understanding the differences between three teleseismic m scalesrichards/my_papers... · 2005. 10....

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Bulletin of the Seismological Society of America, Vol. 95, No. 5, pp. 1809–1824, October 2005, doi: 10.1785/0120040159

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Understanding the Differences between Three Teleseismic mb Scales

by John P. Granville, Paul G. Richards, Won-Young Kim, and Lynn R. Sykes

Abstract We investigate differences between three body-wave magnitude (mb)scales for 2009 earthquakes from 1996 to 1999 listed in the Preliminary Determi-nation of Epicenter (PDE) bulletin having mb between 5.0 and 5.5 and that also havemoment tensor solutions available from the Harvard Centroid Moment Tensor (CMT)catalog. A total of 31,280 broadband seismograms are analyzed, for an average of15 stations per event. Both the PDE and Reviewed Event Bulletin (REB) proceduresfor determining an automated mb are reproduced, thereby eliminating any discrep-ancies that result from using different networks of stations. We compare the repro-duced PDE and REB magnitudes to another magnitude measurement, mb(P), that isbased on the Worldwide Standard Seismographic Network (WWSSN) short-periodinstrument. We find that differences between mb(P), mb(PDE), and mb(REB) arisefrom four factors: response function, length of time window, and corrections forevent depth and epicentral distance. Reproduced mb(PDE) and mb(P) are stronglycorrelated, and we expect that magnitudes assigned from WWSSN short-period in-struments during the 1970s and 1980s are consistent with those assigned by theautomated procedure used since 1991 by the U.S. Geological Survey (USGS), pro-viding stability in mb measurements over several decades. The difference betweenmb(REB) and mb(P) is much greater because of the significantly shorter REB windowlength of 5.5 sec and the high-frequency passband of the REB displacement response.

Online Material: Filter parameters and color versions of Figures 8 and 9.

Introduction

The body-wave magnitude (mb) provides an empiricalestimate of earthquake size that is directly related to thestrength of ground shaking at teleseismic distances. Esti-mates of mb are based on measurements of P-wave amplitudefrom short-period instruments (i.e., period �1.0 sec) and canbe used to determine how strongly the ground moved at aspecific location. Moreover, mb can be used as a crude mea-sure of seismically radiated energy, when direct estimates ofradiated energy (Es) are not available (i.e., for earthquakesof mb ��5.5). Nevertheless, mb is increasingly regarded bysome as a less important or less robust measurement of earth-quake size since a more physically based measurement ofearthquake size, the moment magnitude (Mw), is now avail-able for most moderate and large earthquakes. Yet, mb, un-like Mw, is available for many events of mb �5. Furthermore,empirical mb values have their own importance as a tradi-tional measure of earthquake size assigned from short-periodsignals and are thus distinctly different from Mw values,which are estimated from long-period signals. Therefore,two events can have the same moment but a different mb.For example, for two earthquakes of the same moment, onein a tectonically active region such as the western UnitedStates and one in a stable continental region such as eastern

North America, the event in the tectonically active regionwill be characterized by greater source-to-station attenua-tion. Consequently, the event in the stable region will typi-cally have a higher mb because of stronger ground shaking.Thus, assigning several types of magnitude (both empiricaland physical) to an event allows for greater understandingof the earthquake source and the signals it generates.

This article focuses on teleseismic body-wave magni-tudes assigned by the automated procedures of the UnitedStates Geological Survey (USGS) and the Prototype Inter-national Data Centre (PIDC). Significant discrepancies be-tween short-period teleseismic magnitudes published by theUSGS and PIDC were noted by Murphy and Barker (1996,2003), Willemann (1998), Dewey (1999), and Murphy et al.(2001). These studies of body-wave magnitude discrepan-cies compared mb values published by the two agencies intheir respective bulletins of seismicity—the PIDC’s Re-viewed Event Bulletin (REB) and the USGS’s PreliminaryDetermination of Epicenter (PDE) catalog. By analyzingonly published values of magnitude (and the correspondingamplitude and period from which the magnitude is as-signed), these studies were not able to address any bias inthe actual amplitude and period measurements that results

1810 J. P. Granville, P. G. Richards, W.-Y. Kim, and L. R. Sykes

Figure 1. Locations of the 2009 earthquakes analyzed in this study (PDE bulletinmb 5.0–5.5). Symbol size increases with magnitude of PDE event.

Figure 2. Locations of the 134 seismic stations used in this study. The 22 stationsin our dataset that report data to both the USGS and PIDC are shown as triangles. Thereare 98 stations reporting only to the USGS and they are shown as inverted triangles(none of our stations report data only to PIDC). The remaining 14 stations in the datasetthat do not report data to either the USGS or PIDC are shown as circles. Filled symbolsindicate the 19 stations recording at least 25% of the earthquakes studied.

Understanding the Differences between Three Teleseismic mb Scales 1811

from the different filtering and time window lengths used bythe different agencies and at various times. Moreover, theseprevious studies did not attempt to reproduce the magnitudeprocedures of either the USGS or PIDC.

Differences between published PDE and REB magni-tudes result from different procedures for assigning magni-tude as well as differences in the particular set of stationsfrom which the magnitude is assigned. Only a small numberof seismic stations are common to both the USGS and PIDCseismic networks. This problem of differing networks of sta-tions is further complicated by the fact that many more seis-mic stations are available to the USGS for purposes of as-signing magnitude than to the PIDC. Since the focus of thisstudy is on differences in magnitude procedures and theireffect on seismic magnitudes, we eliminate the problem ofdiffering networks of stations by reproducing the automatedprotocols followed by the USGS and PIDC to assign mb.

To understand these procedures used by the USGS andPIDC to assign mb, we first describe exactly how these twoagencies assign mb from broadband, velocity waveforms andalso how to reproduce their respective protocols and mea-surements. Since PIDC magnitudes were successfully repro-duced by Granville et al. (2002), we follow their procedureto compute the PIDC magnitudes included in this study. TheUSGS procedure for assigning station mb from broadbandwaveforms, on the other hand, has not been published andis not generally known. Guided by advice from USGS per-sonnel (J. Dewey, personal comm., July 1998 to present),we are able to reproduce the automated procedure for as-signing body-wave magnitude at USGS (i.e., mb(PDE)).Thus, we are confident that we understand how the USGSassigns magnitude, and we describe these procedures in de-tail in this article. We investigate differences between theUSGS and PIDC magnitude scales, as well as a third mag-nitude scale, mb(P), that is based on a specific instrumentalresponse—the Worldwide Standard Seismographic Network(WWSSN) short-period seismograph—that was widely usedfor over 20 years. We describe the differences between thethree magnitude scales and then quantify the sources of theobserved differences.

