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

Using velocity profiles from sites in Japan, California, Turkey, and Europe, we find that the time-averaged shear-wave velocity to 30 m (VS30), used as a proxy for site amplification in recent ground-motion prediction equations (GMPEs) and building codes, is strongly correlated with average velocities to depths less than 30 m (VSz, with z being the averaging depth). The correlations for sites in Japan (corresponding to the KiK-net network) show that VS30 is systematically larger for ag ivenVSz than for profiles from the other regions. The difference largely results from the placement of the KiK-net station locations on rock and rocklike sites, whereas stations in the other regions are generally placed in urban areas underlain by sediments. Using the KiK-net velocity profiles, we provide equations relating VS30 to VSz for z ranging from 5 to 29 m in 1-m increments. These equations (and those for California velocity profiles given in Boore, 2004b) can be used to estimate VS30 from VSz for sites in which velocity profiles do not extend to 30 m. The scatter of the residuals decreases with depth, but, even for an averaging depth of 5 m, a variation in logVS30 of � 1 standard deviation maps into less than a 20% uncertainty in ground motions given by recent GMPEs at short periods. The sensitivity of the ground motions to VS30 uncertainty is considerably larger at long periods (but is less than a factor of 1.2 for averaging depths greater than about 20 m). We also find that VS30 is correlated with VSz for z as great as 400 m for sites of the KiK-net network, providing some justification for using VS30 as a site-response variable for predicting ground motions at periods for which the wavelengths far exceed 30 m. Online Material: Estimates of VS30 at K-NET stations.

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Regional Correlations of VS30 and Velocities Averaged Over Depths Less Than and Greater Than 30 Meters

We have estimated ground motions at the site of a bridge collapse during the 1994 Northridge, California, earthquake. The estimated motions are based on correcting motions recorded during the mainshock 2.3 km from the collapse site for the relative site response of the two sites. Shear-wave slownesses and damping based on analysis of borehole measurements at the two sites were used in the site response analysis. We estimate that the motions at the collapse site were probably larger, by factors ranging from 1.2 to 1.6, than at the site at which the ground motion was recorded, for periods less than about 1 sec.

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Estimated Ground Motion From the 1994 Northridge, California, Earthquake at the Site of the Interstate 10 and La Cienega Boulevard Bridge Collapse, West Los Angeles, California

A precise analysis of the influence of topographic and geological effects on the significant ground motions recorded near Pacoima Dam during the San Fernando, California, earthquake of February 9, 1971, is an immensely complicated task. Calculations for simple models give results that suggest the following general conclusions: (1) the topography should have influenced the recorded ground motion, and (2) this influence seems to be an amplification of the higher-frequency accelerations by as much as 50 per cent, but is relatively unimportant at the lower frequencies (which control the maximum particle velocities).

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The effect of simple topography on seismic waves: Implications for the accelerations recorded at Pacoima Dam, San Fernando Valley, California

Recent additions to the strong-motion data set, primarily from earthquakes in California and Italy, are responsible for a large number of papers examining the prediction of ground-motion measures using regression methods. Peak acceleration is still the most common measure being considered, but increasing attention is being given to peak velocity and spectral amplitudes. Although direct comparisons among the studies are hampered by differing definitions of distance and magnitude, in general the various studies give similar answers for peak acceleration in the region of distance and magnitude space in which most of the data are concentrated. As might be expected, the differences are most pronouced for large magnitudes and distances close to the fault, where data are few. Even so, widely differing assumptions about the form of the regression equation and differences in the composition and weighting of the data set can give similar answers. This was true in recent studies by Campbell (1981b) and Joyner and Boore (1981), where the predicted accelerations for large earthquakes at close distances differed by less than 40 per cent. This seemingly large uncertainty is small compared to the scatter in the data about the regression lines. A Monte Carlo study shows that the question of whether the shape of the attenuation curves is magnitude-dependent cannot be resolved by existing data.

The empirical prediction of ground motion

A reanalysis of the available data for the 1966 Parkfleld, California, earthquake (Mr -- 5½) suggests that although the ground breakage and aftershocks extended about 40 km along the San Andreas Fault, the initial dynamic rupture was only 20 to 25 km in length. The foreshocks and the point of initiation of the main event locate at a small bend in the mapped trace of the fault. Detailed analysis of the P-wave first motions from these events at the Gold Hill station, 20 km southeast, indicates that the bend in the fault extends to depth and apparently represents a physical discontinuity on the fault plane. Other evidence suggests that this discontinuity plays an important part in the recurrence of similar magnitude 5 to 6 earthquakes at Parkfield. Analysis of the strong-motion records suggests that the rupture stopped at another discontinuity in the fault plane, an en-echeion offset near Gold Hill that lies at the boundary on the San Andreas Fault between the zone of aseismic slip and the locked zone on which the great 1857 earthquake occurred. Foreshocks to the 1857 earthquake occurred in this area (Sieh, 1978), and the epicenter of the main shock may have coincided with the offset zone. If it did, a detailed study of the geological and geophysical character of the region might be rewarding in terms of understanding how and why great earthquakes initiate where they do.

David M. Boore

Papers

Regional Correlations of VS30 and Velocities Averaged Over Depths Less Than and Greater Than 30 Meters

Estimated Ground Motion From the 1994 Northridge, California, Earthquake at the Site of the Interstate 10 and La Cienega Boulevard Bridge Collapse, West Los Angeles, California

The effect of simple topography on seismic waves: Implications for the accelerations recorded at Pacoima Dam, San Fernando Valley, California

The empirical prediction of ground motion

Control of rupture by fault geometry during the 1966 parkfield earthquake