David M. Perkins

USGS National Seismic Hazard Maps

The U.S. Geological Survey (USGS) recently completed new probabilistic seismic hazard maps for the United States, including Alaska and Hawaii. These hazard maps form the basis of the probabilistic component of the design maps used in the 1997 edition of the NEHRP Recommended Provisions for Seismic Regulations for New Buildings and Other Structures, prepared by the Building Seismic Safety Council and published by FEMA. The hazard maps depict peak horizontal ground acceleration and spectral response at 0.2, 0.3, and 1.0 sec periods, with 10%, 5%, and 2% probabilities of exceedance in 50 years, corresponding to return times of about 500, 1000, and 2500 years, respectively. In this paper we outline the methodology used to construct the hazard maps. There are three basic components to the maps. First, we use spatially smoothed historic seismicity as one portion of the hazard calculation. In this model, we apply the general observation that moderate and large earthquakes tend to occur near areas of previous small or moderate events, with some notable exceptions. Second, we consider large background source zones based on broad geologic criteria to quantify hazard in areas with little or no historic seismicity, but with the potential for generating large events. Third, we include the hazard from specific fault sources. We use about 450 faults in the western United States (WUS) and derive recurrence times from either geologic slip rates or the dating of pre-historic earthquakes from trenching of faults or other paleoseismic methods. Recurrence estimates for large earthquakes in New Madrid and Charleston, South Carolina, were taken from recent paleoliquefaction studies. We used logic trees to incorporate different seismicity models, fault recurrence models, Cascadia great earthquake scenarios, and ground-motion attenuation relations. We present disaggregation plots showing the contribution to hazard at four cities from potential earthquakes with various magnitudes and distances.

A seismic hazard map of India and adjacent areas

Abstract We have produced a probabilistic seismic hazard map showing peak ground accelerations in rock for India and neighboring areas having a 10% probability of being exceeded in 50 years. Seismogenic zones were identified on the basis of historical seismicity, seismotectonics and geology of the region. Procedures for reducing the incompleteness of earthquake catalogs were followed before estimating recurrence parameters. An eastern United States acceleration attenuation relationship was employed after it was found that intensity attenuation for the Indian region and the eastern United States was similar. The largest probabilistic accelerations are obtained in the seismotectonic belts of Kirthar, Hindukush, Himalaya, Arakan-Yoma, and the Shillong massif where values of over 70% g have been calculated.

Spatial Correlation of Probabilistic Earthquake Ground Motion and Loss

Spatial correlation of annual earthquake ground motions and losses can be used to estimate the variance of annual losses to a portfolio of properties exposed to earthquakes. A direct method is described for the calculation of the spatial correlation of earthquake ground motions and losses. Calculations for the direct method can be carried out using either numerical quadrature or a discrete, matrix-based approach. Numerical results for this method are compared with those calculated from a simple Monte Carlo simulation. Spatial correlation of ground motion and loss is induced by the systematic attenuation of ground motion with distance from the source, by common site conditions, and by the finite length of fault ruptures. Spatial correlation is also strongly dependent on the partitioning of the variability, given an event, into interevent and intraevent components. Intraevent variability reduces the spatial correlation of losses. Interevent variability increases spatial correlation of losses. The higher the spatial correlation, the larger the variance in losses to a portfolio, and the more likely extreme values become. This result underscores the importance of accurately determining the relative magnitudes of intraevent and interevent variability in ground-motion studies, because of the strong impact in estimating earthquake losses to a portfolio. The direct method offers an alternative to simulation for calculating the variance of losses to a portfolio, which may reduce the amount of calculation required.