By duplicating the procedures of both the USGS andPIDC, we not only gain an understanding of exactly howmagnitude measurements are made by these two agencies,but we also eliminate any discrepancies that arise from dif-fering networks of stations. Our measurements are based onthe same seismograms, allowing us to focus on the differentprotocols by which body-wave magnitudes are assigned. Wefind that differences between the three magnitude scalesarise from four factors: response function, length of timewindow, corrections for event depth, and corrections for epi-central distance. The automated mb procedure of the USGSis found to be a good surrogate for an mb scale based onsimulated WWSSN short-period instruments for the range ofmagnitudes studied (PDE bulletin mb 5.0–5.5 events). Mag-nitudes based on the automated PIDC procedure, on the otherhand, are significantly smaller than those based on simulated

WWSSN short-period signals. Since the PIDC magnitude,mb(REB), is a higher frequency measurement, it may performbetter than a traditionally measured magnitude such as mb(P)for purposes of applying the mb–Ms discriminant, althoughthis has not yet been demonstrated. Further studies are nec-essary to determine whether the observed relationships be-tween the three magnitude scales apply to events whosemagnitudes are significantly different from those in thisstudy.

For consistency with mb(P) and mb(PDE), the PIDCcould produce a classical mb measurement in addition to itscurrent mb(REB), styled after either the mb(P) or mb(PDE)procedure. This classical measurement would be a very use-ful and important source parameter since it would be basedupon a fixed network of stations and would be consistentwith magnitudes measured using WWSSN short-period in-struments.

Method

Data Acquisition and Processing

The dataset in this analysis consists of seismograms for2009 earthquakes from 1996 to 1999 listed in the Prelimi-nary Determination of Epicenter (PDE) bulletin having mb

between 5.0 and 5.5 and that also have moment tensor so-lutions available from the Harvard Centroid Moment Tensor(CMT) catalog (Fig. 1). In this dataset there are 463 earth-quakes at PDE mb 5.0, 442 at PDE mb 5.1, 364 at PDE mb

5.2, 322 at PDE mb 5.3, 225 at PDE mb 5.4, and 193 eventsat PDE mb 5.5. Although the CMT catalog is not completefor earthquakes of PDE mb 5.0, the body-wave magnitudefor which there are the most events in the CMT catalognevertheless occurs at PDE mb 5.0. This suggests that a largesubset of earthquakes of this size is characterized by suffi-ciently strong long-period signals to enable the computationof a moment tensor solution.

Our dataset consists of events with an associated PDEmb between 5.0 and 5.5 because this range of magnitudesprovides a representative global coverage (Fig. 1). Earth-quakes with a PDE mb less than 5.0 are omitted from thisstudy because the azimuthal gap in station coverage is largeand because there are often only a handful of nonarray sta-tions for which data are available from the Incorporated Re-search Institutions for Seismology (IRIS) data center. Wealso exclude earthquakes with a PDE mb greater than 5.5because mb begins to saturate above 5.5 and because thereare fewer earthquakes at the larger magnitudes (Granville etal., 2002, studied some of them). We chose a time periodfrom 1996 to 1999 for our dataset because the only yearsfor which a complete REB is publicly available are 1995through 1999; however, in 1995, the first year that an REBwas published regularly, the bulletin was plagued by prob-lems such as incorrect instrumental responses and errors inthe PIDC source code used to average the station mb values(Granville et al., 2002).


Figure 3. Histogram showing the number of stations recording an earthquake atdifferent teleseismic distances, for all 31,280 individual station observations in thisstudy. Each bin represents a range of distances with width 5�.

Data consist of broadband, vertical-component recordsfor all Global Seismographic Network (GSN) stations be-tween 20� and 100� from each of the earthquakes (i.e., theteleseismic distance range). Instrumental response informa-tion for all included stations was obtained with the waveformdata. All data were obtained from the IRIS data center. Atotal of 134 seismic stations are used. In Figure 2, we showthe locations of these stations and indicate which of themalso reported data to the USGS and/or PIDC during 1996 to1999. There are 22 stations in this study that reported datato both agencies. An additional 98 stations reported data onlyto the USGS. None of our stations reported data only to thePIDC. Finally, there are 14 stations in the dataset that did notreport data to either the USGS or PIDC.

We find that 19 of the stations in this study recorded atleast 25% of the events analyzed (Fig. 2). These 19 stationsare predominantly located on the Eurasian continent, indi-cating that this region is the best location to record globalearthquakes teleseismically. Moreover, only 2 of the 19 best-recording stations are in the southern hemisphere. Two ofthe stations in our study recorded more than half of the earth-quakes in our dataset—WMQ in Urumqi, China (1177events) and XAN in Xi’an, China (1224 events). The stations

included in this study provide good coverage over the entireteleseismic distance range (20�–100�). In Figure 3 we showthe number of individual station observations in each tele-seismic distance range using 5� bins. Only the farthest tele-seismic distances (90�–100�) are not strongly represented,presumably because the Earth’s core begins to have an effecton signal amplitude and reception.

All station body-wave magnitudes are calculated fromfiltered seismograms using the same general equation:

m � log(A/T) � B(D, h) , (1)b(sta)

where sta is the station, A is the maximum half peak-to-trough amplitude in nanometers, T is the period in secondsmeasured at the maximum amplitude, and B is the correctionfor distance in degrees (D) and depth in kilometers (h). Atotal of 31,280 broadband seismograms are included in thisstudy, for an average of 15 stations per earthquake. Depthestimates are based on values from the Harvard CMT andUSGS moment tensor catalogs. Since we expect the USGSmoment tensor solution to provide the better estimate of hy-pocentral depth for shallow earthquakes, we preferentiallyinclude this depth where available (380 events total, the ma-


Figure 4. Displacement responses of a typicalWWSSN short-period instrument, a broadband stationprocessed according to the USGS procedure (bandpassfiltering from 0.5 to 6.5 Hz and 1.05 to 2.65 Hz), anda broadband station processed according to the PIDCprocedure (zero-phase bandpass filtered from 0.8 to4.5 Hz). Responses are normalized to have the samepeak gain.

jority of which correspond to our PDE mb 5.4 or 5.5 events).Otherwise, we calculate mb using the depth from the HarvardCMT catalog. We use both the Veith–Clawson (1972) cor-rections for distance and depth as well as the Gutenberg–Richter (1956) corrections. Body-wave magnitudes com-puted using the Gutenberg–Richter correction are indicatedas mb

GR, while measurements that include the Veith–Clawsoncorrection are given by mb

VC. Although all body-wave mag-nitudes discussed in this study are computed using equation(1), differences arise between them because of differentlengths of time windows, filters, response functions, and dis-tance corrections.

