A new method for analysing nonlinear and non-stationary data has been developed. The key part of the method is the empirical mode decomposition method with which any complicated data set can be dec...

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The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis

Source parameters for historical earthquakes worldwide are compiled to develop a series of empirical relationships among moment magnitude ( M ), surface rupture length, subsurface rupture length, downdip rupture width, rupture area, and maximum and average displacement per event. The resulting data base is a significant update of previous compilations and includes the additional source parameters of seismic moment, moment magnitude, subsurface rupture length, downdip rupture width, and average surface displacement. Each source parameter is classified as reliable or unreliable, based on our evaluation of the accuracy of individual values. Only the reliable source parameters are used in the final analyses. In comparing source parameters, we note the following trends: (1) Generally, the length of rupture at the surface is equal to 75% of the subsurface rupture length; however, the ratio of surface rupture length to subsurface rupture length increases with magnitude; (2) the average surface displacement per event is about one-half the maximum surface displacement per event; and (3) the average subsurface displacement on the fault plane is less than the maximum surface displacement but more than the average surface displacement. Thus, for most earthquakes in this data base, slip on the fault plane at seismogenic depths is manifested by similar displacements at the surface. Log-linear regressions between earthquake magnitude and surface rupture length, subsurface rupture length, and rupture area are especially well correlated, showing standard deviations of 0.25 to 0.35 magnitude units. Most relationships are not statistically different (at a 95% significance level) as a function of the style of faulting: thus, we consider the regressions for all slip types to be appropriate for most applications. Regressions between magnitude and displacement, magnitude and rupture width, and between displacement and rupture length are less well correlated and have larger standard deviation than regressions between magnitude and length or area. The large number of data points in most of these regressions and their statistical stability suggest that they are unlikely to change significantly in response to additional data. Separating the data according to extensional and compressional tectonic environments neither provides statistically different results nor improves the statistical significance of the regressions. Regressions for cases in which earthquake magnitude is either the independent or the dependent parameter can be used to estimate maximum earthquake magnitudes both for surface faults and for subsurface seismic sources such as blind faults, and to estimate the expected surface displacement along a fault for a given size earthquake.

New Empirical Relationships among Magnitude, Rupture Length, Rupture Width, Rupture Area, and Surface Displacement

This essential reference for graduate students and researchers provides a unified treatment of earthquakes and faulting as two aspects of brittle tectonics at different timescales. The intimate connection between the two is manifested in their scaling laws and populations, which evolve from fracture growth and interactions between fractures. The connection between faults and the seismicity generated is governed by the rate and state dependent friction laws - producing distinctive seismic styles of faulting and a gamut of earthquake phenomena including aftershocks, afterslip, earthquake triggering, and slow slip events. The third edition of this classic treatise presents a wealth of new topics and new observations. These include slow earthquake phenomena; friction of phyllosilicates, and at high sliding velocities; fault structures; relative roles of strong and seismogenic versus weak and creeping faults; dynamic triggering of earthquakes; oceanic earthquakes; megathrust earthquakes in subduction zones; deep earthquakes; and new observations of earthquake precursory phenomena.

The Mechanics of Earthquakes and Faulting

SUMMARY 
We determine best-fitting Euler vectors, closure-fitting Euler vectors, and a new global model (NUVEL-1) describing the geologically current motion between 12 assumed-rigid plates by inverting plate motion data we have compiled, critically analysed, and tested for self-consistency. We treat Arabia, India and Australia, and North America and South America as distinct plates, but combine Nubia and Somalia into a single African plate because motion between them could not be reliably resolved. The 1122 data from 22 plate boundaries inverted to obtain NUVEL-1 consist of 277 spreading rates, 121 transform fault azimuths, and 724 earthquake slip vectors. We determined all rates over a uniform time interval of 3.0m.y., corresponding to the centre of the anomaly 2A sequence, by comparing synthetic magnetic anomalies with observed profiles. The model fits the data well. Unlike prior global plate motion models, which systematically misfit some spreading rates in the Indian Ocean by 8–12mm yr−1, the systematic misfits by NUVEL-1 nowhere exceed ∼3 mm yr−1. The model differs significantly from prior global plate motion models. For the 30 pairs of plates sharing a common boundary, 29 of 30 P071, and 25 of 30 RM2 Euler vectors lie outside the 99 per cent confidence limits of NUVEL-1. Differences are large in the Indian Ocean where NUVEL-1 plate motion data and plate geometry differ from those used in prior studies and in the Pacific Ocean where NUVEL-1 rates are systematically 5–20 mm yr−1 slower than those of prior models. The strikes of transform faults mapped with GLORIA and Seabeam along the Mid-Atlantic Ridge greatly improve the accuracy of estimates of the direction of plate motion. These data give Euler vectors differing significantly from those of prior studies, show that motion about the Azores triple junction is consistent with plate circuit closure, and better resolve motion between North America and South America. Motion of the Caribbean plate relative to North or South America is about 7 mm yr−1 slower than in prior global models. Trench slip vectors tend to be systematically misfit wherever convergence is oblique, and best-fitting poles determined only from trench slip vectors differ significantly from their corresponding closure-fitting Euler vectors. The direction of slip in trench earthquakes tends to be between the direction of plate motion and the normal to the trench strike. Part of this bias may be due to the neglect of lateral heterogeneities of seismic velocities caused by cold subducting slabs, but the larger part is likely caused by independent motion of fore-arc crust and lithosphere relative to the overriding plate.

Current plate motions

Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems

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 .

Stochastic simulation of high-frequency ground motions based on seismological models of the radiated spectra

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

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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

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.

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Simulation of Ground Motion Using the Stochastic Method

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).

Equations for Estimating Horizontal Response Spectra and Peak Acceleration from Western North American Earthquakes: A Summary of Recent Work

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...

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David M. Boore

Papers

Stochastic simulation of high-frequency ground motions based on seismological models of the radiated spectra

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

Simulation of Ground Motion Using the Stochastic Method

Equations for Estimating Horizontal Response Spectra and Peak Acceleration from Western North American Earthquakes: A Summary of Recent Work

NGA-West2 Equations for Predicting PGA, PGV, and 5% Damped PSA for Shallow Crustal Earthquakes: