The 2002 M5 Au Sable Forks, NY, earthquake sequence: Source scaling relationships and energy budget

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1 Click Here for Full Article JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 115,, doi: /2009jb006799, 2010 The 2002 M5 Au Sable Forks, NY, earthquake sequence: Source scaling relationships and energy budget Gisela Viegas, 1 Rachel E. Abercrombie, 1 and Won Young Kim 2 Received 18 July 2009; revised 17 February 2010; accepted 3 March 2010; published 27 July [1] We find invariant high stress drops and radiated energies for a sequence of intraplate earthquakes. We estimate source parameters of the Au Sable Forks, NY, earthquake (M5, 2002) and aftershocks. This intraplate earthquake was the largest to occur in Eastern North America since 1988 and the largest to be recorded by regional broadband networks. We use the empirical Green s function (EGF) method and define a set of qualitative and quantitative rules for the selection of EGF earthquake pairs and for the quality verification of the obtained EGF spectral ratio. We use a multitaper code that performs the complex spectral division with minimum frequency leakage and allows transformation back to the time domain to check the validity of the EGF event. We estimate source parameters for 22 earthquakes (M1 M5) in the sequence. The median stress drop of 104 MPa (using Madariaga source model, and 19 MPa for a Brune model) is significantly larger than estimates for interplate earthquakes. The lower crustal strain rates, and longer fault healing times in intraplate environments, may be responsible for this high average value. We find constant stress drop between M2 and M5, up to the bandwidth resolution limit (80 Hz) of the study, and no evidence of stress drop breakdown for M2 to M1 earthquakes. We find consistently high radiated seismic energy and apparent stress, and a median radiated energy to seismic moment ratio of This is significantly larger than estimates for interplate earthquakes ( ) and consistent with higher stress drops and stronger faults. Citation: Viegas, G., R. E. Abercrombie, and W. Y. Kim (2010), The 2002 M5 Au Sable Forks, NY, earthquake sequence: Source scaling relationships and energy budget, J. Geophys. Res., 115,, doi: /2009jb Introduction [2] In this study we investigate source properties, scaling relationships, and radiated energy of the 2002 Au Sable Forks, NY, earthquake sequence. This intraplate sequence in Eastern North America (ENA) spans four orders of magnitude (M1 to M5) good enough for scaling studies. ENA intraplate earthquakes occur at considerable distances from plate boundaries in a region characterized by compressive stresses [Zoback and Zoback, 1981] with mainly thrust mechanisms [Ma and Atkinson, 2006], low strain and seismic rates, high crustal seismic velocities [Taylor et al., 1980], and low seismic wave attenuation [Frankel et al., 1990]. [3] There are at present two main questions regarding the source characteristics of intraplate earthquakes. The first concerns the amount of stress released during faulting which is thought to be higher than in plate boundary environments [Kanamori and Anderson, 1975; Scholz et al., 1986; and Choy and Boatwright, 1995]. Larger stress drops will give 1 Department of Earth Sciences, Boston University, Boston, Massachusetts, USA. 2 Lamont Doherty Earth Observatory, Columbia University, Palisades, New York, USA. Copyright 2010 by the American Geophysical Union /10/2009JB rise to larger ground accelerations and thus to earthquakes with more destructive capability. The second concerns whether intraplate earthquakes are self similar or whether there is a breakdown in stress drop below a critical magnitude. Constant stress drop is widely accepted as a first order approximation in global and plate boundary studies [Aki, 1967], but a nonconstant scaling relationship has been proposed for ENA [Shi et al., 1998]. A breakdown in stress drop implies fundamental changes in fault dimension and rupture velocity with earthquake size within intraplate settings. [4] Self similarity also implies constant scaled energy, the ratio of radiated energy to seismic moment. The energy scaling relationships is unresolved even for more seismic regions. There are contradictory studies arguing for selfsimilarity where scaled energy and apparent stress (scaled energy multiplied by the medium rigidity) is constant [e.g., McGarr, 1999; Ide and Beroza, 2001; Ide et al., 2003] and for non self similarity where scaled energy decreases with earthquake size [e.g., Abercrombie, 1995; Prejean and Ellsworth, 2001; Mayeda and Walter, 1996]. This decrease in scaled energy suggests differences in frictional behavior during rupture with earthquake size [Kanamori and Heaton, 2000]. [5] Published studies of earthquake source parameters for ENA, using a variety of methods and data, reveal 1of20

2 contradictory results. In comparison with earthquakes in the western United States (WUS), average stress drops for ENA have been found to be anomalously high by some authors [e.g., Nuttli, 1983; Nábělek and Suárez, 1989; Hough and Seeber, 1991] and consistent with WUS by others [e.g., Somerville et al., 1987; Hanks and Johnston, 1992; Li et al., 1995]. This may in part be related to the relatively small number of earthquakes available for study in ENA (a few tens of M4 6 earthquakes compared with hundreds in WUS). Nevertheless, there is an agreement that some ENA earthquakes have an unusually high stress drop, including the largest previously studied M Saguenay earthquake [Hartzell et al., 1994]. Scaling relationship results for ENA are also not in agreement with results indicating constant source scaling similar to WUS [e.g., Somerville et al., 1987; Hanks and Johnston, 1992; Hough and Seeber, 1991; Boatwright and Choy, 1992; Feng and Ebel, 1996; Hartzell et al., 1994]. A dependency of stress drop with seismic moment has been found, either throughout the whole studied magnitude range [e.g., Nuttli, 1983; Xie et al., 1991; Boatwright, 1994; Li et al., 1995] or below a magnitude threshold [Mueller and Cranswick, 1985; Shi et al., 1998] indicating a characteristic rupture dimension for the smaller earthquakes. Finally, a few aftershock sequence studies in ENA estimate high stress drop for the main shock and decreasing values with moment for the aftershock sequence [e.g., Boore and Atkinson, 1989; Atkinson and Boore, 1995]. [6] The disparity of stress drop results reflects the diversity of methods used to retrieve source parameters as well as uncertainties and data quality limitations. All of the above mentioned ENA studies are at best a decade old, and most use individual spectral techniques to retrieve source parameters. Uncertainties in stress drop estimates propagate from seismic moment and source dimension estimates, as stress drop is directly proportional to seismic moment and inversely proportional to the source dimension cubed. Today, most methods estimate seismic moment within a factor of 2, but there are still huge uncertainties in fault dimension estimates. Fault dimension is determined from the corner frequency in spectral analyses or, alternatively, from the source duration in time analyses. Retrieving accurate corner frequencies using individual spectral techniques is challenging as it requires path and site effects corrections, not easily determined, even for stable continental interiors with characteristic low anelastic attenuation [Frankel et al., 1990]. Often, attenuation corrected corner frequencies are smaller than the true corner frequency [Hough et al., 1989; Anderson, 1986; Ide et al., 2003] leading to an underestimation of stress drop, responsible for an apparent nonconstant scaling relationship. Finally, good quality data with high frequency content is also required to estimate corner frequencies of small to moderate earthquakes. Bandwidth limitations introduce a false cutoff at high frequencies and a bias in earthquake selection leading to the underestimation of corner frequency. [7] The empirical Green s function (EGF) method is the best available method to retrieve accurate earthquake source properties, as it empirically corrects for path and site effects. Nevertheless, it depends on the quality of the EGF, not always tested. [8] In the last decades, data quality has been improving with the deployment of broadband networks, and more accurate methods have been implemented. In this study we analyze good quality data recorded at high sampling rates and use the EGF method. The EGF method has been extensively used to retrieve earthquake source information without the need of wave path a priori assumptions [e.g., Mori and Frankel, 1990;Hough, 1997;Ide et al., 2003; Abercrombie and Rice, 2005]. The method requires a colocated smaller earthquake, preferably 1 to 2 magnitudes smaller, with the same focal mechanism, which will act as a medium transfer function. Assuming that the path, site, and instrument effects are the same for both earthquakes, the spectral division of the large earthquake by the small earthquake will give the spectral ratio where the corner frequencies can be measured. Similarly, the time deconvolution of the two earthquakes will give the source time function of the large earthquake. We use the multitaper technique of Prieto et al. [2009] for our spectral estimation. This recently developed technique allows us to perform the complex spectrum division and invert back to time to obtain the earthquake source time function. It is similar to the receiver function analysis method proposed by Park and Levin [2000]. Previous studies that only use amplitude spectra have used the multitaper approach, but source time function studies have used simpler tapers. For a good EGF earthquake pair we expect to obtain a well defined source pulse. Other requirements concerning the quality of the spectral ratio are addressed. Along with a clear source pulse we define a clear qualitative formulation to discriminate between good and unusable EGF spectral ratios. [9] In this study we estimate the source parameters (seismic moment, radius, stress drop, radiated seismic energy, scaled energy, and apparent stress) for 22 earthquakes of the 2002 Au Sable Forks sequence and evaluate scaling relationships. We find a high average stress drop ( 5 times interplate average values) for this set of intraplate earthquakes, and no evidence of scale dependence of stress drop with earthquake size down to a moment of N m. That is, intraplate earthquakes scale the same way as interplate ones but have higher stress drops. For a subset of 9 earthquakes where radiated seismic energy could be calculated, we find high radiated energy (and apparent stress) values ( 4 times interplate average values) and a scale independence of radiated energy with earthquake size, although data uncertainties and scatter are large. 2. The Au Sable Forks Earthquake Sequence [10] The M W 5.0 earthquake that occurred near the town of Au Sable Forks, NY, on 20 April 2002 was the largest earthquake to strike the region since 1988 and the largest to be recorded on modern regional broadband instruments (Figure 1). Shaking was felt over a wide region from Canada to Pennsylvania, characteristic of seismically stable regions with low seismic attenuation [Frankel et al., 1990]. [11] Seeber et al. [2002] described the main characteristics of the earthquake sequence and regional setting. The Au Sable Forks earthquake epicenter is located just west of the Champlain Thrust Belt which divides the Proterozoic Grenville Province (1100 Ma) to the West from the Paleozoic Appalachian Province (400 Ma) to the East (Figure 1). The main 2of20

