Equations for Estimating Horizontal Response Spectra and Peak Acceleration from Western North American Earthquakes: A Summary of Recent Work
TL;DR: In this article, the authors provide tables for estimating random horizontal component peak acceleration and 5 percent damped pseudo-acceleration response spectra in terms of the natural, rather than common, logarithm of the ground-motion parameter.
Abstract: In this paper we summarize our recently-published work on estimating horizontal response spectra and peak acceleration for shallow earthquakes in western North America. Although none of the sets of coefficients given here for the equations are new, for the convenience of the reader and in keeping with the style of this special issue, we provide tables for estimating random horizontal-component peak acceleration and 5 percent damped pseudo-acceleration response spectra in terms of the natural, rather than common, logarithm of the ground-motion parameter. The equations give ground motion in terms of moment magnitude, distance, and site conditions for strike-slip, reverse-slip, or unspecified faulting mechanisms. Site conditions are represented by the shear velocity averaged over the upper 30 m, and recommended values of average shear velocity are given for typical rock and soil sites and for site categories used in the National Earthquake Hazards Reduction Program's recommended seismic code provisions. In addition, we stipulate more restrictive ranges of magnitude and distance for the use of our equations than in our previous publications. Finally, we provide tables of input parameters that include a few corrections to site classifications and earthquake magnitude (the corrections made a small enough difference in the ground-motion predictions that we chose not to change the coefficients of the prediction equations).
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TL;DR: In this article, the authors derived ground motion prediction equations 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.
Abstract: 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
1,512 citations
Cites methods from "Equations for Estimating Horizontal..."
...THE EQUATIONS Following the philosophy of Boore et al. (1993, 1994, 1997), we seek simple functional forms for our GMPEs, with the minimum required number of predictor variables....
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TL;DR: One of the essential characteristics of the method is that it distills what is known about the various factors affecting ground motions into simple functional forms that can be incorporated into practical predictions of ground motion.
Abstract: A simple and powerful method for simulating ground motions is to combine parametric or functional descriptions of the ground motion’s amplitude spectrum with a random phase spectrum modified such that the motion is distributed over a duration related to the earthquake magnitude and to the distance from the source. This method of simulating ground motions often goes by the name “the stochastic method.” It is particularly useful for simulating the higher-frequency ground motions of most interest to engineers (generally, f > 0.1 Hz), and it is widely used to predict ground motions for regions of the world in which recordings of motion from potentially damaging earthquakes are not available. This simple method has been successful in matching a variety of ground-motion measures for earthquakes with seismic moments spanning more than 12 orders of magnitude and in diverse tectonic environments. One of the essential characteristics of the method is that it distills what is known about the various factors affecting ground motions (source, path, and site) into simple functional forms. This provides a means by which the results of the rigorous studies reported in other papers in this volume can be incorporated into practical predictions of ground motion.
1,230 citations
Cites methods from "Equations for Estimating Horizontal..."
...For example, following BOORE et al. (1997) R would be given by R ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi D2 þ h2 p , where D is the closest distance to the vertical projection of the rupture surface onto the ground surface, and h is taken from the empirical results in BOORE et al. (1997)....
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TL;DR: In this article, a new empirical ground motion model for PGA, PGV, PGD and 5% damped linear elastic response spectra for periods ranging from 0.01-10 s was presented.
Abstract: We present a new empirical ground motion model for PGA, PGV, PGD and 5% damped linear elastic response spectra for periods ranging from 0.01– 10 s. The model was developed as part of the PEER Next Generation Attenuation (NGA) project. We used a subset of the PEER NGA database for which we excluded recordings and earthquakes that were believed to be inappropriate for estimating free-field ground motions from shallow earthquake mainshocks in active tectonic regimes. We developed relations for both the median and standard deviation of the geometric mean horizontal component of ground motion that we consider to be valid for magnitudes ranging from 4.0 up to 7.5–8.5 (depending on fault mechanism) and distances ranging from 0 – 200 km. The model explicitly includes the effects of magnitude saturation, magnitude-dependent attenuation, style of faulting, rupture depth, hanging-wall geometry, linear and nonlinear site response, 3-D basin response, and inter-event and intra-event variability. Soil nonlinearity causes the intra-event standard deviation to depend on the amplitude of PGA on reference rock rather than on magnitude, which leads to a decrease in aleatory uncertainty at high levels of ground shaking for sites located on soil. DOI: 10.1193/1.2857546
1,112 citations
Cites background from "Equations for Estimating Horizontal..."
