GEOPHYSICAL RESEARCH LETTERS, VOL. 34, LXXXXX, doi: /2007gl031077, 2007
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1 Click Here for Full Article GEOPHYSICAL RESEARCH LETTERS, VOL. 34, LXXXXX, doi: /2007gl031077, Magnitude scaling relations from P-waves in southern California 3 Louisa L. H. Tsang, 1,2 Richard M. Allen, 1 and Gilead Wurman 1 4 Received 21 June 2007; revised 10 August 2007; accepted 22 August 2007; published XX Month [1] We derive empirical magnitude scaling relationships 7 for southern California using a dataset of 59 past 8 earthquakes recorded in southern California by the 9 Southern California Seismic Network (SCSN) between California and The events range in magnitude from 3.0 to 7.3. We use the maximum predominant period (t max p ) and 12 the peak displacement amplitude (P d ) measured from the 13 first 4 seconds of P-wave arrivals to determine period- 2. Methodology 14 magnitude and amplitude-magnitude scaling relationships 15 respectively. Our calibration study shows that the scaling 16 relationships are similar to those derived for northern 17 California. The average error in magnitude estimates is magnitude units for events with magnitudes smaller 19 than 4.5 (M < = 4.5), 0.3 magnitude units for events with 20 magnitudes ranging from 4.5 to 6.5 (4.5 < M < = 6.5), and magnitude units for events with magnitudes greater than 1988] (M > 6.5). Citation: Tsang, L. L. H., R. M. Allen, and 23 G. Wurman (2007), Magnitude scaling relations from P-waves 24 in southern California, Geophys. Res. Lett., 34, LXXXXX, 25 doi: /2007gl Introduction 28 [2] The proximity of metropolitan cities to active faults 29 within southern California presents a challenge in develop- 30 ing an earthquake early warning system (EEW) capable of 31 providing advance warning of peak ground shaking associ- 32 ated with large earthquakes. 33 [3] Earthquake Alarm Systems (ElarmS) is a methodol- 34 ogy to integrate realtime geophysical data during the course 35 of an earthquake for the purpose of providing warnings 36 prior to damaging ground shaking ( 37 ElarmS uses multiple seismic stations to detect and locate 38 earthquakes, estimate the magnitude from P-waves, and 39 predict the distribution of ground shaking. The methodolo- 40 gy was initially developed by Allen and Kanamori [2003], 41 is described more fully by Allen [2007], and has been 42 extended by Wurman et al. [2007]. ElarmS has been 43 extensively tested offline within northern California, and 44 shown effective as an algorithm for providing accurate 45 estimates of earthquake magnitude, location and the distri- 46 bution of peak ground acceleration within a few to a few 47 tens of seconds after the earthquake origin time. 48 [4] Using the same methodology described by Wurman et 49 al. [2007], we derive empirical magnitude scaling relation- 50 ships exclusively for southern California and evaluate the 51 quality of the calibration using 59 past earthquakes recorded 1 Department of Earth and Planetary Science, University of California, Berkeley, California, USA. 2 Department of Earth Science and Engineering, Imperial College London, London, UK. Copyright 2007 by the American Geophysical Union /07/2007GL031077$05.00 in the region. This provides the necessary scaling relations for future application of ElarmS to southern California. We also compare the magnitude scaling relationships derived in southern California with those derived for northern [5] The ElarmS methodology [Allen and Kanamori, 2003] was developed using past earthquake waveforms to derive empirical scaling relationships between the maximum predominant period (t max p ) of the first 4 seconds of a P-wave arrival at a seismic station, and the final networkrecorded event magnitude. A similar methodology is used in the UrEDAS system implemented in Japan [Nakamura, [6] Wurman et al. [2007] improve upon the accuracy of produced magnitude estimates by incorporating an additional method for magnitude estimation: scaling the peak displacement or velocity amplitude (P d/v ) of the first 4 seconds of a P-wave arrival with the final networkrecorded magnitude via an empirically derived scaling relationship. [Wu et al., 2006]. [7] In this study, we use a dataset of 59 past earthquakes to derive empirical best-fit