3 Figure 1. Regional map showing the Au Sable Forks epicenter location (star) and focal mechanism. The two geological provinces, Grenville and Appalachian, are represented by dark and light gray regions, respectively. Also plotted are the available broadband regional stations which sample data at 100 sps (triangles) and 40 sps (circles). The regional stations used in this study are shown in black. The inset shows the epicenter location in North America. shock has a thrust fault mechanism striking N S, parallel to the geological structural trend observed in the region, and consistent with the general trend of faulting in the area [Yang and Aggarwal, 1981]. The maximum compressive stress is near horizontal striking E W [Seeber et al., 2002], indicating an intermediate orientation between the provinces to the east and west of this transitional region [Du et al., 2003; Zoback and Zoback, 1981; Yang and Aggarwal, 1981]. The estimated source depth of 11 km is consistent with the regional seismicity depth [Ma and Atkinson, 2006]. [12] Over 80 aftershocks were recorded within a year of the main shock, 9 of which were M > 2. The largest aftershock, M3.7, occurred 15 min after the main shock, and 5 of the 9 largest aftershocks occurred within 26 h of the main shock. All M > 2 earthquakes were well recorded by the regional broadband networks at a sampling rate of 40 samples per second (sps) (GSN/imaging riometer for ionospheric studies (IRIS), USNSN, LCSN, CNSN, and Photochemistry of Ozone Loss in the Arctic Region in Summer) and 100 sps (New England Seismic Network, NESN). This higher sampling rate is useful to study the source of small earthquakes that have high frequency content. The main shock and early aftershocks (recorded regionally) were relocated using a master event technique [Kim, 2009]. The relocation shifted the epicenters to the east, correcting for the location bias due to the velocity differences in the two geological provinces (faster seismic velocities in the Grenville Province [Viegas et al., 2010]). [13] Two days after the main shock the Lamont Doherty Earth Observatory deployed a local network of 12 portable stations (200 sps) within a radius of 10 km around the epicenter [Seeber et al., 2002]. Over 8 months, 74 aftershocks with magnitudes 3.1, were recorded, 4 of which were M > 2. The sequence was relocated using the doubledifference method with differential travel times measured from waveform cross correlation [Kim, 2009], to uncertainties of 500 m. [14] We select data for this study based on the empirical Green s function method requirements. We use pairs of earthquakes that need to (1) be collocated and (2) have similar focal mechanisms. Focal mechanism similarity of collocated earthquakes translates into similar waveform shapes (including direct waves polarities at all three components) and close S P times. We select the largest aftershocks from the local data set and find suitable EGF pairs using the cross correlation coefficient of smaller earthquakes for which the location error ellipses [Kim, 2009] overlaps. We use earthquake pairs with a cross correlation coefficient 0.6 and select 22 earthquakes in three clusters (Figure 2 and Table 1). Cluster 1 and 2 include a M3, M2, and several smaller earthquakes. Cluster 3 has two M2 and several smaller earthquakes. Cluster 3 is more spatially distributed as we wished to include the two M2 earthquakes, located further East and shallower relatively to the location of most aftershocks. Figure 3 shows the three component waveforms of cluster 1 earthquakes recorded at three stations. [15] We are unable to find a good EGF pair for the main shock in the regional data. All 9 largest aftershocks show waveform similarity between themselves but distinct from the main shock. The largest aftershock also has a thrust fault mechanism [Kim et al., 2002], but it strikes E W, almost perpendicular to the main shock strike. Bearing the 3of20

4 Figure 2. (a) Local map showing the portable stations locations (black triangles) and the aftershock sequence locally recorded (black circles). We analyze three clusters of locally recorded earthquakes (gray circles) and three earthquakes recorded regionally (gray stars). (b) Cross section showing the hypocenters distribution with depth along the longitude line. (c) Cross section along latitude. Longitude and latitude lines used in the cross section are represented by a box surrounding the bulk of the seismicity in Figure 2a. Note that the depths of the regionally recorded earthquakes are not in good agreement with the locally recorded earthquakes. limitations in mind, we use the largest aftershock as an EGF for the main shock because it has a good signal to noise ratio over a longer frequency band than any of the smaller aftershocks. We get a clear source pulse after the deconvolution. Main shock seismograms were clipped at the two closest NESN stations (see Figure 1), and so we only use 40 sps recordings in its analysis. The largest aftershock was followed by a remarkably similar smaller earthquake (M1.7) suitable for EGF. We use the higher sampled data (100 sps) to analyze the largest aftershock for which the expected corner frequency should be well within the usable bandwidth. Figure 4 shows three component waveforms of the main shock, largest aftershock, and M1.7 aftershock recorded at three stations at regional distances. [16] In summary, we use regional 40 sps records to analyze the main shock, regional 100 sps records for the largest aftershock, and local 200 sps records for the subsequent smaller aftershocks. 3. Empirical Green s Function Method [17] We obtain source parameters using the empirical Green s function (EGF) method following the study of Abercrombie and Rice [2005]. We perform our analyses in the frequency domain. We use a new multitaper approach developed by Prieto et al. [2009] that calculates the complex frequency spectrum, making it possible to perform the complex spectral division and transform back to time, to obtain 4of20

5 Table 1. Earthquakes Selected for Analysis in This Study a ID no. Date b Time c Latitude ( N) Longitude ( W) Depth (km) Magnitude (M w ) Cluster (Local) :50: :04: :08: :40: :49: :26: :53: :39: :51: :48: :41: :42: :27: :37: :51: :46: :48: :29: :05: :53: :40: :56: a Local earthquakes magnitude estimates were determined with an Lg fitting method [Kim and Abercrombie, 2006]. b Date is given as year, month, day. c Time is given as hour, minute, second. Figure 3. Normalized raw velocity seismograms of cluster 1 earthquakes recorded at three stations at local distances. The small numbers above the records indicate the value of the maximum amplitude. 5of20

