Bulletin of the Seismological Socmty of America, Vol 72, No. 2, pp , April MAGNITUDE: THE RELATION OF ML TO m~lg

Transcription

1 Bulletin of the Seismological Socmty of America, Vol 72, No. 2, pp , April 1982 MAGNITUDE: THE RELATIN F ML T m~lg BY RBERT B. HERRMANN AND TT W. NUTTLI ABSTRACT The molg magnitude developed by Nuttli (1973) for the Central United States is adapted to other regions of the world by incorporating a specific term for the spatial coefficient of inelastic attenuation 7. Using region-specific y values, mblg values are determined for earthquakes occurring near the WWSSN stations BKS, GSC, and DUG. A comparison of the molg values with published ML magnitudes shows that these two magnitude scales are essentially equivalent between magnitudes 3 to 5. Because of this observation, we now have a direct way of comparing Eastern and Western United States earthquake sizes for the purpose of adapting western strong motion data bases to the east and also for understanding teleseismic magnitude biases. INTRDUCTIN Earthquake magnitude is an often specified seismic source parameter, is relatively easy to determine under certain circumstances, and at the same time, is poorly understood. A magnitude scale is properly defined in terms of a particular seismic phase observed on a particular seismograph at a particular frequency. Difficulties arise when a magnitude scale in one region must be compared to that in another. Such a situation has arisen in the Eastern United States. Because of the absence of recent destructive earthquakes in the Eastern United States, the strong ground motion data base required for earthquake engineering purposes does not exist. To be able to make some design decisions now, the extensive Western United States strong motion data base is being extrapolated to the Eastern United States. The scaling of strong ground motion is a function of the physics of the earthquake itself and the propagation medium. Recent work by Singh (1981) has provided detail on the variation of 1 and 2 Hz Qz of the Lg phase in the coterminous United States. n the other hand, the earthquake source physics is usually accounted for by a single parameter: magnitude. Herein lies the problem. The ML magnitude is usually used for California earthquakes while an mblg is used for the Central and Eastern United States. To define the mblg magnitude scale, Nuttli (1973) tied it to the teleseismic mb of three Central United States earthquakes. Nuttli et al. (1980) determined mb and Ms for a suite of Central and Eastern United States earthquakes and for a set of larger Western United States earthquakes. Chung and Bernreuter (1981) noted that the mb versus Ms data for the east differed from the corresponding mb versus Ms populations for the west, with the eastern mb being 0.35 mb units larger than the western mb for a given Ms (Figure 1). The difference in populations could be ascribed to the effect of focal mechanism on teleseismic m~, to different spectral content of the eastern and western earthquakes at 1.0 Hz, or to differences in upper mantle Q structure. Chunc and Bernreuter (1981) preferred the upper mantle Q structure explanation since this would also be an explanation of regional variations in mb magnitude station corrections (North, 1976). Nuttli et al. (1980) compiled enough data to permit an empirical relation between western teleseismic rnb and ML for Western United States earthquakes. Assuming that Q structure variations control teleseismic m~, we could attempt to relate mbl~ 389

2 390 RBERT B. HERRMANN AND TT W. NUTTLI m the east to ML by subtracting 0.35 magnitude units from the eastern mbl to estimate an equivalent western teleseismic mb and then use the relation between mb and ML in the west. This approach is unsatisfying since the use of an intermediate empiricism clouds the issue. The object of this paper is to establish a methodology for determining mblg for Western United States earthquakes directly, which will then be correlated with published ML. To do this, we will first review the definitions of ML and mbl~ and then extend the mblg scale to the Western United States by taking into account differences in Lg anelastic attenuation. MAGNITUDE SCALES Richter (1935) developed a method for instrumentally classifying the size of southern California earthquakes. Using a network of Wood-Anderson torsion seismographs {Anderson and Wood, 1925), he developed a local magnitude scale, ML. EAST % _Q E FIG. 1 Plot of mb versus Ms for Eastern and Western United States earthquakes. The lower hne is mb = Ms. The upper hne is raised 0 35 magnitude units vertically above the lower hne Ns The local magnitude of an earthquake is defined by the relation ML = logloa(a) - logloao(h), where A (A) is the maximum trace amplitude in millimeters at an epicentral distance h observed on a horizontal Wood-Anderson torsion seismograph with a natural period of 0.8 sec, a damping factor of 0.8 critical, and a static magnification factor of The Ao(h) curve describes the distance variation of the maximum trace amplitude of a magnitude zero earthquake. The local magnitude scale has been used consistently in central and southern California since its definition and forms a basis for comparing earthquakes of the past 50 yr. However, as noted explicitly by Richter (1958), the definition of local magnitude was not meant to apply to geographical regions other than where it was defined. In order to classify Central United States earthquakes, Nuttli (1973) defined an mbl~ scale which was based on the sustained (third largest peak) Lg amplitude

