Local Magnitude Determinations for Intermountain Seismic Belt Earthquakes from Broadband Digital Data

Transcription

1 Bulletin of the Seismological Society of America, Vol. 97, No. 2, pp , April 2007, doi: / Local Magnitude Determinations for Intermountain Seismic Belt Earthquakes from Broadband Digital Data by James C. Pechmann, Susan J. Nava,* Fabia M. Terra, and Julie C. Bernier Abstract The University of Utah Seismograph Stations (UUSS) earthquake catalogs for the Utah and Yellowstone National Park regions contain two types of size measurements: local magnitude (M L ) and coda magnitude (M C ), which is calibrated against M L. From 1962 through 1993, UUSS calculated M L values for southern and central Intermountain Seismic Belt earthquakes using maximum peak-to-peak (p-p) amplitudes on paper records from one to five Wood Anderson (W-A) seismographs in Utah. For M L determinations of earthquakes since 1994, UUSS has utilized synthetic W-A seismograms from U.S. National Seismic Network and UUSS broadband digital telemetry stations in the region, which numbered 23 by the end of our study period on 30 June This change has greatly increased the percentage of earthquakes for which M L can be determined. It is now possible to determine M L for all M 3 earthquakes in the Utah and Yellowstone regions and earthquakes as small as M 1 in some areas. To maintain continuity in the magnitudes in the UUSS earthquake catalogs, we determined empirical M L station corrections that minimize differences between M L s calculated from paper and synthetic W-A records. Application of these station corrections, in combination with distance corrections from Richter (1958) which have been in use at UUSS since 1962, produces M L values that do not show any significant distance dependence. M L determinations for the Utah and Yellowstone regions for using our station corrections and Richter s distance corrections have provided a reliable data set for recalibrating the M C scales for these regions. Our revised M L values are consistent with available moment magnitude determinations for Intermountain Seismic Belt earthquakes. To facilitate automatic M L measurements, we analyzed the distribution of the times of maximum p-p amplitudes in synthetic W-A records. A 30-sec time window for maximum amplitudes, beginning 5 sec before the predicted Sg time, encompasses 95% of the maximum p-p amplitudes. In our judgment, this time window represents a good compromise between maximizing the chances of capturing the maximum amplitude and minimizing the risk of including other seismic events. Introduction *Present address: ENSCO, Inc., Melbourne, Florida Present address: URS Corporation, Oakland, California Present address: U.S. Geological Survey, St. Petersburg, Florida The University of Utah Seismograph Stations (UUSS) has operated regional seismic networks in the Utah region since 1962 and in the Yellowstone Park region since 1984 (Fig. 1). Earthquake catalogs for these two regions are one of the primary products of the seismic network operations. These catalogs are widely used at the University of Utah and elsewhere for seismic-hazard analyses, basic research, and other purposes. The Utah and Yellowstone regions encompass portions of the Intermountain Seismic Belt (ISB), a north south-trending zone of shallow, intraplate seismicity that extends from southern Nevada to northwestern Montana (Fig. 2; Smith and Arabasz, 1991). Earthquake size measurements in the UUSS catalogs have been based on the local magnitude (M L ) scale since Richter (1935, 1958, pp ) defined local magnitude as M log A log A S (1) L 0 i where the logarithms are to the base 10, A is the maximum 557

2 558 J. C. Pechmann, S. J. Nava, F. M. Terra, and J. C. Bernier Figure 1. Locations of seismograph stations used in this study (labeled) and other high-gain seismograph stations recorded by UUSS in December Italic and regular station labels distinguish, respectively, the USNSN and UUSS broadband stations used. trace amplitude in millimeters on a standard horizontalcomponent Wood Anderson (W-A) torsion seismograph (free period of 0.8 sec, damping constant 0.8, and nominal magnification of 2800), log A 0 is an empirical distance correction, which Richter (1935) arbitrarily fixed to 3.0 at an epicentral distance (D) of 100 km, and S i is an empirical correction for the particular station and/or instrument used. Richter (1958, p. 344) emphasized that an acceptable assignment of magnitude calls for data from a number of stations surrounding the epicenter in order to average out radiation pattern effects. UUSS operated one to five Wood Anderson seismographs in Utah continuously from 1962 until 2005 (see Griscom and Arabasz, 1979, and Table 1). Data from these stations were used to compute M L values for local earthquakes from the earliest days of the Utah regional seismic network (Cook and Smith, 1967; Arabasz et al., 1979). Two W-A seismographs operated by other agencies in southeastern Idaho and southwestern Montana have provided data for computing M L s for earthquakes in these regions and in northwestern Wyoming, including Yellowstone Park. The distance corrections (log A 0 ) used in UUSS M L calculations have traditionally been those developed for southern California earthquakes as a function of D by Richter (1935) and