6 Figure 4. Normalized raw velocity seismograms of the main shock and two aftershocks recorded at three stations at regional distances. The small numbers to the right of the records indicate the value of the maximum amplitude. the earthquake source time function. A clear source pulse indicates the EGF is good in both amplitude and phase. Multitaper methods perform better than standard individual taper methods, such as the cosine taper method, as they are more effective in preventing spectral leakage and preserving the spectral shape [e.g., Park et al., 1987; Thomson, 1982]. Spectral ratios have been calculated using multitapers, but the complex division necessary to obtain the source pulse has rarely, if ever, been performed. [18] We use three component raw velocity seismograms for both P and S waves. We use time windows of 5 and 0.75 s for the regional and local recordings, respectively, to calculate the spectra. All time windows start 0.1 s before P and S wave onsets. Time window length tests [e.g., Ide et al., 2003; Sonley and Abercrombie, 2006] have shown that amplitude spectra are stable over a wide range of lengths above a certain minimum that contains the complete direct wave. We calculate the signal to noise spectral ratio using the same length window duration on the pre P part of the seismogram for the noise data. We calculate the ratio between the complex spectrum of the two earthquakes using the multitapering technique with a time bandwidth product of 4 and 7 Slepian tapers. This technique uses a low pass filter equal to the maximum band frequency instead of a water level to stabilize the spectral division. The spectral ratio is then resampled in a logarithmic scale to even the weight of low and high frequencies when fitting [Ide et al., 2003]. Regional and local data are resampled at log intervals of 0.01 and 0.017, respectively. We model the spectral ratios in the bandwidth in which the signal to noise ratio for both earthquakes is above 3. We fit the spectral ratios to obtain corner frequencies for the large (f c1 ) and small (f c2 ) earthquakes, and the ratio between the two seismic moments (W 0r ) following the study of Abercrombie and Rice [2005], 2 f 1 þ f W r ð f Þ¼W c2 0r þ f f c1 n n ; ð1þ where W r ( f ) is the displacement amplitude spectral ratio, f is the frequency, and g and n are constants (g = n =2) that control the shape of the spectrum curvature around the corner frequency and the high frequency falloff, respectively. We fit the spectral ratio with equation (1) using the Nelder Mead simplex method (in Matlab) to minimize the function res = S N i=1 (log W rm ( f i ) log W rd ( f i )) 2, where the indices M and D refer to model and data, respectively, and N is the number of points in the spectral ratio. We use W 0r, f c1, and f c2 as the free parameters in the fitting and initialize their values with the maximum amplitude ratio value for W 0r and close to the high and low frequency band limits for f c1 and f c2, respectively. The convergence to a local minimum is robust and independent of the initial values, as long as these are selected within the data range. To measure the uncertainty in the corner frequency estimates we refit the data varying f c1 over a range of values around the obtained minimum and using only f c2 and W 0r as free parameters. For each f c1 we calculate the fit variance normalized by W 0r, var = res/(nw 0r ), and take the values where the variance increases by 5% as our possible corner frequency range 6of20

7 Figure 5a. EGF spectral ratio fit analysis. P wave, EGF earthquake pair #56 with #16 at station BILL, east component (p56 16 BILL E). Major features: waveform and spectra similarity, spectral ratio contains both corners within the frequency band, variance shaped as a parabola with well defined minimum, clear source pulse, trade off between W 0r and f c2 when fitting with increasing f c1. (bottom right) P wave raw velocity seismograms. A 0.75 s time window is used for the large (black) and small (gray) earthquakes in the EGF deconvolution. The bottom left number indicates the multiplication factor of the small earthquake in the plot. (top right) Calculated displacement spectra of the seismograms in raw velocity seismogram, after integration and instrument correction. The full lines correspond to wave signal and the dash dotted lines to pre P noise. The black and dark gray colors correspond to large and small earthquakes, respectively. Spectra where signal to noise ratio is below 3 or where frequencies are higher than 80% of the Nyquist frequency (80 Hz) are plotted in light gray. (top center) Fitted EGF spectral ratio. The black line is the EGF spectral ratio, suite of gray lines are the fits for increasing fixed f c1 (corner frequency of large earthquake). f c1 increases from dark gray to light gray (see center bottom). The thick black line is the best fit corresponding to the minimum variance. The star indicates f c1 and W 0r values for the estimated best fit. (bottom center) Fit normalized variance variability for increasing fixed f c1. The variance of the best fit model (star) is set to 1 in this plot. The horizontal line indicates maximum and minimum estimates within 5% for error processing. (bottom left) Fit variability of W 0r (black circles) and f c2 (gray circles) with increasing fixed f c1. (top left) Source time function obtained for the earthquake pair. limit. Figure 5a shows the spectral ratio and best fit for some typical cases. It also shows the variance behavior and f c2 and W 0r variability (Figure 5b) Selecting Earthquake Pairs [19] After the initial selection of EGF earthquake pairs based on the cross correlation coefficient we further assess the quality of the EGF earthquake pair. For a good EGF pair we should obtain, in general, a clear source pulse, corner frequencies well within the frequency band limits and a parabola shaped normalized variance of the fit. In this study we enforced a set of selection criteria to discriminate between good and bad EGF pairs. For a good EGF pair, we ensure that: [20] 1. a clear source pulse is obtained. [21] 2. in the spectral ratio, the corner frequency of the large earthquake f c1 has to be well within the above noise frequency band in order to have relative long period level W 0r and the w 2 roll off well defined. f c1 values estimated close to either frequency band limits risk being spectral ratio irregularities and not the actual source corner frequency. [22] 3. estimates of the corner frequency of the smaller earthquake f c2 are only considered when it is determined well within the above noise frequency band and the highfrequency plateau is well defined. If f c2 is outside the bandwidth we use the limit as minimum estimate. We disregard f c2 estimates which are close to the maximum frequency cutoff [Imanishi and Ellsworth, 2006] as it may be an artifact from instability in the deconvolution (see Figure 5c). 7of20

