence of tectonic seismicity in the archipelago as well. In this article we review the geology and tectonics of the islands as well as recent paleoseismological findings on south Tenerife. We also revise, complete, and decluster the historical and instrumental seismic catalog of the islands. Seismic-hazard analysis is then performed following the standard Cornell (1968) method, defining three seismogenic sources and selecting an appropriate ground-motion attenuation relationship from Hawaiian data. Two hazard maps of the archipelago have been developed for return periods of 475 and 950 yr, as well as hazard curves for the capital cities. Calculated peak ground acceleration values at Santa Cruz de Tenerife and Las Palmas de Gran Canaria are 0.06 and 0.08 g , and 0.05 and 0.07 g , for the 475- and 950-yr return periods, respectively. Finally, we analyze the impact on hazard resulting from uncertainties associated with the seismogenic source model and the ground-motion attenuation relationship.

Implementation of ShakeMap in Ontario: Challenges of Detection and Location in a Sparse Network

ShakeMap is a computer program to map earthquake groundmotion parameters in near real time. It originally was devel oped and implemented using a dense recording network in California (Wald et al. 1999); typical interstation spacing in southern California is about 5 to 50 km, though some sta tions in the Los Angeles metropolitan area are less than 2 km from each other, as seen at http://www.data.scec.org/stations/ CI_station_map.php). For our implementation of ShakeMap in southern Ontario, we have developed an automated earthquake detection program, “EventDetector,” to continuously detect events and trigger ShakeMap in a sparse network where typi cal interstation spacing is about 100 km. The EventDetector is keyed to ShakeMap objectives in that it detects events based on the exceedance of specified ground-motion amplitudes at five or more stations. The specified threshold is set as peak ground velocity (PGV) = 0.003 mm/s. For our network configuration, this criterion should result in ShakeMap triggering on all events of M > 2.8 within the southern Ontario network. When the program detects an event, EventDetector auto matically triggers the ShakeMap program and continues to pro cess the incoming data. The main challenge in event detection is to screen out false triggers caused by teleseismic events or other spurious signals. We distinguish between local/regional and teleseismic events by using the standard deviation of the peak ground velocity, normalized by the mean (denoted NSD) as a discriminant. Events that have NSD < 0.7 are teleseismic events (with a rate of 10% false triggers). To locate the regional earthquake once an event is confirmed by the above criteria, we use the ground-motion centroid concept, originally developed by Kanamori (1993). The centroid provides an estimate of the earthquake moment magnitude ( M) and location from the point of view of ground motion, and it may not coincide with the actual earthquake epicenter and magnitude. The estima tion is based on fitting the observed amplitude data to groundmotion attenuation relations. An additional check on whether the event is a significant earthquake is based on the determined centroid magnitude; events of

Introduction to Dr. Iwasaki’s Paper Entitled “Response Analysis of Civil Engineering Structures Subjected to Earthquake Motions”