3 Local Magnitude Determinations for Intermountain Seismic Belt Earthquakes from Broadband Digital Data 559 Figure 2. Epicenter map of earthquakes (circles) from January 1994 through June 2002 used for (a) calculating M L station corrections (460 events) and (b) checking M L distance corrections (1755 events). The filled diamonds on (a) mark the locations of stations for which we successfully determined M L station corrections (Table 2), including the reference station DUG (labeled). Gutenberg and Richter (1942), and summarized by Richter (1958, p. 342). Griscom and Arabasz (1979; see also Griscom, 1980) concluded that these distance corrections were satisfactory for use in Utah based on analyses of a sparse set of peak amplitude measurements from four Utah W-A seismographs. There have been no such analyses done of M L distance corrections for other parts of the ISB. Most earthquakes in the UUSS catalogs are too small for direct M L determinations using equation (1) and data from the limited number of relatively low-gain W-A seismographs that have operated in and near the Utah and Yellowstone regions. This problem, together with the problem of the limited dynamic range of the other seismological instrumentation available in these regions prior to 1993, motivated Griscom and Arabasz (1979) to develop indirect methods for estimating M L for Utah region earthquakes based on empirical relations between M L, D, and measurements of total signal duration on vertical-component, short-period, high-gain instruments. Later, Smith et al. (1986) developed an analogous empirical relation for Yellowstone region earthquakes. Indirect M L estimates from signal-duration measurements, which we call coda magnitude (M C ), constitute the great majority of the magnitudes in the UUSS earthquake catalogs published from 1979 through the present (e.g., Richins, 1979; Smith et al., 1986; Nava et al., 1990, 1993). The equations developed by Griscom and Arabasz (1979) and Smith et al. (1986) continued to be used for M C calculations throughout the 1980s and 1990s due, in large part, to the lack of a significantly improved M L database for recalibrating them. The number of Utah earthquakes with W-A M L determinations increased more slowly from 1979 to 1993 than previously because during this period there were only two W-A seismographs operating in Utah: at SLC and DUG (Fig. 1). The installation of broadband digital telemetry stations in and around the ISB, beginning with the U.S. National Seismic Network (USNSN) station DUG in 1993, made it possible to determine local magnitudes for a much larger fraction of the earthquakes occurring in this region. M L values can be determined from digital data recorded by non- W-A instruments by deconvolving the instrument response and convolving with the W-A response to produce synthetic Wood Anderson seismograms (Kanamori and Jennings, 1978; Bakun et al., 1978; Uhrhammer and Collins, 1990).

4 560 J. C. Pechmann, S. J. Nava, F. M. Terra, and J. C. Bernier Table 1 Broadband and Wood Anderson Stations Used in This Study Station Code Network Code* Latitude (deg min N) Longitude (deg min W) Elevation (m) Instrumentation (seismometer, digitizer, or recorder) Date Operational (mm/dd/yyyy) AHID US CMG-3NSN, Quanterra 11/12/1997 BGU UU CMG-40T or CMG-3ESP, REFTEK 72A-08 10/24/2001 BUT MB Kinemetrics electronically simulated Wood Anderson, pen recorder 05/06/1983 BW06 US CMG-3NSN or STS-2, Quanterra 05/05/1996 CTU UU CMG-40T, REFTEK 72A-07 08/27/1997 DUG UU Lehner Griffith TS-220 Wood Anderson, photographic recorder 09/20/1963 to 04/08/1994 US CMG-3NSN, Quanterra 02/18/1993 ELK US CMG-3T, REFTEK 72A-08 01/06/1994 HLID US CMG-3NSN, Quanterra 08/10/1998 HVU UU CMG-40T, REFTEK 72A-07 06/01/1998 HWUT US CMG-3NSN or STS-2, Quanterra 03/26/1997 JLU UU CMG-3ESP, REFTEK 72A-08 10/23/2001 KNB US CMG-3T, REFTEK 72A-08 05/17/1995 LDS LB CMG-3ESP, Quanterra 12/13/1996 to 06/17/1998 LKWY US CMG-3ESP, Quanterra 10/11/1995 MPU UU CMG-40T, REFTEK 72A-07 09/01/1998 MVU LB CMG-3ESP, Quanterra 12/08/1998 NLU UU CMG-3ESP, REFTEK 72A-08 10/24/2001 NOQ UU CMG-40T, REFTEK 72A-07 08/27/1997 SLC UU Kinemetrics electronically simulated Wood Anderson, pen recorder; 12-bit digital recording begun 01/05/1994; improved and rebuilt, 07/10/ /02/1976 to 12/26/2005 SRU UU CMG-3T or CMG-40T, REFTEK 72A-07 or REFTEK 72A-08 09/09/1998 YMR WY CMG-40T, REFTEK 72A-07 11/01/1998 *US, U.S. National Seismic Network, U.S. Geological Survey; UU, University of Utah Regional Seismic Network, University of Utah; MB, Montana Regional Seismic Network, Montana Bureau of Mines and Geology; LB, Leo Brady Network, Sandia National Laboratory; WY, Yellowstone Wyoming Seismic Network, University of Utah. The US and LB stations are collectively referred to as USNSN stations in this article because the LB stations are part of the U.S. National Seismic Network. Through 30 June 2003; all the digitizers are 24-bit (except at SLC), with sampling rates of 40 Hz for US and LB data and 100 Hz for UU and WY data. This technique was previously applied, on a trial basis, to digital recordings of analog telemetry data from the UUSS network which are available back to 1 January However, these data were not well suited for M L determinations because the dynamic range was only about 50 db and there were few stations with horizontal components. As of 30 June 2002 the end date for the primary data set used in this study there were 10 USNSN and 13 UUSS broadband digital telemetry stations operating within the area shown in Figure 1, plus two W-A seismographs. The best measurement of earthquake size is now considered to be moment magnitude, M W, as defined by Kanamori (1977) and Hanks and Kanamori (1979). M W can be directly determined by using broadband digital data, but with the current broadband station spacing in the ISB routine, rigorous M W determinations would be possible only for earthquakes of M W 3.0 to 3.5 or greater. Studies in California have found that, on the average, M W and M L determinations for earthquakes of 3.0 M L 7 agree very well (Hanks and Boore, 1984; Thio and Kanamori, 1995; Zhu and Helmberger, 1996; Uhrhammer et al., 1996). Because M L is compatible with M W and much simpler to determine, M L is expected to remain the primary size measurement in the UUSS earthquake catalogs for the foreseeable future. In this article, we report on development and testing of a methodology for using broadband digital telemetry data to compute M L s for ISB earthquakes which are consistent with UUSS M L s computed using paper W-A seismograms from 1962 through This methodology has enabled UUSS to do the following: (1) maintain continuity in the basic size measurement in the earthquake catalogs while taking advantage of the new instrumentation available, (2) directly determine M L for many more of the earthquakes located, (3) automatically compute an M L within minutes after an earthquake and utilize it for earthquake alerts via pager and , and (4) assemble an expanded and improved M L data set for calibrating better M C scales for the Utah and Yellowstone regions that can be applied retroactively to the time that digital seismic recording began in these regions. We begin by describing our determination of station corrections that minimize differences between M L values determined from synthetic and paper W-A seismograms. Next, we verify the adequacy of Richter s distance corrections for use in the ISB. We then examine the times of maximum p-p amplitudes in synthetic W-A records to guide the development of efficient and reliable algorithms for automatic M L determinations. Finally, we show that our M L s are consistent with available M W determinations for ISB earthquakes.