period-magnitude and amplitude-magnitude scaling relationships for southern California. These events occurred in southern California between 1992 and 2003, and range in magnitude from 3.0 to 7.3. The dataset includes the three largest magnitude earthquakes for which digital recordings are available. The 1992 Landers event (M = 7.3), the 1994 Northridge event (M = 6.7) and the 1999 Hector Mine event (M = 7.1). The waveforms were recorded by seismic stations within the Southern California Seismic Network (SCSN) and obtained from the Southern California Earthquake Center (SCEC). Figure 1 shows a map of all the events and SCSN stations used in this study. [8] We plot observations of t max p measured within the first 4 seconds of a P-wave arrival versus the network magnitude, and fit a least squares linear regression line to the observations. We define the period-magnitude scaling relationship as the equation of this line. Likewise, we obtain the amplitude-magnitude scaling relationship using observations of the peak displacement amplitude (P d ) within the first 4 seconds of a P-wave arrival. We define the ElarmS magnitude estimate as the linear average of the magnitude estimates obtained from t max p and P d. [9] Using the derived best-fit relationships and algorithmic components from ShakeMap specific to southern California [Newmark and Hall, 1982; Joyner and Boore, 1988; Boore et al., 1997; Wald et al., 1999, 2005], we run ElarmS on the 59 events in our dataset, and determine the associated magnitude errors and uncertainties in peak ground acceleration estimates at alarm-time (defined as the time when LXXXXX 1of5
2 multiple stations have usually triggered by the time of the first magnitude estimate Quality of the Calibration [13] The average magnitude error using t max p observations from a single seismic station is 1.1 magnitude units. This is greater than an average error of 0.4 magnitude units that we find using the peak displacement amplitude (P d ) observations from a single station. Figure 3 shows a scatter plot of ElarmS magnitude versus network-recorded magnitude (M w or M L ). The dashed line on the plot represents a Figure 1. Map showing the location of the 59 earthquakes (circles) and Southern California Seismic Network (SCSN) stations (squares) used in this study seconds of data is available from 4 different channels), in 105 order to evaluate the quality of the calibration Results Period-Magnitude Scaling Relationship 108 [10] We obtain the following best-fit relationship between 109 t max p in the first 4 seconds of a P-wave arrival at a station, 110 and the event magnitude: M ¼ 6:36 þ 6:83 log 10 t max p 113 [11] The solid line in Figure 2a shows a plot of this 114 relationship through the maximum predominant period 115 observations from the 59 events used for the calibration. 116 The variance of the observed t max p values from the best fit 117 line is log units in period Amplitude-Magnitude Scaling Relationship 119 [12] We obtain the following best-fit relationship between 120 P d in the first 4 seconds of a P-wave arrival at a station, and 121 the event magnitude: ð1þ M ¼ 1:24 log 10 ðp d Þþ 1:65 log 10 ðrþþ 5:07 ð2þ 123 where R is the distance between the station and the 124 epicenter, in kilometers. Here the variance between 125 observed P d and the model is log units in amplitude. 126 The solid line in Figure 2b shows a plot of this relationship 127 through the peak displacement observations from the events used for the calibration. Using this relation to 129 estimate magnitude in a realtime early warning environment 130 requires a good estimate of the epicentral distance and 131 therefore the event location. This does not cause a problem 132 when using the dense regional networks in California as Figure 2. Plot of (a) maximum predominant period vs. network magnitude and (b) peak displacement amplitude vs. network magnitude for all 59 events (each peak value has been corrected to an epicentral distance of 1 km). Each point represents an individual station measurement using the first 4 seconds of a P-wave arrival. The solid line in each of the plots shows the best fit linear scaling relation. The dashed line in each of the plots shows the respective scaling relationships derived for northern California [Wurman et al., 2007]. 2of5