Seismic design of Japanese bridges started in 1925, triggered by the extensive damage of the 1923 Kanto earthquake. "Drafted Structural Details of Road Structures," issued by Japan's Ministry of the Interior in 1925, recommended the use of static seismic analysis based on working stress design, which was used for a long time. "Design Specifications of Steel Bridges," issued by the Japan Road AssoCiation in 1964, was an important code used for design of a number of bridges during restoration after World War II and the early high economic growth periods that followed. There was no independent seismic design code in those days, so only limited descriptions were provided for seismic design, e.g., pages in the code related to seismic design numbered only 2 or 3, and seismic knowledge was limited. Most bridges damaged in the 1995 Kobe earthquake were designed based on this code. Extensive damage in the 1964 Niigata earthquake initiated intensified research on the structural response and seismic design of bridges. Accomplishments of research were reflected in the 1971 "Guide Specifications on Seismic Design of Bridges" (Japan Road Association), the first design guidelines focusing on the seismic design of bridges. Pages of the main text and explanations related to seismic design increased to 30, and included the natural period dependent lateral seismic coefficient and preliminary evaluation of soil liquefaction assessment and unseating prevention devices. This was the first time that preliminary liquefaction assessment and unseating prevention devices innovated by Japanese bridge engineers were included in bridge codes. The 1971 Guide Specification of Seismic Design of Bridges was compiled with other design codes and issued in 1980 as "Part V Seismic Design" of "Design Specifications of Highway Bridges" (Japan Road Association). Assessment of soil liquefaction based on FL was introduced in Part V, but other parts remained almost unchanged. Part V was completely revised in 1990 to include (1) new static analysis evaluating lateral force in continuous bridges based on the stiffness of superstructures and substructures, (2) safety evaluation (level 2) ground motion for the design of reinforced concrete columns, and (3) design response spectra and design-spectra-compatible ground acceleration for dynamic response analysis. This was the first in Japan to include safety evaluation ground motion and static design for ductility evaluation of bridge columns. Pages on code related to seismic design increased to 96 greatly enhanced as a modern seismic design code. Based on the extensive damage sustained in the 1995 Kobe earthquake, Part V on seismic design was further revised in 1996 and 2002 to include lessons learned from this damage. Pages of code related to seismic design increased to 227 in the 1996 code and 280 in the 2002 code. Figure 1 shows the increase in the number of pages related to seismic design. Extensive improvement was conducted in 1990 and 1996. Although we have had over 80 years in experience of seismic bridge design, only in the last 15 years has seismic bridge design been enhanced to include modern requirements. Codes before the 1971 Guide Specification and the 1980 Part V on seismic design had insufficient scientific knowledge, although they were used for design in a number of bridges. The paper by Dr. Iwasaki has contributed much to establishing modern seismic design codes for bridges. His contributions include, but are not limited to, the clarification of dynamic response characteristics of bridges based on extensive field measurements, the deployment of strong motion recording networks, the development of soil liquefaction evaluation based on FL, and the development of ground motion attenuation equations. All of his activities and research helped enhance seismic design codes for bridges in Japan.

Revising the areal extent of post-earthquake inspections of dams in Quebec

Post-earthquake inspection is required by many dam safety regulations. Typically, based on the magnitude of the earthquake, the guidelines define an area within which dams should be inspected. The areas are established on ground-motion relations derived for the western United States. In eastern North America (ENA), the attenuation is slower with distance from the earthquake epicentre, and as a consequence the inspection area should be significantly larger than that recommended by the current guidelines. We review the state of knowledge on earthquake damage to dams, the factors used to define post-earthquake inspections, and the earthquake characteristics used to define the guidelines. We recommend new radii of inspections for dams applicable in ENA, including the Province of Quebec. Derived from historical earthquake information, the proposed new radii of inspections are twofold to sixfold larger than the 1988 guidelines of the International Commission on Large Dams. It is also suggested that a half-magnitude unit be added to every magnitude “rapidly” released by seismological organizations to include the intrinsic uncertainty in magnitude values and types. Our proposed approach is only one avenue that dam owners can follow to comply with dam safety regulations. Irrespective of the avenue chosen, however, this paper emphasizes the need for dam owners to consider the lower ground motion attenuation in ENA.Key words: earthquake, damage, dam, inspection, natural hazards, emergency response.

Attenuation of the peak ground motion for the special case of Vrancea intermediate-depth earthquakes and seismic hazard assessment at NPP Cernavoda

Attenuation specific from Vrancea intermediate-depth focus toward SE is revised at length in order to re-evaluate the seismic hazard at the nuclear power plant (NPP) Cernavoda. To this aim, we took into consideration all the strong motion data available for the region and test a large range of relationship types. Since the instrumental data are limited as magnitude and depth intervals, the extrapolation based on the attenuation laws deduced from these data to great magnitudes is very instable and must be carefully considered. The extrapolation outside the characteristic domain of the available database leads to large deviations, especially at large magnitudes and for the relations which contain the depth as independent parameter.

