NUREG/CR-1655 UCRL-53004

XA04NO347

fNIS-XA-N--048 The Effect of Regional Variation of Seismic Wave Attenuation on the Strong Ground Motion from Earthquakes

D. H Chung and D. L. Bernreuter

Prepared for U.S. Nuclear Regulatory Commission

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The Effect of Regional Variation of Seismic Wave Attenuation on the Strong Ground Motion from Earthquakes

Manuscript Completed: July 1981 Date Published: October 1981

Prepared by D. H. Chung and D. L. Bernreuter

Lawrence Livermore Laboratory 7000 East Avenue Livermore, CA 94550

Prepared for Office of Nuclear Regulatory Research U.S. Nuclear Regulatory Commission Washington, D.C. 20555 NRC FIN No. A0139 Availability of Reference Materials Cited in NRC Publications Most documents cited in NRC publications will be available from one of the following sources: 1 . The NRC Public Document Room, 1717 H Street., N.W. Washington, DC 20555 2 The NRC/GPO Sales Program, U.S. Nuclear Regulatory Commission, Washington, DC 20555 3. The National Technical Information Service, Springfield, VA 22161 Although the listing that follows represents the majority of documents cited in NRC publications, it is not intended to be exhaustive. Referenced documents available for inspection and copying for a fee from the NRC Public Document Room include NRC correspondence and internal NRC memoranda-, NRC Office of Inspection and Enforce- ment bulletins, circulars, information notices, inspection and investigation notices, Licensee Event Reports; vendor reports and correspondence; Commission papers; and applicant and licensee documents and correspondence. The following documents in the NUREG series are available for purchase from the NRC/GPO Sales Pro- gram: formal NRC staff and contractor reports, NRC-sponsored conference proceedings, and NRC booklets and brochures. Also available are Regulatory Guides, NRC regulations in the Code of Federal Regulations, and NuclearRegulatory Commission Issuances. Documents available from the National Technical Information Service include NUREG series reports and technical reports prepared by other federal agencies and reports prepared by the Atomic Energy Commis- sion, forerunner agency to the Nuclear Regulatory Commission. Documents available from public and special technical libraries include all open literature items, such as books, journal and periodical articles, transactions, and codes and standards. FederalRegister notices, federal and state legislation, and congressional reports can usually be obtained from these libraries. Documents such as theses, dissertations, foreign reports and translations, and non-NRC conference pro- ceedings are available for purchase from the organization sponsoring the publication cited. Single copies of NRC draft reports are available free upon written request to the Division of Technical Infor- mation and Document Control, U.S. Nuclear Regulatory Commission, Washington, DC 20555. ABSTRACT

Attenuation is caused by geometric spreading and absorption. Geometric spreading is almost independent of crustal geology and physiographic region, but absorption depends strongly on crustal geology and the state of the earth's upper mantle. Except for very high frequency waves, absorption does not affect ground motion at distances less than about 25 to 50 km. Thus, in the near-field zone, the attenuation in the eastern United States is similar to that in the western United States. Beyond the near field, differences in ground motion can best be accounted for by differences in attenuation caused hy differences in absorption. The stress drop of eastern earthquakes may be higher than for western earthquakes of the same seismic moment, which would affect the high-frequency spectral content. But we believe this factor is of much less significance than differences in absorption in explaining the differences in ground motion between the East and the West. The characteristics of strong ground motion in the conterminous United States are discussed in light of these considerations, and estimates are made of the epicentral qround motions in the central and eastern United States.

iii

CONTENTS

Abstract ...... Figures ...... vi

Tables ...... vii Foreword ...... ix

Glossary of Symbols ...... xi

Executive Summary ...... 1

Introduction ...... 3 Evidence for Regionalization ...... 7

Evidence from P- and S-Wave Velocities ...... 7 Evidence from Surface-Wave Studies ...... 14

Implications of Regionalization: Discussion ...... 23 Strong Ground Motion Characteristics in the

Conterminous United States ...... 32 Inferring EUS Attenuations: Four Possible Methods ...... 33

Method 1 ...... 36 Method 2 ...... 36

Method 3 ...... 37 Method 4 ...... 38

Examples and Discussion ...... 39 Estimates of the Epicentral Ground Motion in the

Central and Eastern United States ...... 46 Approach and Results ...... 47

Comparison with Nuttli's Analysis ...... 55 Appendix: Published Attenuation Functions ...... 57

References ...... 65

v FIGURES

1. Typical ground motion attenuation ...... 4

2. The Pn-velocity distribution in the conterminous

United States ...... 8

3. Contour map of mean teleseismic P-wave station corrections for the conterminous United States ...... 9

4. Seismic-wave transmission characteristics in North America . . . 12

5. Seismograms along three profiles from the Salmon nuclear

explosion ...... 15

6. Comparison of the upper-mantle Q models for the eastern and western United States ...... 21

7. Contours of upper mantle a from Pn paths in the conterminous United States ...... 22

8. Peak particle velocity as a function of distance from a

salvo-type underground nuclear explosion source (Buggy) . . . . 25

9. Attenuation of vertical ground velocity from the 1971

San Fernando earthquake ...... 26

10. Comparison of vertical components of velocity from

earthquakes in the western United States with magnitudes between 4.5 and 5.8 ...... 27

11. Variation of amplitude ratio with epicentral distance for

three frequencies ...... 31

12. The intensity attenuation relationships for five historical

events in the EUS ...... 40

13. A comparison between the results of the four attenuation

models, for an event with b = 65 ...... 42

Vi 14. Measured peak accelerations from the Rio Blanco event as a function of distance ...... 49

15. Estimated peak horizontal acceleration for the 1811-1812 New Madrid earthquake series, based on the 1968 southern Illinois event ...... 53