5 Local Magnitude Determinations for Intermountain Seismic Belt Earthquakes from Broadband Digital Data 561 Data and Methodology The data for this study came from 19 broadband digital telemetry stations (labeled diamonds, Fig. 1) and three W- A seismographs (circles, Fig. 1; Table 1). One of the latter was located at the same site as the broadband station DUG. The DUG W-A seismograph, which operated from 1963 to 1994, was an original-design photographically recording W-A instrument (Anderson and Wood, 1925; Richter, 1958, p. 222). The other two W-A seismographs, located at BUT and SLC (Fig. 1), were electronically simulated W-A instruments with pen-and-ink recorders. Digital (12-bit) recording of the SLC W-A began in January 1994 and ended in December 2005 when SLC was closed. However, because the digital records are noisier than the paper records, we used the paper records except when they were clipped or unavailable due to recorder malfunctions. Michael C. Stickney, Montana Bureau of Mines and Geology, kindly provided us with the measurements from the BUT paper records that we utilized in this study. We used data from all earthquakes with M L measurements from two or more stations that occurred between 1 January 1994 and 30 June 2002, in the area shown in Figure 2, with the exception of one small region. Earthquakes in this region (42 30 to N, to W) were excluded to prevent the large number of aftershocks from the 1994 M W 5.7 Draney Peak, Idaho, earthquake (Pechmann et al., 1997; Brumbaugh, 2001) from dominating the data set. In terms of the ISB subdivisions defined by Smith and Arabasz (1991), our study area (Fig. 2) encompasses all of the southern and central ISB and the southern third of the northern ISB. We restricted our data set to measurements from D 600 km because that is the range of Richter s (1958) distance corrections and he warned that path-specific distance corrections are needed at greater distances (Richter, 1958, p. 345). To create a synthetic W-A seismogram from a broadband record, we do the following processing: (1) remove the mean, (2) apply a 5% cosine taper to both ends, (3) pad the end of the record with 5 sec of zeroes, (4) deconvolve the instrument response, and (5) convolve the standard W-A instrument response. The last two steps are done in the frequency domain. Comparisions of actual and synthetic W-A records from DUG, the only station from which both are available, show good agreement in waveform shape but a systematic amplitude difference. The geometric mean ratio between maximum p-p amplitudes on the actual and synthetic W-A records is (2r; see Fig. 3), with the latter being larger. Based on step-function calibrations, which we carried out in collaboration with USNSN personnel in 1999, we believe that the DUG broadband instrument responses we used are accurate to within 5%. Therefore, it appears that the gain of the DUG W-A seismograph is a factor of about smaller than the design gain of 2800 (Anderson and Wood, 1935), or This conclusion is consistent with the findings of Uhrhammer and Figure 3. Plot of M L from synthetic W-A seismograms, M L (digital), versus M L from photographic W-A seismograms, M L (paper), for 42 earthquakes of the 1994 Draney Peak, Idaho, sequence (distances, 300 to 322 km) recorded at the Dugway, Utah, USNSN station (DUG). Both M L s were computed using the DUG photographic W-A station correction of 0.2. For the 10 earthquakes with p-p amplitudes 1 mm on the paper records, there is a systematic M L difference of (2r) as shown by the line. To account for this difference, we adjusted the station correction for the DUG synthetic W-A records. Collins (1990), who present calibration data and a theoretical analysis indicating that the actual gain of the standard W-A seismograph is Following Kanamori et al. (1993), we decided to use the nominal W-A gain of 2800 to construct our synthetic W-A seismograms and use station corrections to account for the gain difference between synthetic and actual W-A records. Various different procedures are in use for measuring the maximum trace amplitude in equation (1) and for combining readings from different stations and components into a single M L estimate (see, e.g., Wald et al., 1992; Hutton and Jones, 1993). To maintain continuity in the catalog, we follow the established UUSS procedures for these tasks that have been in use since at least the late 1970s. The p-p amplitude of the largest single swing anywhere in the W-A record is measured and divided by two to determine the maximum amplitude, A. The arithmetic mean of the amplitude measurements from the north south and east west components is then used in equation (1) to calculate an M L estimate for each station. Finally, the M L estimates for two or more stations are averaged to obtain the M L value for the earthquake. These procedures are the same as those described by