8 Figure 5b. P wave, EGF earthquake pair #45 with #50 at station BARN, vertical component (p45 50BARN Z). Major features: waveform and spectra similarity, spectral ratio contains only f c1 corner within the frequency band, variance shaped as a parabola with well defined minimum, clear source pulse, decreasing W 0r with increasing f c1, and infinite scattered f c2. See panel description in Figure 5a. [23] 4. when both corner frequencies are estimated in the fit, the amplitude difference between the two frequency plateaus (frequencies below f c1 and above f c2 ) are large enough to make sure we are fitting the corner frequencies and not spectral oscillations (see Figure 5d). To differentiate between spectral bumps and real source corner frequencies, it is helpful to estimate the expected theoretical values of the f c values for a certain seismic moment and compare with the value obtained with the fit. [24] 5. the normalized variance of the fit has preferably a parabola shape for a sequence of fixed f c1 values, with the minimum corresponding to the best fit. Although desirable, the parabola shape is not always obtained [Ide et al., 2001; Sonley and Abercrombie, 2006], particularly when f c1 is close to the low frequency cutoff and the step increase in f c1 starts at values outside the bandwidth. In this case we only consider the f c1 estimated value if it is consistent with values obtained at other stations or components. In this study we obtain parabola shaped variances in 80% of our preferred pairs. [25] 6. the variance normalized by W 0r is smaller than [26] We consistently obtain higher P wave corner frequencies than S wave corner frequencies. The ratio of P to S corner frequencies is, on average, 1.5 for the local data and 1.3 for the regional data. This frequency shift is a source effect, since path (attenuation) is corrected for by the EGF technique, and reflects the source finiteness. The ratio is consistent with the source model by Madariaga [1976] that we used to calculate the fault radius. The estimated corner frequencies and fault radii are listed in Table 2. [27] We use the corner frequency estimates from the large earthquake in the EGF pair when possible. The exceptions are the smallest earthquakes in the data set, which all have corner frequencies >80 Hz, and the smaller regional aftershock. In theory, both corner frequencies can be estimated, but in practice, deconvolution instability, noise, and nonlinearity of site effects contaminate the higher frequencies of the spectral ratio. Noise in the data introduces high frequency oscillations in the spectral ratio with amplitude drops, masking the corner frequency of the small earthquake and the low amplitude plateau. We investigate the variability in corner frequency estimates for earthquakes used both as large and small in the EGF pair. Earthquakes #16 (M2.2) and #31 (M1.3) from cluster 1 fit the criteria. We find that, for the same earthquake (at the same station and component), the variability in f c2 is higher than in f c1 by an average factor of 17. We also observe that the variability is larger (factor of 24) for the smaller earthquake (#31) than for the larger earthquake (#16) (factor of 2). That is, variability increases for earthquakes with corner frequencies closer to the maximum limiting bandwidth. The increase in uncertainty for corner frequencies estimated from f c2 instead of f c1 was also observed by Hough and Dreger [1995] in a study of source parameters of the 1992 Joshua Tree sequence (M6 M2). We also investigate the corner frequency stability with increasing 8of20

9 Figure 5c. P wave, EGF earthquake pair #44 with #50 at station BARN, north component (p44 50BARN N). Major features: waveform similarity at large amplitude peaks, spectra similarity, spectral ratio contains only f c1 corner within the frequency band, variance shaped as a parabola with well defined minimum, clear complex source pulse, trade off between W 0r and f c2 when fitting with increasing f c1, with f c2 jumping to infinite values for higher f c1. See panel description in Figure 5a. hypocentral distance between earthquake pairs (or with added noise). We apply the EGF method to earthquake #45 (M2.5) from cluster 1 paired with smaller earthquakes from cluster 2 and 3 (S waves, station JEEP, E and Z components). We find that corner frequency estimates decrease by 30% above a cutoff hypocentral distance of 400 m (±500 m), consistent with the cutoff distance obtained by Mori and Frankel [1990] when analyzing source pulse width variability with distance. This emphasizes the importance of selecting collocated earthquakes when using the EGF method to obtain accurate estimates of source parameters. [28] We also compare our results using the multitaper procedure with results using a more standard 5% cosine taper method [e.g., Abercrombie and Rice, 2005] to look for possible bias between the two methods. We compare corner frequency and relative W 0 estimates (P and S waves) for three M2 M1 earthquake pairs (#16 with #15, #31 with #30, and #45 with #42). We find that the differences in estimates are negligible, varying less than 10% (median of 9% for f c, and 2% for relative W 0 ). Sonley and Abercrombie [2006] compared results obtained with the two methods and also found the differences negligible. [29] The multitaper method performs better than the 5% cosine taper method in both frequency and time domain. The multitaper produces more stable spectra at both high and low frequencies, allowing for the inclusion of more spectral ratios in the study and the reduction of modeling uncertainties. The multitaper method also produces much stronger and clearer source time functions (STFs) and reduced noise. The STF obtained with the multitaper method are independent of the small changes in window length that strongly affect the results of the cosine tapered deconvolution. The multitaper method retrieves 100% of the amplitude of the delta function, obtained by self deconvolution, versus 85% with the cosine taper method. The principal drawback of the multitaper method is a decrease in resolution of the STF. The duration of the delta function, increases by 2 samples (by 40%, from 5 samples to 7 samples, for the 5% cosine taper and multitaper method, respectively). The loss in STF resolution has no impact in this study because we estimate the source parameters from the spectral ratio. In this study the duration of the delta function is and 0.07 s, for the locally (200 sps) and regionally (100 sps) recorded data, respectively. The multitaper method is very sensitive to the start time of the two earthquake waves within the involving time window. It requires the same start time for both waves, in order to avoid a STF phase change, which distorts the shape of the source pulse. 4. Individual Spectral Analysis for Seismic Moment [30] The EGF method only resolves relative seismic moments, and so we perform an individual spectral analysis 9of20