TABLES

1. Values for the constants A. in Eq. 14) ...... 39 1 2. Peak ground accelerations (in cm/s2) calculated for three body-wave magnitudes, using methods 3 and 4 ...... 44 3. Attenuation coefficients for selected events ...... 54

vii

FOREWORD

This report was prepared as part of Phase I of the Seismic Safety Margins Research Program at the Lawrence Livermore National Laboratory. It was supported by the U.S. Nuclear Regulatory Commission under a memorandum of understanding with the U.S. Department of Energy.

ix

GLOSSARY OF SYMBOLS

a Wave amplitude; exponential constant in Eq. 12)

A Wave amplitude in Eq. 12)

ah Peak horizontal ground acceleration C(z) Factor to account for the variation of Q with depth

f Wave frequency GMP Ground motion parameter

I0 Epicentral intensity

Is Site intensity L Length of salvo explosion array

M Generalized earthquake magnitude

mb Body-wave magnitude

ML Local magnitude PGA Peak ground acceleration PGV Peak ground velocity

PSA Peak spectral amplitude

Generalized seismic quality factor

a Seismic quality factor for P-waves Seismic quality factor for S-waves r Hypocentral distance R Epicentral distance; hypocentral or epicentral distance in Eq. 4)

s Ray path coordinate (p. 11) S Factor to account for geometric spreading

V Group velocity z Depth a Compressional wave velocity

Shear-wave velocity Coefficient of anelastic attenuation

Epicentral distance

Exponent in attenuation equation on page 5 W Angular frequency

xi

EXECUTIVE SUMMARY

Attenuation is the decay in the amplitude of earthquake motion--motion generated by sudden release of the earth's strain about the earthquake source. The key factors influencing attenuation are the source conditions, the transmission path characteristics, and the local site conditions. The source conditions influence the initial level and frequency content of the motion. The transmission path characteristics influence the path length and the rate of amplitude decay. The local site conditions further influence the level and frequency content of the motion. The attenuation of ground motion from an earthquake is complex in nature, owing in part to the complexity of the ground motion, which consists of a combination of harmonic motions of varying frequency. The frequency dependency of typical ground motion attenuation shows that higher frequency motions attenuate faster than lower frequency motions. The composition of frequencies and the percentage of strong motion caused by different waves i.e., P waves, SH and SV waves, surface waves, etc.) undergo changes along the transmission path. During the travel of both the body and surface waves, the amplitudes decay with distance because of geometric spreading and damping within the material. In the conterminous United States, a regional propagation difference between the eastern and western United States is inferred from seismic observations. The much larger felt areas of earthquakes in the East require consideration of the effect of distant large events such as the 1811 New Madrid and 1886 Charleston events. What evidence do we have for these differences of ground motion attenuation between the East and the West? At distances less than about 100 km from the source, how does the damping of large eastern earthquakes differ from that of the 1906 San Francisco event? What is the implication of the "lown attenuation observed in the East upon observed ground motion? These are some of the more important questions to be answered in the development of our methodology in connection with the seismic hazard analyses for the Seismic Safety Margins Research Program.

1 In this report, we first present all types of seismological and other geophysical evidence (pertinent to the questions above) from our consideration of (1) P and waves, Pn and S nvelocity distributions, and associated seismic quality factors Q (when known); 2 direct measurements of attenuation

(1/Q) along various propagation paths of different seismic-wave velocity; and

(3) propagation characteristics of surface waves. In the near-field zone, attenuation of seismic waves apppears to be the same in the eastern United

States as in the western states; this is because the absorption is not important at small distances. We observe a regional difference in attenuation

(as well as velocity) between the eastern and western United States in the teleseismic distances. We investigate te implications of this regionalization of both the attenuative property and the propagation of seismic wave velocities for ground motion attenuation in the intermediate fields. we conclude that the attenuation characteristics of seismic motion in the East are definitely different from those in the West. These conclusions are based primarily on our consideration of (1) attenuation of intensity with increasing epicentral distance, 2 far-field measurements of the amplitude of various wave types, and 3 other seismological and geophysical evidence, as discussed above. It appears that the sources do not provide much insight into the relationship among the peak ground motion parameters, earthquake source parameters, and epicentral distance for distances of less than about 25 km, except for very large earthquakes. Several interpretations of the basic data can be made, leading to significantly different conclusions. There are too few data to make other than gross judgments at this time. A systematic comparison of peak velocities of earthquakes recorded in the central and western United States, as computed using the CIT-EERL Strong Motion Data Processing corrected records for those earthquakes of magnitude range

3.9 < ML< 54, is presented. For a given magnitude and epicentral distance, the central U.S. data points are well above average. The peak velocities for the central United States appear to be higher that those for the western United States. A review of the spectra of the records obtained in the central United States at about 100 km shows these spectra to be richer in high frequencies than those obtained in the western United States.

