This paper contains ground-motion prediction equations (GMPEs) for average horizontal-component ground motions as a function of earthquake magnitude, distance from source to site, local average shear-wave velocity, and fault type. Our equations are for peak ground acceleration (PGA), peak ground velocity (PGV), and 5%-damped pseudo-absolute-acceleration spectra (PSA) at periods between 0.01 s and 10 s. They were derived by empirical regression of an extensive strong-motion database compiled by the “PEER NGA” (Pacific Earthquake Engineering Research Center’s Next Generation Attenuation) project. For periods less than 1s , the analysis used 1,574 records from 58 mainshocks in the distance range from 0 km to 400 km (the number of available data decreased as period increased). The primary predictor variables are moment magnitude M, closest horizontal distance to the surface projection of the fault plane R JB , and the time-averaged shear-wave velocity from the surface to 30 m VS30. The equations are applicable for M =5–8 , RJB 200 km, and VS30= 180– 1300 m / s. DOI: 10.1193/1.2830434

/pdf/ground-motion-prediction-equations-for-the-average-1pxmyzur8d.pdf

Ground-motion prediction equations for the average horizontal component of PGA, PGV, and 5%-damped PSA at spectral periods between 0.01 s and 10.0 s

PART 1 DEALS WITH THE DYNAMIC ASPECTS OF THE SUBJECT: MATHEMATICAL ANALYSIS OF SYSTEMS SUBJECTED TO INDEPENDENT VIBRATIONS BY MEANS OF MATHEMATICAL MODELS. THE ANALYTICAL SYSTEMS USED ARE NON-LINEAR SYSTEMS, HYDRODYNAMICS AND NUMERICAL METHODS. PART 2 EXAMINES SEISMIC MOVEMENTS, THE DYNAMIC BEHAVIOUR OF STRUCTURES AND THE BASIC CONCEPTS OF THE SEISMIC DESIGN OF STRUCTURES.

Fundamentals of earthquake engineering

The true performance of ground-motion prediction equations is often not fully appreciated until they are used in practice for seismic hazard analyses and applied to a wide range of scenarios and exceedance levels. This has been the case for equations published recently for the prediction of peak ground velocity (PGV), peak ground acceleration (PGA), and response spectral ordinates in Europe, the Middle East, and the Mediterranean (Akkar and Bommer 2007a,b). This paper presents an update that corrects the shortcomings identified in those equations, which are primarily, but not exclusively, related to the model for the ground-motion variability.

Strong-motion recording networks in Europe and the Middle East were first installed much later than in the United States and Japan but have grown considerably over the last four decades. The databanks of strong-motion data have grown in parallel with the accelerograph networks, and in addition to national collections there have been concerted efforts over more than two decades to develop and maintain a European database of associated metadata ( e.g. , Ambraseys et al. 2004).

As the database of strong-motion records from Europe, the Mediterranean region, and the Middle East has expanded, there have been two distinct trends in terms of developing empirical ground-motion prediction equations (GMPEs): equations derived from a large dataset covering several countries, generally of moderate-to-high seismicity; and equations derived from local databanks for application within national borders. We refer to the former as pan-European models, noting that this is for expedience since the equations are really derived for southern Europe, the Maghreb (North Africa), and the active areas of the Middle East. The history of the development of both pan-European and national equations is discussed by Bommer et al. (2010), who also review studies that consider the arguments for and against the existence of consistent regional …

Empirical Equations for the Prediction of PGA, PGV, and Spectral Accelerations in Europe, the Mediterranean Region, and the Middle East