Three types of body-wave magnitude are discussed inthis article: mb(P), mb(PDE), and mb(REB). The first, mb(P),is based on simulated WWSSN short-period signals and fol-lows the procedure recommended by an International As-sociation of Seismology and Physics of the Earth’s Interior(IASPEI) manual (Willmore, 1979). The second, mb(PDE), isbased on a reproduction of the automated procedure usedsince 1991 by the USGS to assign station magnitudes in itsPDE bulletin. Finally, mb(REB) values are based on the au-tomated procedure used by the PIDC to generate station mag-nitudes for its REB. We choose mb(P) as our standard againstwhich to compare PDE and REB mb values because mb(P) isa Richter-type magnitude (Richter, 1935) that follows awell-defined protocol and is based on a specific instrumentalresponse—the WWSSN short-period seismograph—used forabout two decades before broadband data became generallyavailable. Neither the USGS nor PIDC magnitude scale isbased on a particular instrumental response.

mb(P) Procedure

To obtain a measurement of mb(P) from the broadbandP-wave recorded at a particular station, we first simulate aWWSSN short-period (SP) signal. This is done by decon-volving the response of the instrument to obtain ground dis-placement and then convolving the resulting waveform withthe WWSSN SP displacement response (Luh, 1977). Thisshort-period response is shown in Figure 4. Then, using thearrival times published in the International SeismologicalCentre (ISC) bulletin, the waveform is extracted for a 15-secwindow beginning at the P-wave arrival time (referred to aseither mb(P)GR,15s or mb(P)VC,15s, depending on the distanceand depth corrections). The arrival times in the ISC bulletinare based on information contributed by several differentagencies including the USGS and PIDC and are chosen forthis study because the ISC reviews the contributed arrivaltimes and selects the most accurate arrival time available fora given phase onset at a particular station. Measurements ofmb from the ISC bulletin are not included in this analysisbecause the ISC relies entirely upon contributed measure-ments of amplitude and period (including those publishedby the USGS and PIDC) instead of directly analyzing seis-mograms.

Amplitude and period are then measured from the sim-ulated WWSSN SP waveforms in the 15-sec time window,and an mb is assigned based on equation (1). Measurementsof amplitude and period follow a traditionally used protocoldescribed in the Manual of Seismological Observatory Prac-tice (Willmore, 1979, p. 84), which states, “For earthquakesof small size, motions may be measured up to 20 secondsfrom the time of the first onset. For very large earthquakes,up to 60 seconds may be allowed.” Earlier guidelines gavea 15-sec window, followed here. The amplitude is measuredfrom trough-to-peak (or peak-to-trough) and then halved toestimate the peak-to-zero ground motion in nanometers. Pe-riod is measured as peak-to-peak at the maximum amplitude.The quantity mb(P)VC,15s is identical to the parameter re-ferred to as Veith–Clawson mb by Granville et al. (2002).The corresponding mb(P) measurement that includes insteadthe Gutenberg–Richter distance and depth corrections is in-dicated as mb(P)GR,15s.

Reproduced mb(PDE) Procedure

To assign mb(PDE) at a particular station, we follow aninternal USGS memorandum that describes that agency’s au-tomated procedure for measuring mb (J. Dewey, personalcomm., 1998). It is important to point out, however, thatalthough we are able to reproduce the automated mb proce-dure of the USGS, our mb(PDE) values may differ from themb values published by the USGS in its PDE bulletin for tworeasons. First, a USGS analyst may override the automatedprocedure (for example, by following Willmore (1979) andselecting the maximum signal amplitude using a time win-dow whose length exceeds the automated 10 cycle lengthand can be as long as 60 sec for very large earthquakes).


Figure 5. (a) Histogram showing the distribution of offsets between the reproducedPDE station mb and the PDE bulletin station mb for all earthquakes in the dataset (PDEbulletin mb 5.0–5.5). Each bin represents a range of offsets with width 0.05 magnitudeunits; (b) Histogram showing the distribution of offsets between the reproduced REBstation mb and the published REB station mb for all events. Each bin represents a rangeof offsets with width 0.05 magnitude units.

Second, the USGS publishes mb values in its PDE bulletinthat are contributed by other agencies. In fact, during thetime period of our study (1996 to 1999) only �30%–40%of the amplitude (A) and period (T) measurements publishedin the PDE bulletin for mb �4.5 earthquakes were measuredinternally by the USGS (J. Dewey, personal comm., 2003).The remainder of the (A), T measurements were contributedby agencies such as the Australian Geological Survey Or-ganization, the Geological Survey of Canada, and the La-boratoire de Detection et de Geophysique, France. Althougha significant number of station magnitudes published in thePDE bulletin are based on contributed values rather than theautomated mb procedure, we focus on the automated pro-cedure because it is rigorously defined and can be accuratelyreproduced. The percentage of mb measurements in the PDEbulletin that are based on the automated procedure has in-creased from around 15% in 1991 to about 45% in 2003 formb �4.5 events (J. Dewey, personal comm., 2004). Thus,there is an ongoing effort at USGS to standardize mb mea-surements—that is, to base their measurements on an auto-mated procedure.

We reproduce the automated procedure of the USGS byfirst demeaning the broadband, velocity record. Next, thesignals are filtered using two bandpass filters: a second-orderbutterworth filter with cutoffs at 1.05 Hz and 2.65 Hz (2zeros and 4 poles) and another second-order butterworth fil-ter with cutoffs at 0.5 Hz and 6.5 Hz (2 zeros and 4 poles).The displacement response of these two bandpass filters isshown in Figure 4. ( E The poles and zeros for these filtersare given in Appendix 1, which is available in the electronicedition of BSSA.)

To measure amplitude and period, the filtered wave-forms are then extracted for a 15-sec window beginning atthe P-wave arrival, according to the ISC arrival time. Sincethe USGS uses a time window length of 10 cycles, beginningat the P-wave arrival, we obtain two slightly different mea-surements of maximum amplitude—one using a time win-dow length of 15 sec (e.g., mb(PDE)GR,15s, mb(PDE)VC,15s)and one using a length of 10 sec (e.g., mb(PDE)GR,10s,mb(PDE)VC,10s). The measurement using a 15-sec time win-dow is included to be consistent with mb(P) while the mag-nitude measured in a 10-sec window is intended to approx-imate the time window used by the USGS (assuming a 1-secperiod for 10 cycles). The amplitudes are measured fromtrough-to-peak (or peak-to-trough) and then halved to esti-mate the peak-to-zero amplitude. Periods are measured aspeak-to-peak at the maximum amplitude.