3 MAGNITUDE: THE RELATIN F ML T mblg 391 recorded on a short-period vertical WWSSN seismograph. This seismograph consists of a Benioff short-period vertical seismometer with a natural frequency of 1.0 Hz and a galvanometer with a natural frequency of 1.3 Hz. Because of the large seismometer inductance, the system response falls off more rapidly above 3.0 Hz than expected for a simple seismometer-galvanometer system. The Lg phase is the largest amplitude arrival and travels with a group velocity of about 3.5 km/sec. It is well recorded in eastern North America, even out to distances of 20. To specify the decrease of the observed amplitude with distance, Nuttli (1973) noted that the observed amplitudes could be fit by the model A(A) = AoA-5/%xp(-- ),h), (2) where 3, is the anelastic attenuation coefficient. Equation (2) represents the spatial decay of an Airy phase of a surface wave propagating in an anelastic medium. Using data from three earthquakes, Nuttli (1973) was able to specify ~, for the Central United States. Fortunately, the earthquakes used to specify 7 were large enough to be recorded teleseismically so that Ao could be defined in terms of teleseismic mb. Nuttli (1973) presented his mblg relation in the form mble = logma + loglo(a/t), (3) where h is the epicentral distance in degrees, A is the instrument-corrected vertical component sustained ground motion in microns, and T is the period of the Lg wave in seconds. Equation (3) is valid in the distance range of 4 to 30 and was constrained by noting that the amplitude decay with distance of equation (2) could be fit by a straight-line segment in the given distance range. A more general formula would be to use equation (2) directly to yield mbng = -- 1ogl0A0 + (~)logl0 A + ~/51ogl0e + logt0a, (4) where we now restrict the use of (4) to T = 1.0 _ 0.2 sec and choose A0 such that an mblg = 5.0 earthquake is one with an amplitude of 115 #m at an epicentral distance of 10 km. Using this definition of mblg to specify Ao, equation (4) becomes mblg = log10 h + ~/(h )logme + logma (5) where/~ is in degrees and A is in microns, and (5) is valid only for periods near 1.0 sec. Equation (4) is quite general, but requires a determination of ), before it can be used. Establishing a region-specific form for equation (5) was not too difficult to do in the central, southeastern, and northeastern United States (Nuttli, 1973; Street, 1976; and Bollinger, 1979) because it turned out that 7 varied so little in these regions, that a broad distribution of seismograph stations could be used to obtain 7 from a study of a single, well-recorded earthquake. Nuttli (1973) estimated ~/= 0.07 deg -1 for the Central United States; Street found 7 = 0.11 deg -1 for the northeastern United States, and Bollinger (1979) found values for ~/between 0.07 deg -1 and 0.10 deg -1 for the southeastern United States. A direct determination of y in the Western United States from observed Lg amplitudes has not yet been attempted because of expected variations in ~, and poor seismograph station distribution. Until recently, these problems have not permitted the extension of mblg to the Western United States. Herrmann (1980) developed a