Evidence for a Global Seismic-Moment Release Sequence

Temporal clustering of the larger earthquakes (foreshock-mainshock-aftershock) followed by relative quiescence (stress shadow) are characteristic of seismic cycles along plate boundaries. A global seismic-moment release history, based on a little more than 100 years of instrumental earthquake data in an extended version of the catalog of Pacheco and Sykes (1992), illustrates similar behavior for Earth as a whole. Although the largest earthquakes have occurred in the circum-Pacific region, an analysis of moment release in the hemisphere antipodal to the Pacific plate shows a very similar pattern. Monte Carlo simulations confirm that the global temporal clustering of great shallow earthquakes during 1952–1964 at M ≥ 9.0 is highly significant (4% random probability) as is the clustering of the events of M ≥ 8.6 (0.2% random probability) during 1950–1965. We have extended the Pacheco and Sykes (1992) catalog from 1989 through 2001 using Harvard moment centroid data. Immediately after the 1950–1965 cluster, significant quiescence at and above M 8.4 begins and continues until 2001 (0.5% random probability). In alternative catalogs derived by correcting for possible random errors in magnitude estimates in the extended Pacheco–Sykes catalog, the clustering of M ≥ 9 persists at a significant level. These observations indicate that, for great earthquakes, Earth behaves as a coherent seismotectonic system. A very-large-scale mechanism for global earthquake triggering and/or stress transfer is implied. There are several candidates, but so far only viscoelastic relaxation has been modeled on a global scale.

Treatment of Parameter Uncertainty and Variability for a Single Seismic Hazard Map

The inputs to probabilistic seismic hazard studies (seismic source zones, earthquake rates, attenuation functions, etc.) are uncertain, being based on subjective judgments and interpretations of limited data. In the face of this uncertainty, we consider (a) how one might “reasonably” determine the ground-motion levels to show on a single probabilistic seismic hazard map, and (b) the extent to which uncertainty in the calculated levels can be meaningfully represented on such a map. If the “best guess” estimates of the earthquake rate, the Gutenberg-Richter b-value and the maximum magnitude for a single source zone are regarded as uncorrelated and the uncertainty in each parameter can be regarded as symmetric about the estimated value, then the probabilistic ground-motion levels calculated using these best estimates represent both most likely values and also approximate mean values.

Losses to Single-Family Housing from Ground Motions in the 1994 Northridge, California, Earthquake

The distributions of insured losses to single-family housing following the 1994 Northridge, California, earthquake for 234 ZIP codes can be satisfactorily modeled with gamma distributions. Regressions of the parameters in the gamma distribution on estimates of ground motion, derived from ShakeMap estimates or from interpolated observations, provide a basis for developing curves of conditional probability of loss given a ground motion. Comparison of the resulting estimates of aggregate loss with the actual aggregate loss gives satisfactory agreement for several different ground-motion parameters. Estimates of loss based on a deterministic spatial model of the earthquake ground motion, using standard attenuation relationships and NEHRP soil factors, give satisfactory results for some ground-motion parameters if the input ground motions are increased about one and one-half standard deviations above the median, reflecting the fact that the ground motions for the Northridge earthquake tended to be higher than the median ground motion for other earthquakes with similar magnitude. The results give promise for making estimates of insured losses to a similar building stock under future earthquake loading.

Direct Calculation of the Probability Distribution for Earthquake Losses to a Portfolio

We demonstrate a direct method for the calculation of the annual frequency of exceedance for earthquake losses (or the probability distribution for annual losses) to a portfolio. This method parallels the classic method of probabilistic seismic hazard analysis for the calculation of the annual frequency of exceedance for earthquake ground motions. The method assumes conditional independence of the random component of ground motions and losses at different sites for each earthquake, given magnitude, distance to the sites, and so-called interevent epsilon. Examples show that the method is realizable, and can take into account different loss functions and site conditions in the portfolio. The main advantage of this method is that it does not require a separate set of scenario earthquakes, as do Monte Carlo-based approaches, but can be calculated directly from the inputs used for hazard maps.

Are secular correlations between sunspots, geomagnetic activity, and global temperature significant?