...In such cases, the following equation can be used to calculate this standard deviation: Arb = T2 + C2 18 where C is given by the equation (Boore 2005) C 2 = 1 4N j=1 N ln y1j − ln y2j 2 19 and yij is the value of the ground motion parameter for component i of recording j and N is the total number…...
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TL;DR: In this article, empirical response spectral attenuation relations for the average horizontal and vertical component for shallow earthquakes in active tectonic regions were derived using a database of 655 recordings from 58 earthquakes.
Abstract: Using a database of 655 recordings from 58 earthquakes, empirical response spectral attenuation relations are derived for the average horizontal and vertical component for shallow earthquakes in active tectonic regions. A new feature in this model is the inclusion of a factor to distinguish between ground motions on the hanging wall and footwall of dipping faults. The site response is explicitly allowed to be non-linear with a dependence on the rock peak acceleration level.
1,026 citations
TL;DR: In this article, ground motion prediction equations for computing median and standard deviations of average horizontal component intensity measures (IMs) for shallow crustal earthquakes in active tectonic regions were provided.
Abstract: We provide ground motion prediction equations for computing medians and standard deviations of average horizontal component intensity measures (IMs) for shallow crustal earthquakes in active tecton...
1,024 citations
Cites methods from "Equations for Estimating Horizontal..."
...As with Boore et al. (1997) and BA08, we sought simple functions for our GMPEs, with the smallest number of predictor variables required to provide a reasonable fit to the data....
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References
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Book•
31 Jan 1986TL;DR: Numerical Recipes: The Art of Scientific Computing as discussed by the authors is a complete text and reference book on scientific computing with over 100 new routines (now well over 300 in all), plus upgraded versions of many of the original routines, with many new topics presented at the same accessible level.
Abstract: From the Publisher:
This is the revised and greatly expanded Second Edition of the hugely popular Numerical Recipes: The Art of Scientific Computing. The product of a unique collaboration among four leading scientists in academic research and industry, Numerical Recipes is a complete text and reference book on scientific computing. In a self-contained manner it proceeds from mathematical and theoretical considerations to actual practical computer routines. With over 100 new routines (now well over 300 in all), plus upgraded versions of many of the original routines, this book is more than ever the most practical, comprehensive handbook of scientific computing available today. The book retains the informal, easy-to-read style that made the first edition so popular, with many new topics presented at the same accessible level. In addition, some sections of more advanced material have been introduced, set off in small type from the main body of the text. Numerical Recipes is an ideal textbook for scientists and engineers and an indispensable reference for anyone who works in scientific computing. Highlights of the new material include a new chapter on integral equations and inverse methods; multigrid methods for solving partial differential equations; improved random number routines; wavelet transforms; the statistical bootstrap method; a new chapter on "less-numerical" algorithms including compression coding and arbitrary precision arithmetic; band diagonal linear systems; linear algebra on sparse matrices; Cholesky and QR decomposition; calculation of numerical derivatives; Pade approximants, and rational Chebyshev approximation; new special functions; Monte Carlo integration in high-dimensional spaces; globally convergent methods for sets of nonlinear equations; an expanded chapter on fast Fourier methods; spectral analysis on unevenly sampled data; Savitzky-Golay smoothing filters; and two-dimensional Kolmogorov-Smirnoff tests. All this is in addition to material on such basic top
12,662 citations
Book•
01 Jan 1980
TL;DR: This work has here attempted to give a unified treatment of those methods of seismology that are currently used in interpreting actual data and develops the theory of seismic-wave propagation in realistic Earth models.