4 392 RBERT B. HERRMANN AND TT W. NUTTLI method for estimating coda Q from the records of short-period WWSSN seismographs. He was also able to show that the coda Q obtained was quite consistent with 7. He was able to estimate y by using the coda to correct for earthquake size and then estimate y by using data from many earthquakes recorded at a single station. He found ~/= _ 0.14 deg -1 for a broad region about BKS and Y = _ 0.11 deg -] for a region about DUG. Recently Singh (1981) applied the technique developed by Herrmann (1980) to provide contour maps of coda Q at 1.0 Hz for the coterminous United States. He was also able to estimate Y values, obtaining 0.66 _+ 0.16,deg -1 for the region about GSC. Using these recently determined 7 values, we are able to use (5) to estimate mblg for earthquakes occurring in places other than the Eastern or Central United States. mblg VERSUS ML The data used in the analysis are earthquakes recorded by the WWSSN shortperiod vertical seismographs at Goldstone, California (GSC), Berkeley, California 5 BKS (D o~-~/ / en3 ~ ~ E i 2 3 ~ 5 HL FIG 2. Plot ofmblg versus ML from the BKS data Hypocenter reformation and ML values were taken from Bolt and Miller (1975) (BKS), and Dugway, Utah (DUG). These stations were chosen because earthquake catalogs published at Pasadena (Hileman et al., 1973). Berkeley (Bolt and Miller, 1975), and Salt Lake City (Richins, 1979) list ML's for the local earthquakes. In the case of the Pasadena and Berkeley bulletins, the ML used is as defined by Richter (1935), while the ML used at Salt Lake City is based on Wood-Anderson records, and the southern California ML calibration function for larger events, and an empirical ML relation using coda duration for smaller events. Even though the y values given above indicate a difference in attenuation between California and Utah, the Salt Lake data were from distances less than 200 km, so that the effect of a different attenuation relation on magnitude should be less than 0.2 magnitude units. The Utah events studied are those which had a Wood-Anderson ML estimate. The analysis performed is very straightforward. Selecting earthquakes for which ML is given in the regional catalogs, l-sec sustained Lg amplitudes were read from the short-period vertical WWSSN seismograph in the respective region. Using a Y

5 MAGNITUDE: THE RELATIN F ML T mblg 393 value for that region, the instrument magnification corrected ground motion amplitude was used with equation (5) to calculate ruble. These data were then plotted versus the ML listed in the catalogs. We used 7 = 0.55 deg -~ for BKS and GSC and y = 0.39 deg -~ for Utah earthquakes recorded at DUG, GL, ALQ, and TUC. Figures 2 to 4 show the results for BKS, GSC, and Utah, respectively. In each of GSC (!) ~'4fi~m 8 o E 2 o 1 0 o i 5 4 g ML FIe. 3. Plot of ruble versus ML from GSC data. Hypoeenter reformation and ML values were taken from Htleman et al. (1973) 5 DUG 0 AL@ [] GL ±,~ TUC <> J 5 2 'A 05 1 ML FxG. 4. Plot of mblg versus ML for Utah data. Hypocenter reformation and MI. values were taken from Rmhlns (1979) these figures, a straight line mblg = ML is plotted. In the case of GSC, one can conclude that mblg -~ ML over a range of 2.5 orders of magnitude. The correlation coefficient between mble and ML is 0.81 with a standard error of 0.35 mble units about the relation mb = ML. For BKS, mble overestimates ML for smaller magnitude events but estimates ML fairly well for magnitudes greater than 3.5. The correlation