6 562 J. C. Pechmann, S. J. Nava, F. M. Terra, and J. C. Bernier Gutenberg and Richter (1956), except that maximumamplitude measurements from P waves are not disregarded. In selecting the largest p-p amplitude on synthetic W-A records, we generally ignore waveform complications having p-p amplitudes less than one-tenth that of the overall swing. The rationale is that these small-waveform complications are not usually visible on paper W-A records. We reject p-p amplitude measurements from synthetic W-A records that are not at least twice the p-p amplitude of the preevent noise. Because the pre-event noise is usually dominated by microseisms, which have significantly longer period than local-earthquake signals, we estimate that this guideline limits the noise-induced amplitude error to less than 20%. For p-p amplitude measurements from paper W-A records, we restrict ourselves in this study to values of 1.0 mm or larger based, in part, on the discussion of Figure 3 in the next section. Our total data set consists of 11,352 p-p amplitude measurements from 1755 earthquakes of M L 0.5 to 5.7. Station Corrections Some ambiguity exists in the relationship between absolute earthquake size and M L as defined by Richter (equation 1) due to the uncertainty about the gains of W-A instruments and the effects of regional variations in average log A 0, focal depth, and site amplification on seismic wave amplitudes at D 100 km (Boore, 1989). Although station corrections can account for systematic site-amplification differences among stations, the site conditions corresponding to any specific station correction are not part of Richter s M L definition. Consequently, the mean M L station correction for a seismic network is typically set to zero. With this constraint on the station corrections, the M L values calculated are a function of the average site amplification for the stations in the network. This dependence, combined with differences in average site amplification among networks, can lead to nonuniformity in M L determinations. Note that station corrections for rock sites can span at least 0.6 magnitude units (e.g., Table 2; Uhrhammer et al., 1996). For our M L determinations, we decided to choose M L from the DUG W-A seismograph paper records as the standard. DUG is the only station for which we have both actual and synthetic W-A records and it also has a long recording history. W-A recording at DUG began on 20 September 1963, years after the starting date of the UUSS instrumental earthquake catalog, which is 1 July Therefore, using the DUG W-A M L s as the standard serves to minimize discontinuities with previous magnitude measurements in the UUSS catalog, which are based directly or indirectly on M L determinations from W-A instruments at DUG and four other stations (see Griscom and Arabasz, 1979; Richins, 1979; Richins et al., 1981). Another advantage of DUG as a reference station is that it is located on granitic rock (early Tertiary) and is therefore unlikely to have an unusual site response. Station Code Table 2 Local Magnitude Station Corrections Station Correction, S i Std. Dev. of S i, s(s i ) No. of Measurements AHID BGU BUT BW CTU DUG-paper* 0.20 DUG-digital 0.08 ELK HLID HVU HWUT JLU KNB LDS LKWY MPU MVU NLU NOQ SLC SRU YMR *Station correction from Griscom and Arabasz (1979). See text and Figure 3 for explanation. Station correction derived from paper record data but applied to magnitudes from both paper and digital records for earthquakes after 10 July 1985, when the SLC Wood Anderson instrument was rebuilt; for earlier events, we used Griscom and Arabasz s (1979) station correction of 0.0. In calculating M L s from the DUG W-A paper records, we adopt the station correction of 0.2 determined by Griscom and Arabasz (1979). This station correction is the same as that for station PAS in southern California, as determined by Richter (1958, p. 343) and confirmed by Hutton and Jones (1993). PAS is one of the seven W-A stations that Richter (1935) used in developing the M L scale and is also located on granitic rock (early Cretaceous). As mentioned previously, we found a systematic difference between maximum p-p amplitudes on DUG synthetic and actual W-A records. The evidence for this difference is shown in Figure 3, where we have plotted M L from DUG synthetic W-A seismograms versus M L from DUG photographic W-A seismograms, both computed using a station correction of 0.2. The data are from 42 earthquakes that occurred near Draney Peak, Idaho, between 1 February and 7 April 1994, when both the W-A and broadband instruments were operating at DUG. For the 10 earthquakes with p-p amplitudes 1 mm on the paper records, the M L s from the synthetic (digital) records are higher than those from the actual (paper) records by an average of (2r), as illustrated by the line. To remove this difference, we set the station correction for the DUG synthetic W-A records to The data for events with p-p amplitudes 1 mm on the paper records show a similar systematic difference between the two sets of M L s, but with considerably more scatter due to the larger