2 INTRODUCTION

Ground motion due to earthquakes consists of a combination of harmonic motions of varying frequency. The attenuation of this motion with distance is, therefore, complex, as suggested by Fig. 1: High-frequency motions are

attenuated faster than low-frequency motions. As a consequence, the frequency content and the percentage of strong motion caused by different waves (i.e., P waves, SH and SV waves, surface waves, etc.) change along the transmission path. In the near and intermediate field, the body waves carry a significant -n portion of strong ground motion, which diminishes in amplitudes as R where R is the distance from the epicenter. (We define the near field as the area within about 25 km of the epicenter; the intermediate field extends from about 25 km to about 150 or 200 km; the far field extends beyond about 200 km.) Surface waves carry a significant portion of the strong motion in the far field and diminish as Rm, where n > m. The value of m itself varies with epicentral distance (Nuttli, 1973a), but the essential difference between n and m remains. This difference accounts for the change in attenuation rates between the intermediate and far fields. Along the transmission path, the amplitudes of both body and surface waves decay with distance because of geometric spreading and because of damping due to the earth's material. As we shall discuss in the next section, a regional propagation difference is evident between the eastern and western regions of the conterminous United States. Similar-sized earthquakes in the

Fast are felt more widely and can cause more widespread damage; therefore, we must consider the effects of distant large events such as the 1811 New Madrid and 1886 Charleston earthquakes. At distances less than about 150 km, how was ground motion damping during these earthquakes in the East different from that during the 1906 San Francisco event? In general, what is the implication of the lown attenuation observed along propagation paths in the East? Because of the potential for serious damage to structures and for injury over large areas in the East, predictions of future ground motion due to earthquakes in the eastern United States are of much more than academic interest. Consideration of possible seismic activity is especially important

- 3 - Near Intermediate Far field field field

.+10 CU High" frequency dominant

C

E Total ground motion

cox :E ow" frequency dominant

Distance

FIG. 1. Typical ground motion attenuation. The figure illustrates schematically the more rapid attenuation of high-frequency components (steeper dashed line), compared to low-frequency components (flatter dashed line).

- 4 - in selecting sites for nuclear power plants and in their design. More than 80% of the plants in existence, under construction, or being planned are

located east of the Mississippi River, most of them concentrated in the

northeastern states. Among the design criteria for nuclear power plants, the most difficult to

establish is the maximum level of ground motion from regional earthquakes that the plant must withstand. The reasons for the difficulty are our poor

understanding of intraplate earthquake occurrences and the difficulty in quantifying attenuation of strong ground motion in the eastern United States.

The approach to this problem in the past has been to associate the maximum intensity with a maximum ground acceleration, using empirical relationships, and to use reported intensities of past earthquakes in the region to infer the maximum ground acceleration that might be experienced in the future at a given location. However, because so little strong ground motion data exist for the East, inferences must be made about the attenuation of strong ground motion by studying systematic differences or similarities between the eastern United States and other regions of the world. The available information, which is often only indirectly related to ground motion, includes intensity data, local crustal models, and attenuation of both surface and body waves in the intermediate and far fields. In this report, we discuss in depth the evidence developed in a number of diverse studies which suggests that there is a significant difference in attenuation between the eastern United States and the western United States. (We shall now define the eastern United States as the conterminous United States east of the Rocky mountains and shall abbreviate it as EUS. The western United States--WUS--is the conterminous United States west of the Rockies, excluding coastal California.) We shall attempt to unify these studies to see what can be concluded about the attenuation of strong ground motion in the EUS. The important evidence includes:

o Modified Mercalli (MM) intensity attenuates more slowly in the EUS than in the WUS, based on historical intensity data (see Nuttli and

Zollweg, 1974; Nuttli et al., 1979; Street and Turcotte, 1977). 9 There are higher propagation velocities at depth in the EXJS than in

the WUS (see Herrin and Taggart, 1962, 1968; Hales and Herrin, 1972; Cleary and Hales, 1966; Doyle and Hales, 1967; Molnar and Oliver,

1969).

5 • There are higher seismic quality factors values), thus lower damping, in the EUS than in the WUS (see Sutton et al., 1967; Molnar and Oliver, 1969; Nuttli, 1973a, b, c; Necioglu and Nuttli, 1974; Solomon and Toksoz, 1970; Lee and Solomon, 1975, 1979; Der et al.,

1975; Der and McElfresh, 1976; Biswas and Knopoff, 1974; Mitchell, 1975; Archambeau et al., 1969; Chung, 1980). • There is a less pronounced low-Q zone in the upper mantle of the EUS (see Solomon and Toksoz, 1970; Lee and Solomon, 1975, 1979; Chung, 1980; Archambeau et al., 1969; Mitchell, 1975). • Propagation and prominent characteristics of surface waves in the EUS are different from those in the WUS (see Nuttli et al., 1979; and Bollinger, 1979). • There are systematic differences among magnitude determinations used in the EUS and the WUS (see Nuttli, 1979; Chung and Bernreuter, 1980).

- 6 - EVIDENCE FOR RBGIONALIZATION

Earthquake energy travels in the form of body waves and surface waves. The body waves consist of both compressional waves (P waves) and shear waves (SH and SV waves), and carry a significant amount of energy within

approximately 50 to 100 km from the source of an earthquake having a magnitude

greater than about mb = 5.0. In general, high-frequency surface waves carry significant energy -- even in the near-field. Surface waves, which consist of

Rayleigh and Love waves, dominate at distances beyond 100 to 200 km from the source. The amplitudes of both body and surface waves decay with distance because of geometric spreading and damping (caused by internal friction) within the earth's materials. Geometric spreading results in a more or less continuous decrease in amplitude as the radiating wavefront expands. The rate of this geometric attenuation depends on the velocity distribution in the transmitting medium and, to some extent, on the size and shape of the rupture

surface. The second source of attenuation, damping, is frequency dependent. It is generally observed that higher-frequency motions attenuate more rapidly than others; thus, the frequency content of the ground motion changes with distance.

Most transmission paths have complex geometries and include layers with

dissimilar physical properties. In this section, we present seismological evidence for regionalization within the conterminous United States. The evidence comes from the propagation characteristics of both body and surface waves.

