Regional Bias in Estimates of Earthquake Ms Due to Surface-Wave Path Effects

Bulletin of the Seismological Society of America, Vol. 84, No. 2, pp. 377-382, April 1994 Regional Bias in Estimates of Earthquake Ms Due to Surface-Wave Path Effects by Rachel E. Abercrombie Abstract Continental earthquakes have long been known to have anomalously high surface-wave magnitudes relative to their seismic moments. A recent global study of shallow earthquakes by Ekstrrm and Dziewonski (1988) confirmed this and found other regional, systematic anomalies in the Ms-Mo relationship. It is important to determine the source of these anomalies in order to understand the controls on earthquake-source radiation and to obtain accurate estimates of historical seismic strain rates. In this study the magnitudes of 82 earthquakes from eight different tectonic regions are recalculated using a simple surface-wave path correction to determine whether path effects are responsible for the observed anomalies. The magnitudes of continental earthquakes are reduced by an average of 0.2 magnitude units, an improvement in fit to the global average significant at the 98% level. Surface-wave path effects are clearly responsible for the high Ms observed in continental areas. There is a small decrease in scatter in the other areas, but lateral refraction of the surface waves at plate boundaries prevents the simple correction from having a significant effect. There is no evidence in the observed anomalies, however, for any dependence of earthquake-source type on tectonic setting. It is clear that to obtain reliable, unbiased estimates of regional seismic strain rate and hazard, a local moment-magnitude relationship should be preferred to a global one. Introduction A reliable relationship between magnitude and seismic moment is an important tool in many branches of seismology, with uses such as determining regional seismic hazard and earthquake recurrence rates. Relationships determined for recent events are used to assign seismic moments (M0) to historical events for which only a magnitude estimate (typically from surface waves, Ms) is available. However, a recent study of shallow earthquakes by Ekstrrm and Dziewonski (1988) found systematic regional deviations with respect to the global average relationship between Ms and M0, calculated from their centroid moment tensor (CMT) solutions. These deviations are dependent on tectonic setting with Ms~log (M0) high for most continental earthquakes, low for mid ocean ridges, and varying for subduction zones. The anomalies are of the order of 0.3 magnitude units, corresponding to a factor of 2 to 3 in moment, depending on the relationship between moment and magnitude. If they are not the result of measurement errors they imply that earthquake sources vary with tectonic setting. This has been suggested (e.g., Main and Burton, 1989, 1990), but no such dependence has been observed. An explanation of these anomalies is required in order to increase our understanding of the controls on earthquake sources and to make reliable estimates of historical seismicity. For example, Jackson and McKenzie (1988) estimate the seismic strain rate in the Aegean area to be three times greater than do Ekstrrm and England (1989) simply by using a different Ms-Mo relationship. Ms is simple to measure, but purely empirical and is commonly defined as: Ms = logl0(t)+ 1.66 log~o(a) + 3.3 (1) (the Prague formula). The term A is the maximum amplitude of surface waves recorded, T is the period at which it is measured, and A is the distance in degrees (Vanek et al., 1962). The term M0 is defined from the mechanics of a dislocation source as Mo = fa I~ud12, (2) where/x is the shear modulus, u is the slip, and 1) is the fault area (Aki, 1966). 377