7 Local Magnitude Determinations for Intermountain Seismic Belt Earthquakes from Broadband Digital Data 563 relative uncertainty in these smaller amplitude measurements. For each of the other stations we calculated an empirical M L station correction, S i, which would minimize the mean difference between the station-corrected M L s from that station and DUG: S M (DUG-digital) M (i) (2) i L L where the overbar indicates the mean value, M L (i) is the uncorrected M L from station i, and M L (DUG-digital) is the M L from the DUG synthetic W-A records after applying the 0.08 station correction. One key assumption underlying these station correction calculations is that Richter s M L distance corrections are adequate for use within our study area (Figs. 1 and 2). This assumption is checked and verified in the next section. A second assumption is that the distribution of epicenters for the earthquakes used is sufficiently random that path and radiation pattern effects will average out in calculating S i from (2). This latter assumption might not be very well satisfied for some of the stations around the edges of our study region, but it is difficult to avoid this problem given our data set and station distribution (Fig. 2a). We consider a station correction to be acceptable if (1) it was determined by using data from at least 10 earthquakes and (2) it has a standard deviation, s(s i ), less than or equal to 0.10, where s(s i) s [M L(DUG-digital) M L(i)]/ N, (3) s is the sample standard deviation, and N is the number of earthquakes used. The station corrections appear to be stable to within a few hundredths once data from at least 10 welldistributed earthquakes are available. The 20 station corrections that meet our acceptance criteria range from 0.43 to 0.21 and were determined using 10 to 259 earthquakes (Table 2). Stations for which an acceptable correction could not be determined using data from the period January 1994 through June 2002 are not used in the work reported here. Distance Correction Check As pointed out by Richter (1958, p. 345), his distance corrections cannot be assumed to apply outside southern California. M L distance corrections determined for northern California by Bakun and Joyner (1984) and Uhrhammer et al. (1996) and for the western Great Basin by Savage and Anderson (1995) are very similar to Richter s over most of the applicable distance range. However, published M L distance corrections for some regions differ significantly (e.g., Boore, 1989; Alsaker et al., 1991; Langston et al., 1998; Bragato and Tento, 2005). Furthermore, revised distance corrections for southern California derived by Hutton and Boore (1987) diverge from Richter s at hypocentral distances less than 50 km and more than 200 km. In this section, we test the accuracy of Richter s (1958) distance corrections in our ISB study region by examining the distance dependence of M L residuals calculated using his corrections. We define an M L residual as the difference between the M L from a single station and the mean M L from all stations reporting an M L for a given earthquake. Figure 4 shows plots of mean M L residuals versus epicentral distance, both without (Fig. 4a) and with (Fig. 4b) station corrections, for the earthquakes in our ISB data set (Fig. 2b). Comparison of Fig. 4a and b shows that the station corrections reduce the mean M L residuals, as expected. On both plots, there is a trend of increasing residuals with distance, which suggests that attenuation in the ISB might be slightly less than in California. Both plots also show a trough in the residuals between 200 and 250 km distance. This feature is more prominent on the plot for the stationcorrected M L s, mostly because of the reduced scatter elsewhere. Figure 5 shows M L residual plots analogous to those in Figure 4, but for earthquakes in the Utah region only (Fig. 2b). The station corrections reduce the residuals more dramatically for the Utah region data set than for the ISB data set. On the Utah region plot for the station-corrected M L s, the trough in the residuals between 200 and 250 km is smaller in amplitude than on the corresponding ISB region plot. Both Utah region plots show a trend of increasing residuals with distance as noted for the ISB region plots, but this trend is weak on the plot for the station-corrected M L s. If significant, this trend would imply that attenuation of W-A peak amplitudes in the Utah region is somewhat less than in California. Griscom (1980) reached the opposite conclusion based on a much smaller data set from W-A paper records. The most important observation to be made from Figures 4 and 5 is that, after applying station corrections, the mean M L residuals are all small. The absolute values of the mean residuals are all less than or equal to 0.16 and, in the ISB and Utah regions, respectively, 87% and 86% have absolute values less than 0.1. Moreover, the 95% confidence limits (vertical bars) of all the means extend to within 0.1 magnitude units of the zero line. From these results, we conclude that Richter s distance corrections are suitable for use in our ISB study region and the Utah region. As discussed by Boore (1989), there is observational evidence from four separate studies that Richter s distance corrections lead to underestimation of M L at D 40 km in California: (1) Luco (1982), (2) Jennings and Kanamori (1983), (3) Bakun and Joyner (1984), and (4) Hutton and Boore (1987). At least for focal depths between 5 and 15 km, these studies found that the largest underestimation occurs at a horizontal distance of 20 km and ranges from 1/4 to 1/2 unit, depending on the focal depth and the study. In contrast, our station-corrected results for the ISB and Utah regions show much smaller systematic deviations from mean M L satd 40 km, with a maximum underestimation of units (Figs. 4b and 5b). Similarly, distance corrections derived by Uhrhammer et al. (1996) for northern

8 564 J. C. Pechmann, S. J. Nava, F. M. Terra, and J. C. Bernier Figure 4. Graphs of mean M L residuals versus epicentral distance for ISB earthquakes (Fig. 2b), computed by using Richter s distance corrections both without (a) and with (b) station corrections. The 5676 M L residuals are the differences between each single-station M L and the mean M L for the same earthquake from two or more stations. The horizontal bars indicate the widths of the distance bins used to compute the means: 10 km at distances less than 380 km but up to 60 km at greater distances to include enough data points for a meaningful average. The vertical bars show the 95% (2 standard deviation) confidence limits on the means. California and by Savage and Anderson (1995) for the western Great Basin are within 0.15 units of Richter s values in the epicentral distance range 0 to 40 km. We suspect that these differing results concerning the accuracy of Richter s distance corrections at close distances are due primarily to differences in the types of data and methods used. The three studies (including ours) that find good agreement with Richter s corrections used data sets dominated by small earthquakes and distance corrections that are not constrained to match any particular functional form. The primary differences between these studies and those of Luco (1982) and Jennings and Kanamori (1983) are that the latter two did not use station corrections and analyzed data only from moderate to large earthquakes, 5.2