This article presents the latest generation of ground-motion models for the prediction of elastic response (pseudo-) spectral accelerations, as well as peak ground acceleration and velocity, derived using pan-European databases. The models present a number of novelties with respect to previous generations of models (Ambraseys et al. in Earthq Eng Struct Dyn 25:371–400, 1996, Bull Earthq Eng 3:1–53, 2005; Bommer et al. in Bull Earthq Eng 1:171–203, 2003; Akkar and Bommer in Seismol Res Lett 81:195–206, 2010), namely: inclusion of a nonlinear site amplification function that is a function of $$\text{ V }_\mathrm{S30}$$
 and reference peak ground acceleration on rock; extension of the magnitude range of applicability of the model down to $$\text{ M }_\mathrm{w}$$
 4; extension of the distance range of applicability out to 200 km; extension to shorter and longer periods (down to 0.01 s and up to 4 s); and consistent models for both point-source (epicentral, $$\text{ R }_\mathrm{epi}$$
 , and hypocentral distance, $$\text{ R }_\mathrm{hyp}$$
 ) and finite-fault (distance to the surface projection of the rupture, $$\text{ R }_\mathrm{JB}$$
 ) distance metrics. In addition, data from more than 1.5 times as many earthquakes, compared to previous pan-European models, have been used, leading to regressions based on approximately twice as many records in total. The metadata of these records have been carefully compiled and reappraised in recent European projects. These improvements lead to more robust ground-motion prediction equations than have previously been published for shallow (focal depths less than 30 km) crustal earthquakes in Europe and the Middle East. We conclude with suggestions for the application of the equations to seismic hazard assessments in Europe and the Middle East within a logic-tree framework to capture epistemic uncertainty.

/pdf/empirical-ground-motion-models-for-point-and-extended-source-440ttrey95.pdf

Empirical ground-motion models for point- and extended-source crustal earthquake scenarios in Europe and the Middle East

Although the methodological framework of probabilistic seismic hazard analysis is well established, the selection of models to predict the ground motion at the sites of interest remains a major challenge. Information theory provides a powerful theoretical framework that can guide this selection process in a consistent way. From an information-theoretic perspective, the appropriateness of models can be expressed in terms of their relative information loss (Kullback–Leibler distance) and hence in physically meaningful units (bits). In contrast to hypothesis testing, information-theoretic model selection does not require ad hoc decisions regarding significance levels nor does it require the models to be mutually exclusive and collectively exhaustive. The key ingredient, the Kullback–Leibler distance, can be estimated from the statistical expectation of log-likelihoods of observations for the models under consideration. In the present study, data-driven ground-motion model selection based on Kullback–Leibler-distance differences is illustrated for a set of simulated observations of response spectra and macroseismic intensities. Information theory allows for a unified treatment of both quantities. The application of Kullback–Leibler-distance based model selection to real data using the model generating data set for the Abrahamson and Silva (1997) ground-motion model demonstrates the superior performance of the information-theoretic perspective in comparison to earlier attempts at data-driven model selection (e.g., Scherbaum et al. , 2004).

Model Selection in Seismic Hazard Analysis: An Information-Theoretic Perspective

The complete characterization of earthquake ground motion includes the length of the interval of strong shaking as well as the amplitude and frequency content of the time series. There are relatively few published equations available for the prediction of strong-motion duration from earthquakes, which may in part be a consequence of the fact that the duration of shaking has generally not been considered in structural engineering. Recognizing that there are many applications for which an estimate of the duration of ground motion is needed, this study presents new empirical predictive equations for a number of definitions of strong-motion duration using the records from the Next Generation of Attenuation (NGA) global database of accelerograms from shallow crustal earthquakes. The equations can be used to estimate ground-motion durations from shallow crustal earthquakes of magnitude between M w  4.8 and 7.9 at distances up to 100 km from the source.