Recent studies have led to speculation that solar-terrestrial interaction, measured by sunspot number and geomagnetic activity, has played an important role in global temperature change over the past century or so. We treat this possibility as an hypothesis for testing. We examine the statistical significance of cross-correlations between sunspot number, geomagnetic activity, and global surface temperature for the years 1868–2008, solar cycles 11–23. The data contain substantial autocorrelation and nonstationarity, properties that are incompatible with standard measures of cross-correlational significance, but which can be largely removed by averaging over solar cycles and first-difference detrending. Treated data show an expected statistically-significant correlation between sunspot number and geomagnetic activity, Pearson p < 10^(−4), but correlations between global temperature and sunspot number (geomagnetic activity) are not significant, p = 0.9954, (p = 0.8171). In other words, straightforward analysis does not support widely-cited suggestions that these data record a prominent role for solar-terrestrial interaction in global climate change. With respect to the sunspot-number, geomagnetic-activity, and global-temperature data, three alternative hypotheses remain difficult to reject: (1) the role of solar-terrestrial interaction in recent climate change is contained wholly in long-term trends and not in any shorter-term secular variation, or, (2) an anthropogenic signal is hiding correlation between solar-terrestrial variables and global temperature, or, (3) the null hypothesis, recent climate change has not been influenced by solar-terrestrial interaction.

Probabilistic Estimates of Maximum Seismic Horizontal Ground Acceleration on Rock in Alaska and the Adjacent Continental Shelf

Estimates of ground motion hazard from earthquakes in Alaska and the adjacent continental shelf indicate that, for all the exposure times considered, the predicted values of peak acceleration are highest in the Gulf of Alaska and near the major active strike-slip faults of southern Alaska. The evaluations assume a Poisson model of earthquake occurrence and are based on seismic source zones delineated from regional geologic considerations and the historical record of earthquakes. Calculated peak acceleration values for a return period of 100 years range as high as 0.4 g in the Gulf of Alaska sector between Kodiak and Kayak Islands, are about 0.2 g near Anchorage, and 0.1 g near Fairbanks. Values for most of the rest of the state are estimated to be less than .04 g; however, most of the southern Alaska industrial and population base lies within the 0.2 g contour. For a return period of 500 years, peak accelerations are estimated as high as 0.8 g for parts of southeastern Alaska near the Fairweather fault, 0.6 g or greater for part of the Gulf of Alaska, and are about 0.45 g and 0.2 g, respectively, for the Anchorage and Fairbanks areas. Values of acceleration for a return period of 2,500 years exceed 0.6 g for much of southern Alaska and are 0.8 g or greater near the Fairweather and central Denali faults; estimated values are 0.1 g or greater for nearly all of onshore Alaska and for the continental shelf areas of the Bering Sea, Norton and Kotzebue Sounds, southern Chukchi Sea and southeastern Beaufort Sea.

Earthquake Hazard in the Eastern United States: Consequences of Alternative Seismic Source Zones

The regional variability in expected ground motion associated with six different characterizations of seismic source zones for probabilistic ground motion assessment is examined for the eastern United States. Three of the seismic source zone models are based on types of geologic structure: (1) regions characterized by late-Precambrian faulting; (2) middle-to-late Paleozoic thrust tectonics; and (3) early-to-middle Mesozoic extensional features. Two other seismic source zone configurations considered are based on data related to vertical crustal movements, and the final source zone model investigated is that of Algermissen and others (1982). Maintaining the same maximum magnitude among all zones and for all source zone configurations, a comparison of results indicates a factor of 3 difference among source zone models for calculated acceleration levels in eastern Massachusetts, southeastern Maine, and the Cape Fear arch of eastern North Carolina; a factor of about 2 or greater difference for most other eastern seaboard areas; and a factor of 1.5 or less for much of the Appalachian region extending from New Brunswick to the Gulf Coast. Results show that certain source zone models based exclusively on speculative geologic hypotheses result in considerably lower ground-motion hazard than otherwise implied by accepting historical seismicity as a guide to future hazard. Significantly, variation in the seismic hazard estimates at probability levels of 1 in 500 due to uncertain earthquake causal structures or processes is considerably higher in the heavily populated northeast region than in the Charleston, South Carolina, area.