9 Local Magnitude Determinations for Intermountain Seismic Belt Earthquakes from Broadband Digital Data 565 Figure 5. Graphs of mean M L residuals versus epicentral distance for 995 Utah region earthquakes (see Fig. 2b), computed both without (a) and with (b) station corrections. The distance bins (horizontal bars) for the 3615 residuals are 10 km wide out to a distance of 250 km and up to 60 km at larger distances. See Figure 4 for additional explanation. Note that the mean station-corrected residuals shown here and in Figure 4 are all relatively small, which justifies the use of Richter s distance corrections in the ISB and Utah regions. M L 7.2. Although Luco (1982) and Jennings and Kanamori (1983) took into account the spatial extent of their earthquake sources by using distance measurements based on the rupture location rather than the epicenter, this change might not fully compensate for finite-source effects at close distances. Bakun and Joyner (1984) and Hutton and Boore (1987) used mostly small earthquakes to determine M L distance and station corrections for northern and southern California, respectively. Both assumed the distance corrections to be a simple analytical function of hypocentral distance, r, with an anelastic attenuation factor of 10 Kr and a geometrical spreading factor of r n, where K and n are constants and n 1. The deviation of their distance corrections from Richter s for D 40 km might be an artifact of this simple functional form. It appears that this function varies too smoothly with distance to be able to match Richter s corrections over their entire distance range (see figure 7 of Bakun and Joyner, 1984).

10 566 J. C. Pechmann, S. J. Nava, F. M. Terra, and J. C. Bernier Richter s (1958) distance corrections for D 30 km are taken from Gutenberg and Richter (1942). Hutton and Boore (1987) and Boore (1989) argue that these distance corrections are incorrect because although the recent work supports a geometrical spreading close to 1/r, Gutenberg and Richter (1942) assumed a geometrical spreading of 1/r 2 and an average focal depth of 18 km..., both of which are inappropriate for southern California, in their modification of the original log A 0 values (Richter, 1935) for closer distances (Hutton and Boore, 1987, p. 2082). We question this assessment for two reasons. First, Gutenberg and Richter (1942) calculated their distance corrections for D 30 km from the equation log A log r, (4) 0 which they justified empirically, not theoretically, using seven magnitude-corrected amplitude measurements in the distance range 22 D 80 km. They make no explicit mention of assumptions about geometrical spreading in this equation, although it is possible that such assumptions influenced its form. Second, Frankel et al. (1990) showed that S waves from a buried point source in a realistic layered elastic model of the crust can decrease with amplitude at a rate much faster than r 1. In fact, Frankel et al. (1990) successfully modeled S-wave amplitude decay in southern California using a geometrical spreading factor proportional to r and a frequency-independent quality factor (Q) of 800. In northern Utah, Pankow and Pechmann (2005) showed that ground motions at Paleozoic rock sites decrease with distance at rates of r in the frequency range 0.5 to 2.5 Hz and r in the frequency range 2 to 10 Hz. We conclude that the r 2 amplitude decrease in Gutenberg and Richter s (1942) distance corrections for D 30 km is plausible. However, Gutenberg and Richter (1942) assumed a focal depth of 18 km in calculating their corrections, and the median focal depth of southern California earthquakes is probably only about half of that (see Corbett, 1984; Doser and Kanamori, 1986). The effect of this error is significant ( 0.1) for their distance corrections for D 0, 5, and 10 km. Based on the results in Figures 4 and 5, and the preceding discussion, we conclude that there is little to be gained by determining a new set of M L distance corrections for the ISB. Figures 4b and 5b show that when Richter s distance corrections are applied, along with empirical station corrections, systematic variations of M L residuals with epicentral distance are small and comparable to the 95% confidence limits in the station corrections, which range from 0.04 to 0.16 (Table 2). We realize that there is usually some tradeoff between M L distance corrections and station corrections, and that consequently a formal inversion of our data set for both might produce somewhat different sets of corrections. However, judging from the results of other such inversions (e.g., Hutton and Boore, 1987), the improvement in the fit to the data would probably be small. Furthermore, different methods of inverting for station and distance corrections can produce differences in the latter that are at least as large as our mean station-corrected M L residuals (see Savage and Anderson, 1995). Therefore, in the interest of maintaining homogeneity in the M L (and indirectly, M C ) values in the UUSS earthquake catalogs, we decided to continue to use Richter s (1958) distance corrections for routine M L determinations in the ISB. We note that for similar reasons, the University of California, Berkeley (Uhrhammer et al., 1996), and the University of Nevada, Reno (Savage and Anderson, 1995), decided to continue using Richter s (1958) distance corrections for M L computations in northern California and the western Great Basin, respectively. Although it would be preferable to have distance corrections based on hypocentral distance instead of epicentral distance, we do not have enough events in our data set with well-constrained focal depths to calibrate the corrections as a function of hypocentral distance. However, it might be necessary to develop a revised set of distance corrections at short distances, based on hypocentral distance, for special studies in which many of the M L measurements are from epicentral distances less than 10 km or one focal depth. Maximum Peak-to-Peak Amplitude Times To determine M L s automatically, it is necessary to define a time window within which to search for maximum p- p amplitudes. This search window should be as short as possible to maximize the efficiency of the search and minimize the chances of including seismic waves from other events, which can lead to large M L errors. It should also be long enough to encompass most, if not all, of the maximum p-p amplitudes. To help guide the selection of optimal time windows for automatic M L determinations, we examined the distribution of maximum p-p amplitude times (t(max p-p)) on the synthetic W-A records used in this study, excluding a few which had timing problems. There are 10,500 times in the data set we used: two per station with at least two stations per earthquake. We define t(max p-p) as the mean of the times of the peak and trough with the maximum amplitude difference, measured relative to the earthquake origin time. Figure 6 is a plot of t(max p-p) versus epicentral distance, D. The solid lines labeled Pg and Sg show simple approximations to the arrival times of these phases: D/V Pg and D/V Sg, where V Pg and V Sg are the average Pg and Sg velocities, respectively. We set V Pg 5.9 km/sec and V Sg 3.39 km/sec based on the velocity model used by UUSS for earthquake locations in north-central Utah (Keller et al., 1975; Richins et al., 1979, 1981). It is evident from Figure 6 that most, but not all, of the maximum p-p amplitudes occur within the S wave. Figure 7 shows the same data as Figure 6 on a plot of reduced t(max p-p) versus M L, where reduced t(max p-p) t(max p-p) D/3.39 km/sec. Based on Figure 7, there does not appear to be any systematic relationship between t(max p-p) and M L. The trend in the lower bound