/pdf/empirical-equations-for-the-prediction-of-the-significant-2nfs54he9e.pdf

Empirical Equations for the Prediction of the Significant, Bracketed, and Uniform Duration of Earthquake Ground Motion

A key issue in the assessment of seismic hazard in regions of low- to-moderate seismicity is the extent to which accelerograms obtained from small- magnitude earthquakes can be used as the basis for predicting ground motions due to the larger-magnitude events considered in seismic hazard analysis. In essence, the question is whether empirical ground-motion prediction equations can be applied outside their strict range of applicability as defined by the magnitude and distance ranges covered by the datasets from which they are derived. This question is explored by deriving new spectral prediction equations using an extended strong-motion da- taset from Europe and the Middle East covering the magnitude range Mw 3.0-7.6 and comparing the predictions with previous equations derived using data from only Mw 5.0 and above events. The comparisons show that despite their complex func- tional form, including quadratic magnitude-dependence and magnitude-dependent attenuation, the equations derived from larger-magnitude events should not be extra- polated to predict ground motions from earthquakes of small magnitude. Moreover, the results suggest not only that ground-motion prediction equations cannot be used outside the ranges of their underlying datasets but also that their applicability at the limits of these ranges may be questionable. Although only tested for smaller magni- tudes, the results could be interpreted to suggest that predictive equations also cannot be reliably extrapolated to higher magnitudes than those represented in the dataset from which they are derived, a finding that has important implications for seismic hazard analysis. The conclusion of the study is that empirical derivation of ground-motion pre- diction equations should be based on datasets extending at least one unit below the lower limit of magnitude considered in seismic hazard calculations. The inclusion of small-magnitude recordings results in a significant increase in the aleatory varia- bility of the equations, although it is yet to be established whether this is due to greater uncertainty in the associated metadata or whether ground-motion variability is gen- uinely dependent on earthquake magnitude.

The Influence of Magnitude Range on Empirical Ground-Motion Prediction

Peak ground velocity (PGV) has received much less attention in the technical literature than more widely-used parameters such as peak ground acceleration (PGA) and response spectral ordinates. However, there are many examples of the use of PGV in engineering seismology and earthquake engineering, including as a parameter from which to estimate macroseismic intensity and structural damage. PGV is also employed in some methods for the assessment of liquefaction potential and, because of its relationship to ground strains, in the seismic design and assessment of buried pipelines. One of the most important uses of PGV has been in the construction of elastic response spectra. There are relatively few predictive equations for PGV, compared to those for PGA and spectral ordinates, but 25 such equations are reviewed and summarised. The issue of scaling PGV from response spectral ordinates is explored and it is shown that the common practice of scaling PGV from spectral accelerations at 1.0 second should not be co...

The prediction and use of peak ground velocity

Correlations between duration and number of effective cycles of earthquake ground motion

The Bojnurd region of NE Iran experienced a Mw 6.4 earthquake on February 4, 1997. By combining results from teleseismic body-waveform analysis, field observations of structural damage, coseismic deformation, geomorphology, and analysis of the resulting strong ground-motions, we build a coherent picture of the faulting associated with this earthquake. The earthquake resulted from almost pure right-lateral strike-slip motion (0.5–1.0 m), which ruptured a ∼15 km long section of fault, striking ∼340° at its northern end, which changes to ∼320° at its southern end. This fault can be seen clearly on the geological map and satellite imagery. The village of Sheikh lies ∼10–15 km SE of the fault rupture, yet was severely damaged during the earthquake. Analysis of strong-motion records, recorded by the Building and Hazard Research Center of Iran, particularly their significant duration, the polarization of the fault-normal component, and the velocity pulse, indicates a probable directivity effect, in which the rup...

The 4th February 1997 Bojnurd (Garmkhan) Earthquake in NE Iran: Field, Teleseismic, and Strong-Motion Evidence for Rupture Directivity Effects on a Strike-Slip Fault

John E. Alarcón

Papers

Empirical Equations for the Prediction of the Significant, Bracketed, and Uniform Duration of Earthquake Ground Motion

The Influence of Magnitude Range on Empirical Ground-Motion Prediction

The prediction and use of peak ground velocity

Correlations between duration and number of effective cycles of earthquake ground motion

The 4th February 1997 Bojnurd (Garmkhan) Earthquake in NE Iran: Field, Teleseismic, and Strong-Motion Evidence for Rupture Directivity Effects on a Strike-Slip Fault