Trevor I. Allen

Topographic Slope as a Proxy for Seismic Site Conditions and Amplification

We describe a technique to derive first-order site-condition maps di- rectly from topographic data. For calibration, we use global 30 arc sec topographic data and VS 30 measurements (here VS 30 refers to the average shear-velocity down to 30 m) aggregated from several studies in the United States, as well as in Taiwan, Italy, and Australia. VS 30 values are correlated against topographic slope to develop two sets of parameters for deriving VS 30 : one for active tectonic regions where to- pographic relief is high, and one for stable shields where topography ismoresubdued. By taking the gradient of the topography and choosing ranges of slope that maximize the correlation with shallow shear-velocity observations, we can recover, to first order, many of the spatially varying features of site-condition maps developed for California. Our site-condition map for the low-relief Mississippi Embayment also predicts the bulk of the VS 30 observations in that region despite rather low slope ranges. We find that maps derived from the slope of the topography are often well cor- related with other independently derived, regional-scale site-condition maps, but the latter maps vary in quality and continuity, and subsequently, also in their ability to match observed V S 30 measurements contained therein. Alternatively, the slope-based method provides a simple approach to uniform site-condition mapping. After validating this approach in regions with numerous V S 30 observations, we subsequently estimate and map site conditions for the entire continental United States using the respective slope correlations.

A Revised Ground-Motion and Intensity Interpolation Scheme for ShakeMap

Wedescribe aweighted-average approach for incorporating varioustypes of data (observed peak ground motions and intensities and estimates from ground- motion prediction equations) into theShakeMap ground motion and intensity mapping framework.ThisapproachrepresentsafundamentalrevisionofourexistingShakeMap methodology. In addition, the increased availability of near-real-time macroseismic intensitydata,thedevelopmentofnewrelationshipsbetweenintensityandpeakground motions, and new relationships to directly predict intensity from earthquake source information have facilitated the inclusion of intensity measurements directly into ShakeMap computations. Our approach allows for the combination of (1) direct observations (ground-motion measurements or reported intensities), (2) observations converted from intensity to ground motion (or vice versa), and (3) estimated ground motionsandintensities frompredictionequationsornumerical models.Critically,each oftheaforementioneddatatypesmustincludeanestimateofitsuncertainties,including those caused by scaling the influence of observations to surrounding grid points and those associated with estimates given an unknown fault geometry. The ShakeMap ground-motion and intensity estimates are an uncertainty-weighted combination of these various data and estimates. A natural by-product of this interpolation process is an estimate of total uncertainty at each point on the map, which can be vital for comprehensive inventory loss calculations. We perform a number of tests to validate this new methodology and find that it produces a substantial improvement in the accuracy of ground-motion predictions over empirical prediction equations alone.

An atlas of ShakeMaps for selected global earthquakes

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Attenuation of Ground-Motion Spectral Amplitudes in Southeastern Australia

A dataset comprising some 1200 weak- and strong-motion records from 84 earthquakes is compiled to develop a regional ground-motion model for southeastern Australia (sea). Events were recorded from 1993 to 2004 and range in size from moment magnitude 2.0 ≤ M ≤ 4.7. The decay of vertical-component Fourier spectral amplitudes is modeled by trilinear geometrical spreading. The decay of low- frequency spectral amplitudes can be approximated by the coefficient of R −1.3 (where R is hypocentral distance) within 90 km of the seismic source. From approximately 90 to 160 km, we observe a transition zone in which the seismic coda are affected by postcritical reflections from midcrustal and Moho discontinuities. In this hypocentral distance range, geometrical spreading is approximately R +0.1 . Beyond 160 km, low-frequency seismic energy attenuates rapidly with source–receiver distance, having a geometrical spreading coefficient of R −1.6 . The associated regional seismic-quality factor can be expressed by the polynomial: log Q ( f ) = 3.66 − 1.44 log f + 0.768 (log f ) 2 + 0.058 (log f ) 3 for frequencies 0.78 ≤ f ≤ 19.9 Hz. Fourier spectral amplitudes, corrected for geometrical spreading and anelastic attenuation, are regressed with M to obtain quadratic source scaling coefficients. Modeled vertical-component displacement spectra fit the observed data well. Amplitude residuals are, on average, relatively small and do not vary with hypocentral distance. Predicted source spectra (i.e., at R = 1 km) are consistent with eastern North American (ena) models at low frequencies ( f less than approximately 2 Hz) indicating that moment magnitudes calculated for sea earthquakes are consistent with moment magnitude scales used in ena over the observed magnitude range. The models presented represent the first spectral ground-motion prediction equations developed for the southeastern Australian region. This work provides a useful framework for the development of regional ground-motion relations for earthquake hazard and risk assessment in sea.