11 Local Magnitude Determinations for Intermountain Seismic Belt Earthquakes from Broadband Digital Data 567 Figure 6. Plot showing time of maximum p-p amplitude on synthetic W-A records versus epicentral distance. The solid lines show approximate Pg- and Sg-arrival times, which are calculated for a surface source and constant Pg and Sg velocities of 5.9 and 3.39 km/sec, respectively. The dashed lines mark the bounds of our recommended search window for automatic maximum p-p amplitude measurements. Figure 7. Plot showing reduced time of maximum amplitude on synthetic W-A records versus M L. Note that the maximum amplitude time does not have any obvious dependence on M L, except that the pre-sg time range of the data increases with M L because of the increased distance range of the observations. See Figure 6 and the text for further explanation.

12 568 J. C. Pechmann, S. J. Nava, F. M. Terra, and J. C. Bernier of the data distribution between magnitudes 1.2 and 3.0 is an artifact of the magnitude-dependent distance limit, and hence Sg-P time limit, out to which amplitudes can be measured. The dashed lines on Figures 6 and 7 show our recommended search window for automatic maximum p-p amplitude measurements: a 30-sec time window beginning 5 sec before the predicted Sg time. This search window encompasses 95.6% of the data, and appears to be a good compromise between minimizing the search window length and maximizing the chances of capturing the maximum amplitude. However, because the optimal trade-off between these two considerations is a matter of judgment, there is a range of other reasonable choices available (Table 3). For example, a search window of 12 sec beginning 2 sec before the Sg time is significantly shorter, but still encompasses 85.1% of the data. A search window beginning with the P-wave arrival and extending to 25 sec after the Sg arrival encompasses 99.5% of the data, but has a duration that increases with distance to more than 100 sec at 600 km. Revision of M L Values in the UUSS Earthquake Catalogs, We recomputed all of the M L s in the UUSS earthquake catalogs for the Utah and Yellowstone regions for 1981 through 2002 using Richter s distance corrections, the station corrections in Table 2, and the p-p amplitude criteria described in the Data and Methodology section. (For a few events outside these two regions, we used some p-p amplitudes 1 mm from DUG paper records.) M L s for subsequent Table 3 Percentage of Maximum Peak-to-Peak Amplitude Times in Selected Time Windows Time Window (sec Relative to Sg Arrival Time) Percentage of Data (10,500 Points) 2 to to to to to to * 5 to P to P to P to P to P to *Recommended search window for automatic maximum peak-to-peak amplitudes. earthquakes have been computed using the same basic methodology, but with an expanded station set after June M L s are included in the catalogs only if they are average values from two or more stations. We used M L s for earthquakes from 1983 to 2001 to calibrate new M C equations for the Utah and Yellowstone regions based on gain-corrected signal duration measurements from vertical-component, short-period, digital data (Pechmann et al., 2001, 2006). All non-m L magnitudes in the revised catalogs are M C s calculated using these new equations. Figure 8. The percentage of earthquakes with M L s in the Utah region (squares) and Yellowstone region (circles) catalogs each year from 1981 (Utah) or 1982 (Yellowstone) through The same quantity is also shown for the Utah region catalog with coal-mining-related seismicity removed (triangles). This removal was accomplished by deleting all events from two polygonal regions similar to those shown in Figure 1 of Arabasz et al. (2005).