The amplitudes are then corrected for the effect of thebandpass filtering and for instrumental response. The atten-uating effect of the two bandpass filters is removed by di-viding the measured amplitude by the amplitude of the filterresponse at the measured period (where the filter responseconsists of the combination of the two bandpass filters). Thisfilter correction is quite large (a factor of 1.55 at 1 Hz) andis used to compensate for significant attenuation causedlargely by the narrowband 1.05-to 2.65-Hz filter. The in-strumental response (which is typically broadband and al-most flat to velocity) is then removed by dividing the am-plitude by the transfer function (to displacement) of theinstrument at the measured period, providing an estimate ofground motion in nanometers. A body-wave magnitude isassigned for each of these amplitudes and their respective


Figure 6. Simulated vertical records at HIA(Hailar, China) from the PDE mb 5.1 earthquakeof 20 December 1997 in the Sea of Okhotskregion (h � 612 km). Maximum amplitude(peak-to-trough or trough-to-peak) is markedby horizontal bars at the peak and trough of themeasured amplitude and corresponding periodis indicated by vertical bars. Note that for theUSGS and WWSSN signals a full cycle periodis measured whereas for the PIDC data a halfcycle period is used. Maximum amplitude val-ues, which are halved to estimate peak-to-zero(or zero-to-trough) amplitude, are given. Forthe simulated USGS short-period record, thecorresponding displacement amplitude is 241nm, with a period of 0.6 sec; the simulatedPIDC short-period record has displacement am-plitude of 204 nm, with a period of 0.5 sec.Waveforms begin at P-wave arrival time.

periods using equation (1). Since the USGS uses the Guten-berg–Richter corrections for distance and depth, the stationmagnitude corresponding to the mb value published in thePDE bulletin is indicated by mb(PDE)GR,10s.

In Figure 5a we show the offset between our repro-duced station mb(PDE) and PDE bulletin station mb for the20,205 observations that have an amplitude and period pub-lished in the PDE bulletin. The difference between the twomagnitudes is �0.0171 on average and the standard devi-ation (r) is 0.196. Agreement between the two quantities isnot exact because, as previously stated, in many cases ananalyst at the USGS will override the amplitude and periodvalues assigned by the automated procedure and becausemany of the magnitudes published in the PDE bulletin arebased on values contributed to the USGS by other seismo-logical centers. The fact that our reproduced station mb(PDE)measurements are on average less than the correspondingvalues in the PDE bulletin is likely the result of analyst over-ride at USGS. When overriding the automated measure-ments, an analyst may determine the maximum signal am-plitude using a longer time window (up to 60 sec for largeearthquakes) and therefore may assign a larger amplitude.Nevertheless, we are confident that our mb(PDE) accurately

reproduces the automated procedure stated by the USGS forassigning body-wave magnitude from a particular broadbandrecord.

Reproduced mb(REB) Procedure

The Reviewed Event Bulletin (REB) magnitude is re-produced by following the PIDC protocol for assigning mb

described in IDC Processing of Seismic, Hydroacoustic, andInfrasonic Data (International Data Centre, 1999) and isconsistent with the method used by Granville et al. (2002)to reproduce magnitude values published in the REB. TheREB magnitudes published by the PIDC are all measuredusing their automated procedure and there is minimal analystoverride. It is important to point out, however, that althoughwe are able to reproduce the automated mb procedure of thePIDC, only 22 of the 134 stations in this study contributeddata to the PIDC during 1996 to 1999. Therefore, our eventmagnitudes are based on a very different seismic networkthan those published by the PIDC.

To reproduce REB measurements, first the velocity sig-nals are bandpass filtered using a third-order butterworth fil-ter with cutoff frequencies at 0.8 Hz and 4.5 Hz. Since the


Figure 7. Simulated vertical records at BJT(Beijing, China) from the PDE mb 5.0 earth-quake of 15 August 1999 in Leyte, PhilippineIslands region (h � 34 km). Maximum ampli-tude (peak-to-trough or trough-to-peak) ismarked by horizontal bars at the peak andtrough of the measured amplitude, and corre-sponding period is indicated by vertical bars.Note that for the USGS and WWSSN signals, afull-cycle period is measured, whereas for thePIDC data, a half-cycle period is used. Maxi-mum amplitude values, which are halved toestimate peak-to-zero (or zero-to-trough) am-plitude, are given. Since the maximum ampli-tudes for the reproduced USGS and PIDC wave-forms arrive after the USGS- and PIDC-definedtime windows (10 sec and 5.5 sec, respec-tively), we also indicate the maximum ampli-tudes that would be selected using the shortertime windows. For the simulated USGS short-period record, the corresponding displacementamplitude is 28.3 nm (with period of 1.0 sec)using a time window length of 10 sec and 27.4nm (with period of 0.85 sec) using a 15-secwindow. The simulated PIDC short-period sig-nal has corresponding displacement amplitudeof 16.5 nm (with period of 0.9 sec) using a timewindow length of 5.5 sec and 19.7 nm (withperiod of 0.7 sec) using a 15-sec window.Waveforms begin at P-wave arrival time.

PIDC uses a zero-phase, infinite impulse response (IIR) filter,the time series is then reversed in time and the data are fil-tered a second time, using the same bandpass filter. By fil-tering the data in both the forward and reverse directions,the waveform’s shape is preserved, but the amplitudes areattenuated twice as much. The complete PIDC filter responsethus consists of 12 poles and 6 zeros (each of the 6 uniquepole values appears twice since the same filter is applied twotimes). The displacement response of these two bandpassfilters is shown in Figure 4. ( E The corresponding poles andzeros are given in Appendix 2, which is available in theelectronic edition of BSSA.) The waveform is then extractedfor a 15-sec window beginning at the P-wave arrival time.Then, we obtain two measurements of maximum amplitudefrom this waveform. The first amplitude measurement ismeasured using a 15-sec time window (e.g., mb(REB)GR,15s,mb(REB)VC,15s), to be consistent with mb(P). The second isbased on a window length of 5.5 sec (e.g., mb(REB)GR,5.5s,mb(REB)VC,5.5s), to be consistent with the PIDC procedure forassigning mb. The PIDC actually uses a time window lengthof 6.0 sec, beginning 0.5 sec before the P-wave arrival, how-ever, we will refer to this time window length as 5.5 secsince this corresponds to the length of time after the P-wave

arrival. This nomenclature is consistent with measurementsbased on 10-sec and 15-sec time window lengths, since thosewindow lengths are measured from the P-wave arrival time.

The amplitudes are measured as half trough-to-peak (orpeak-to-trough). Periods are estimated as twice the time be-tween the peak and trough corresponding to the measuredamplitude. Then, the peak-to-zero amplitude is corrected forthe instrumental response at the estimated period. The resultis displacement amplitude in nanometers at the estimatedperiod. Body-wave magnitude is assigned for each of theamplitudes and corresponding periods using equation (1).Since the PIDC uses Veith–Clawson corrections for distanceand depth, the magnitude corresponding to the mb publishedin the REB is indicated by mb(REB)VC,5.5s.