6 394 RBERT B. HERRMANN AND TT W. NUTTLI coefficient is 0.83 while the standard error is 0.51 mbl units. Fewer data are available for the Utah events, so data from DUG, ALQ, TUC, and GL were combined on the assumption that $ did not vary significantly over the region. The correlation coefficient between mblg and ML is 0.81 v~ith a standard error of 0.35 mblg units about the model mblg = ML. There is a great deal of scatter in these plots, somewhat more than usually found in magnitude determinations. It should be recalled however that the mbng determinations are single station determinations rather than better behaved network averages. NV 16, 1964 m b 4.5 M L ~ = mblg 4.94 BKS \ t]) z rr 10- Z 7= 0035kin -1 CR TUC _ AMPLtTUDES CRRECTED FR R -5/6 SPREADING T 10 KM BZ LN o o \ GL o I I I I I I I KM FIc. 5. Plot of geometrical spreading corrected Lg amphtudes versus epmentral distance for the earthquake of I6 November 1964, 36,93 N, W, 02 46:41,6 UTC. Figures 2 to 4 indicate that m~lg - ML is a reasonable inference. It is possible to test this inference using a display introduced by Nuttli (1980). Sustained Lg amplitudes, corrected for instrument response, are obtained from a number of seismographs recording the same earthquakes. The amplitudes are corrected for the h -5/~ geometrical spreading back to a reference distance of 10 km = These reduced amplitudes are next plotted versus distance in a semi-logarithmic plot. According to equation (2), the effect of anelastic attenuation would appear as a

7 MAGNITUDE: THE RELATIN F ML T mblg 395 straight line in such a plot. Assuming that m~lg = ML, a straight line, constrained by the appropriate 10-km intercept, is passed through the data. This was done for two earthquakes studied by Nuttli et al. (1980). The data for these two earthquakes are plotted in Figures 5 and 6. In both cases, the straight line slope corresponded to y = km -1 = 0.39 deg-', which represents an average y for the paths to the WWSSN stations used. These figures are interpreted as supporting the inference that mbl = ML. SEP 25,1965 m b 4.7 NI L z o n- 10- c.) TUC o ~ DUG _ AMPLITUDES CRRECTED FR R -516 SPREADING T 10 KN CR\ I I I I I l I KM Fl6. 6. Plot of geometrical s!dreading corrected Lg amphtudes versus epmentral distance for the earthquake of 25 September 1965, 34.69~N, W, 17.43:43.7 UTC. DISCUSSIN The conclusion of this study is that mblg = ML, in the magnitude range 3 to 5. By this we mean only that the numbers obtained are almost identical. This agreement is accidental, but is pleasant nonethe]ess. It is accidental because the ML magnitude used the peak amplitude recorded on a Wood-Anderson horizontal torsion seismograph, irrespective of frequency or wave type. The concept of magnitude was extended to teleseismic P waves by Gutenberg to establish the m scale which used periods greater than 1.0 sec. The mb scale for teleseismic P waves uses the Gutenberg

8 396 RBERT B. HERRMANN AND TT W. NUTTLI attenuation form, but uses periods only near 1.0 sec. Finally, Nuttli (1973) used the teleseismic mb to establish mblg. If we accept the inference that mblg = ML, we can now address the relationship between these quantities and teleseismic mb. Chung and Bernreuter (1981) performed a regression between teleseismic m~ and ML for the Western United States data given in Table 1 of Nuttli et al. (1980). Assuming that My is error-free, they found mb = 0.99ML Since we have inferred that ML = mblg and since mole was tied to teleseismic mb in the east by definition, we would conclude that mb(west) = 0.99m~(east) , which is similar to the inference obtained from Figure 1. Since both mb and mblg sample 1.0-sec source excitation and because we use a region-specific ~, value to correct for anelastic attenuation in the crustal waveguide, through which the Lg propagates, we attribute the east-west mb bias to differences in upper mantle structure. Because this bias may exist in other parts of the world, mblg would seem to be able to give better estimates of the l-sec spectral characteristics of the seismic source than teleseismic mb would. Nuttli (1980) found that Iranian earthquakes with teleseismic mb= 5.0 have a 10-km Lg-amplitude intercept of 270 /Am, which is equivalent to a 0.37 magnitude unit teleseismic mb bias with respect to the Central United States. This paper also suggests some changes in the use of data contained in Table 1 of Nuttli et al. (1980). Regressions should not be made between seismological parameters such as Io, Ms, or others and mb without recognizing the inherent bias between the Eastern and Western United States. Regressions would be better performed using mblg and/or ML. ne source of possible teleseismic bias not considered is the effect of different earthquake focal mechanisms on teleseismic P-wave magnitudes. We realize that we have not demonstrated the equivalence of mblg and ML for magnitudes greater than 5.0. It is these larger magnitudes which are of engineering significance. However, it should be possible to pass the vertical components of strong ground motion acceleration records through a numerical short-period WWSSN seismic instrument in a manner similar to that used by Kanamori and Jennings (1978) to synthesize Wood-Anderson records for large nearby earthquakes. nly by doing this would we be able to define the relation between mblg and ML more precisely. ACKNWLEDGMENTS We wish to thank Suleiman Ahmed for reading the necessary seismograms This research was sponsored in part by the U S Nuclear Regulatory Commission under Contract NRC , by the U S Geologmal Smvey under Contract , by NSF Grant PFR , and by the Defense Advanced Research Projects Agency (monitored by the Air Force ffice of Scmntlfic Research) under Contract F C REFERENCES Anderson, J. A and H. Wood (1925). Descnphon and theory of the torsion selsmometer, Bull Se~sm. Soc Am 15, 1-72 Bolhnger, G A (1979) Attenuatmn of the Lg phase and the determination of m~ m the southeastern Umted States, Bull Selsm. Soc. Am. 69,