378 R.E. Abercrombie The M0 value is corrected for the depth and radiation pattern of the earthquake, unlike Ms. However, the regional anomalies are not depth dependent and earthquakes recorded by enough stations giving good coverage of the focal sphere show deviations from the global relationship. Moment is dependent on the period at which it is measured (e.g., Silver and Jordan, 1983), but the CMT moments are determined from constant long periods (-60 sec) so this effect cannot cause the regional anomalies. Main and Burton (1989, 1990) suggest that regional variations in source complexity could affect the long-period moment, but Abercrombie (1991) shows that the failure of CMT solutions to include the known source complexity of shallow continental earthquakes does not cause systematic underestimation of the moment. Therefore, the most probable cause of the systematic anomalies in the global Ms-Mo relationship is a failure to correct magnitude for surface-wave path effects. The dispersion characteristics of a particular surface-wave path have a considerable effect on shaping the amplitude envelope of the surface-wave train. For example, large amplitude Airy phases propagate on paths through continental shield, but not through oceanic crust overlain by thick sediment. Marshall and Basham (1973) determined the group velocity curves of four different surface-wave paths (oceanic, continental Eurasia, continental North America, and intercontinental, mixed), and used them to propose the magnitude scale: Ms = loglo(a) + B'(A) + p(a), (3) where B'(A) is the distance correction, as in the Prague formula. The term p(a), which is used to correct for the period at which A is measured and the path type, is a function of the group velocity curve. Marshall and Basham (1973) show that the amplitude of Rayleigh waves of under 20 sec period that traveled a continental path could be up to l0 times higher than that of waves on other paths. Here the magnitudes of earthquakes from a range of tectonic settings are recalculated to determine whether a simple path correction can account for the anomalies observed by Ekstr6m and Dziewonski (1988). Note that applying a more complex correction to magnitude estimates would defeat the purpose of estimating magnitude at all. Recalculation of Ms Surface-wave magnitudes are recalculated using equation (3) for 82 earthquakes from eight regions around the world, representing a cross section of tectonic environments (Table 1). The earthquakes are selected to cover a broad magnitude range (5.3 to 7 Ms), have CMT solutions published by Harvard, and, in common with those considered by Ekstr6m and Dziewonski (1988), are less than 50 km deep, to minimize the effects of depth. The amplitude and period readings used are those reported in the International Seismology Centre (ISC) Bulletins. At least 50% are made at less than 20 sec period and 90% are made on vertical component seismograms, and hence are of Rayleigh waves. The p(a) and B'(A) are obtained from the tables in Marshall and Basham (1973). If the percentage of the surface-wave path in continental crust was 90% or greater the path was deemed continental; if 10% or less, oceanic and all others were considered mixed. Ten percent or more of the path being oceanic is enough to destroy a continental