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

Our ground-motion predictions equations (GMPEs) (Boore and Atkinson, 2007 and 2008) (BA07 and BA08), include a non-linear site amplification term that requires a value of peak acceleration (PGA)) for the magnitude and distance for which the equations are being evaluated. We call this quantity pga4nl. We obtained an equation for pga4nl during our initial regression work, as described in BA07. That equation is given by the regression coefficients in the first row of Tables 4.2 and 4.4 in BA07. The observed data were modified to a reference condition of 30 760 m/s S V = , using the initial regression equation for pga4nl, and the final ground-motion prediction equations (GMPEs) were developed using this modified set of observed data. The peak accelerations for the reference site condition from the final regression coefficients (the second row in Tables 6 and 7 in BA08) are not the same as given by the coefficients from the initial regression. This has the unfortunate consequence that a plot of site amplification against peak acceleration developed from our GMPEs will show a dependence on magnitude, distance, and fault type, if the points used in the plot are developed in the following reasonable way (for a given oscillator period):

Notes on the equation to use for pga4nl

Accessibility of pre‐exposure prophylaxis (PrEP) in Canada remains complex as publicly funded coverage and delivery differs by province. In January 2018, PrEP became publicly funded and free of charge in British Columbia (BC), whereas PrEP coverage in Ontario and Montreal is more limited and may require out‐of‐pocket costs. We examined differences over time in PrEP uptake and assessed factors associated with PrEP awareness and use.

Examining provincial PrEP coverage and characterizing PrEP awareness and use among gay, bisexual and other men who have sex with men in Vancouver, Toronto and Montreal, 2017–2020

While crystal methamphetamine use by gay, bisexual, and other men who have sex with men (GBM) is associated with increased risk for sexually transmitted infection (STI) transmission, less is understood about the causal pathways between crystal methamphetamine use and STIs. We examined whether the association between greater crystal methamphetamine risk and prevalent bacterial STI diagnosis among GBM was mediated by two types of attitudinal variables: attitudes toward condoms, and sexual escape motives, defined as the use of substances to escape self-awareness during sex, and by sexual behaviors.We used computer-assisted self-interview questionnaires from 2449 sexually active GBM (18% living with HIV; median age = 33, interquartile range, 27-45) recruited via respondent-driven sampling in Vancouver, Toronto, and Montreal, Canada. Using the baseline data from the Engage cohort study, we fit a series of structural mediation models of the associations between greater crystal methamphetamine risk and bacterial STI (syphilis, gonorrhea, and chlamydia) diagnosis. We estimated indirect paths from greater crystal methamphetamine risk, attitudes toward condoms, sexual escape motives, and sexual risk behaviors, adjusting for self-reported demographic variables.In the mediated model, the direct association between greater crystal methamphetamine risk and bacterial STI diagnosis was non-significant; however, five indirect paths were significant. Greater crystal methamphetamine risk was associated with bacterial STIs via condom use attitudes and escape motives, which in turn were associated with number of male anal sex partners, condomless anal sex, and oral sex.Public health and counselling interventions for GBM who use crystal methamphetamine and who are at higher risk for STIs should target evidence-based causal paths that consider sexual attitudes and sexual practices. 

Crystal methamphetamine use and bacterial sexually transmitted infections (STIs) among gay, bisexual and other sexual minority men in Canada.

Accelerations near faults that have moved during moderate-sized earthquakes

In 1982, we published equations for the prediction of various measures of ground motion as a function of earthquake magnitude, distance from the earthquake rupture, and site geology. Many more strong-motion recordings have been obtained since we published our equations. The predictions of the ground motions from our published equations are in reasonable agreement with the peak accelerations from the new data. The increased number of data, however, allow us to refine our predictions for some regions of magnitude and distance space, and perhaps for other variables.

David M. Boore

Papers

Notes on the equation to use for pga4nl

Examining provincial PrEP coverage and characterizing PrEP awareness and use among gay, bisexual and other men who have sex with men in Vancouver, Toronto and Montreal, 2017–2020

Crystal methamphetamine use and bacterial sexually transmitted infections (STIs) among gay, bisexual and other sexual minority men in Canada.

Accelerations near faults that have moved during moderate-sized earthquakes

Empirical prediction of strong ground motion