Tectonophysics, 93 (1983) 207-223

Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands

207

EMPIRICAL MAGNITUDE AND SPECTRAL SCALING RELATIONS FOR MID-PLATE AND PLATE-MARGIN EARTHQUAKES

OTTO W. NUITLI

Department of Earth and Atmospheric Sciences, Saint Louis University, St Louis, MO 63103 (U.S.A.)

(Received September 23. 1982)

ABSTRACT

Nuttli, O.W., 1983 Empirical magnitude and spectral scaling relations for mid-plate and plate-margin

earthquakes, In: S.J. Duda and K. Aki (Editors), Quantification of Earthquakes. Tectonophysics. 93:

207-223.

Published values of body-wave magnitude mb, surface-wave magnitude, MS, and seismic moment, M,,

for mid-plate and plate-margin earthquakes, are analyzed, to determine their inter-relationship and to

develop scaling laws for earthquake spectra. All of the plate-margin earthquakes used in the study

occurred near the border of the Pacific Ocean. The mid-plate earthquakes occurred in both continental

plate interiors and oceanic plate interiors.

For mid-plate earthquakes the m,,- M, relation can be represented by two straight lines, of slope one

and two. The intersection of the two lines corresponds to the body-wave magnitude for which the comer

period of the spectrum is at 1 sec. The Mb- MS relation for plate-margin earthquakes is more

complicated, because the derived spectra exhibit two corner periods.

A principal feature of the mb- M, and MS-M, relations is the fact that the large plate-margin

earthquakes have a higher M, value than the mid-plate earthquakes, for the same m b or Ms. Because m b

is a measure of the spectral amplitude for frequencies at which damaging ground motion occurs, and M,

is a measure of the spectrum at very long periods, it follows that mb is a good estimator of strong ground

motion, whereas a moment-derived magnitude is not. The latter, however, is a good measure of fault

rupture area.

The derived spectra of the mid-plate earthquakes are flat at the long periods, and have a slope of two

at the short periods. Their seismic moment varies as the fourth power of the corner period, implying that

the stress drop increases as the moment increases. For the large plate-margin earthquakes the derived

spectra are flat at the long periods, have a slope of one at intermediate periods, and a slope of two at short

periods. The stress drops are almost independent of moment for the larger plate-margin earthquakes.

The moment-magnitude relations for mid-plate earthquakes indicate that an MS = 8.7 event requires a

fault rupture length of only 60 km, for a fault width of 20 km. A plate-margin earthquake of M, = 8.7 and

fault width of 20 km would require a fault length of 6000 km, obviously impossible. Assuming a fault

width of 20 km, an MS = 8.2 earthquake has a rupture length of about 850 km, which is as large as can be

expected for strike-slip faults, such as the San Andreas of California. Subduction zone earthquakes, on the

other hand, if they have fault widths as great as 200 km, can give rise to MS = 8.7 earthquakes.

tNTRODUCTION

The first magnitude scale. which was proposed by Richter ( 1935). was the local

magnitude, M,, for southern California earthquakes. To assign magnitudes to

earthquakes in other parts of the world, Gutenberg and Richter (1936) developed a

surface-wave magnitude, A4,, and Gutenberg f 1945a.b) a body-wave magnitude, ~2~.

Gutenberg and Richter attempted to adjust the arbitrary constants in the ?I~ and MS

equations so that the numerical values of M,, mh and MS would be the same for a

given earthquake. However, earthquake spectra do not scale in a manner which

allows this objective to be achieved. Later this fact was realized by Richter and

Gutenberg, who developed empirical equations to relate the three types of magni-

tude to one another {see, e.g., Richter, 1958). However, seismologists and engineers

still often speak of a magnitude of an earthquake, without specifying the scale

being used. Many published studies of strong ground-motion attenuation suffer

from a mixture of the various magnitudes. without correcting for their numerical

differences. For example, in Californiait is common to call Richter magnitude the

N, value for earthquakes for which Mt. is approximately less than 6.5. and the MS

value for the larger earthquakes. But an M, of 6.5 is equivalent to an M, of 7.5.

which introduces a discontinuity into the relation. It would be desirable to reserve

the term Richter magnitude exclusively for Mr. By this logic the 1906 San

Francisco earthquake had a Richter magnitude of 6.75-7 (Jennings and Kanamori,

1979). but an MS of 8.25 (Bolt, 1968).