Airy phase (P. Marshall, personal comm.). Results and Discussion The recalculated magnitudes (MBMs) are shown in Table 1, together with the hypocentral parameters and the ISC magnitudes (IMs). The results for the 82 earthquakes are shown in Figure 1, and Figure 2 shows just the earthquakes from continental areas. The variances of IMs and MBMs with M0 about the EkstrSm and Dziewonski (1988) curve were calculated and the statistical significance of any observed decrease in variance of MBMs with respect to IMs determined (Table 2). Some decrease in variance is observed in most separate areas, and in the data set as a whole. The continental areas show decreases significant at the 98% level. The surface-wave path type is clearly responsible for some of the scatter seen in plots of magnitude against moment. This is shown by the decrease in variance of magnitude on log moment in the entire data set after making the simple path correction. The largest decrease in variance (by 73%) was observed for the Tibetan earthquakes. Surface waves from events in this area travel on continental paths to all but the furthest recording stations. Correcting for path type reduced the magnitude of these events by an average of 0.17 magnitude units. This systematic decrease is primarily the result of correcting Ms measurements made from amplitude readings at less than 20 sec period. In all areas studied, slightly over 50% of the readings are made at less than 20 sec, and Marshall and Basham (1973) show that magnitude estimates from these readings using the Prague formula are too high by up to 0.75 magnitude units for totally continental paths. The success of this simple correction implies that the high magnitudes observed for intracontinental earthquakes are principally the result of continental surface-wave paths and not a source effect as suggested by Ekstr6m (1987). The curve he proposed to fit continental events (Ekstr6m, 1987; Ekstr6m and England, 1989) does not account for the systematic errors in magnitude determinations for events less than about magnitude 6 (Fig. 2). The path correction used here is probably too simple to have much effect in the other areas. Most surface-

Regional Bias in Estimates of Earthquake Ms Due to Surface-Wave Path Effects 379 Table 1 Hypocentral Parameters of the Earthquakes Used in This Study* Time Depth CMT M0 Date (hr min sec) Lat. ( ) Long. ( ) (kin) IMs MBMs (x 1016 Nm) N % MIX Aleutian Islands 1 Dec. 87 12 3 56.1 53.03N 142.73W 10 5.7 5.6 53 15 80 7 Feb. 88 18 15 6.2 50.76N 173.44E 0 6.1 6.0 330 38 87 16 Feb. 88 4 22 36.3 51.56N 175.00E 33 5.8 5.7 110 38 92 29 Feb. 88 5 31 36.6 55.16N 167.40E 0 7.0 6.9 2600 40 43 8 Mar. 88 16 27 19.0 51.32N 176.83E 33 5.6 5.6 62 35 94 29 Mar. 88 8 31 32.1 52.28N 168.24W 33 5.5 5.4 57 30 90 26 Apr. 88 1 47 31.9 57.84N 143.02W 10 5.8 5.6 65 27 63 22 May 88 9 39 56.2 53.62N 163.30W 0 5.9 5.8 100 87 52 18 Jul. 88 13 22 11.5 54.60N 168.43E 23 5.7 5.6 97 35 63 New Hebrides Islands 19 May 86 20 54 2.8 12.65S 167.23E 44 5.5 5.5 66 15 67 13 Dec. 86 18 31 53.8 17.96S 167.62E 26 5.6 5.6 51 6 67 16 Apr. 87 13 23 40.5 22.27S 171.81E 37 5.7 5.7 74 19 53 28 Sep. 87 7 15 39.9 18.36S 168.21E 46 5.9 5.9 150 26 67 27 Nov. 87 13 5 50.7 16.17S 168.11E 18 5.5 5.6 23 3 67 21 Jan. 88 8 22 23.7 18.21S 168.10E 49 5.8 5.8 190 33 70 16 May 88 23 7 40.3 13.94S 166.26E 39 5.7 5.7 120 44 80 12 Jun. 88 13 39 40.2 10.77S 165.16E 35 6.4 6.4 690 42 74 17 Jun. 88 12 52 3.9 10.65S 165.22E 49 5.5 5.5 64 26 65 23 Jul. 88 14 25 37.1 22.07S 174.89E 19 6.1 6.1 440 23 61 