EVIDENCE FROM P- AND S-WAVE VELOCITIES

Herrin and Taggart 1962) were the first to present clear evidence of the existence of significant regional differVces in Pn velocity in the conterminous United States. Figure 2 generalizes their conclusions regarding velocities, and Fig. 3 illustrates their observations of regional variations of teleseismic travel time residuals. Herrin and Taggart 1968) noted that the teleseismic P-wave residuals to the east of the Texas Panhandle are generally negative, while those to the west are positive, increasing to a value of 0.7 s in the middle of the Basin and Range Province. Herrin and Taggart 1968, p. 1335) thus concluded that the station corrections due to these regional variations are positive in the WUS, where Pn velocities are

- 7 - 7.9 8.0 8.1 8.1 8.2

7.9 8. 8.

8.1

8. 8.1 13.0 .0 8.2

Estimated Pn velocity 8 1 (k M/sec)

FIG. 2 The Pn-velocity distribution in the conterminous United States (after Herrin, 1969, based on Herrin and Taggart, 1962, 1968).

8 0. -0.5

0.5 5

+0 5 +0.

75

.0

Seismic del y times in seconds

FIG. 3 Contour map of mean teleseismic P-wave station corrections for the conterminous United States (after Herrin and Taggart, 1968).

9 relatively low 780 km/s) , but that the corrections are negative in the higher Pn velocity ( 8.10 k/s) regions of the EUS. (Both of these figures represent only broad regional variations. Recent work by Taylor and oksoz (1979) and by Zandt 1978) point up far greater complexity in lateral heterogeneity.) Crustal thicknesses in general are less in the West. Jackson and Pakiser (1965) reported thicknesses of 25 to 40 km in the Basin and Range Province, Colorado Plateau, and Middle Rocky Mountains; and 50 km in the Southern Rockies and Great Plains. The estimate of crustal thickness in the Basin and Range Province s somewhat arbitrary because there is not a true Moho present in this region. The upper layer, interpreted as granitic, is 19 km thick, with a 6.0-km/s P-wave velocity. The lower layer, 10 to 12 km thick, is probably basaltic, with a P-wave velocity of about 67 km/s (Chung, 1977) At the boundary with the Columbia Plateau, the lower layer thickens and the upper layer thins. The 6.0-km/s layer may be absent beneath this region, in agreement with the presumed replacement of continental crust by basalt here (Chung, 1977). Pn velocities are lower in the West: Herrin and Taggart (1962, 1968) reported 78 km/s for the mid-Rockies, Colorado Plateau, and the Basin and Range Province; 8.0 km/s for the Southern Rockies; and 82 km/s under the Great Plains in the EUS (see Fig. 2. These observations of P n velocity, and the average short-period P-wave amplitude residuals determined by Cleary 1967) and Booth et al. 1974) were used by Marshall and Springer 1976) to illustrate an empirical relationship between mean station amplitude residuals and the local Pn velocities. These observations strongly suggest that the local Pn velocity is indeed a measure of the regional seismic attenuation properties of the earth's upper mantle beneath the seismic station. A high local P n velocity implies a positive station magnitude bias; a low local Pn velocity, a negative station bias. Also implied here is that the regions with lower P n velocities would show higher attenuation of P amplitudes. This empirical relationship is of fundamental importance, because, for many parts of the world, it allows estimates to be made of Q in the earth's upper mantle, as well as estimates of corresponding amplitude residuals, given only measured P n velocities. It seems reasonable, then, tat regional amplitude variations are caused by the corresponding variations in Q (neglecting local effects such as amplification by low-velocity surface layers). From these amplitude variations, one can

-10 conclude that upper-mantle Q correlates with the velocity of P n and that the observed high Q and high Pn velocities in the EEJS may be caused by physical mechanisms unique to the properties of the stable shield regions and distinctly different from those in the West. Lateral variations in the structure and physical state of the crust and upper mantle of the earth bear directly on these differences in velocities and Q's. Solomon and Toksoz 1970) have observed the attenuation of Pnand S waves over the conterminous United States. The regions of high attenuation (thus low Q) for both types of waves lie between the Rockies and the Sierra Nevada. The regions of low attenuation (thus high Q) are the central and eastern regions and along the Pacific Coast. Again, it appears that the attenuation results correlate well with apparent heat flow data and seismic-wave velocities. Molnar and Oliver 1969) used the S n velocity as a discriminant to test the continuity of the lithosphere in many regions of the world, including North America. Regions of stable lithosphere, such as shields or ocean basins, transmit Sn waves efficiently, while regions of discontinuity, such as spreading centers (for example, the Rio Grande Rift zone) or descending plates, do not transmit Sn waves. As shown in Fig. 4 S n waves are transmitted efficiently in the Canadian shield and the entire EUS. However, over paths in the WUS, the Gulf of California, and the Mexican Plateau, n waves are either severely attenuated or not transmitted at all. Cleary and Hales 1966) observed regional variations in P-wave travel-time residuals across North America. The arrivals were as much as s early in the central United States and up to 1 s late in the Basin and Range Province in the West. Doyle and Hales 1967), in a similar study of waves, found a range of travel-time anomalies of about s, with negative values generally occurring in the eastern and central United States. As observed by Hales and Herrin 1972), the travel-time anomalies in the conterminous United States associated with local station conditions are:

• S-wave residuals have a range of over 8 s, while the P-wave residuals range over 3 s. • In the West, travel times of both P and waves are slow relative to the Jeffreys-Bullen curves, while the times are fast in the East.

- 11 KTG) v4li :CCG COL

DH

Canadian hield

na ian, LON Shield are,, ItCOR 1'g__ LA _'pBOZ SFA Basin I RCD SHF BKS *DU IVINN M G Ra C

BEC

Indian rc

FIG. 4 Seismic-wave transmission characteristics in North America. Efficient transmission is indicated by solid lines; insufficient transmission by dashed lines (after Molnar and Oliver, 1969).