Hanks and Kanamori (1979) pointed out that saturation of the mh scale occurs at

around 7 when 1-set period waves are used. They noted that mh prior to 1960 was

obtained by using longer period wave amplitudes. which gave mh values consider-

ably greater than 7. They also noted that no California earthquake had an M,

greater than 6.8 or an MS greater than 8.3. These saturation levels (about 7 for 1-set

~lr,., and 8.5 for 20set MS) exist because for large enough earthquakes, all of these

narrow-band time domain amplitude measurements no longer measure gross faulting

characteristics but only limited conditions on localized failure along crustal fault

zones (Hanks and Kanamori, 1979). To overcome these saturation problems they

proposed a scale of moment magnitude, which they empirically related to the

radiated seismic energy under the assumption that the stress drop is constant for shallow earthquakes. This moment magnitude is directly proportional to the very

long period amplitude level of the spectrum. When it was empirically related to Mt,,

mh and Ms. by Hanks and Kanamori (t979), the assumption was made that stress

drop is independent of seismic moment. It will be shown later that this assumption

of constant stress drop is valid for most California earthquakes, which Hanks and

Kanamori (1979) were considering, but is not valid for mid-plate earthquakes. Thus

the best magnitude scales for estimating near-field strong ground motion remain M,~

and mb, because they are a direct measure of the amplitude of the ground motion at

periods near 1 sec. The moment magnitude, on the other hand. is a measure of the

209

fault rupture area and the seismic moment, gross source properties of interest for

some geophysical problems, but not for estimating strong motion. Moment magni-

tude can be related to short period ground motion in the manner described by

Hanks and Kanamori (1979) only if the average stress drop is constant over the

observed range of seismic moments.

The data to be presented in this paper are empirical, taken from the published

works of many investigators. They consist of pairs of mb, Ms and IV, values. For

some earthquakes all three parameters have been determined, resulting in three pairs

of values. For other earthquakes only two of the parameters are available, and thus

just one of three possible pairs. The data are broken down into two basic types,

plate-margin earthquakes and mid-plate earthquakes. In this study the former have

been restricted to earthquakes occurring near the margin of the Pacific Ocean. The

latter include both mid-continental and mid-oceanic plate earthquakes. Not used

were data from earthquakes that sometimes are called intra-plate, such as in the

Himalayas, China, and the Colorado Plateau and Basin and Range regions of the

western United States, which probably are intermediate in character between true

plate-margin and mid-plate earthquakes.

m b - Ms RELATIONS

Figure 1 shows the relation between mb, obtained from I-set period waves, and

Ms, obtained from 20-set period waves, for mid-plate earthquakes. The letter

symbols indicate the paper from which the data are taken, as given in Table I. The

solid-line curve is not a fit to the data, in the sense of fitting a mathematical function

by least squares or some similar method, but rather the relation between mb and MS

which is obtained from the derived spectrum scaling relations. That is, the trends of

the m,-MS, m,-MO and MS-M, data are used to generate a set of spectra, and these

TABLE I

References to letter symbols used in figures

Letter Reference

Stein (1978)

Stein and Okal (1978) Wang et al. (1979)

Richardson and Solomon ( 1977)

Nuttli et al. (1979)

House and Boatwright (1980)

Nuttli and Kim (1975)

Herrmann ( 1979)

Stem ( 1979)

Letter Reference

Street and Turcotte (1977)

Hasegawa and Wetmiller (1980)

Geller ( 1976)

Liu and Kanamori (1980)

Kanamori and Anderson (1975)

Kanamori( 1977)

Street et al. (1975)

Herrmann et al. (1981)

Singh et al. (1981)

, ! / / I I 9- MID-PLATE EARTHQUAKES

8- 1

-I

7-

6-

MS .

5-

3-

2-

I-

I

Ol 2 3 4 5 6 7 8 mb

Fig. I. mb- Ms relation for mid-plate earthquake>.

scaling relation shown in Fig. 7.

The solid-line is obtained from the spectral

spectra in turn are employed to obtain the curves shown in Fig. 1 and in similar

figures.

The curve of Fig. 1 consists essentially of two straight-line segments. For magni-

tudes less than mb = 4.5, the slope of the curve is unity, indicating that the comer

periods of the corresponding spectra are less than one second. For mb < 3, the data

points fall below the curve. The m,, and MS values of these small earthquakes were

obtained from spectral amplitudes, and possibly are in error. For 4.5 5 mh s 7.0, the slope of the m,-MS curve for mid-plate earthquakes is 2.