10 Figure 5d. S wave, EGF earthquake pair #42 with #51 at station SCRF, east component (s42 51SCRF E). Major features: waveform and spectra similarity, flat spectral ratio with both corners outside the frequency band, variance not shaped as a parabola, stars corresponds to best fit with 3 parameters as variables, algorithm fitting bumps in the spectral ratio, and estimating f c1 > f c2, clear complex source pulse. We assume f c1 and f c2 > 80 Hz. W 0r slightly increasing with f c1. See panel description in Figure 5a. of each earthquake to obtain the absolute seismic moment, following the study of Abercrombie [1995]. This analysis also estimates the corner frequency (f c ) and attenuation quality factor (Q). Seismic moment estimates from the individual spectrum are more reliable than corner frequency estimates, because it is measured from the more stable long period part of the displacement spectrum less affected by attenuation. We do not expect f c and Q to be very accurate, as we place no constraints on Q, but we expect the long period moment to be reliable. [31] We analyze all three components individually for both P and S waves when available. We first correct the recorded velocity seismogram for instrument response and integrate to displacement. We then calculate the Fourier displacement amplitude spectra and resample it. We use the same time window, multitaper parameters, and log frequency intervals as before. We model the displacement spectrum in the bandwidth where the signal to noise ratio is above 3, following the study by Boatwright [1980], W 0 e ft Q Wðf Þ¼ 1 þ f ; ð2þ n 1 f c where W( f ) is the displacement amplitude spectrum, W 0 the long period level of the spectrum, and t is the travel time of the seismic wave of interest (P or S). We use the Nelder Mead simplex method to fit the spectra using W 0, f c, and Q as variables. The travel time is calculated from the delay time between S and P waves arrivals. Throughout this study we assume a P wave velocity p ffiffiffi at the source a = 6.5 km/s, a S wave velocity b = a/ 3, and a crust density r = 2900 kg/m 3 [Viegas et al., 2010]. Uncertainties for the corner frequency estimates f c are determined similarly to uncertainties in f c1 in the EGF analysis. Here we vary f c over a range of values and keep W 0 and Q as free parameters in the fit. The f c uncertainty range is determined by a variance increase of 5%. Corresponding values are attributed to W 0 and Q. Figure 6a shows two typical examples of individual spectral modeling. When fitting the individual spectrum, there is a trade off between the corner frequency and Q; Q decreases as f c increases. In some cases this trade off prevents constraining f c, as the normalized variance remains constant with increasing f c (Figure 6b), particularly when the estimated corner frequency is larger than the maximum cutoff frequency. In these cases, we only consider the more stable W 0 estimates and disregard f c and Q. In most cases, f c and Q are poorly constrained, but W 0 is always very well constrained. For example, in Figure 6b bottom left, while f c varies by a factor of 170, W 0 only varies by a factor of 1.5 (disregarding the outlier point). Using only individual spectra for which we can constrain f c and Q, we obtain Q P 10 of 20

11 Table 2. Earthquake Source Parameters Obtained With the EGF Method a ID no. M W M 0 (N m) f cp (Hz) f cs (Hz) r (m) Ds (MPa) E S (J) ~e s a (MPa) Ds/s a E E E E E E E E E E E E E E E E E E E E+11 >80 >80 <12.4 > E+11 >80 >80 <12.4 > E E E+11 >80 >80 <12.4 > E E E+11 >80 >80 <12.4 > E E E E+11 >80 >80 <12.4 > E+10 >80 >80 <12.4 > E+10 >80 >80 <12.4 > E+10 >80 >80 <12.4 > E+10 >80 >80 <12.4 > E+10 >80 >80 <12.4 > E+10 >80 >80 <12.4 > E+10 >80 >80 <12.4 > E+10 >80 >80 <12.4 > E+10 >80 >80 <12.4 >3.3 a Seismic moment was calculated with the individual spectral analysis method. Figure 6a. Individual displacement spectrum fit of earthquake #42 at station JEEP, north component, S wave (42 JEEP S n). (top left) Instrument corrected displacement seismogram. The two top lines indicate the time windows used to obtain the noise (dash dotted) and wave (solid) spectra. (top right) Individual displacement spectrum (black) fit. Gray lines correspond to fits for increasing fixed f c. f c increases from dark gray to light gray (see bottom right). The star indicates the best fit values estimated for f c and W 0, corresponding to a minimum variance. (bottom right) Fit normalized variance variability for increasing fixed f c. The variance of the best fit model (star) is set to 1 in this plot. The horizontal line indicates maximum and minimum estimates within 5% for error processing. (bottom left) Fit variability of W 0 (black circles) and Q (graycircles)withincreasingfixedf c. The trade off between f c and Q can be observed. W 0 is more stable, especially within the range of the 5% variance, showing a slight increase with increasing f c. 11 of 20