Tonga-Kermadec Islands 6 Oct. 87 4 19 6.0 17.93S 172.24W 16 7.0 7.0 8900 34 68 3 Nov. 87 8 14 54.2 17.07S 173.81W 34 5.6 5.7 240 12 58 11 Dec. 87 2 3 9.7 21.95S 174.87W 0 5.8 5.8 120 19 63 12 Jan. 88 7 29 30.3 28.71S 177.45W 27 6.3 6.4 790 41 34 13 Jan. 88 11 47 29.9 32.43S 179.67W 15 5.5 5.5 26 8 50 27 Feb. 88 13 46 13.7 20.93S 173.76W 15 5.3 5.2 22 18 80 2 Apr. 88 14 26 29.1 15.40S 173.09W 33 6.0 6.0 280 35 71 6 May 88 19 14 53.0 33.09S 178.65W 15 5.7 5.7 45 9 44 11 Jun. 88 12 17 26.6 15.21S 173.53W 42 6.1 6.1 t60 32 75 16 Jul. 88 16 55 0.9 27.15S 176.80W 30 5.3 5.3 37 17 65 East Indian Ridge 28 Oct. 86 15 11 23.0 30.51S 60.14E 10 5.5 5.6 74 11 91 11 Nov. 86 18 57 13.6 49.02S 31.38E 10 5.9 5.9 130 12 83 28 Dec. 86 20 4 36.8 38.78S 78.77E 10 6.0 6.0 280 9 89 13 Apr. 87 8 6 41.1 37.29S 78.21E 10 5.7 5.7 47 5 100 22 Oct. 87 0 4 33.3 26.00S 71.24E 10 5.4 5.2 9.1 1 0 8 Dec. 87 19 56 54.5 40.57S 44.58E 10 5.3 5.4 21 3 100 26 Feb. 88 6 17 31.9 37.28S 48.02E 10 6.7 6.7 1800 46 96 11 Mar. 88 2 36 59.6 37.35S 48.07E 10 5.3 5.4 12 3 100 12 Apr. 88 20 26 19.6 33.77S 56.34E 10 6.4 6.4 34 13 100 31 Jul. 88 15 22 48.7 31.89S 57.47E 10 5.8 5.9 77 23 100 Mid Atlantic Ridge 6 Jun. 85 2 40 13.3 0.97N 28.44W 10 6.5 6.5 560 37 95 28 Jul. 87 1 44 10.3 0.67N 25.99W 10 5.5 5.4 91 15 100 15 Jan. 88 21 7 12.0 27.12S 11.34W 10 5.5 5.5 49 12 95 23 Mar. 88 15 50 19.0 10.77N 43.49W 10 5.7 5.7 200 19 95 20 Apr. 88 4 25 36.7 0.97N 30.27W 10 5.4 5.3 20 7 100 18 May 88 5 39 51.4 13.45N 44.85W 10 5.5 5.5 56 10 100 20 May 88 14 58 43.6 8.11N 34.41W 10 6.0 6.0 120 34 100 21 May 88 15 15 43.5 0.78N 30.35W 10 5.5 5.6 81 7 100 21 Jun. 88 6 26 16.9 24.87N 45.87W 26 5.5 5.5 45 20 90 29 Jun. 88 10 30 16.9 42.88S 16.02W 10 5.4 5.4 14 7 100 Andes 5 Feb. 88 14 1 2.7 24.77S 70.46W 0 6.8 6.8 6600 22 95 5 Feb. 88 18 49 30.6 24.92S 70.55W 22 6.2 6.3 410 15 93 22 Feb. 88 19 13 13.0 20.77S 69.77W 28 6.3 6.4 890 29 93

380 R.E. Abercrombie Table 1--Continued Time Depth CMT M0 Date (hr rain sec) Lat. ( ) Long. ( ) (kin) lms MBMs ( 1016 Nm) N % MIX 9 Mar. 88 21 33 53.7 17.35S 74.18W 33 5.8 5.9 91 19 95 13 Mar. 88 11 31 32.8 33.69S 72.22W 42 5.9 5,9 70 7 86 30 Mar. 88 23 50 56.3 24.90S 70.44W 35 5,7 5,7 230 13 85 13 Apr. 88 0 39 30.8 17.34S 72.55W 16 6.2 6,3 220 5 100 21 May 88 14 28 40.0 32.91S 71.71W 46 5.6 5.5 180 5 80 4 Jul. 88 13 54 14.1 17.68S 71.75W 20 5.5 5.5 54 13 92 California 10 Feb. 84 16 51 21.3 28.29N 112.14W 3 6.2 6.2 130 15 80 9 Oct. 84 23 2 32.4 24.90N 109.05W 37 5.4 5.2 30 8 63 4 Aug. 85 12 1 56.3 36.13N 120.15W 12 5.9 5,8 160 24 83 31 Mar. 86 11 55 39.1 37.53N 121.62W 0 5.6 5,6 32 14 93 13 Jul. 86 13 47 9.1 33.08N 117.88W 10 5.8 5.8 65 23 91 25 Sep. 86 6 15 54.9 23.00N 108.18W 5 5.8 5.8 120 20 70 7 Feb. 87 3 45 15.7 32.51N 115.27W 6 5.5 5,6 21 8 88 24 Nov. 87 13 15 56.6 33.12N 116.02W 2 6.6 6,6 720 27 81 12 Feb. 88 5 23 57.3 30.05N 113.77W 10 5.6 5,7 54 14 86 18 Jun. 88 22 49 42.4 26.81N li1.04w 10 6.8 6,8 1100 61 92 Tibetan Plateau 22 Feb. 80 3 2 44.8 30.55N 88.65E 14 6.3 6.1 400 4 25 24 Jun. 80 7 35 44.7 33.00N 88.55E 3 5.6 5.5 51 14 7 29 Jul. 80 14 58 41.6 29.63N 81.09E 23 6.5 6,4 830 39 28 7 Oct. 80 9 32 8.7 35.62N 82.14E 32 5.5 5,4 56 22 18 23 Jan. 82 17 37 29.2 31.68N 82.28E 25 6.5 6,3 380 23 17 5 Nov. 83 19 48 24,6 33.92N 89.95E 33 5.4 5.3 31 12 17 21 Apr. 85 13 21 27.5 35.56N 87.28E 31 5.7 5,4 28 7 14 20 May 85 15 11 38.9 35.56N 87.20E 19 6.1 5,8 61 15 7 20 Jun. 86 17 12 47.2 31.22N 86.82E 33 6.2 6.0 140 32 56 6 Jul. 86 19 24 23.1 34.45N 80.20E 9 6.1 6.0 100 32 38 Aegean 9 Jill, 80 2 11 57 39.26N 22.71E 3 6.4 6.4 870 5 