A comparison between our reproduced station mb(REB)and the published REB station mb is shown in Figure 5B forthe 4294 observations that have an amplitude and periodpublished in the REB catalog. The difference between thetwo magnitudes is �0.0140 on average, with r � 0.124.Since the PIDC uses an automated procedure with minimalanalyst override of measurements, we are able to match theirmeasurements better than those of the USGS, where analystoverride is more frequent. We do not include a correction


for the effect of the PIDC filter on the measured amplitudes,although the PIDC documentation does indicate that such acorrection is applied (International Data Centre, 1999). Incontrast to the large filter correction applied by the USGS,we expect this correction to be quite small—less than 10%on average. The frequency dependence of the PIDC displace-ment response in the 1 to 2 Hz frequency range of interest(Fig. 4) results almost entirely from the velocity-propor-tional instrument response.

Results

Individual Station Magnitudes

For each of the 31,280 broadband seismograms in thisstudy, we measure the signal amplitude (A) and period (T)using five different automated procedures to generate fivedifferent measurements: mb(P) from simulated WWSSNshort-period signals, mb(PDE) using time window lengths of10 sec and 15 sec, and mb(REB) using time windows of 5.5-sec and 15-sec duration. Moreover, for each of the five mea-surements of A and T, we compute an mb using both theVeith–Clawson and Gutenberg–Richter distance and depthcorrections; therefore, our results include 10 measurementsof mb per station for each event.

Effect of Focal Depth on Seismograms

Examples of waveforms processed using these differentprocedures are shown in Figures 6 and 7. In Figure 6 weshow the raw broadband signal as both velocity and dis-placement as well as the simulated WWSSN short-period rec-ord, the reproduced USGS short-period signal, and the re-produced PIDC short-period signal. The signals correspondto a deep (h � 612 km) earthquake with PDE bulletin mb

5.1, as recorded by station HIA (Hailar, China). For this verydeep earthquake, the simulated WWSSN, USGS, and PIDCwaveforms are strongly correlated and the correspondingamplitude and period values are similar (AWWSSN � 224 nm,TWWSSN � 0.6 sec, AUSGS � 241 nm, TUSGS � 0.6 sec, APIDC

� 204 nm, TPIDC � 0.5 sec). The maximum amplitude foreach of these three waveforms arrives within the first threeseconds after the P-wave arrival, so the choice of time win-dow is not an issue. The mb

GR values associated with theserecords are nearly equal: mb(P)GR � 5.93, mb(PDE)GR �5.96, and mb(REB)GR � 5.96. Although the amplitude mea-sured from the reproduced USGS short-period record inFigure 6 is smaller than the amplitude measured from repro-duced PIDC short-period signal, the corresponding displace-ment amplitude for the simulated USGS signal is larger thanthe PIDC displacement amplitude because the USGS appliesa large filter correction to their amplitude measurements.This filter correction is intended to compensate for the sig-nificant attenuation in signal amplitude that results from ap-plying the two USGS bandpass filters.

For a shallow earthquake, on the other hand, the simu-lated WWSSN, USGS, and PIDC waveforms can appear quite

different (Fig. 7). We show the raw broadband signal (inboth velocity and displacement) as well as the simulatedWWSSN short-period record, the reproduced USGS short-period signal, and the reproduced PIDC short-period signalin Figure 7. The records correspond to a shallow (h � 34km) PDE earthquake of mb 5.0 recorded at station BJT (Bei-jing, China). For this shallow event, the maximum ampli-tudes arrive much later in the wavetrain than for a deepevent. In this case, since the USGS and PIDC assign theirmagnitudes using time window lengths of less than 15 sec(10 sec and 5.5 sec, respectively), the amplitude that wouldbe assigned by these agencies is smaller than the maximumamplitude within the full 15-sec window (Fig. 7). For thesimulated USGS short-period waveform, the correspondingdisplacement amplitude is 28.3 nm (with a period of 1.0 sec)when measured in a window of length 10 sec and 27.4 nm(with a period of 0.85 sec) using a 15-sec window. The sim-ulated PIDC waveform has displacement amplitude of 16.5nm (with a period of 0.9 sec) when measured with a windowof length 5.5 sec and 19.7 nm (with period of 0.7 sec) usinga 15-sec window. The corresponding mb(PDE)GR,10s � 4.91and mb(PDE)GR,15s � 4.97; mb(REB)GR,5.5s � 4.72 andmb(REB)GR,15s �4.91. The simulated WWSSN SP signal hasmb(P)GR � 4.89. Since the USGS displacement amplitudehas been corrected for the effect of two filters, this displace-ment amplitude is greater than the corresponding PIDC dis-placement amplitude (even though the opposite is true forthe velocity amplitudes).

Relationship between mb(P), mb(PDE), and mb(REB)

One goal of this study is to investigate how well cor-related the automated USGS magnitude scale is to one basedon the WWSSN short-period instrumental response. In Fig-ures 8a and 8b, we show the relationship between mb(PDE)and mb(P) and find that the two measurements are stronglycorrelated over all depth ranges. ( E Color versions of thesefigures that include results for all six subsets of earthquakes[PDE bulletin mb 5.0 to 5.5] are available in the electronicedition of BSSA.) We expect that the depth range where thechoice of time window (either 5.5 sec, 10 sec, or 15 sec)will have the greatest effect on mb is from 15 to 50 km. Thisis because the direct-arrival P phase is often much smallerin amplitude than the surface-reflected depth phases pP andsP for earthquakes occurring at those depths. The arrival ofthe P-wave amplitude will also be affected by differences insource complexity. Many larger earthquakes are character-ized by slowly emerging P-wave amplitudes, and the max-ima are significantly delayed with respect to initial P-wavearrival times.

Since many of the shallow earthquakes studied are as-signed a default depth of 15 km in the Harvard CMT catalogand an exact depth is not available, we treat these eventsseparately. The mb(PDE) shown in Figure 8a uses a timewindow length of 10 sec, similar to the PDE procedure; incontrast, the window length for mb(PDE) in Figure 8b is


Figure 8. (a) Reproduced event mb(PDE) as a function of event mb(P) for PDEbulletin mb 5.0 and 5.5 earthquakes. Reproduced PDE measurements are made using atime window length of 10 sec (to approximate the time window used in the PDE bul-letin). Measurements of mb(P) are made using a 15-sec time window and the distanceand depth corrections for all magnitudes shown are Gutenberg–Richter (to match PDEbulletin). Correlation coefficient value (R) is shown for each plot. (b) Reproduced eventmb(PDE) as a function of event mb(P) for PDE bulletin mb 5.0 and 5.5 earthquakes. Bothmagnitude types are measured using a 15-sec time window. Distance and depth cor-rections for all magnitudes shown are Gutenberg–Richter. Correlation coefficient value(R) is shown for each plot. ( E Color versions of Figures 8a and 8b that include resultsfor all six subsets of earthquakes [PDE bulletin mb 5.0 to 5.5] are available in theelectronic edition of BSSA.)