12 Figure 6b. Individual displacement spectrum fit of earthquake #14 at station JEEP, north component, S wave (14 JEEP S N). See panel description in Figure 6a. A variance minimum is not obtained in this example and we discard the unconstrained f c and Q values, but the more stable W 0 can still be used. and Q S >10 4 for 66.7% and 34.0% of the cases, respectively. For the remaining 33.3% (Q P ) and 66.0% (Q S ) of the cases, we obtain median values of and and a standard deviation of and 826.2, respectively. [32] We calculate the seismic moment M 0 for each component and wave type from the long period part of the displacement spectrum following the study of Brune [1970], M 0 ¼ 4c3 RW 0 FU ; ð3þ where c is the velocity of the wave of interest, R the hypocentral distance (measured from S P arrival times), F the free surface parameter (F = 2), and U the mean radiation pattern (U = 0.52 for P waves and U = 0.63 for S waves [Aki and Richards, 1980]). We use the mean radiation pattern because a clear dominant mechanism was not established for this earthquake sequence. To calculate the seismic moment, we calculate the geometric mean of the three components at each station. If one or two components are not available, we consider the missing components as the average of the available ones. The earthquake seismic moment is calculated by the logarithmic average of the estimates at all stations [Archuleta et al., 1982] for both P and S waves [Ide et al., 2001]. We calculate moment magnitude M W following Hanks and Kanamori [1979]. Our M W estimates are in good agreement (average difference of 1.6%) with the M W estimates of Kim and Abercrombie [2004] using the individual fitting of Lg waves method of Shi et al. [1998], when comparing the common earthquakes of both studies. [33] For the regional data (main shock and largest aftershock) we use available seismic moment estimates determined by moment tensor inversion of regional broadband recordings [from Seeber et al., 2002 and Kim et al., 2002, respectively]. We prefer these estimates as they include more stations in the moment calculations (12 instead of 4) thus being less affected by radiation and site effects. The seismic moment of the aftershock used as the EGF for the largest aftershock is estimated from the relative long period level and the moment of the largest aftershock. [34] We compare the corner frequencies obtained from individual and EGF methods (Figure 7). Previous studies [e.g., Sonley and Abercrombie, 2006; Ide et al., 2003] have shown that EGF methods are more reliable in obtaining source parameters largely affected by attenuation, such as corner frequency, than individual spectral analysis methods, because they empirically correct for attenuation and site effects without the need of simplified a priori models required by the later methods. We see that individual corner frequencies are underestimated for smaller earthquakes and more scattered for larger earthquakes. This is largely due to the lack of a correction for site effects and an unsuitable attenuation correction. Following the study of Ide et al. [2003] we compare the EGF spectral ratios with attenuation curves and find that uncorrected site effects are obscuring the corner frequencies. We also find that attenuation is underestimated by at least a factor of 4, which explains the lower corner frequency estimates with the individual method. Poor attenuation and site effect corrections together with limited bandwidth are likely responsible for the apparent breakdown in the scaling of fault length with earthquake size for small earthquakes in most studies in ENA [e.g., Shi et al., 1998, Boatwright, 1994, Li et al., 1995]. The corner frequencies obtained with the individual method appear to saturate at a lower frequency than the EGF corner frequencies (maximum 12 of 20

13 moment of Nm. Below that the radii are invariant with moment, indicating a minimum source dimension of 100 m. As discussed, this is an artifact of poor attenuation and site effect corrections. [36] We estimate the static stress drop Ds from the seismic moment and source radius using the circular static solution by Eshelby [1957], D ¼ 7 M 0 16 r 3 : ð5þ Figure 7. Corner frequency versus seismic moment. Comparison of corner frequency results obtained with the EGF method (dark gray) with the ones obtained with the individual fitting method (light gray) for both P (stars) and S (circles) waves. Earthquakes with estimated corner frequencies above our bandwidth limit of 80 Hz are plotted at the limit with upward arrows, indicating this is a lower threshold of maximum resolution. Stress drops obtained with the EGF method appear to be invariant with earthquake moment (Figure 8). A breakdown is only possible for the small earthquakes in the data set where corner frequencies are above the detection threshold. Stress drops obtained with the individual fitting method show an expected dependency with moment because of inaccurate estimates of corner frequencies discussed above. We plot for comparison EGF results from other studies in ENA [Xie et al., 1991; Li et al., 1995; Shi et al., 1998]. We select the results that clearly lie within the data resolution limits. We exclude EGF results of earthquakes for which corner frequencies are close to or above the maximum frequency resolution limit, or for which source pulse durations are near the time resolution limit. In tests deconvolving earthquakes bandwidth limit), explaining why Shi et al. [1998] assumed their results to be accurate. 5. Source Dimension and Stress Drop [35] Once we obtain the source parameters seismic moment and corner frequency, we can calculate the source dimension and the stress released by faulting. We do it for both the EGF and the individual fitting results. We assume a circular fault model and use the dynamic solution of Madariaga [1976] to calculate the fault radius r, r ¼ k f c ; ð4þ where k is a constant (k = 0.32 for P waves and k = 0.21 for S waves). The source model implicitly assumes a constant rupture velocity. The earthquake source radius is then determined by the arithmetic mean of all the available corner frequency estimates. For the corner frequency estimate of the largest earthquake in the EGF pair, we also average between pairs that use different EGF earthquakes, when available. Source radii obtained with the EGF method scale with seismic moment throughout the whole magnitude spectrum until the maximum resolution is reached. Because we cannot resolve corner frequencies above 80 Hz, we use f c = 80 Hz to estimate the source radii of the smaller earthquakes, for which the corner frequency is outside the available bandwidth. These source radii correspond to a maximum radii threshold, with the real source radii smaller than the estimates (Figure 10). Source radii obtained with the individual method decrease with decreasing moment until a Figure 8. Stress drop versus seismic moment. Comparison of stress drop results obtained with the EGF method (solid black circles) with the ones obtained with the individual fitting method (solid gray circles). Also included are stress drop estimates from other ENA studies with the EGF method (solid black symbols) and with the Lg fitting method (open symbols). ENA results were converted to a Madariaga source model for comparison purposes. Arrows indicate a minimum stress drop estimate. Solid and dash dotted diagonal lines mark the band limit cutoff for stress drop estimates set at 80 Hz for this study and at 40 Hz for the Shi et al. [1998] study, respectively. Data points are Au Sable Forks, NY (EGF and Ind, this study), Au Sable Forks, NY (Lg fit) [Kim and Abercrombie, 2006], ENA (Lg fit and EGF) [Shi et al., 1998], Goodnow, NY [Xie et al., 1991], and Charlevoix, Quebec [Li et al., 1995]. 13 of 20