13 Local Magnitude Determinations for Intermountain Seismic Belt Earthquakes from Broadband Digital Data 569 The percentage of earthquakes with M L s in the catalogs increases dramatically beginning in the late 1990s and reaches 28% and 13% in the Utah and Yellowstone regions, respectively, in 2002 (Fig. 8). The deviation from this trend for the Utah catalog during 2000 and 2001 (squares, Fig. 8) is mostly due to the inclusion of a large number of small mining-related events without M L s from a special study conducted during this period (Arabasz et al., 2005). If all the mining-related seismicity in east-central Utah is removed from the Utah region catalog, the percentage of M L sinthe catalogs increases almost monotonically between 1996 and 2002 (triangles, Fig. 8). The increase in the percentage of earthquakes with M L s was made possible by the increase in the number of broadband digital telemetry stations in the region available for use in M L determinations. For the period 1981 through 1993 the Utah region catalog contains only 46 M L s, all of which were determined using paper records from the DUG and SLC W-A instruments (Fig. 1). All but one of these 46 M L s are for M L 3 earthquakes and there is no magnitude level above which M L s are available for all earthquakes (Fig. 9a). In contrast, the Utah region catalog for 2002 contains 302 M L s, which were determined using up to 16 of the 20 stations listed in Tables 1 and 2. In both the Utah and Yellowstone region catalogs for 2002, M L s are available for all earthquakes of M 3, about half of the earthquakes of 2 M 3, and some earthquakes of M 1 (Figs. 9b and c). The size threshold for M L determinations is lowest in north-central Utah and in central Yellowstone Park, where the density of broadband digital telemetry stations is the highest (Fig. 1). Comparison between M L and M W As a test of the absolute accuracy of our M L s, we compared them with M W s compiled from several web sites and the published literature (Tables 4 and 5; Fig. 10). The M W s for most of the 47 earthquakes we used in this comparison are from either J. Nabelek and his colleagues at Oregon State University (OSU; 20 events, ) or from R. B. Herrmann of Saint Louis University (SLU; 14 events, ). The M W s for the other 13 earthquakes ( ) are from a variety of sources (Table 5). All of these M W s are from inversions of either long-period waveforms or surfacewave spectra. We chose to exclude the seismic-moment measurements of Doser and Smith (1982) because they were done using a less reliable method: spectral analysis of body waves recorded at local to teleseismic distances. If there were multiple M W s from waveform inversion or surfacewave spectra available for the same earthquake, we used the mean of the different values. However, for events for which SLU reported solutions from more than one technique, we used whichever solution was indicated as preferred for that earthquake. Figure 10 shows that UUSS M L s for ISB earthquakes are reasonably consistent with available M W determinations. The UUSS M L is within 0.5 units of the M W for 89% of the Figure 9. Histograms showing the percentage of earthquakes with M L s as a function of magnitude (M C or M L ) for the regions and periods indicated. earthquakes. For the data set in Figure 10, M L tends to overestimate M W for earthquakes of M L 4.5 and underestimate M W for smaller earthquakes. However, it is possible that these systematic differences are, at least in part, an artifact of the data limitations. One of these limitations is that the M W determinations were done with a variety of different methods and velocity models, both of which can affect the M W values. Furthermore, the sources of the M W determinations are not uniformly distributed with magnitude. For example, note that the M W s for earthquakes of M L 4.5 are predominantly from the OSU Moment Tensor Catalog (circles, Fig. 10). The OSU M W s are in general higher than the UUSS M L s, with a mean difference that averages 0.15 and does not appear to be magnitude dependent. Another limitation of the data set is that for all five M L 5.5 earthquakes, the M L s are from stations DUG and SLC only and the DUG-SLC azimuth difference is quite small

14 570 J. C. Pechmann, S. J. Nava, F. M. Terra, and J. C. Bernier Table 4 Earthquakes with Both an M W and a UUSS M L : January 1981 through June 2003 Date (mm/dd/yyyy) Time (UTC) Latitude (deg min N) Longitude (deg min W) Geographic Area No. of Stations Used in M L UUSS M L M W * 05/24/ Sevier Valley, Utah /28/ Borah Peak, Idaho /29/ Borah Peak, Idaho /09/ Cove Fort, Utah /22/ Borah Peak, Idaho /02/ St. George, Utah /04/ Draney Peak, Idaho /11/ Draney Peak, Idaho /07/ Borah Peak, Idaho /25/ Caribou Range, Idaho /27/ Wellsville, Utah /28/ Yellowstone Region, Wyoming /28/ Yellowstone Region, Wyoming /06/ Wasatch Range, Utah /06/ San Rafael Swell, Utah /16/ Draney Peak, Idaho /11/ Yellowstone Park, Wyoming /15/ Yellowstone Park, Wyoming /16/ Yellowstone Park, Wyoming /17/ southeastern Idaho /13/ southern Utah /30/ Hebgen Lake Region, Montana /02/ Beaver, Utah /30/ southern Utah /16/ southern Utah /10/ Milford, Utah /18/ southern Utah /19/ southeastern Idaho /20/ western Wyoming /03/ southeastern Idaho /23/ Teton Range, Wyoming /26/ Teton Range, Wyoming /28/ Tobacco Root Mts., Montana /20/ southwestern Montana /22/ Parowan Valley, Utah /22/ Southern Wasatch Plateau, Utah /24/ western Montana /26/ central Wyoming /27/ Paradox Valley, Colorado /24/ Yellowstone Park, Wyoming /23/ Pavant Range, Utah /21/ Grays Range, Idaho /19/ Fish Lake Plateau, Utah /29/ Jackson Hole, Wyoming /22/ Wyoming-Idaho border /03/ Huntsville, Utah /17/ Levan, Utah *See Table 5 for references. ( 13 ). When the azimuthal distribution of the stations used for an M L determination is limited, the M L can be biased by radiation pattern and/or path effects. Four of the five M L 5.5 earthquakes are in the Borah Peak region of central Idaho, which is centered at 44 15, (Figs. 1 and 2). The fifth earthquake is the 1992 M L 5.9 St. George earthquake in southwestern Utah. The azimuthal distribution of stations for the St. George earthquake M L determination can be improved by adding data from southern California stations ( azimuth) with station corrections from Kanamori et al. (1993). These additional data lower the M L slightly from 5.93 to 5.81, which is in satisfactory agreement with the M W of 5.54 (Tables 4 and 5) considering the uncertainties in both.