- 12 - • The scatter in the data is too great to try to correlate residuals with provinces. • The correlation coefficient of the P- and S-wave anomalies is 075, and the slope of the regression line is 372 1.0, implying that regions with a P-wave anomaly have a corresponding though much larger S-wave time anomaly. The magnitudes of the P- and S-wave anomalies suggest that the apparent effects of partial melting in the upper mantle may be an important factor in the delay times, since a mechanism that changes the Poisson's ratio is needed. A constant Poisson's ratio implies that the ratio of the travel-time anomalies is inversely proportional to the ratio of the P- and Swave velocities, implying a slope of 17 to 1.8. What is observed from the seismic data is that Pisson's ratio in the West is about 5% to 10% higher than the more or less constant value in the East. These observations are most easily explained by lateral variations in the velocity and attenuation structures of the earth's upper mantle and lower crust in going from the East to the West. The relative attenuation of body waves passing through the upper mantle beneath North America has been the subject of several recent studies. Solomon and Toksoz 1970) determined a differential attenuation

St* = Tr fQl(sf) _'(s) ds path where is the shear-wave velocity and is the departure of the true anelasticity, at a point along the ray path, from a radially symmetric Q_1distribution. Positive values of t* indicate greater than normal attenuation and vice versa. The results of Solomon and Toksoz 1970) for both P and waves indicate high attenuation between the Rocky Mountains and the Sierra Nevada-Cascade ranges and low attenuation throughout most of the central and eastern portions of the conterminous United States.

- 13 - Der et al. 1975) observed consistent patterns of attenuation for short-period teleseismic P and waves. Their analysis shows that greater attenuation occurs for both types of waves in the WUS than in the EUS. In a later study, Der and McElfresh 1976) determined average Q values for ray paths from the Salmon nuclear explosion in Mississippi to various Long Range Seismic Measurements (RSK) stations. They observed Q values between 1600 and

2000 for paths confined to eastern North America, whereas they obtained values of about 400 to 500 for paths crossing into the WUS. Figure , reproduced from Der and McElfresh 1976), shows that as the Northwest profile crosses over the Rocky Mountain front, the dominant period of P waves increases to about 1 s, while those with paths located entirely in the EUS have dominant periods around 03 to 0.5 s. This change in spectral content dramatically illustrates the attenuation characteristics of high-frequency waves for paths traversing the upper mantle of the WUS, compared to the same frequencies for the other paths (i.e., the northeast and north profiles).

EVIDENCE FROM SURFACE-WAVE STUDIES

For the purpose of inferring regional structures, surface-wave data are very valuable. In addition, the anelastic attenuation of surface waves is of practical importance to a proper description of ground motions caused by earthquakes (see Nuttli, 1973a, b, c). Love- and Rayleigh-wave dispersions are most sensitive to shear-wave velocity distributions, which are in general difficult to measure using the usual waves. Also, surface waves in the period ranges detected on long-period World-Wide Standard Seismograph Network

(Wr4SSN) instruments are sensitive to the details of the upper 400 km of the earth's interior, which corresponds to body-wave arrivals less than 30 0 from the source. In practice, body-wave arrivals in this distance range are very difficult to interpret: The amplitudes are often small and multiple phases appear within short periods of time on the seismograms. Because of focusing of rays, the amplitudes in some cases are very large. In recent years, the body waves at these distances have been used to determine the fine structure of the upper mantle, by constructing synthetic seismograms.

- 14 - U4 0

OA 4.)

ol di 0 i tW a 0 w 4i 4i %W -4 to IL

01 4 C: 4i 0 to -4 0 En 0 1-4 4) 04 C x 4.) '44 0

CL

4J E 4i 0 lu L4 :3 44 CO a 0 44 0 w L4 04 (D cc wi 43 CO 4 r=

to 4i

> rz0 to

fit

c 04 -4 4i

15 Surface-wave measurements over the conterminous United States were made by Pilant 1967) for periods between 20 and 50 s. A sharp gradient in the phase velocity of Rayleigh waves across the Rockies and much lower phase velocities in the West are prominent features at these periods. Also, evidence is seen in the records of higher phase velocities at the western coastal margins. The structure that Pilant inferred for the western region has a low upper-mantle velocity, compared with the CANSD model of Brune and Dorman 1963). Pilant's conclusion is consistent with heating and partial melting of the upper mantle below the crust in the West. No evidence exists for the presence of a low-velocity zone in the ast. Biswas and Knopoff 1974) reported results of two-station Rayleigh-wave phase-velocity measurements in the conterminous United States in the period range between 20 and 250 s. They found three subregions, which they labeled the western United States, the southcentral United States, and the northcentral United States. The western U.S. region corresponds to the physiographic provinces west of the Rockies. Five two-station paths in the western United States were found to have phase velocities that agreed to within about at all periods, but that showed differences of up to 10% when compared with the eastern regions. Phase velocities for the eastern provinces were much higher, especially in the northcentral United States, where velocities become indistinguishable from the values observed in the Canadian Shield regions. A few determinations of upper-mantle Q beneath the United States have been reported; among them are those by Lee and Solomon 1975, 1979) in the EUS, and by Archambeau et al. 1969), Solomon and Toksoz 1970), Biswas and Knopoff 1974), Lee and Solomon 1975, 1979), and Kanamori 1967) in the WUS. The Q values range from 300 to 1100 in the EUS and from 20 to 500 in the WUS, and these Q values were obtained under the assumption of frequency-independent Q. These observations have qualitatively established that low values of upper-mantle Q predominate in the West and that high Q values predominate in the East. Recent work (Mitchell, 1979) shows that Q varies with frequency. Mitchell's studies have been carried out in the frequency domain. The Rayleigh-wave amplitude spectra, after correction for source radiation effects and focal depth, show a decrease with epicentral distance. Using the spectra at a number of stations, the spatial attenuation was calculated as a function

