- © 2005 by the Seismological Society of America
We have developed empirical relations that describe ground-motion amplitudes from earthquakes of 2 < M < 6 at regional distances of 10-500 km in southeastern Canada and the northeastern United States, for ShakeMap applications. The predictive ground-motion parameters are peak ground velocity, peak ground acceleration, and response spectra at frequencies of 1, 2, 5, and 10 Hz. The relations differ from previous relations developed by Atkinson and Boore (1995) in their focus on applicability to the small to moderate regional events important to reliable ShakeMap development. Because of this focus, they are empirical, rather than being based on a stochastic ground-motion model. The stochastic model predictions of Atkinson and Boore (1995) are used at larger magnitudes (M > 4), however, to ensure reasonable values over a broad range of magnitudes (2 to 6).
The new relationships are used to estimate ground-motion parameters for ShakeMaps in Ontario. The ShakeMap program combines predicted ground-motion values with recorded ground-motion values to produce an interpolated map of ground-motion amplitudes. It is essential that the predicted ground-motion values be consistent with recorded values in order to generate reliable ShakeMaps. We found that with our new predictive relations, we obtain ground-motion estimates that closely resemble the recorded ground motions for the small events (2 < M < 4) that occur relatively frequently in eastern North America and are often felt. Thus we recommend the use of our predictive relations for ShakeMap applications in southeastern Canada and the northeastern United States. They are not intended for engineering predictions for large rare earthquakes (M > 6).
ShakeMap, originally conceived by Wald et al. (1999), is a Web-based near-real-time map that shows the spatial distribution of recorded peak ground motions (velocity, acceleration, and response spectra) and estimates the corresponding felt effects. ShakeMap begins by determining ground-motion amplitudes for a network of grid points on the map. At grid points where no actual records are available, ShakeMap uses prediction equations to estimate ground-motion parameters as a function of the event's magnitude and location. ShakeMap combines these estimated ground motions with the recorded values to produce contour maps of ground-motion parameters. These parameters are then used to estimate the felt effects, based on empirical relations between ground motions and Modified Mercalli Intensity (MMI).
In eastern North America (ENA), ShakeMaps are required for the relatively frequent small to moderate events that are often felt, as well as for larger, potentially damaging events (M 5 to 6). It is important to provide timely information on the shaking from such events. Of course, very large events (M > 6) are also possible but occur only rarely (about once every hundred years) in most ENA regions. These rare events are important for engineering design but are not the focus of our ShakeMap applications. Our ShakeMaps are based on seismographic instrumentation that may go off-scale for such large events at close distances.
Kaka and Atkinson (2004) have shown that for small to moderate events (moment magnitude M < 5), peak ground velocity (PGV) values estimated using common ENA ground-motion relations such as those of Atkinson and Boore (1995) (AB95), Toro et al. (1997), and Campbell (2003) are significantly higher than recorded values. This is a consequence of the focus of these relations, which aim to be most accurate for moderate to large events (M 5-7) at close distance (R < 100 km). A new relation is required for ShakeMap applications with better applicability to small to moderate events (M 3-5) over a broad range of distances (1 to 500 km). It is important to produce reliable maps for these common felt events because operators of critical facilities, such as nuclear power plants, must be able to provide timely information on the ground motions associated with felt events to both the public and regulatory authorities.
In this study, we perform regression analyses to develop empirical relations for peak ground velocity (PGV), peak ground acceleration (PGA), and 50/0 damped response spectra (PSA) at frequencies of 1, 2, 5, and 10 Hz for small to moderate events from southeastern Canada and the northeastern United States. The regression is based on a vertical-component database of 3,097 digital seismograms from 205 earthquakes of Nuttli magnitude (MN) greater than 2.0 that occurred between 1980 and 2004. The great majority of records were obtained on hard-rock sites, but a few southern Ontario stations are on firm soil. The effect of soil amplification is considered negligible because we use the vertical component as the basic ground-motion measure. (Note that the horizontal-to-vertical component ratio technique for estimating site response is based on the assumption that amplification of the vertical-component motion is negligible; see Siddiqqi and Atkinson, 2002). Our ShakeMap implementation is based on input vertical-component motions, which are then amplified to horizontal-component motions according to the site conditions (soil response). The final step of ShakeMap, the conversion of ground-motion amplitudes to intensity, has been dealt with in a previous study (Kaka and Atkinson, 2004) and will not be discussed in this paper.
DATA SET FOR THE STUDY
Our data set is composed of all available broadband three-component and short-period data from the Canadian National Seismographic Network (CNSN) and Portable Observatories for Lithospheric Analysis and Research Investigating Seismicity (POLARIS) network recorded from November 1993 through March 2004 in the study region, plus short-period vertical-component seismograms recorded from 1980 to 1990 on the Eastern Canada Telemetered Network (ECTN) as compiled by Atkinson and Mereu (1992). We also include United States National Seismic Network stations (USNSN) in the study region. Figure 1 shows the locations of seismographic stations and study events. Figure 2 shows the distribution of the compiled database in magnitude and distance. Table 1 lists the date, latitude, longitude, depth, Nuttli magnitude (MN), and moment magnitude (M) for each of the 205 earthquakes analyzed in this study. All the information (except for M) is taken from the Canadian National Earthquake Database (NEDB) published by the Geological Survey of Canada and can be searched at their Web site (http://www.seismo.nrcan.gc.ca/nedb/eq_db_e.php). M values are taken from Atkinson (2004), as calculated from the long-period spectral amplitudes. The regressions use M as the predictive magnitude variable, as do our relationships between instrumental ground-motion parameters and Modified Mercalli Intensity (MMI) (Kaka and Atkinson, 2004).