60 24 Feb. 81 20 53 37 38.10N 22.84E 5 6.6 6.6 1290 17 82 25 Feb. 81 21 58 7 38.14N 23.05E 5 6.3 6.3 430 16 75 4 Mar. 81 15 43 52 38.18N 23.17E 3 6.4 6.2 348 18 44 *Origin time, epicenter, and depth are from the ISC Bulletins, excepting the Aegean events where the epicenter is from Jackson et al. (1982) and the depth is from Abercrombie (1991). The CMT seismic moments are from Dziewonski et al. (1988) and the ISC Bulletins. The term N is the number of readings used to calculate the magnitudes, and %MIX is the percentage of those that traveled an intercontinental path. wave paths to these areas are mixed and any variation between paths of 10 and 90% oceanic crust is left uncorrected. Also, the Marshall and Basham (1973) curves are most reliable for continental paths where the most data were used to constrain them. Surface waves traveling on mixed paths or from oceanic earthquakes must cross plate boundaries to reach a recording station. Various studies have shown that surface waves suffer significant lateral refraction as they cross such major structural boundaries (e.g., McGarr, 1969; Capon, 1970). Focusing and defocusing of the rays leads to variations of up to a factor of 10 in amplitude (McGarr, 1969) and could produce regional errors in magnitude estimates comparable to those seen by Ekstr6m and Dziewonski (1988). The poorest performance of the path correction applied here is for mid ocean-ridge earthquakes. The majority of the surface-wave paths from these earthquakes (>85%) are of the mixed type for which the Marshall and Basham (1973) correction has the least effect. Also, they all cross plate boundaries to the land-based stations, so the waves experience considerable lateral refraction. It is possible that the higher attenuation of oceanic crust is, in part, responsible for the low magnitude measurements of mid ocean-ridge earthquakes. Canas and Mitchell (1981) show that Rayleigh wave attenuation across the Atlantic and Pacific oceans is approximately twice as high as the average value (Q = 400) assumed by Marshall and Basham (1973) in the construction of their curves. As predicted by Ekstr6m and Dziewonski (1988), surface-wave path effects cannot explain the opposite anomalies seen at the New Hebrides and Tonga-Kermadec subduction zones. These two areas are close and Ms measurements of the earthquakes are made at the same range of stations on surface waves that have traveled similar paths. It is difficult to attribute the differences to

Regional Bias in Estimates of Earthquake Ms Due to Surface-Wave Path Effects 381 lateral refractions for the same reasons. Two other options are considered to explain the anomaly: depth and radiation pattern. Depth estimates of shallow earthquakes are known to be rather inaccurate, especially for small events. However, Zhangand Schwartz (1992) find the depth distribution of moment release in the New Hebrides and Tonga subduction zones to be remarkably 7.5 "10 = e- 6.5 II) ~ 5.5 't if) 4.5 16.5 7.0 -o 6.5 e- ~ 6.0 Figure 1. A ISC Magnitude Marshall & Basham Magnitude - Ekstrom & Dziewonski curve A ~. ~ A a i i i 17.5 18.5 19.5 Log Seismic Moment (Nm) Surface-wave magnitude and seismic moment of all 82 earthquakes with the curve of EkstrOm and Dziewonski (1988). The recalculated Marshall and Basham (1973) magnitudes (solid circles) exhibit less scatter than the ISC magnitudes (open triangles). -- Ekstrom & Dziewonski curve,- j /X ISC Magnitude / ' ~ f Mk~tho all, &Br;?har mamag nitude.""" A A A "'" o,//''~o 2,, Jt similar, with mean depths of 23.7 