This can be satisfied by having the short-period portion of the spectrum fall off as

the square of the frequency, such as in Akis (1967) w model, in Brunes (1970)

model, and in the model of Hanks (1979). For mh > 7, which is near the upper limit

of observed mb values, the curve of Fig. 1 has a decreasing slope, corresponding to

spectral comer periods greater than 20 sec. There are no observational data to

support this predicted phenomenon.

Figure 2 presents the m,-MS data for plate-margin earthquakes. The first

impression is that there is much more scatter than in Fig. 1. This might be expected,

for plate-margin earthquakes frequently involve complex rupture processes which differ from event to event. A part of the curve is dashed to indicate that the

earthquakes of this size which were used in the study did not have seismic moment

determinations. The segment of the curve corresponding to 4.2 -C mh 5 5.1 has a

211

$1 I I t b 1 I1 * 1

6_ PLATE MARGIN EARTHQUAKES

?-

6- l

Fig. 2. mb- Ms relation for plate-margin earthquakes. The solid-line portion of the curve is obtained from

the spectral scaling relation shown in Fig. 8. The dashed line part of the curve corresponds to magnitude

values for which no seismic moment data were available.

slope of unity. The portion between 5.1 5 mb g 5.4 has a slope of about 4, and the slope of the portion between 5.4 5 mb K 6 is about 2.5.

For the large magnitude earthquakes most of the data points of Fig. 2 lie to the right of the curve. For these mag~tudes the curve may be looked upon as a boundary or limiting relation, rather than an average-value one. The two most anomalous points, which have the symbol e and are of mb 6.2, are for the 1965 Washington earthquake and the 1971 San Fernando, California earthquake, which more properly should be classified as intra-plate rather than plate-margin earth- quakes. Earthquakes involving movement on the San Andreas Fault would be called plate-margin earthquakes.

MAGNITUDE-MOMENT RELATIONS

Figure 3 presents the m,--MO data for mid-plate earthquakes. The curve, with two linear segments of slope 1 and 2, is in reasonable agreement with the data except at small magnitudes. The data of this figure, taken together with those of Figs. 1 and 5,

1 1 6 7

Fig. 3. m b - M, relation for mid-plate earthquakes. The solid-line curve is obtained from the spectral scaling relation shown in Fig. 7.

I 1 I I ! 1030 - PLATE MARGIN EARTHQUAKES

1029 -

1028 -

E

k lot7 J

f lo=-

to=-

10243 4 1 5 I 6 I 7 1 8 I

mbob+ 0.4

Fig. 4. m,-h4, relation for plate-margin earthquakes, with 0.4 added to mb obtained from teleseismic

P-wave amplitudes to account for anomalous absorption in asthenosphere below the epicenter. The

solid-line portion of the curve is obtained from the spectral scaling relation shown in Fig. 8.

02f------ MID-PLATE EARTHWAKEs 101

IO2

I

:

IO

102

IO I

Fig. 5. MS-M, relation for mid-plate earthquakes. The solid-line curve is obtained from the spectral

scaling relation shown in Fig. 7.

I I I I I 3 4 5 6 7 8

Fig. 6. Ms- M,, relation for plate-margin earthquakes. The solid-line curve is obtained from the spectral

scaling relation shown in Fig. 8.

214

suggest that mb has been overestimated for the small earthquakes. Street and

Herrmann (1976) showed that nz,, could be overestimated by 0.5 units for M,, values

of 102 dyne-cm and less.

Figure 4 shows the m,-MO data for plate-margin earthquakes. In order to agree with the curves obtained from the spectral scaling law, it was necessary to add 0.4

units to the observed mb values. Chung and Bernreuter ( 1980) showed that nrh

values of California earthquakes obtained from I-set period teleseismic P-wave

amplitudes are underestimated by approximately 0.4 units due to anomalously large

absorption in the asthenosphere beneath the epicenter. Presumably this occurs for

most shallow plate-margin earthquakes. although the correction for all of them may

not be exactly 0.4 units.

The MS-M,, relation for mid-plate earthquakes is given in Fig. 5. The straight-line curve of unit slope indicates there is a one-to-one relation between MS and M, for 6

orders of magnitude. The spectra predict that the slope should increase at about

MS = 8.5, where the corner period exceeds 20 sec. There are no data to test this

expected behavior.

The MS-MO data for plate-margin earthquakes,as given in Fig. 6, show reasonable agreement with the relation predicted by the spectra. This figure further suggests

that some of the large scatter in the mb-MS relation of Fig. 2 results from difficulty

in accurately determining m,, for plate-margin earthquakes.

