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...

/pdf/the-empirical-mode-decomposition-and-the-hilbert-spectrum-qkmom366dy.pdf

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

Scattering of body waves to surface waves is a means for converting energy with essentially infinite horizontal wavelength to motion with short wavelengths. This process, of interest to engineers designing structures with large horizontal dimensions such as pipelines, tunnels, and bridges, has received little attention from seismologists. Finite-difference calculations have been performed for the simple case of vertically incident SV and P waves impinging on a step change in surface elevation. These calculations predict scattered Rayleigh waves with amplitudes as large as 0.4 times the amplitude of the surface motion of the incident waves in the absence of any topographic relief, even for incident wavelengths several times the height of the step. Both vertical and inclined steps are examined.

Wave scattering from a step change in surface topography

The digital accelerograph network installed in Taiwan produced a rich set of records from the 20 September 1999 Chi-Chi, Taiwan earthquake (Mw 7.6). Teledyne Geotech model A-800 and A-900A* digital accelerographs were colocated at 22 stations that recorded this event. Comparisons of the amplitudes, frequency content, and baseline offsets show that records from several of the A-800 accelero- graphs are considerably different than those from the colocated A-900A accelero- graphs. On this basis, and in view of the more thorough predeployment testing of the newer A-900A instruments, we recommend that the records from the A-800 instruments be used with caution in analyses of the mainshock and aftershocks. At the Hualien seismic station two A-900A and one A-800 instruments were colocated, along with a Global Positioning System instrument. Although the records from the two A-900A instruments are much more similar than those from a colocated A-800 instrument, both three-component records contain unpredictable baseline offsets, which produced completely unrealistic ground displacements derived from the ac- celerations by double integration, as do many of the strong-motion data from this event; the details of the baseline offsets differ considerably on the two three- component records. There are probably numerous sources of the baseline offsets, including sources external to the instruments, such as tilting or rotation of the ground, and sources internal to the instruments, such as electrical or mechanical hysteresis in the sensors. For the two colocated A-900A records at the Hualien seismic station, however, the differences in the baseline offsets suggest that the principal source is some transient disturbance within the instrument. The baseline offsets generally man- ifest themselves in the acceleration time series as pulses or steps, either singly or in combination. We find a 0.015-Hz low-cut filter can almost completely eliminate the effects of the baseline offsets, but then information regarding the permanent dis- placements is lost. The causative mechanisms of the baseline offsets are unknown presently. Hence, it is very difficult to recover the permanent displacements from the modern digital records, although for records close to large earthquakes, the signal- to-noise ratio should theoretically be adequate to obtain ground motions with periods of hundreds of seconds. This study reinforces our conclusion from previous studies that the sources of baseline offsets occurring in digital strong-motion records are very complex and often unpredictable, and that, therefore, it is difficult to remove the baseline effects to maximize the information content of the record. The baseline offsets only affect very long period motions (e.g., 20 sec), however, and therefore are of little or no engineering concern.

/pdf/some-observations-on-colocated-and-closely-spaced-strong-30ta30t9u0.pdf

Some Observations on Colocated and Closely Spaced Strong Ground- Motion Records of the 1999 Chi-Chi, Taiwan, Earthquake

/pdf/ground-motion-values-for-use-in-the-seismic-design-of-the-ix4hf3euak.pdf

Ground motion values for use in the seismic design of the Trans-Alaska Pipeline system

Most digital accelerograph recordings are plagued by long-period drifts, best seen in the velocity and displacement time series obtained from integration of the acceleration time series. These drifts often result in velocity values that are nonzero near the end of the record. This is clearly unphysical and can lead to inaccurate es- timates of peak ground displacement and long-period spectral response. The source of the long-period noise seems to bevariations in the acceleration baseline in many cases. These variations could be due to true ground motion (tilting and rotation, as well as local permanent ground deformation), instrumental effects, or analog-to-digital con- version. Very often the trends in velocity are well approximated by a linear trend after the strong shaking subsides. The linearity of the trend in velocity implies that no vari- ations in the baseline could have occurred after the onset of linearity in the velocity time series. This observation, combined with the lack of any trends in the pre-event motion, allows us to compute the time interval in which any baseline variations could occur. We then use several models of the variations in a Monte Carlo procedure to derive a suite of baseline-corrected accelerations for each noise model using records from the 1999 Chi-Chi earthquake and several earthquakes in Turkey. Comparisons of the mean values of the peak ground displacements, spectral displacements, and resid- ual displacements computed from these corrected accelerations for the different noise models can be used as a guide to the accuracy of the baseline corrections. For many of the records considered here the mean values are similar for each noise model, giving confidence in the estimation of the mean values. The dispersion of the ground-motion measures increases with period and is noise-model dependent. The dispersion of in- elastic spectra is greater than the elastic spectra at short periods but approaches that of the elastic spectra at longer periods. The elastic spectra from the most basic proces- sing, in which only the pre-event mean is removed from the acceleration time series, do not diverge from the baseline-corrected spectra until periods of 10-20 sec or more for the records studied here, implying that for many engineering purposes elastic spec- tra can be used from records with no baseline correction or filtering.

/pdf/on-baseline-corrections-and-uncertainty-in-response-4fngmecpr6.pdf

On Baseline Corrections and Uncertainty in Response Spectrafor Baseline Variations Commonly Encounteredin Digital Accelerograph Records

INTRODUCTION 

Shear-wave velocity profiles are used in a variety of engineering and seismological applications, and several methods are available to determine the velocities, including borehole and surface-wave methods (Woods and Stokoe, 1985; Stokoe et al. , 1988; Stokoe etal. , 1994; Poran et al. , 1994; Poran et al. , 1996). Surface-wave methods offer the advantage of being non-invasive and less costly than boreholes, but their reliability needs to be established by comparison with more direct methods. The best way to do this is a “blind” test in which the velocities determined independently from surface-wave and borehole measurements at the same site are compared. By “blind” we mean that the determination of the shear-wave velocity profile by the two methods were done independently of one another. It is surprisingly difficult to find situations in which the velocity determinations are truly independent of one another. We report on one such case in this paper. In...

Comparing Shear-Wave Velocity Profiles From Inversion of Surface-Wave Phase Velocities with Downhole Measurements: Systematic Differences Between the CXW Method and Downhole Measurements at Six USC Strong-Motion Sites

David M. Boore

Papers

Wave scattering from a step change in surface topography

Some Observations on Colocated and Closely Spaced Strong Ground- Motion Records of the 1999 Chi-Chi, Taiwan, Earthquake

Ground motion values for use in the seismic design of the Trans-Alaska Pipeline system

On Baseline Corrections and Uncertainty in Response Spectrafor Baseline Variations Commonly Encounteredin Digital Accelerograph Records

Comparing Shear-Wave Velocity Profiles From Inversion of Surface-Wave Phase Velocities with Downhole Measurements: Systematic Differences Between the CXW Method and Downhole Measurements at Six USC Strong-Motion Sites