and 21.5 kin, respectively. Earthquakes from the Kermadec zone have a deeper mean depth (41.7 km) but constitute less than 10% of the total moment release in the Tonga-Kermadec zone. If their greater depth did bias Ms measurements, then it would be in the opposite direction to the observed anomaly. A combination of earthquake radiation pattern and station distribution appears to be a more plausible cause. Over two-thirds of the stations recording the earthquakes from these two subduction zones with magnitudes less than about 6 lie in the range of azimuths 270 to 350. If the majority of events are assumed to be 45 dip slip (thrusts) with strikes parallel to the strike of the zone (New Hebrides 160, Tonga-Kermadec 195 ) then the stations will receive surface waves from a minimum in the Rayleigh wave radiation pattern from New Hebrides and a maximum from Tonga-Kermadec. This is entirely consistent with the systematically high Ms observed at Tonga-Kermadec and low Ms observed at New Hebrides. The difference between the maximum and minimum in the surface-wave radiation pattern is about a factor of 2, comparable to the observed anomaly. Of course, if data are available from horizontal-component seismograms it would be useful to demonstrate that the Love wave radiation is in agreement with the above hypothesis, but this is beyond the scope of this article, which is restricted to bulletin data. Conclusions Surface-wave path type is clearly responsible for the high Ms observed in continental areas, causing systematic overestimation by about 0.2 magnitude units. In other areas the path correction is less effective, probably as a result of lateral refraction of the surface waves and re- Table 2 Regression Results: Variances of Both Magnitudes About the Curve of Ekstrrm and Dziewonski (1988), and the Probability of Their Being Significantly Different 1= 5.5 ~o / i 5.0 17.0 17.5 18.0 i 18.5 t 19.0 Log Seismic Moment (Nm) Figure 2. Surface-wave magnitude and seismic moment of the 14 continental earthquakes (Tibet and Greece), symbols as in Figure 1. All but two of the ISC magnitudes are higher than predicted. Correction for the surface-wave path brings them significantly closer to the global average. Also shown is the curve (dashed) for continental events, Ekstrrm (1987). It fits the original data no better than the global curve below about magnitude 6. 19.5 Variance Variance Probability of Region MBMs IMs Significant Difference Aleutian Islands 0.0117 0.0205 0.56 New Hebrides Islands 0.0387 0.0291 0.32 Tonga-Kermadec 0.0476 0.0634 0.32 East Indian Ridge 0.2321 0.2381 0.03 Mid Atlantic Ridge 0.0626 0.0659 0106 Andes 0.0819 0.0673 0.21 California 0.0760 0.0632 0.21 Tibet 0.0272 0.1014 0.95 Aegean 0.0053 0.0179 0.65 Subduction Zones 0.0318 0.0356 0.28 Mid Ocean Ridges 0.1396 0.1440 0.06 Continental Areas 0.0201 0.0743 0.98 Other Boundaries 0.0744 0.0615 0.3 l All Earthquakes 0.0639 0.0721 0.42

382 R.E. Abercrombie gional variations in Q. Path effects cannot explain the difference between the closely located subduction zones of the New Hebrides and Tonga-Kermadec, but it is shown that these anomalies are consistent with the azimuthally restricted recording-station distribution combined with the source radiation patterns. The anomalies in the global Ms-Mo relationship can easily be accounted for by the "errors" in the Ms measurements and provide no evidence for regional variations in regional source type or complexity. Clearly, to obtain accurate estimates of moment from magnitude of historical events