The ground-motion equations were obtained by a simple linear regression of the compiled data set to obtain each ground-motion parameter as a function of M and hypocentral distance. The distribution of empirical data, as shown in Figure 2, is insufficient to predict reliable ground motions for larger events (M > 5). It is important that the predictive ground-motion relations predict not only ground motion at low to moderate magnitudes but also be applicable for the larger magnitudes that occur infrequently in the region. Consequently, we added to the empirical database the predicted ground-motion values for 5.0 ≤ M ≤ 7 (in 0.5 magnitudeunit increments, with hypocentral distance in increments of 0.1 log units), as generated by Atkinson and Boore (1995) using the stochastic model. This will ensure that the relations are reasonable when extended to magnitudes greater than those in the recorded database. Thus the ground-motion equations we obtain are based on recorded ground motion at low magnitudes, plus predictions from the Atkinson and Boore (1995) model for M ≥ 5. Table 2 lists the regression coefficients and their standard errors for the fit of the compiled data set to the predictive ground-motion equations, which are of the form (1) where Y is the vertical-component ground-motion parameter (PGV in mm/s, PGA and PSA(f) in cm/s2), R is hypocentral distance in km, and M is moment magnitude.
To evaluate the performance of the regression equations, we analyzed the residuals, defined as the difference between the log of the observed ground-motion value and the log of the predicted value. Figure 3 plots the PGV residuals as a function of distance and moment magnitude. Plots for PGA and PSA(f) are similar in their trends. We use different symbols to distinguish between observed ground-motion values and those generated by the Atkinson and Boore (1995) (AB95) stochastic model. Notably, there is an apparent magnitude trend, attributable to the mismatch between the empirical predictions at low M and the AB95 stochastic model predictions at M > 5. We recognize that there is a strong likelihood that our new empirical relations might overestimate ground-motion values for M ≥ 6 events, as suggested by the decreasing residual trend at large magnitudes seen in Figure 3. This is not a great concern for us, since these events are not the focus of our ShakeMap applications. For ShakeMap, we are interested in accurate prediction of ground motions for the more frequent small to moderate (3 < M < 5) events that are very typical in Ontario. Regression residuals in Figure 3 suggest that for M ≤ 6 events, we obtain reliable ground-motion estimates on average. We note the relatively high standard deviation (σ) (from 0.31 to 0.37 log units) of residuals for the regression analysis; this is expected due to the large magnitude and distance range of our compiled data (see Figure 2).
In Figure 4 we compare our empirical ground-motion relations with those of the AB95 model for an event of M 4.0 near Maniwaki, Québec which occurred on 12 October 2003. Our empirical ground-motion equations closely predict the recorded ground motions, while the AB95 relations significantly overpredict ground-motion values for this event. This result is typical. Similar comparisons for other events (e.g., 1999/03/16 M 4.5, 2003/08/20 M 3.0, 2003/10/18 M 3.0) also indicate overprediction of recorded amplitudes for small events by the AB95 relations. This is not entirely surprising, since the AB95 relations were developed primarily for M ≥ 5 events.
We have developed empirical ground-motion equations based on regression of a vertical-component database of 3,097 digital seismograms from 205 earthquakes of moment magnitude (M) 2 to 6 that occurred between 1980 and 2004. The relations are useful for the purpose of generating reliable ShakeMaps in Ontario for small to moderate regional events. The predicted parameters are peak ground velocity (PGV), peak ground acceleration (PGA), and 5% damped response spectra (PSA) at frequencies of 1, 2, 5, and 10 Hz. Our predictive equations differ from previous relations developed by Atkinson and Boore (1995) in their applicability to smaller events, and our emphasis on fit to empirical data rather than to model predictions (although model predictions are used to ensure reasonable ground motions for larger magnitudes). Our relations are appropriate for use as the interpolation basis in ShakeMaps for southeastern Canada and the northeastern United States. They are not intended for engineering ground-motion predictions for rare moderate to large events.
Time series data for the CNSN and POLARIS stations were obtained from the Geological Survey of Canada (GSC) Automatic Data Request Manager (http://www.seismo.nrcan.gc.ca/nwfa/autodrm). The CNSN and ECTN data from 1990-2002 were accessed through http://www.seismo.nrcan.gc.ca/nwfa/events. The U.S. stations were obtained from the U.S. Geological Survey's Automatic Data Request Manager (httpc//neic.usgs.gov/neis/autodrm). Short-period data from 1980 to 1990 were complied by Atkinson and Mereu (1992). Our compiled database of ground-motion amplitudes is available upon request to .