Abstract: In the past decade, seismology has matured as a quantitative science through an extensive interplay between theoretical and experimental workers. Several specialized journals have recorded this progress in thousands of pages of research papers, yet such a forum does not bring out key concepts systematically. Because many graduate students have expressed their need for a textbook on this subject and because many methods of seismogram analysis now used almost routinely by small groups of seismologists have never been adequately explained to the wider audience of scientists and engineers who work in the peripheral areas of seismology, we have here attempted to give a unified treatment of those methods of seismology th at are currently used in interpreting actual data. We develop the theory of seismic-wave propagation in realistic Earth models. We study specialized theories of fracture and rupture propagation as models of an earthquake, and we supplement these theoretical subjects with practical descriptions of how seismographs work and how data are analyzed and inverted. Our text is arranged in two volumes. Volume I gives a systematic development of the theory of seismic-wave propagation in classical Earth models, in which material properties vary only with depth. It concludes with a chapter on seismometry. This volume is intended to be used as a textbook in basic courses for advanced students of seismology. Volume II summarizes progress made in the major frontiers of seismology during the past decade. It covers a range of special subjects, including chapters on data analysis and inversion, on successful methods for quantifying wave propagation in media varying laterally (as well as with depth), and on the kinematic and dynamic aspects of motions near a fault plane undergoing rupture. The second volume may be used as a texbook in graduate courses on tectonophysics, earthquake mechanics, inverse problems in geophysics, and geophysical data processing.n
5,291 citations
TL;DR: In this article, the authors proposed a frequency-domain scaling model for predicting seismic motions as a function of source strength, which can be applied to any time series having a stochastic character, including ground acceleration, velocity and the oscillator outputs on which response spectra and magnitude are based.
Abstract: Theoretical predictions of seismic motions as a function of source strength are often expressed as frequency-domain scaling models. The observations of interest to strong-motion seismology, however, are usually in the time domain (e.g., various peak motions, including magnitude). The method of simulation presented here makes use of both domains; its essence is to filter a suite of windowed, stochastic time series so that the amplitude spectra are equal, on the average, to the specified spectra. Because of its success in predicting peak and rms accelerations (Hanks and McGuire, 1981), an ω -squared spectrum with a high-frequency cutoff ( f m), in addition to the usual whole-path anelastic attenuation, and with a constant stress parameter (Δ σ ) has been used in the applications of the simulation method. With these assumptions, the model is particularly simple: the scaling with source size depends on only one parameter—seismic moment or, equivalently, moment magnitude. Besides peak acceleration, the model gives a good fit to a number of ground motion amplitude measures derived from previous analyses of hundreds of recordings from earthquakes in western North America, ranging from a moment magnitude of 5.0 to 7.7. These measures of ground motion include peak velocity, Wood-Anderson instrument response, and response spectra. The model also fits peak velocities and peak accelerations for South African earthquakes with moment magnitudes of 0.4 to 2.4 (with f m = 400 Hz and Δ σ = 50 bars, compared to f m = 15 Hz and Δ σ = 100 bars for the western North America data). Remarkably, the model seems to fit all essential aspects of high-frequency ground motions for earthquakes over a very large magnitude range .
Although the simulation method is useful for applications requiring one or more time series, a simpler, less costly method based on various formulas from random vibration theory will often suffice for applications requiring only peak motions. Hanks and McGuire (1981) used such an approach in their prediction of peak acceleration. This paper contains a generalization of their approach; the formulas used depend on the moments (in the statistical sense) of the squared amplitude spectra, and therefore can be applied to any time series having a stochastic character, including ground acceleration, velocity, and the oscillator outputs on which response spectra and magnitude are based .
1,708 citations
01 Jan 1981
TL;DR: In this paper, a magnitude-independent shape based on geometrical spreading and anelastic attenuation was proposed for the attenuation curve, which decouples the determination of the distance dependence of the data from the magnitude dependence.
Abstract: We have taken advantage of the recent increase in strong-motion data at close distances to derive new attenuation relations for peak horizontal acceleration and velocity. This new analysis uses a magnitude-independent shape, based on geometrical spreading and anelastic attenuation, for the attenuation curve. An innovation in technique is introduced that decouples the determination of the distance dependence of the data from the magnitude dependence. The resulting equations are log A = − 1.02 + 0.249 M − log r − 0.00255 r + 0.26 P r = ( d 2 + 7.3 2 ) 1 / 2 5.0 ≦ M ≦ 7.7 log V = − 0.67 + 0.489 M − log r − 0.00256 r + 0.17 S + 0.22 P r = ( d 2 + 4.0 2 ) 1 / 2 5.3 ≦ M ≦ 7.4
where A is peak horizontal acceleration in g , V is peak horizontal velocity in cm/ sec, M is moment magnitude, d is the closest distance to the surface projection of the fault rupture in km, S takes on the value of zero at rock sites and one at soil sites, and P is zero for 50 percentile values and one for 84 percentile values.
We considered a magnitude-dependent shape, but we find no basis for it in the data; we have adopted the magnitude-independent shape because it requires fewer parameters.
1,020 citations