SPECTRAL SCALING RELATIONS

Figure 7 presents the spectral scaling relation for mid-plate earthquakes, as

derived from the empirical data of Figs. 1. 3 and 5. It is characterized by a flat or

level portion at long periods. by a segment of slope 2 at short periods, and by a

corner frequency w which satisfies Mow4 = constant. A similar moment-corner

frequency relation had been proposed by Street et al. (1975). Street and Turcotte

(1977) and Herrmann and Nuttli (1980) from spectral data of earthquakes in the

central and eastern United States. This relation implies that stress drop increases as

seismic moment increases, which differs from the usual assumption that stress drop

is independent of moment (Aki, 1967; Hanks and Kanamori. 1979) or that Mow3 =

constant.

Figure 7 was derived by assuming that the I-set spectral amplitude is directly

proportional to mb, and the 20-set spectral amplitude directly proportional to Ms.

By trial and error the corner period was shifted back and forth until the Mb-MS, m,-MO and MS-MO relations thus obtained appeared to give a satisfactory fit to the

data of Figs. 1, 3 and 5. Subjective judgment was used to evaluate the quality of the

fit, rather than mathematical curve-fitting. The upper curve of Fig. 7 corresponds to an m,, of 7.2 and an MS of 8.7, which

are taken as likely upper limits for these scales on the basis of historical earthquake

information. However, the spectra themselves do not place such an upper limit on

215

T bed

Fig. 7. Derived spectral scaling relation for mid-plate earthquakes. The seismic moment varies as the

fourth power of the comer period, as indicated by the dashed line.

these mb and MS values, i.e., there is no saturation of either scale implied by this

particular form of spectral scaling.

The relation Moo4 = constant and the spectral slope of 2 at the shorter periods

leads to MS increasing twice as fast as Mu for mb > 4.5, where 4.5 is the mb value at

which the comer period is 1 sec. The data of Fig. 1 require that such a relation be

satisfied. Much more difficulty was experienced in attempting to derive a set of spectra for

plate-margin earthquakes that satisfy the data of Figs. 2, 4 and 6, because the data

do not seem to conform to such simple relations as observed for mid-plate earth-

quakes and because there is a large amount of scatter in the data. Figure 8 presents a

scaling relation for plate-margin earthquakes, obtained by trial-and-error in an

attempt to satisfy the data of Figs. 2, 4 and 6. This spectral scaling relation may be

considered to be an extreme or limiting case, as probably also is the mid-plate

spectral scaling relation of Fig. 7, with spectra of many earthquakes lying between

the two.

A distinctive feature of the spectra of Fig. 8 is the presence of a segment of slope

1030 T,, I 1 llll!, I I I ,,>,, I I I ,llil, , , , ,/ .,,, , , PLATE MARGIN EARTHQUAKES ;

102g-

102e-

2 102?--

E % 1026_

P

iO23-

I

I

I

, 6-

~~ .,,,,,,,,,,i

,

102 5-

lo 0.1 b us

IO loo 1000 T (set)

Fig. 8. Derived spectral scaling relation for plate-margin earthquakes. The mb value is corrected by adding

0.4 units to account for absorption in the asthenosphere.

equal to 1, in addition to the flat part at the long periods and the part of slope 2 at

the short periods. Thus there are two corner periods. For the longer of the two

corner periods the relation Mow4 = constant applies for M, B 1O28 dyne-cm, but this relation breaks down for smaller moments, as can be seen by the dashed line in the

figure. The lesser of the two corner periods appears to bear no simple relation to

seismic moment, except that it increases as the moment increases. Although this

paper presents no supporting data, for MO < 10 23 dyne-cm the spectra of Figs. 7 and

8 presumably would be coincident. Savage (1972) showed that the lesser of the two comer periods is proportional to

the fault rupture width and the greater is proportional to the fault length. In Figs. 7

and 8 the lesser comer periods are approximately the same for a given mb, whereas

the greater comer period is larger for the plate-margin spectra. This implies that the

rupture widths are similar for the two classes of earthquakes, but that plate-margin

earthquakes have relatively larger rupture lengths for a given ltrb value.

The mb values indicated in Fig. 8 actually are not the observed teleseismic P-wave

values, but rather values which are corrected for anomalous absorption of I-set

217

P-wave energy in the asthenosphere. As discussed for Fig. 4, this correction is

assumed to be 0.4 mb units for most plate-margin earthquakes.