9 MAGNITUDE: THE RELATIN F ML T mblg 397 Bolt, B A and R. D Miller (1975) Catalogue of Earthquakes m Northern Cahfoyma and Adjommg Areas" 1 January December 1972, Seismographic Stations, University of Cahforma, Berkeley, Cahforma, 567 pp. Chung, D H and D L Bernreuter (1981) Regional relationships among earthquake magmtude scales, Rev Geophys Space Sct. 19, Herrmann, R B. (1980) Q estimates usmg the coda of local earthquakes, Bull Selsm Soc Am. 70, Hfleman, J. A., C R. Allen, and J M Nordqmst (1973). Se~smtctty of the Southern Cahfornm Regton 1 January 1932 to 31 December 1972, Seismological Laboratory, California Institute of Technology, Pasadena, California Kanamola, H. and P. C. Jennmgs (1978) Determination of local magnitude, ML from strong-motion accelerograms, Bull. Se~sm Soc. Am. 68, North, R G. (1976) Station biases in body-wave magnitude (abstract), Transacttons, American Geophystcal Umon ES 57, 955. Nutth,. W (1973). Seismic wave attenuation and magnitude relations for eastern North Amerma, J. Geophys Res 78, Nutth, W. (1980) The excitation and attenuation of seismic crustal phases in Iran, Bull. Se~sm. Soc Am. 70, Nutth, W., G. A. Bolhnger, and D W. Griffiths (1980). n the relation between modified Mercalli mtenslty and body-wave magnitude Bull Se~sm Soc Am 69, Richms, W. D. (1979). Earthquake data for the Utah region, 1850 to 1978, in Earthquake Studtes m Utah 1850 to 1978, W. J Arabasz, R B Smith, and W. D. Richms, Editors, University of Utah Seismograph Stations, Department of Geology and Geophysics, University of Utah, 552 pp. Richter, C. F. (1935). An instrumental magnitude scale, Bull. Setsm Soc Am 25, Richter, C F. (1958}. Elementary Seismology, W H. Freeman and Company, San Francisco, Singh, S (1981) Regionalizatlon of crustal Q in the continental United States, Ph.D. D~ssertatmn, Samt Louis University, St. Lores, Missouri, 184 pp Street, R. L. (1976). Scaling northeastern Umted States/southeastern Canadian earthquakes by their Lg waves, Bull. Setsm Soc Am. 66, DEPARTMENT F EARTH AND ATMSPHERIC SCIENCES SAINT LUIS UNIVERSITY P.. BX 8099, LACLEDE STATIN SAINT LUIS, MISSURI Manuscript received 29 September 1980