Seismic hazard analysis: a comparative study

The quantitative seismic hazard maps for the 1970s National Building Code of Canada were evaluated using the Davenport–Milne method. The Cornell–McGuire method is employed to develop recent seismic hazard maps of Canada. These methods incorporate the information on seismicity, magnitude-recurrence relations, and ground motion (or response) attenuation relations. The former preserves and depends completely on details of the historical seismicity; the latter smoothes the irregular spatial occurrence pattern of the historical seismicity into seismic source zones. Further, the Epicentral Cell method, which attempts to incorporate the preserving and smoothing aspect of these methods, has been developed. However, the impact of the adopted assumptions on the estimated quantitative seismic hazard has not been investigated. This study provides a comparative seismic hazard assessment using the above-mentioned methods and simulation-based algorithms. The analysis results show that overall the Davenport–Milne method gives quasi-circular seismic hazard contours near significant historical events, and the Cornell–McGuire method smoothes the transition of contours. The Epicentral Cell method provides estimates approximately within the former and the latter. Key words: epicentral cell method, probability, seismic hazard, Thiessen polygon, Voronoi, uniform hazard spectra.

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.

An ML Scale for the La Paz-Los Cabos Region, Baja California Sur, Mexico

We have developed a local magnitude scale to quantify the size of earthquakes in the La Paz–Los Cabos region, Baja California Sur, a seismically active region with little seismic history reported. For this, we used digital data from 501 local and regional earthquakes recorded by temporary networks that were deployed in the region from October 1998 to December 2003. A multiple linear regression analysis applied to 3328 average zero-to-peak synthetic Wood–Anderson amplitudes produced the following results: a −log A attenuation function for the region, the local magnitude for each earthquake, and a magnitude correction for each station. Regarding the attenuation function, our best fit to the regressed data is −log A ;eq (1.2052 ± 0.0177) log ( r /100) + 0.0016 ± 0.0003) ( r − 100) + 3, where r is the hypocentral distance. The ground-motion attenuation represented by this relationship is similar to the attenuations reported for the Peninsular Ranges of Baja California and for the southern California region. In addition, the station magnitude corrections obtained from our regression analysis range from −0.46 to 0.23. As it should be expected, positive station corrections correlate well with hard-rock sites, whereas negative corrections correlate with soft or sedimentary rock sites. The combined use of Richter’s definition of magnitude with the attenuation function and station corrections determined here give reliable and homogeneous estimations of the local magnitude.

SEISMIC WAVE ATTENUATION FOR VRANCEA EVENTS REVISITED

New aspects of the frequency-dependent attenuation of the seismic waves travelling from Vrancea subcrustal sources toward NW (Transylvanian Basin) and SE (Romanian Plain) are evidenced by the recent experimental data made available by the CALIXTO'99 tomography experiment. The observations validate the previous theoretical computations performed for the assessment, by means of a deterministic approach, of the seismic hazard in Romania. They reveal an essential aspect of the seismic ground motion attenuation that has important implications on the probabilistic assessment of seismic hazard from Vrancea intermediate-depth earthquakes. The attenuation toward NW is shown to be a much stronger frequency-dependent effect than the attenuation toward SE and the seismic hazard computed by the deterministic approach fits satisfactorily well the observed ground motion distribution in the low-frequency band (<1Hz). The apparent contradiction with the historically-based intensity maps arises mainly from a systematic difference in the eigenperiods (type and size) of the buildings in the intra- and extra-Carpathians regions, thus the existing macroseismic data, based on buildings of small dimensions, i.e. with high eigenfrequency (5–10 Hz), can hardly be representative of the real hazard for new and large dimension, tall buildings, with eigenfrequency above 1 Hz.

Site-Specific Probabilistic Seismic-Hazard Assessment: Direct Amplitude-Based Approach

Conventional probabilistic seismic-hazard assessment (PSHA) is difficult to apply in regions lacking sufficient information concerning geological setting, active faults, and so forth. Also, for a PSHA, site effects arising from both crustal rock and overlying soil sediments are generally not assessed rigorously. This is of particular importance for those metropolitan cities having a significant proportion of reclaimed land, because the site-to-site variability of such site effects can be very large. The objective of this article is to demonstrate an alternative procedure for assessing seismic hazard, developed from the conventional source-based Cornell-McGuire PSHA approach, based on considering an infinite number of sources. The proposed new procedure is termed the direct amplitude-based (DAB) approach. The major advantage of the proposed DAB approach is that it is not necessary to characterize any seismic sources. Moreover, if a site-specific and event- specific ground-motion attenuation model is available, a more accurate PSHA could be performed. Also, a generic analytical solution for the proposed procedure has been derived to avoid the need for a lengthy integration process. Using the proposed approach, peak ground velocities have been computed at different return periods, to form a seismic hazard curve, citing Hong Kong as a case study.