DISCUSSION

Figure 9 compares the m,-MS relations obtained in this study with that of

Gutenberg and Richter (Richter, 1958), namely mb = 1.59 MS - 3.97. The latter

relation is commonly used, even though the mb values were based on amplitudes of

P waves of 5-10 set period, whereas present practice uses the amplitude of P waves

of 1-set period. Thus it is not surprising that the Gutenberg-Richter mb values, for a

given MS, are larger. Except for MS values between 4 and 6, the m,-MS curves for

mid-plate and plate-margin earthquakes are almost parallel, the separation being 0.4

mb units.

Figure 10 compares the m,-MO relations for mid-plate and plate-margin earth-

quakes. For a given mb, (corrected for anelastic attenuation in the upper mantle for

plate-margin earthquakes), M,, is larger for the plate-margin earthquakes. This figure

illustrates the difficulty encountered in trying to assess a size to the two classes of

, I 1 1 1 I ....-. GUTENBERG-RICHTER --- PLATE MARGIN EARTHQUAKES - MID-PLATE EARTHQUAKES

9-

4-

3-

2-

I-

Fig. 9. Comparison of mb- Ms relations. The tnb of plate-margin and mid-plate earthquakes is obtained

from l-xc P-wave amplitudes, whereas the mb of the Gutenberg-Richter relation was obtained from S- to

IO-set P-wave amplitudes. The rnb value for plate-margin earthquakes is the observed, or uncorrected,

value.

Fig. 10. Comparison of m b - M, relations for plate-margin and mid-plate earthquakes. The m h vatue. for

plate-margin earthquakes is the value corrected for absorption in the upper mantle, not the observed

value.

earthquakes, in the sense of making statements that one earthquake is greater than another. If the amplitude of the high frequency, strong ground motion (and thus the damage resulting from ground shaking) is of concern, then mb is the proper parameter to use to compare mid-plate and plate-margin earthquakes. If, on the other hand, fault rupture area is of concern, then MO is the parameter to use for comparison. Thus, from the earthqu~e engineers point of view, m,, would be the parameter of most value for quantifying earthquakes, whereas the structural geolo- gist would prefer MO (or M, the moment magnitude).

Figure 11 compares Ms-M, relations for the two classes of earthquakes. For mid-plate earthquakes Ms is in a one-to-one relation with MO over almost the emire range of moments, whereas for plate-margin earthquakes the relation only is valid for A4s < 6.5,

Figure 12 shows how the spectra relate to one another. For periods less than 10 set the two types of spectra do not differ greatly from each other. However, at longer periods the plate-margin spectral amplitudes rise far above the mid-plate amplitudes. One possible explanation of the intermediate slope of unity for the plate-margin

219

---- PLATE MARGIN EARTHQUAKES / 1;;

9

Fig. 11. Comparison of Ms- M, relations for plate-margin and mid-plate earthquakes.

earthquakes is fractional stress drop (Brune, 1970). Another is a ratio of fault length

to fault width appreciably greater than one (Savage, 1972).

Seismic moment, M,, can be related to average stress drop, Au, and fault rupture

TABLE II

Source characteristics of mid-plate and plate-margin earthquakes

Type MS Mo ii A2 L W A0 (dyne-cm) (m) (km2) (km) (km) (bars)

Mid-plate 8.7 4.0.102 10 1,200 60 20 230

8.5 2.5. lo* 7 1,100 55 20 170 7.5 2.5. 1O26 2 380 25 15 130

6.5 2.5. IO* 1 75 15 5 90

5.5 2.5. 1O24 0.3 25 8 3 50 4.5 2.5. 1O23 0.1 7.5 5 1.5 30

Plate-margin 8.2 4.0. 102* 7 17,000 865 20 43 (Strike-slip) 7.5 1.6. 102 2 2,400 160 15 33 Plate-margin 8.7 6.0. 1O29 15 120,000 600 200 35 (Subduction) 8.2 4.0.102s 7 17,000 170 100 43

-- MID-PLATE / i

1029 I

.I-*----7 I

#I I

1028 , _a, .f _____----- I

T (sac)

Fig. 12. Comparison of spectral scaling relations for plate-margin and mid-plate earthquakes. The mb value for plate-margin earthquakes is the value corrected for absorption in the upper mantle, not the observed value.

area, A, using (Aki, 19661.