Prompt Assessment of Global Earthquakes for Response (PAGER): A System for Rapidly Determining the Impact of Earthquakes Worldwide

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Empirical Attenuation of Ground-Motion Spectral Amplitudes in Southwestern Western Australia

A dataset comprising some 389 strong- and weak-motion records for 69 events from the Burakin 2001–2002 earthquake swarm, and additional recent events, is compiled to develop a regional ground-motion model for the Yilgarn Craton, southwestern Western Australia. Events range in size from moment magnitude 2.2 ≤ M ≤ 4.6. The decay of horizontal-component spectral amplitudes can be approximated by a geometrical attenuation coefficient of R −1.0 within 80 km of the source. The associated regional seismic quality factor can be expressed as Q ( f ) = 457 f 0.37 for frequencies 1.07 ≤ f ≤ 25.0 Hz. Average corner frequencies for events with magnitude M >3.0 do not vary significantly with seismic moment M 0 , indicating a steep distribution of M 0 versus corner frequency. This causes anomalously low estimates of stress drop for smaller magnitude events ( M Fourier spectral amplitudes, corrected for geometric and anelastic attenuation, were regressed with M to obtain quadratic attenuation coefficients. Modeled horizontal-component displacement spectra fit the observed data well. Amplitude residuals (predicted–observed amplitudes) are, on average, relatively small and do not vary significantly with hypocentral distance. Source spectra (i.e., at R = 1 km) predicted from the regression parameters give self-consistent amplitudes at low frequency ( f less than approximately 2 Hz), equivalent to predictive models from eastern North America (ena) for the same moment magnitude. However, our model predicts lower spectral amplitudes with increasing frequency as a consequence of the low- stress-drop events. This is particularly apparent for the smaller magnitudes. Western Australian source spectra begin to converge with ena models at increasing magnitudes. If hypocentral distance is increased (i.e., R ≫ 1 km), the models begin to diverge at low frequencies owing to differences in geometrical attenuation coefficients. The bulk of these data were recorded from an earthquake swarm with very shallow focal depths ( h

The Challenges of Probabilistic Seismic‐Hazard Assessment in Stable Continental Interiors: An Australian Example

In stable continental regions (SCRs), the process of probabilistic seismic‐hazard assessment (PSHA) remains a scientific and technical challenge. In producing a new national hazard model for Australia, we developed several innovative techniques to address these challenges. The Australian seismic catalog is heterogeneous due to the variability between magnitude types and the sparse networks. To reduce the resulting high epistemic uncertainty in the recurrence parameters, a and b , the magnitudes of pre‐1990 earthquakes have been empirically corrected to account for changes in magnitude formulas around 1990. In addition, existing methods for estimating recurrence parameters (e.g., maximum likelihood estimation) were found to be unstable. To overcome this problem, a new method was developed that removes outlier earthquakes before applying a regression. The incorporation of a model of episodic seismicity into the new hazard model required deviation from the more conventional method of PSHA. The selection of the maximum earthquake magnitude M max is based on the analysis of surface ruptures from paleoearthquakes, with M max thought to vary between geological domains (e.g., 7.2–7.6 in nonextended SCR and 7.4–7.8 in extended SCR). The sensitivity of PSHA to M max, source zone boundary location, recurrence parameters, and ground‐motion prediction equations (GMPEs) was examined in this study. The hazard was found to be generally insensitive to M max in the estimated preferred magnitude range. The uncertainty in recurrence parameters was found to contribute a variation in hazard comparable to the epistemic uncertainty associated with the different GMPEs used in this study. For sites near source zone boundaries, a similar variation in hazard was observed by reasonable changes in the position of the boundaries. Aleatory variability and epistemic uncertainty in GMPEs are routinely incorporated in PSHAs, as is variation in M max. However, the uncertainties in recurrence parameters and source zone boundaries are generally given less attention.

Comparison of earthquake source spectra and attenuation in eastern North America and southeastern Australia

Abstract The paucity of ground-motion data in Stable Continental Regions (SCRs) remains a key limitation when developing relations that seek to predict effects of strong ground-shaking from large damaging earthquakes. It is desirable to combine data from more than one SCR in order to increase database size, but this raises questions as to whether the source and attenuation properties of the SCRs are equivalent. We merge recently- compiled spectral-amplitude databases from small-to-moderate events (moment magnitudes 2.0 ≤ M ≤ 5.0) in both southeastern Australia and eastern North America in order to compare the key characteristics of ground motion in these two regions. Both are SCRs, but are widely separated, spatially and in tectonic history. We statistically compare ground motions by plotting mean and standard deviations of spectral amplitudes for data grouped in magnitude and distance bins. These comparisons show that the source and attenuation properties of the two regions are very similar, particularly at shorter hypocentral distances

Advancements in Casualty Modelling Facilitated by the USGS Prompt Assessment of Global Earthquakes for Response (PAGER) System

The advent of the U.S. Geological Survey (USGS) Prompt Assessment of Global Earthquakes for Response (PAGER) system, in conjunction with several recent advances and trends in related data sources and research efforts, bring to light new opportunities within the overlapping realms of earthquake hazard, earthquake engineering, and earthquake epidemiological studies. While casualty modelling has admittedly often suffered from the lack of epidemiological rigour on the part of earth scientists and engineers, comparable laxity is also evident in some analyses of related hazard complexities on the part of social scientists. These limitations have often been due to insufficient oversight or interaction, or more commonly, insufficient data availability. Thanks to improved data sets, modelling approaches, and collaborations, there are now fewer obstacles to performing comprehensive casualty estimation, though formidable challenges remain. Under the auspices of the PAGER system, a global set of ShakeMaps has been produced for all significant earthquakes in the past 34 years (1973–2007). These event-specific ShakeMaps, constrained by any available data, are then combined with new global population data sets to develop systematic hazard and loss analyses. These and other important advancements, as well as their limitations, and their potential for contributing to casualty modelling are discussed. Example studies and applications are presented.