3 Figure 3. Plot of ElarmS magnitude estimate vs. networkrecorded magnitude (in M w or M L ) for all 59 earthquakes. The triangles represent magnitude estimates using the maximum predominant period (t max p ) observations, the squares represent the magnitude estimates using the peak displacement amplitude (P d ), and the circles represent the magnitude estimates calculated by averaging magnitudes estimated using t max p and P d, for each earthquake :1 relationship between the estimated magnitude and the 144 observed magnitude. We can therefore evaluate the accura- 145 cy of the ElarmS magnitude calibrations by analyzing the 146 scatter of the observation points about this line. The 147 triangles plotted on Figure 3 show the magnitude estimates 148 from t p max. They show little scatter for small events (M < = ), but more scatter for events with magnitudes greater 150 than 4.5. The squares in Figure 3 represent the magnitude 151 estimates from P d. They lie remarkably close to the plotted 152 dashed line when event magnitudes are smaller than However, at magnitudes larger than 5.5, more scatter 154 occurs. Joint t p max and P d magnitude estimates are plotted as circles in Figure 3. The scatter in the combined ElarmS 155 magnitude is significantly less than that of t max p and P d 156 magnitude estimates individually, at a given network- 157 recorded magnitude. This justifies using both estimators 158 to provide the most accurate estimate the earthquake 159 magnitude. 160 [14] For small events (we define these as events with 161 M < = 4.5), the average error in ElarmS magnitude 162 estimates is 0.2 magnitude units. For moderate-sized events 163 (4.5 < M < = 6.5), this error is slightly larger: 0.3 magnitude 164 units. This is reflected by the greater scatter in Figure 3 at 165 larger magnitudes. Since we are primarily concerned with 166 the accuracy in parameter estimates of large earthquakes, 167 which potentially cause the most socio-economic damage in 168 cities, we evaluate the accuracy of the calibration for the 169 three largest events in the dataset. In the case of the M7.3 Landers earthquake, the magnitude is underestimated 171 by 1.0 magnitude units. The magnitude error is primarily 172 max due to the fact that there were only 2 stations to report t p 173 and P d measurements within 100 km of the epicenter at the 174 time of earthquake. We find the ElarmS magnitude error for 175 the 1999 M7.1 Hector Mine earthquake to be lower: magnitude units. For the 1994 M6.7 Northridge earth- 177 quake, despite the fact that only 2 stations were located 178 within 100 km of the epicenter, the magnitude is only 179 underestimated by less than 0.1 magnitude units. The 180 average ElarmS magnitude error for these three large events 181 is 0.5 magnitude units. 182 [15] ElarmS provides realtime predictions of peak ground 183 acceleration (PGA), peak ground velocity (PGV), and 184 Modified Mercalli Intensity (MMI) using a similar approach 185 to that used by ShakeMap. Here we present only the errors 186 for PGA due to space limitations, however, they are repre- 187 sentative of the errors in PGV and MMI also. Figure shows the error in PGA estimates for all 59 events. This is 189 expressed as the log (PGA) error, which is calculated by 190 subtracting the logarithm of the observed peak ground 191 acceleration from the logarithm of the estimated peak 192 ground acceleration. An error of 1 represents an overpre- 193 diction of the peak ground acceleration by a factor of The plots in Figure 4 show that the log (PGA) error 195 decreases from an average error of 0.5 initially (i.e second after event detection) (Figure 4a) to 0.0 at 197 alarm-time meaning that the PGA estimates are centered 198 on the true value (Figure 4b). The standard deviation of the 199 Figure 4. Histograms showing the error in peak ground acceleration (log (PGA) error) (a) initially (1 second after the first detected P-wave arrival) and (b) at alarm-time (time when 4 seconds of data is available from 4 different channels). 3of5