Liquefaction Limit during Earthquakes and Underground Explosions: Implications on Ground-Motion Attenuation

Liquefaction of saturated soils and sediments documented during earthquakes shows an empirical relation log R max = 2.05 (±0.10) + 0.45 M , where R max is the liquefaction limit in meters (i.e., the maximum distance from liquefaction site to the hypocenter) and M is the earthquake magnitude. Combining this with an empirical relation between M and the seismic energy of an earthquake, we obtain a relation between the liquefaction limit and the seismic energy: E = A R β max. The prefactor corresponds to a threshold energy for liquefaction ranging from 0.004 to 0.1 J/m3; the exponent, ranging from 3.2 to 3.3, implies that the energy density of ground motion attenuates with distance according to 1/ r 3.2–3.3, where r is the distance from the hypocenter. The value of the threshold energy suggests a preliquefaction degradation of the shear modulus of soils by more than 3 orders of magnitude. Liquefaction documented during underground explosions is characterized by a threshold energy several orders of magnitude greater than that for liquefaction during earthquakes but shows a similar functional relation between E and R max as that for liquefaction during earthquakes and implies a similar attenuation relation between ground-motion energy density and distance.

Band of precariously balanced rocks between the Elsinore and San Jacinto, California, fault zones: Constraints on ground motion for large earthquakes

A spectacular band of precariously and semiprecariously bal- anced rocks extends from Riverside to near Borrego Valley, Cali- fornia, about halfway between the Elsinore and San Jacinto fault zones. The rocks are distributed in a band a few kilometers wide midway between the San Jacinto and Elsinore fault zones, an in- dication that the distribution is caused by attenuation of strong ground motion from numerous large events along these two fault zones. These rocks have apparently been in place for thousands of years, and thus place important constraints on ground motions from earthquakes. On the basis of field tests and photographic analysis, the estimated quasi-static toppling accelerations for the precariously balanced rocks are ;0.32 6 0.10 g (g 5 gravitational acceleration). The dynamic toppling accelerations are within this range for earthquakes with waveforms similar to those recorded during the Izmit and Denali earthquakes. These constraints are roughly consistent with the median predicted value of ground mo- tion for M7 earthquakes, but somewhat lower than 11s ground motion curves, and much lower than the values from the 2% in 50 yr hazard maps. The evidence from these rocks has importance for some of the assumptions that go into calculating probabilistic seismic hazard assessment, including median and standard devia- tion of ground motion attenuation curves (especially for hard rock, for which few instrumental data are available), the possible exis- tence of random background earthquakes, and the smoothing dis- tance for historical seismicity.

An Assessment of the Impact of the 2003 EPRI Ground-Motion Prediction Models on the USGS National Seismic-Hazard Maps

Ground-motion attenuation relations have an important impact on seismic hazard analyses. Ground-motion modeling is particularly sensitive to assumptions about wave-propagation attenuation (crustal Q and geometrical spreading), as well as source and site conditions. Studies of path attenuation from earthquakes in eastern North America (ena) provide insights into the appropriateness of specific attenuation relations. An Electric Power Research Institute (EPRI) (2003, 2004) study combines published ena ground-motion attenuation relations into four model forms: single-corner, double-corner, hybrid-empirical, and finite-fault. When substituted in the U.S. Geological Survey 2002 national seismic hazard maps for the five ena relations originally used in those hazard calculations, the EPRI (2003) relations predict similar ground motions and hazard at short periods ( 0.5 sec), relative to the 2002 national maps. A major reason for this difference is due to the crustal seismic-wave attenuation model assumed in a few of the ena relations combined into the EPRI (2003, 2004) models. Although appropriate differences in geometrical spreading models among ena relations can also be significant, a few ena relations have 1-Hz Q -values ( Q ) that are below the EPRI (1993) consensus range for Q when coupled with a geometrical spreading of R −0.5. The EPRI (2003, 2004) single-corner relation is strongly influenced by the inclusion of ena relations with assumed Q below the EPRI (1993) range, which explains much of the discrepancy in predictions at longer periods.