- 16 - of wave frequency. Both fundamental-mode and higher-mode Rayleigh waves were used in the analysis. From these data, Mitchell determined by inversion a Q model in which Q varies both with depth in the crust and upper mantle and with wave frequency. He found for eastern North America (Mitchell, 1979) that for periods of to 40 s the data satisfy the relation

Q PZ = WWC where refers to shear waves, w is angular frequency, C(z) expresses the dependence of Q, on depth, and has a constant value of 0.5 for eastern North America. The theory allows for to be a variable, but the data indicate that it is constant in this period range. The coefficient of anelastic attenuation decreases monotonically from a value of 1.0 X 10 -3 km-1 at a period of 1 s to about 0.1 x 10- 3 km-1 at a period of 10 s for eastern North America. The Q, model that Mitchell found for eastern North America has a minimum at a depth of to 7 km and then i monotonically with depth in the crust. The minimum values of Q are approximately 700 at a period of 1 s, 200 at periods of 10 to 20 s, and 10 at a period of 40 s. At a depth of 30 km, they are about 10,000, 2000, and 800, respectively. Recent studies of Q for short-period seismic waves indicate the dependence, if any, of Q on wave frequency. Herrmann 1980), for example, using the coda of local earthquakes, developed a number of techniques for obtaining values of Q and the coefficient of anelastic attenuation from the codas of local earthquakes, based on the hypothesis that the codas represent scattered waves. In the first of his methods, one measures the frequency of the coda waves as a function of travel time. A plot of such data can be used to give both the Q value at a 1-s period and the parameter by comparing the data with a master curve that takes account of the filter characteristics of the seismograph. Herrmann also gives two other methods of determining Q from the coda of surface waves. In the second method, the peak-to-peak coda amplitude is plotted as a function of travel time, and curve matching is used to compare the observed variation of coda amplitude with time against theoretical values for a particular seismograph system. In the third method, the envelope of the coda is matched with a theoretical envelope for a

- 17 - particular Q. The amplitude ratio of the codas is a measure of the seismic moment of the earthquake. When the amplitudes are corrected for this moment, the coefficient of anelastic attenuation can be calculated. Herrmann applied these techniques to data from stations at Blacksburg, Va., Berkeley, Calif., Dugway, Utah, and Gratio, Tenn. His data were fitted by the model in which = . His result for Q at Blacksburg corresponds closely to that obtained by Bollinger 1969) for the southeastern United States, and his Q value for Gratio is similar to that obtained by Nuttli 1978, 1980) for the central Mississippi value. Nuttli 1978, 1980) used a number of techniques, principally amplitude measurements in the time domain, to estimate the anelastic attenuation of L 9 and other crustal phases, and thus Q. The first technique uses the observed decrease of amplitude with distance for a single earthquake, and fits the data with a theoretical attenuation curve for dispersed surface waves, in which the coefficient of anelastic attenuation y is a parameter. For a half-space model,

= f/QV where f is the wave frequency and V is the group velocity. If the earth model is layered, Q represents an apparent Q. This method is applied for a number of earthquakes in a particular region, and values of y are averaged to give a mean y for the region. For 1-Hz, higher-mode Rayleigh waves, Nuttli (1973a) obtained y = 00006 m for eastern North America. In a later paper (Nuttli, 1978), for the Mississippi valley he obtained y = 0006 km-1 for 10-Hz, higher-mode Rayleigh waves. These results, taken together, indicate that the apparent Q for 1- and 10-Hz L waves is 1500. A variation of this method is to use the body-wave magnitude of an earthquake, as determined from teleseismic P waves, to obtain a near-field value (at, say, an epicentral distance of 10 km) of the extrapolated L amplitude at I Hz. (This uses the fact that throughout the world there appears to be a similar relation between mb values and 10-km extrapolated L amplitudes.) Using theoretical attenuation curves, the observed L amplitude at one station for a single earthquake can be used to give an average value of y for the path from the epicenter to the station. Nuttli 1980) used this method to

- 18 determine attenuation in Iran and (in unpublished work) throughout southern Asia. Nuttli has also applied Herrmann's first method to get Q from the variation of the wave frequency of the coda of L with travel time. For stations in Iran, Afghanistan, and Pakistan, he obtained low Q values and found that for periods of to 5 s Q varies with frequency as Q(f) 0.5 QO f , where Q is the value at Hz. This is the same value of the exponent as Mitchell found for eastern North America. Also, independently for Iran, by amplitude measurements in the time domain, Nuttli obtained Q = 200 for 1-s L waves and Q = 00 for waves of 3-s period, implying a relation of 90.5 Q(f) = Q 0f for this period range. Nuttli 1979) has also applied the fitting of a theoretical surface-wave attenuation curve to ground accelerations and velocities of the 1971 San Fernando earthquake, as well as to-other western U.S. earthquakes. For the San Fernando earthquake, he found that for waves of approximately 5-Hz frequency the coefficient of anelastic attenuation for the acceleration data was 00135 km The maximum velocity values occurred at lower frequencies (about 2 Hz), and for these data, the coefficient of anelastic attenuation was 0.010 km-1. These results imply that Q = 80 at 2 Hz, and Q = 333 at Hz. Dwyer, Herrmann, and Nuttli (Numerical Study of Attenuation of High-Frequency L Waves in the New Madrid Seismic Region, to appear as an Open-File Report of the U.S. Geological Survey) used data recorded on magnetic tape for the New Madrid seismic region. The data were narrow-bandpass filtered, and the data of each frequency were fitted by a theoretical surface-wave attenuation curve. A statistical treatment allowed the data of all the earthquakes recorded at all the stations to be considered simultaneously. The result was values of the coefficient of anelastic attenuation at discrete frequencies, along with confidence limits. The results confirmed Nuttli's value of Q = 500 at I Hz, but gave Q = 3090 at 0 Hz, as opposed to Nuttli's value of 1500. These results indicate that, for 0.3 to 10-Hz L waves in the central Mississippi valley, Q(f) = Q f 9 0 The only Q model pertaining to the upper mantle beneath the EUS, where the tectonics resemble those of shield regions, was derived by Lee and Solomon (1975, 1979) from simultaneous inversions of surface-wave phase-velocity and attenuation data. Although the model shows much scatter, it does not require