4 200 error in the log (PGA) estimates is 0.8 initially, and 201 decreases to 0.5 at alarm-time. The log (PGA) errors 202 associated with all three of the largest events at alarm- 203 time were small. For the Northridge event, we find the 204 average log (PGA) error to be 0.2 with a standard 205 deviation 0.3 ( 0.2 ± 0.3). This corresponds to an average 206 underestimation of peak ground acceleration by a factor of The log (PGA) errors for Landers and Hector Mine 208 were less, ( 0.1 ± 0.2) and (0.0 ± 0.2) respectively. It is 209 worth noting that the PGA errors at alarm-time do not 210 correlate with the size of the magnitude errors Discussion 213 [16] Figure 2a shows that compared to northern Califor- 214 nia, shorter maximum predominant periods (higher frequen- 215 cies) are found within southern California, for any given 216 network magnitude. While the slight difference in scaling 217 slope between northern and southern California is statisti- 218 cally insignificant with this dataset, the difference in scaling 219 offset is a statistically significant result, with greater than % confidence (Student-t value of 7.17 with degrees of freedom). Presently we are unsure of reasons 222 for this, although fault rupture dynamics and regional 223 crustal structure may play a role in explaining this obser- 224 vation. For the amplitude-magnitude calibration, we find 225 that measuring the peak amplitude in displacement (P d ) 226 yields the lowest errors for both velocity sensors and 227 accelerometers. This therefore allows us to derive a single 228 best-fit scaling relationship using P d measurements only. By 229 contrast, in northern California two individual amplitude- 230 magnitude scaling relationships were necessary for velocity 231 sensors and accelerometers; peak amplitude in displacement 232 (P d ) was used for velocity instruments, whereas peak 233 amplitude in velocity records (P v ) were used for acceler- 234 ometers (for a full discussion to justify deriving scaling 235 relationships for individual channels, refer to Wurman et al. 236 [2007]). The lower errors associated with using peak 237 amplitude in displacement in southern California may be 238 attributed to the housing of accelerometers at stations 239 located at lower noise sites. We speculate that the larger 240 number of stations further from the coast in southern 241 California are subject to less noise due to ocean waves 242 and tides. Since we are able to obtain P d measurements 243 from both velocity sensors and accelerometers in southern 244 California, we have a larger number of P d data points on 245 our scatter plot of P d vs. network magnitude providing for 246 a more robust fit. This ensures that we can obtain a 247 well-constrained amplitude-magnitude scaling relationship. 248 Figure 2b shows the similarity between the P d amplitude- 249 magnitude scaling relationships obtained for southern and 250 northern California respectively. 251 [17] The dataset we use in this calibration study includes 252 large magnitude events recorded by seismic networks when 253 the density of station coverage was much lower than that of 254 the present day. Hence the accuracy of rapid-magnitude 255 estimates determined from ElarmS in this study would be 256 further improved if we were able to include within our 257 dataset large magnitude earthquake data recorded by a 258 seismic network similar to today s station coverage density. 259 This study therefore exemplifies the threshold accuracy of 260 magnitude and peak ground acceleration estimates ElarmS can provide for large magnitude earthquake events. We calculate that if a repeat Hector Mine-sized earthquake occurs along the Lavic Lake/Bullion fault, ElarmS could potentially provide the following warning times for populated cities at alarm-time : 10 seconds for Barstow (located 75 kilometers from the epicenter); 20 seconds for Moreno Valley/Riverside (located approximately 104 kilometers away), and 30 seconds for downtown Los Angeles (located 190 kilometers away). The warning times given here indicate the amount of time available before the S-wave arrival, which is the earliest time at which peak ground shaking would occur. It should be noted that these times do not take into account delays due to transmission of data over seismic networks which would likely be a few seconds. The density of the seismic network in 1999 was similar to that of today, therefore these warning times are a good indication of the warning time ElarmS could provide. 