14 same problems that affect our individual estimates, that is, inaccurate attenuation and site corrections at high frequencies. Earthquake source parameters must be estimated with extreme care to avoid the main sources of bias that affect scaling relationships. Accurate corrections for wave path and site effects as well as careful consideration of the data quality limitations are fundamental to source parameter calculations. 6. Radiated Seismic Energy [37] We calculate the earthquake radiated energy E S for all the large earthquakes in the EGF pairs with a corner frequency within the available bandwidth (<80 Hz). Energy estimates for all three components of P and S waves are determined following the study of Boatwright and Fletcher [1984], Figure 9. Energy is calculated from the squared spectral ratio. We use real data between two cutoff frequencies and model data for the remaining frequency band up until a decade above and below the corner frequency. Low frequency cutoff is set for signal to noise ratio above 3. The high frequency cutoff is set when the ratio of the EGF fit model to the individual fit model is above 1.5%. with themselves, we find the duration of a delta function to be 5 and 7 samples in the 5% cosine taper and multitaper analyses, respectively. We cannot account for the lack of any high stress drop earthquakes at low magnitudes due to selection bias, in these studies. We convert all the results to a Madariaga source model, by raising stress drop estimates by a factor of 5.5 for the studies which used a Brune source model. Xie et al. [1991] and Li et al. [1995] estimated the source radius from the source rise time using the source model by Boatwright [1980]. Tomic et al. [2009] found that this model is not consistent with a Madariaga source model for S waves. Xie et al. [1991] analyzed P and S waves, and Li et al. [1995] analyzed only S waves. To avoid introducing bias in our comparison we convert these source pulse duration t to corner frequency f c, using f c =2/pt [Lay and Wallace, 1995]. The other ENA EGF results are consistent with our results down to their resolution limit, equivalent to a moment of Nm[Xie et al., 1991; Shietal., 1998] and Nm[Li et al., 1995]. Also plotted are source parameters determined by fitting Lg waves of ENA earthquakes [Shi et al., 1998] and of the Au Sable Forks sequence [Kim and Abercrombie, 2006]. We see that stress drop estimated with the Lg fitting method is constant down to a moment of N m, after which there is a breakdown with decreasing stress drop with decreasing moment. Shi et al. [1998] analyzed different types of data with various sampling rates up to a maximum band limit of 40 Hz (80% Nyquist frequency) for the smaller earthquakes in their data set, further reduced to 30 Hz by signal to noise constraints. The apparent breakdown in stress drop for this data set is probably an artifact of limited data resolution and selection bias. The breakdown observed for the Au Sable stress drop estimates with the Lg fitting method is probably due to the Z E S ¼ 4cR2 f2 F 2 j Wðf _ Þj 2 df ; ð7þ f 1 where _ W(f) is the Fourier velocity amplitude spectrum, and f 1 and f 2 are the integration limits. The velocity spectrum is obtained by differentiation of the EGF spectral ratio, after setting the long period level of the spectral ratio equal to the long period level of the displacement spectrum obtained in the individual fitting step. We calculate the energy from f 1 = f c /10 to f 2 =10f c to obtain at least 90% of the total radiated energy [Ide and Beroza, 2001]. The available bandwidth does not always reach one or both of those limiting frequencies so we use the modeled spectral ratio to fill the gaps. The EGF spectral ratio contains two corner frequencies and starts diverging from a w 2 source model [Brune, 1970] in the vicinity of the smaller earthquake corner frequency. To avoid this distortion at high frequencies, we only use the data spectral ratio until a certain cutoff frequency is reached and use a w 2 source model for the remaining frequency interval. The cutoff frequency is set when the modeled spectral ratio starts diverging from the modeled w 2 source by more than 1.5% (Figure 9). The data contribution to the energy estimate corresponds, on average, to 36%. Lower magnitude earthquakes, with corner frequencies closer to the limiting frequency, have a larger contribution of the model energy to fill the high frequencies gap. Earthquakes deconvolved by closer magnitude EGF earthquakes also have a larger model contribution for the energy estimate at high frequencies. The total energy radiated by an earthquake is calculated by summing the contributions of P and S wave energies [Ide et al., 2003] after we logarithmically average over all the stations the sum of the estimated energies at all the 3 components [Abercrombie, 1995]. Similarly to seismic moment estimates, when not all the components are available, we set them equal to the average energy value of the available ones. Not all earthquakes have P and S energy estimates due to clipping, signal to noise threshold limitation, and EGF quality choices. Four local earthquakes (#03, #16, #31, and #45) have estimates of both P and S wave energies (E Sp and E Ss, respectively). We use the ratio of S to P energy from these four earthquakes to estimate the missing wave energy on the remaining earthquakes thus avoiding underestimating the earthquake total radiated energy. We obtain a median value of E Ss /E Sp equal to 17.06, consistent with previous published 14 of 20