Figure 9. (a) Reproduced event mb(REB) as a function of event mb(P) for PDEbulletin mb 5.0 and 5.5 earthquakes. Reproduced REB measurements are made using atime window length of 5.5 sec (to match the time window used in the REB catalog).Measurements of mb(P) are made using a 15-sec time window and the distance anddepth corrections for all magnitudes shown are Veith–Clawson (to match REB catalog).Correlation coefficient value (R) is shown for each plot. (b) Reproduced event mb(REB)as a function of event mb(P) for PDE bulletin mb 5.0 and 5.5 earthquakes. Both mag-nitude types are measured using a 15-sec time window. Distance and depth correctionsfor all magnitudes shown are Veith–Clawson. Correlation coefficient value (R) is shownfor each plot. ( E A Color versions of Figures 9a and 9b that include results for all sixsubsets of earthquakes [PDE bulletin mb 5.0 to 5.5] are available in the electronic editionof BSSA.)


Figure 10. Histogram showing the distribution ofoffsets between reproduced PDE event mb and PDEbulletin event mb for all earthquakes in the dataset.Each bin represents a range of offsets with width 0.1magnitude units.

15 sec to match mb(P) and eliminate any differences causedby different time window lengths. We find that mb(PDE) andmb(P) are strongly correlated for the range of magnitudesand depths studied. When the magnitudes are compared us-ing identical 15-sec time windows, the scatter is reduced(Fig. 8b); however, there exists a small offset between thetwo magnitudes, with mb(P) being slightly larger on average.

We also analyze the relationship between mb(REB) andmb(P), using both a 5.5-sec time window length (Fig. 9a)and a window length of 15 sec (Fig. 9b) to measure mb(REB).( E Color versions of these figures that include results for allsix subsets of earthquakes [PDE bulletin mb 5.0 to 5.5] areavailable in the electronic version of BSSA.) Unlike themb(PDE)–mb(P) relationship, we find a strong depth depen-dence when mb(REB) is compared to mb(P). Since the PIDCdisplacement response is peaked at a frequency that is muchhigher than 1 Hz (Fig. 4), this response is not suitable forshallow earthquakes because high frequencies are toostrongly attenuated. Although the USGS displacement re-sponse is also peaked at a frequency much higher than 1 Hz,magnitudes based on the USGS response are not as stronglyaffected as those based on the PIDC response because theresponses are shaped differently and because the PIDC re-sponse has a peak around 3.4 Hz, whereas the USGS re-sponse peaks around 2.6 Hz. Because the PIDC displacementresponse causes strong attenuation of high frequencies,mb(REB) values are too low compared to traditional mag-nitudes, for shallow earthquakes. The scatter is reducedwhen equivalent time window lengths are used (Fig. 9b),although the mb(REB)–mb(P) differences are still greater thanthe mb(PDE)–mb(P) differences. We find that because of dif-ferent time windows and response functions, mb(P) is greaterthan mb(REB) for almost every event. The fact that differ-ences between the magnitude scales decrease with increasingfocal depth, independent of time window length, suggeststhat these differences should also decrease with decreasingsource size as the dominant periods of P waves decrease.However, we expect that the events in this study are onlyslightly affected by this magnitude dependence since therange of magnitudes studied is narrow (i.e., PDE bulletin mb

5.0 to 5.5 events).

Discussion

Effect of Differing Seismic Networks on Event mb

Though we have emphasized the differences in mea-surement procedures for different magnitude scales as theyapply to station mb values, a strong contributor to differentvalues for published event mb is the fact that the USGS, thePIDC, and the ISC all use different sets of stations whenaveraging station mb values to obtain an event mb. The USGS,for example, maintains a strong interest in tectonic areassuch as the western United States and therefore receivesmore data from stations in those areas. Since stations in tec-tonic areas experience more attenuation than those in stable

continental regions, this leads to a network mb that is biasedlow. An example of the differences that can result from usingdifferent networks of stations is shown in Figure 10, whichcompares the reproduced event mb(PDE) with the PDE bul-letin event mb, for all 2009 earthquakes in our dataset. Thedifference between the two event magnitudes is �0.024 onaverage, with r � 0.16. This average difference of �0.024magnitude units is similar to the �0.0171 magnitude unitdifference observed between the reproduced station mb(PDE)and published station mb(PDE) shown in Figure 5a. An im-portant difference between Figures 5a and 10, however, isthat Figure 5a compares station magnitudes whereas Figure10 compares event magnitudes. Moreover, the two magni-tudes compared in Figure 10 are based on different networksof stations (Fig. 2) and the 120 stations in this study thatreported data to the USGS during 1996 to 1999 are only asubset of the complete USGS seismic network. Nevertheless,although the event magnitudes compared in Figure 10 arebased on different networks, on average, there is only a�0.024 magnitude unit difference between the magnitudes.

Because of discrepancies that can result from using dif-ferent networks of stations to assign event mb, we insteadreproduce the procedures of the USGS and PIDC so that wecan base our measurements on the same seismograms andfocus on the different protocols. Thus, for each broadbandseismogram we measure mb(P), mb(PDE), and mb(REB). Fora particular station, each of these magnitudes is computedusing the same distance and depth information; therefore,only the amplitudes and periods (i.e., log(A/T) in equation[1]) are different.


Table 1Comparisons between mb(P), USGS PDE mb, and PIDC REB mb

Average Event mb

(Using Gutenberg–Richter Distance and Depth Corrections) � r

Depth (km)No. ofEvents

mb(P)(tw*: 15 sec)

ReproducedPDE mb

(tw: 10 sec)

ReproducedPDE mb

(tw: 15 sec)

ReproducedREB mb

(tw: 5.5 sec)

ReproducedREB mb

(tw: 15 sec)Harvard

CMT Mw

PDE mb 5.0 Events h � 15 (fixed)† 172 5.02 � 0.15 4.96 � 0.17 5.00 � 0.16 4.72 � 0.20 4.81 � 0.18 5.38 � 0.2315 � h � 50 165 5.07 � 0.14 5.02 � 0.15 5.06 � 0.14 4.87 � 0.16 4.95 � 0.15 5.29 � 0.2150 � h � 300 107 4.98 � 0.18 4.98 � 0.18 4.99 � 0.17 4.87 � 0.17 4.90 � 0.17 5.25 � 0.17

300 � h � 700 19 5.05 � 0.19 5.06 � 0.19 5.06 � 0.19 4.97 � 0.19 4.97 � 0.19 5.42 � 0.18

PDE mb 5.1 Events 0 � h � 15 4 5.28 � 0.21 5.19 � 0.25 5.26 � 0.21 4.90 � 0.34 5.01 � 0.26 5.90 � 0.28h � 15 (fixed) 150 5.10 � 0.15 5.04 � 0.16 5.07 � 0.15 4.81 � 0.21 4.89 � 0.19 5.40 � 0.2115 � h � 50 161 5.14 � 0.15 5.09 � 0.15 5.13 � 0.15 4.93 � 0.17 5.01 � 0.15 5.33 � 0.2050 � h � 300 100 5.09 � 0.16 5.09 � 0.16 5.10 � 0.16 4.97 � 0.18 5.00 � 0.18 5.30 � 0.17