M, = pAfi

and (Geller, 1976):

ho = (7/16)M,[m/( LW)j3

where p is the rigidity modulus of the crustal rocks, taken to be 3.3 . 10 dynes/cm,

B is the average fault displacement, L is fault rupture length and W = A/L is fault

rupture width. Combining these equations with the data of Fig, 11, estimates of fault

rupture area and average stress drop can be made for mid-plate and plate-margin

earthquakes, as shown in Table I.

In Table II the values of L> have been assumed. If smaller values were used, the

rupture area would be larger and the stress drop smaller. Also, the breakdown of the area, A, into a length, L, and a width, W, is arbitrary, but considered to be

reasonable.

221

Table II offers an explanation as to how the 18 1 l- 18 12 New Madrid earthquakes could have such relatively short rupture lengths and large surface-wave magnitudes. Nuttli (1980) estimated the December 16, 1811 event to have an MS of 8.6, the January 23, 1812 to have an Ms of 8.4, and the February 7, 1812 event to have an MS of 8.7. He also observed that the December earthquake occurred on the southern branch of the fault system, of length 125 km, that the January earthquake probably occurred on the 60 km long central branch, and that the February earthquake occurred on the 75 km long northern branch. A reasonable value for rupture width is 20 km, as the earthquakes had their foci in the crust and may have broken the earths surface. Table II shows that such large magnitude earthquakes could occur in a mid-plate en~ronment, and would not require large rupture lengths or areas. Table II also shows that a mid-plate earthquake the size of the 1886 Charleston, South Carolina event (MS of about 7.5) would have only a 25 km rupture length.

Table II indicates that the 1906 San Francisco earthquake of MS = 8.25 likely represents the maximum earthquake for the San Andreas fault, because of the large value of the rupture length. The rupture width cannot be much greater than 20 km for this strike-slip, plate-margin earthquake. Even if the average fault displacement were doubled, to 15 m, the rupture length would be 400 km. Hanks and Kanamori (1979) concluded that California earthquakes of width 15-20 km must have an upper seismic moment limit of approximately 1O28 dyne-cm if fault lengths do not exceed several hundred kilometers.

It has been observed that subduction zones can generate earthquakes of MS = 8.7, e.g. the 1964 Alaska earthquake. If a 200 km rupture width is permitted, Table II shows that the rupture length would be approximately 600 km. These values are large, but within the realm of possibility.

Hanks (1979) noted that the logarithmic mean of the stress drops of California earthquakes is approximately 30 bars, which is consistent with the stress drops given for the plate-margin earthquakes in Table II. However, for mid-plate earthquakes the stress drop increases with moment, as shown in the table. For smaller mid-plate and plate-mar~n earthquakes than those considered in Table II, the average stress drop likely would be in the range of I- 10 bars, as observed by Street and Turcotte (1977) for eastern North America earthquakes.

CONCLUSIONS

Empirical Mu, MS and h4, interrelations suggest that the spectra of mid-plate and plate-margin earthquakes scale in a different manner. The mid-plate spectra behave in a way that indicates that the average stress drop increases with seismic moment, whereas the plate-margin earthquakes have a nearly constant stress drop.

Although the seismic moment is directly proportional to the long period spectral amplitude and to the fault rupture area, for mid-plate earthquakes it is not directly related to the short-period portion of the spectrum, the part which is related to

272

damaging strong ground motion. Thus for mid-plate earthquakes a moment magni-

tude. M. is not a good measure of the damage potential of an earthquake. The

definition of M is based on western United States empiricisms, which, from what we

have seen, are not applicable for other tectonic environments.

The two classes of earthquakes considered in this paper, mid-plate and plate-

margin, likely represent extreme conditions. That is. there probably are a large

number of earthquakes whose spectra and magnitude-moment relations lie some-

where between those presented in this paper. In particular, earthquakes with

hypocenters near plate margins but not associated with plate-margin movement

itself can be expected to lie in this intermediate category. However, only further

research can determine if this intuitive reasoning is correct.

ACKNOWLEDGMENTS

I wish to thank Dr. R.B. Herrmann for helpful discussion, and Dr. S.J. Duda for

inviting me to present this paper at the meeting of the International Association of

Seismology and Physics of the Earths Interior in London, Canada. The research

reported in this paper was supported in part by the Defense Advanced Research

Projects Agency, monitored by the Air Force Office of Scientific Research, under

Contract F49620-79-C-0025, and in part by NSF Grant PFR-7909795 of the

Earthquake Hazards Mitigation Program, Division of Civil and Envirionmental

Engineering.

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