- 19 a low-Q zone in the upper mantle of the EUS to give an adequate f it to the data (Fig. 6 In the WUS, the model shows clear evidence of a low-Q zone in

the upper mantle. In summary, a regional attenuation (as well as velocity) difference is apparent between the WUS and the EUS. Figure 7 shows our estimates for Q a along paths in the upper mantle of the conterminous United States, calculated from Pn velocities.. The contour intervals are 250 in the EUS (where we took the Pn velocity to be 82 km/s) and 100 in the WUS (where we took the velocity to be 76 km/s). Closer intervals would require subjective judgments about the areal extent represented by a single path determination, as well as judgments about the reliability of such determinations. What then are the implications of this regionalization of both attenuative properties and propagation velocities for ground motion attenuation at near fields? The next

section will address this question.

- 20 - 0.06

Eastern United States

0.04 -

7,xx

0.02 -

0

0.08

Western United States 0.06 -

0.04 -

0.02 -

O.h=RA I I 0 100 200 300 Depth (km)

FIG. 6 Comparison of the upper-mantle Q models for the eastern and western United States (after Lee and Solomon, 1975, 1979). The shaded areas indicate the seismological model variations.

- 21 - C) C)

250 13

I 1000 750 0

FIG. 7 Contours of upper-mantle a from Pn paths in the conterminous United States.

- 22 - IMPLICATIONS OF RBGIONALIZATION: DISCUSSION

The ground motion attenuation we refer to here is the decay in the amplitude of motion that is generated by sudden slippage at an earthquake source. Key factors influencing attenuation are the source conditions, transmission path characteristics, and local site conditions themselves. Near the source, at strain levels of > -6 , attenuation may depend on amplitude as well. Q might decrease twofold or more when strains are high

(see Johnson and Toksoz, 1980); however, we shall not pursue this dependence here. In the foregoing section, we presented seismological evidence related principally to the transmission path characteristics. The source conditions influence the initial level of the ground motion and the frequency content of the motion. Local site conditions further influence the level and frequency content of ground motion. The transmission path characteristics influence the path length and the rate of amplitude decay. To compare ground motion from different earthquakes, we need a methodology to extrapolate, for each earthquake, the observed ground motion into the near field. The attenuation of the peak ground motion with epicentral range is of particular interest for several other reasons as well. First, the high-frequency end of the spectrum is fixed by the peak acceleration. Second, estimates of the stress drop can be obtained if estimates of the peak velocity in the near field can be made. Finally, the interpretation for the attenuation of the high-frequency parts of the ground motion can be made in terms of the peak acceleration or velocity. The problem is too complex to derive the appropriate law directly; however, our observations from both point-source and line-source (salvo-type) explosions show that

A GM P (r = (1) n r

23 - where

GMP = ground motion parameter (peak ground acceleration, velocity, or displacement), r = hypocentral distance, n A = constants dependent on the ground motion parameter, geological parameters, and the yield of the explosion.

A single value for the constant n appears adequate to cover the range L/r < 025, where L/r is the ratio of the length of the salvo explosive array to the hypocentral distance, for both near and far fields. Bernreuter 1978) gives a number of examples. Figure shows typical results: These data were obtained from the Buggy experiment, a salvo-type underground nuclear explosion, performed in 1968 to test the feasibility of using nuclear devices for canal excavation. The exponent n is in the neighborhood of 17 for the peak particle velocity. As shown by Bernreuter 1978), the same result (n 17) is found for all available data from the underground nuclear explosion experiments. Figure 9 shows the attenuation of vertical ground velocity from the 1971 San Fernando earthquake. Again, the velocity attenuates as the inverse of n r ,where n 165. In fact, Eq. (1), with n n 17, fits all the available earthquake data for the attenuation of peak acceleration; with n = 17 it fits all available data for peak velocity. Therefore, we believe that the 1/rnlaw is general for the attenuation of peak velocity. One implication of these findings is that the nonlinear behavior of the ground during the passage of strong motion may not be very important compared to uncertainties introduced by other geological and seismological parameters. Nuttli (1973c) presented estimates of "peak sustained values of the vertical component of the velocity' from the 1968 Illinois earthquake (body-wave magnitude 5.5). These data, collected from seismograph stations throughout the Midwest and eastern North America, are plotted in Fig. 10, along with earthquake data from the WUS for magnitudes between 45 and 5.8. It is important to note that these data were obtained from the WSSN

- 24 - 104

103

102

E Slope 1.7 lo' 0

E 100 - M CL

co 0

lo 1

lo 2

lo- 3 I 0 lo 2 lo 1 100 lo' 102 103 Distance (km)

FIG. 8. Peak particle velocity as a function of distance fro a salvo-type underground nuclear explosion source (Buggy). The open circles represent data from velocity gauges; the triangles represent spall measurements.

- 25 - 102 F

lo'

0 E 0 000 > 100 lope 1.65 0

lo-'

> lo 2

A

lo 3 I \ J 100 lo, lo2 103 104 Epicentral distance (km)

FIG. 9 Attenuation of vertical ground velocity from the 1971 San Fernando earthquake. The open circles represent strong-motion data; the triangles are based on the surface-wave magnitude.