300 � h � 700 27 5.09 � 0.15 5.10 � 0.16 5.10 � 0.16 5.01 � 0.16 5.02 � 0.16 5.46 � 0.16


300 � h � 700 12 5.22 � 0.09 5.23 � 0.09 5.23 � 0.09 5.12 � 0.10 5.13 � 0.11 5.58 � 0.19


300 � h � 700 14 5.38 � 0.15 5.41 � 0.14 5.41 � 0.14 5.33 � 0.14 5.33 � 0.14 5.65 � 0.25


300 � h � 700 10 5.41 � 0.14 5.42 � 0.14 5.42 � 0.14 5.34 � 0.13 5.35 � 0.14 5.73 � 0.24


300 � h � 700 8 5.48 � 0.16 5.48 � 0.17 5.49 � 0.17 5.38 � 0.18 5.39 � 0.18 5.88 � 0.28

*Length of time window used to make the measurements, beginning at the P-wave arrival time.†No PDE mb 5.0 events with a focal depth less than 15 km are present in our dataset.

Differences between mb(P), mb(PDE), and mb(REB)

A summary of the differences we observe betweenmb(P)GR, mb(PDE)GR, and mb(REB)GR is shown in Table 1.Events are separated according to depth and PDE bulletinmagnitude. All body-wave magnitudes in Table 1 includeGutenberg–Richter distance and depth corrections (GR);therefore, any differences between the magnitudes resultfrom different time window lengths and response functions.Although the magnitudes published in the REB use Veith–Clawson corrections for distance and depth (VC), in Table1 we show mb(REB) using the Gutenberg–Richter correctionterms (i.e., mb(REB)GR), to be consistent with the other mag-nitude scales. By comparing the three magnitude scales us-ing the same distance and depth correction terms, we areable to examine the effects of different time window lengthsand response functions. We find that average mb(P)GR,15s andaverage mb(PDE)GR,10s are similar to one another, suggestingthat magnitudes based on the automated USGS procedure—

which has been used since 1991—are very similar to thosebased on simulated WWSSN short-period instruments with aslightly longer time window. Thus, we expect that magni-tudes assigned from WWSSN short-period instruments dur-ing the 1970s and 1980s are consistent with those assignedby the automated procedure used since 1991 by the USGS,providing stability in mb measurements over several decades.For mb(PDE)GR values assigned using a time window lengthof 15 sec instead of 10 sec, the 15-sec window producesmagnitudes that are only slightly larger than those based ona 10-sec window.

On the other hand, we find that for the mb(REB)GR mea-surements the short window length of 5.5 sec often resultsin a lower magnitude for shallow events. Assigningmb(REB)GR using the PIDC-defined time window length of5.5 sec, instead of 15 sec, lowers mb(REB)GR by an averageof approximately 0.1 magnitude units for shallow events. Incontrast, the deepest earthquakes show almost no depen-


Table 2Differences in mb Resulting from Different Time Window Lengths, Responses, and Corrections for Distance and Depth,

as a Function of Depth (PDE Bulletin mb 5.0–5.5 events)

Average Difference between Event mb Values

Depth (km)mb(P)GR,15s] �

[mb(PDE)GR,10s][mb(P)GR,15s] �

[mb(PDE)GR,15s][mb(P)GR,15s] �

[mb(REB)GR,5.5s][mb(P)GR,15s] �

[mb(REB)GR,15s][Average BGR] �

[Average BVC]

0 � h � 15 0.06 0.02 0.34 0.23 0.09h � 15 (fixed) 0.06 0.02 0.31 0.22 0.1215 � h � 50 0.05 0.01 0.20 0.13 0.1850 � h � 300 0.01 0.00 0.12 0.09 0.24

300 � h � 700 �0.01 �0.01 0.08 0.07 0.42

BGR, correction for distance and depth based on Gutenberg and Richter (1956); BVC, correction for distance and depth based on Veith and Clawson(1972).

dence on time window length. This result applies to bothmb(PDE)GR and mb(REB)GR, indicating that the length of thetime window used to measure amplitude matters only forshallow earthquakes, where the depth phases (pP and sP)are often the largest arrivals. Regardless of time windowlength, however, mb(REB)GR is substantially lower thanmb(P)GR for shallow earthquakes because of differences be-tween the PIDC displacement response and WWSSN dis-placement response (Fig. 4). The PIDC response, which ispeaked at a much higher frequency than the WWSSN re-sponse, is not suitable for shallow earthquakes because thedominant frequencies in the radiated signal are oftenstrongly attenuated. Although the USGS displacement re-sponse is also peaked at a frequency much higher than theWWSSN response, magnitudes based on the USGS responseare not as strongly affected as those based on the PIDC re-sponse since the PIDC response is peaked at a significantlyhigher frequency than the USGS response (3.4 Hz vs.2.6 Hz).

Moment magnitudes from Harvard CMTs are also givenin Table 1 and are found to be greater on average than allof the body-wave magnitudes. ( E A discussion of the rela-tionship among mb(P), Mw, and Ms for the events studied isavailable in the electronic edition of BSSA.)

Summary of Factors Contributing to DifferencesBetween the mb Scales

In Table 2, we give a summary of the factors contrib-uting to the observed differences between the mb scales stud-ied. When equivalent 15-sec time windows are used, theaverage difference between mb(P)GR and mb(PDE)GR is closeto zero for all depth ranges. On the other hand, if mb(PDE)GR

is measured using a time window length of 10 sec, a dis-crepancy does exist between mb(P)GR and mb(PDE)GR forshallow earthquakes (h � 50 km). In this case, the shorter10 sec window misses some of the larger depth phase arriv-als, causing the amplitudes to be underestimated; thus,mb(P)GR,15 sec will exceed mb(PDE)GR,10 sec by 0.05 to 0.06magnitude units.

For earthquakes with focal depths of 15 km or less, theaverage mb(P)GR is 0.22 to 0.23 magnitude units greater thanmb(REB)GR when equivalent 15-sec time windows are used.If mb(REB)GR is measured using the PIDC-defined windowlength of 5.5 sec, however, then the mb(REB)GR value willbe lowered by an additional 0.10 to 0.11 magnitude units(when h � 15 km). While the choice of time window—either5.5 sec or 15 sec—for the REB magnitudes has almost noeffect for the deepest earthquakes (h � 300 km), an averagedifference of 0.07 magnitude units exists betweenmb(P)GR,15s and mb(REB)GR,15s for deep events because ofdifferences between the PIDC and WWSSN responses.