5. Conclusions [18] The results of our calibration study show that the scaling relationships between t max p and P d measured from the first 4 seconds of the P-wave and earthquake magnitude are similar but not identical to those of northern California. Combining these scaling relations to determine the ElarmS magnitude estimate we find that the uncertainty for small magnitude events (M < = 4.5) is 0.2 magnitude units. For 4.5 < M < = 6.5 events the uncertainty is 0.3 and for M > 6.5 the uncertainty is 0.5. It is a challenge to estimate the accuracy for large events given the small waveform dataset available due to few events and fewer stations providing t max p and P d measurements at the time of the events. Errors in the peak ground acceleration estimates have a mean and standard deviation of (0.0 ± 0.5) at alarm-time. The errors for the three largest events were ( 0.2 ± 0.3), ( 0.1 ± 0.2) and (0.0 ± 0.2) for Northridge, Landers and Hector Mine respectively. The errors are smallest for the most recent Hector Mine earthquake by which time many more stations were operating in southern California. For this earthquake 11 channels were providing data about the earthquake at alarm-time while only 4 were available for both Northridge and Landers. [19] Given the present day density of station coverage in southern California, these magnitude scaling relationships can potentially provide rapid and accurate real-time magnitude and ground motion estimates for populated areas in epicentral regions. This would allow existing seismic networks to provide seconds to tens of seconds warning prior to damaging ground shaking. [20] Acknowledgments. The authors thank Pete Lombard for assistance in incorporating ShakeMap algorithms for southern California into ElarmS. This project was made possible by an exchange program between the Department of Earth Science and Engineering at Imperial College London, and the Department of Earth and Planetary Science at University of California Berkeley. Support for this work was provided by USGS/ NEHRP grant 06HQAG0147. References Allen, R. M. (2007), The ElarmS earthquake early warning methodology and its application across California, in Earthquake Early Warning Systems, edited by P. Gasparini, G. Manfredi, and J. Zschau, pp , Springer, New York. Allen, R. M., and H. Kanamori (2003), The potential for earthquake early warning in southern California, Science, 300, of5
5 322 Boore, D. M., W. B. Joyner, and T. E. Fumal (1997), Equations for estimat- 323 ing horizontal response spectral and peak acceleration from western 324 North American earthquakes: A summary of recent work, Seismol. Res. 325 Lett., 68, Joyner, W. B., and D. M. Boore (1988), Measurement, characterization and 327 prediction of strong ground motions, in Proceedings of the Conference 328 on Earthquake Engineering and Soil Dynamics II, Geotech. Spec. Publ., 329 vol. 20, pp , Am. Soc. of Civ. Eng., Park City, Utah. 330 Nakamura, Y. (1988), On the Urgent Earthquake Detection and Alarm 331 System (UrEDAS), paper presented at Ninth World Conference on Earth- 332 quake Engineering, Int. Assoc. for Earthquake Eng., Tokyo, 2 9 Aug. 333 Newmark, N. M., and W. J. Hall (1982), Earthquake spectra and design, 334 Geotechnique, 25, Wald, D. J., V. Quitoriano, T. H. Heaton, H. Kanamori, C. W. Scrivner, and 336 C. B. Worden (1999), TriNet ShakeMaps: Rapid generation of instru- mental ground motion and intensity maps for earthquakes in southern California, Earthquake Spectra, 15(3), Wald, D. J., B. C. Warden, V. Quitoriano, and K. L. Pankow (2005), ShakeMap manual: Technical manual, user s guide and software guide, Tech. Methods 12-A1, U.S. Geol. Surv., Golden, Colo. Wu, Y.-M., H.-Y. Yen, L. Zhao, B.-S. Huang, and W.-T. Liang (2006), Magnitude determination using initial P waves: A single-station approach, Geophys. Res. Lett., 33, L05306, doi: /2005gl Wurman, G., R. M. Allen, and P. Lombard (2007), Toward earthquake early warning in northern California, J. Geophys. Res., 112, B08311, doi: /2006jb R. M. Allen, L. L. H. Tsang, and G. Wurman, Department of Earth and Planetary Science, University of California, 307 McCone Hall, Berkeley, CA , USA. (rallen@berkeley.edu) of5
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