a local relationship should be preferred to a global one. Use of such a local relationship will prevent path type, radiation pattern, and mean depth from biasing the results of local studies of seismic hazard and strain rate. Acknowledgments I thank John Young and Phil Abercrombie for their help with data collection and analysis, and Peter Marshall and Steve Lund for much appreciated input and advice. I am grateful to Goram Ekstrrm for providing me with his Ms-Mo relationship for continental earthquakes. The comments of Brian Mitchell, Art McGarr, and an anonymous reviewer greatly improved this manuscript. This work was completed whilst PEA was supported by a Southern California Earthquake Center (SCEC) fellowship. SCEC publication number 75. References Abercrombie, R. E. (1991). Earthquake rupture dynamics and neotectonics in the Aegean region, Ph.D. Thesis, Reading University, United Kingdom. Aki, K. (1966). Generation and propagation of G waves from the Niigata earthquake of June 16, 1964, Bull. Earthquake Res. Inst. Tokyo Univ. 44, 23-88. Canas, J. A. and B. J. Mitchell (1981). Rayleigh wave attenuation and its variation across the Atlantic Ocean, Geophys. J. R. Astr. Soc. 67, 159-176. Capon, J. (1970). Analysis of Rayleigh-wave multipath propagation at LASA, Bull. Seism. Soc. Am. 60, 1701-1731. Dziewonski, A. M., G. Ekstrrm, J. E. Franzen, and J. H. Wood- house (1988). Global seismicity of 1980: centroid moment tensor solutions for 515 earthquakes, Phys. Earth Planet. Interiors 50, 127-154. Ekslxrm, G. (1987). A broadband method of earthquake analysis, Ph.D. Thesis, Harvard University, Cambridge, Massachusetts. Ekstrrm, G. and A. M. Dziewonski (1988). Evidence of bias in estimations of earthquake size, Nature 332, 319-323. Ekstrrm, G. and P. England (1989). Seismic strain rates in regions of distributed continental deformation, J. Geophys. Res. 94, 10231-10257. Jackson, J. A., J. Gagnepain, G. Houseman, G. C. P. King, P. Papadimitriou, C. Soufleris, and J. Virieux (1982). Seismicity, normal faulting and the geomorphical development of the Gulf of Corinth: the Corinth earthquakes of February and March 1981, Earth Planet. Sci. Lett. 57, 377-397. Jackson, J. A. and D. P. McKenzie (1988). The relationship between plate motions and seismic moment tensors, and the rates of active deformation in the Mediterranean and Middle East, Geophys. J. 93, 45-73. McGarr, A. (1969). Amplitude variations of Rayleigh waves--horizontal refraction, Bull. Seism. Soc. Am. 59, 1307-1334. Main, I. G. and P. W. Burton (1989). Seismotectonics and the earthquake frequency-magnitude distribution in the Aegean area, Geophys. J. Int. 98, 575-586. Main, I. G. and P. W. Burton (1990). Moment-magnitude scaling in the Aegean area, Tectonophysics 179, 273-285. Marshall, P. D. and P. W. Basham (1973). Rayleigh wave magnitude scale, Ms, Pure Appl. Geophys. 103, 406-414. Silver, P. G. and T. H. Jordan (1983). Total-moment spectra of fourteen large earthquakes, J. Geophys. Res. 88, 3273-3293. Vanek, J., A. Zfitopek, V. K~nik, N. Kondorskaya, Yu. V. Riznichenko, Ye. F. Savarensky, S. L. Solov'ev, and N. V. Shebalin (1962). Standardisation of magnitude scales, Bull. Acad. ScL USSR. Geophys. Ser. 2, 108. Zhang, Z. and S. Schwartz (1992). Depth distribution of moment release in underthrnsting earthquakes at subduction zones, J. Geophys. Res. 97, 537-544. Southern California Earthquake Center Department of Geological Sciences University of Southern California Los Angeles, California 90089-0740 Manuscript received 11 August 1992.