Although the difference between mb(P) and mb(REB) issmallest for deep earthquakes, a large discrepancy betweenREB and PDE bulletin magnitudes exists for earthquakes atall depths (Murphy et al., 2001). This is because the PIDCand USGS use different corrections for distance and depth(Veith–Clawson and Gutenberg–Richter, respectively) whenassigning mb. The Gutenberg–Richter corrections are greaterfor all depths and become increasingly greater than theVeith–Clawson corrections as depth increases. We find thatthe Gutenberg–Richter corrections are an average of 0.42magnitude units higher for the deepest earthquakes (h � 300km). This large observed difference between the Veith–Clawson and Gutenberg–Richter corrections for deep earth-quakes agrees with Murphy and McLaughlin (1998), whofound that the difference between the two corrections canexceed 0.6 magnitude units for earthquakes in the 600- to700-km-depth range. Thus, a large offset exists betweenpublished REB and PDE magnitudes for deep earthquakeseven though the attenuating effects of the PIDC filter areminimal. Differences between published REB and PDE mag-nitudes for shallow earthquakes result primarily from thedifferent responses, whereas for deep earthquakes the dif-ferences are primarily the result of different corrections fordistance and depth.

The average period for all station observations, whenmeasured in 15-sec time windows, is 0.99 sec for the sim-ulated WWSSN SP signals, 0.86 sec for the reproduced PDEwaveforms, and 0.80 sec for the simulated REB records.Since these periods are all measured using the same time


window length, the differences between them are mainly theresult of different response functions (Fig. 4) and differencesin the type of signal from which the period is measured (i.e.,WWSSN waveforms are simulated from displacement sig-nals; PDE and REB records are simulated from velocity seis-mograms). Since the average periods of the PDE and REBrecords differ by only 0.06 sec the differences between thetwo for a fixed time window are also due in part to a depen-dence on source corner frequency. This is only a slight ef-fect, however, and not as big as the factors we address inthis study since the range of magnitudes studied is narrow(i.e., PDE bulletin mb 5.0 to 5.5 events). Because the averagereproduced PDE and REB periods are less than 1.0 secs thiswill increase the log(A/T) portion of the mb calculation rela-tive to WWSSN signals with periods near 1.0 sec. Repro-duced PDE and REB records have periods much less than 1.0sec because of the high-frequency passbands of the USGSand PIDC responses and because the periods are measuredfrom velocity seismograms.

Conclusions

We obtain body-wave magnitude (mb) measurementsfor 2009 earthquakes from 1996 to 1999 listed in the PDEbulletin having mb between 5.0 to 5.5 and that also havemoment tensor solutions available from the Harvard CMTcatalog. A total of 31,280 broadband seismograms are ana-lyzed for an average of 15 stations per event. The seismicstations recording the largest number of earthquakes are lo-cated predominantly on the Eurasian continent. For eachbroadband seismogram studied, three different types of mag-nitude are assigned: mb(PDE), mb(REB), and mb(P). We re-produce both the automated protocol followed by the USGSto assign body-wave magnitude, mb(PDE), and the auto-mated procedure used by the PIDC to assign magnitude,mb(REB). By reproducing the automated procedures of theseagencies, we can base our measurements on the same seis-mograms and eliminate the discrepancies that result fromusing different networks of stations. Since neither the PDEnor the REB magnitude scale is based on a specific instru-ment, we compare the reproduced PDE and REB magnitudesto a traditional magnitude measurement, mb(P), that is basedon the Worldwide Standard Seismographic Network(WWSSN) short-period instrument, used for about 20 yearsbefore digital instruments became widely available. The tra-ditional method (mb(P)) is based on displacement measure-ments, whereas the PDE and REB measurements are basedon velocity signals.

Differences between mb(PDE), mb(REB), and mb(P) arisefrom four factors: response function, time window length,corrections for hypocentral depth, and corrections for epi-central distance. We find that mb(PDE) and mb(P) arestrongly correlated for the range of magnitudes and depthsstudied, with mb(P) being larger by an average of 0.04 mag-nitude units, when mb(PDE) is measured using a 10-sec time

window. The PDE window length of 10 sec when comparedto a traditional window length of 15 sec, has only a minoreffect on mb(PDE). When equivalent 15-sec, time windowsare used, magnitudes based on WWSSN short-period instru-ments are very similar to those based on the automated pro-cedure used since 1991 by the USGS.

In contrast to the similarity between mb(PDE) and mb(P),we find a strong dependence on depth, response function,and time window length when mb(REB) is compared tomb(P). Because the PIDC displacement response is peakedat a much higher frequency (�3.4 Hz) than either the USGS(�2.6 Hz) or WWSSN response (�1.6 Hz), magnitudesbased on the PIDC procedure (i.e., mb(REB)) are too smallfor shallow earthquakes. The high-frequency passband of thePIDC response causes the short-period portion of the signalto be attenuated too strongly, compared to a traditional mea-surement. The observed differences between REB and PDEbulletin magnitudes for shallow earthquakes result primarilyfrom the different response functions whereas for deep earth-quakes the differences are primarily the result of differentcorrections for distance and depth. For consistency withmb(P) and mb(PDE), the PIDC could produce a classical mb

measurement in addition to its current mb(REB), styled aftereither the mb(P) or mb(PDE) procedure. This classical mea-surement would be a very useful and important source pa-rameter since it would be based on a fixed network of sta-tions and would be consistent with magnitudes measuredusing WWSSN short-period instruments. We also recom-mend that the PIDC continue to assign magnitudes using itscurrent procedure since the PIDC mb, being a higher fre-quency measurement, may work better than a traditionallymeasured magnitude such as mb(P) for purposes of applyingthe mb–Ms discriminant.

Since PDE bulletin magnitudes are based on Gutenberg–Richter distance and depth corrections, whereas publishedREB magnitudes are based on Veith–Clawson corrections,using different correction terms causes additional differencesbetween the two magnitudes. The Gutenberg–Richter cor-rections are greater for all depths and become increasinglygreater than the Veith–Clawson corrections as depth in-creases. The deepest earthquakes show an average separa-tion of 0.4 magnitude units between the Gutenberg–Richterand Veith–Clawson correction terms.

Acknowledgments

We would like to thank Jack Murphy and an anonymous reviewer fortheir helpful reviews of the manuscript. We benefited greatly from com-ments by Ray Buland, Jim Dewey, and Scott Phillips. Data were retrievedfrom the Incorporated Research Institutions in Seismology (IRIS), DataManagement Center in Seattle, Washington. The Generic Mapping Tools(GMT) software package of Wessel and Smith (1998) was used to makeFigures 1 and 2. This research was sponsored partly by the Defense ThreatReduction Agency under Contract DTRA01-00-C-0074 and DTRA01-00-C-0031 and also partly by the Department of Earth and EnvironmentalSciences, Columbia University. This is Lamont-Doherty Earth ObservatoryContribution Number 6808.


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understanding the differences between three teleseismic m scalesrichards/my_papers... · 2005. 10....

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