- 26 - 102 F F I FI I I F I F I I F I

A lo' A

A AA AA E 100 A Al& t A A

0 lo I 76 Slope -1.55 0 L_ lo 2 a) > 0 O 6

lo 3 \lo

lo 4 I I I j I L I If I i I 11 I I I tj 100 lo' 102 103 lo4 Epicentral distance (km)

FIG. 10. Comparison of vertical components of velocity from earthquakes in the western United States with magnitudes between 45 and 5.8. The open circles (from Nuttli, 1973c) are for the 1968 central Illinois earthquake, body-wave magnitude 5.5.

- 27 - were obtained from the WSSN seismographs, which were not designed to read velocity directly. Velocity must be estimated by determining the period and computing the amplitude-to-period ratio. Because of the inherent instrument response characteristics, the high-frequency part of the ground velocity is filtered out by the seismographs. In addition, it must be kept in mind that Nuttli (1973c) reported the peak sustained value, which is about 07 of the true peak velocity. The comparison of vertical components of velocity from various earthquakes in the western United States (with local magnitudes between 45 and 5.8) with Nuttli's (1973c) data for the 1968 central Illinois earthquake (mb =5.5) is made in Fig. 10. Several important features should be noted in Fig. 10. First, it is evident that Eq. (1) fits the data well. Second, if the WUS data are extrapolated into the far field using Eq. (1) with the exponent n = .55, we see very little difference between the vertical velocity observed in the West and that observed in the central United States in this distance range. The WUS data are for such a small distance range, all within 100-km distance range. As noted earlier, there is no big difference between the EUS and WUS data in the near-field distance because absorption is not important in the near-field. Thus, for the same magnitude, the excitation level (near-fled value) is the same for the WUS and EUS, but at intermediate- and far-field distances, absorption becomes important and EUS motions are attenuated less than WUS motions. The damage area and the felt area are typically much larger in the central United States than in California. This raises the important question: Why this large difference in damage and felt areas? Part of the difference might be attributed to differences in construction. But there is a more basic reason, at least for the difference in felt areas. Human response to vibrations plays an important role in establishing the local mm magnitude scale. One would expect human reaction to be similar in the Fast and the West (except possibly at the lower end of the MM scale), but we are most sensitive to vibrations at frequencies near resonant conditions for different parts of the body. Goldman and von Gierke (1961) showed tat the typical natural frequencies of the thora-abdomen system is between 3 and 4 Hz. For sitting men, the fundamental frequency of the whole body is between 4 and 16 Hz. For standing men, this frequency is between and 12 Hz. Resonance of the head relative to the shoulders falls between 20 and 30 Hz. If, as expected, human response to vibrations is

- 28 - strongly influenced by these resonant conditions, one would expect a much greater human awareness of earthquake motion in the range of 2 to 20 Hz.

Considering the spectral content of earthquake ground acceleration, then, it would appear that man is sensitive to the higher frequencies. This fact, and a two- or threefold difference in the specific seismic attenuation factor 1/Q could well explain the differences observed between felt and damage areas

in the central United States and those in California. Similar reasoning may apply to the differences between the EUS and WUS as well.

The ground velocity is primarily associated with the longer-period waves; this is usually the case even in the near field. The frequency of peak ground

velocity is greater than that of peak acceleration, but in the near-field the peak velocity may have a frequency of 10 Hz. It is generally assumed that the

attenuation of seismic energy is due to geometric spreading, as well as material properties that cause both attenuation and dispersion. Attenuation

(see Gutenberg and Richter, 1956; Knopoff, 1964; Press, 1964) is expressed as

a(rf) = SW exp (- 'f)r (2) VQ where

a(rf) = amplitude of a given wave, S(r) = factor to account for geometric spreading, f = frequency of wave harmonic (in Hz), V = appropriate group velocity.

It is reasonable to assume that the geometric spreading term S(r) is the same in both the East and the West. The major differences in the amplitude of the ground motion are then related to Q and, to some extent, to differences in the appropriate average group velocity. Let us assume for the sake of a simple illustration that the appropriate value of V in Eq. 2 is approximately the same for the East and the West. The ratio of the amplitude of the various harmonics is then given by

- 29 - a ITf QE aW = exp -7 - r JI (3) E _TEW

where the subscripts denote the WUS and the EUS.

From the earlier sections, we take Q values for the East and West as Q E

660 and W = 330 for the purpose of our illustration. (Even greater

differences between the two Q values could be readily justified.) Fig. 1 is

a plot of Eq. 3 for these values of Q E and QW and for three values of f.

For periods greater than 1 s, we observe very little difference in attenuation

out to about 00 km. Because velocity in the far field is primarily

associated with longer-period waves, Fig. 11 thus illustrates that one would

indeed expect to see difference between the far-field values of ground velocity observed in the East and those observed in the West. The value of Q has a strong effect upon the higher-frequency components of the ground motion,

as seen in Fig. 11. Thus, in the East, at the same epicentral distance and

for the same ground velocity, we would expect to see a higher peak

acceleration than in the West.

In addition, the source size not only affects the corner frequency, but

also the total seismic energy. Combining the factor related to the difference

in attenuation with a factor related to source size leads to a prediction of

about an order of magnitude increase of the ground motion in the East compared

to the West. We conclude then that the differences observed between the East

and West may be related to an average difference in source parameters (e.g.,

stress drop, focal depth, etc.), as well as the differences in absorption.

The other important factor in the apparent difference of ground motion

attenuation is that for some western earthquakes the fault breaks the earth's

surface, resulting in larger ground motion. No eastern earthquakes are known

to have broken the earth's surface by faulting. The stress drop of eastern

earthquakes may be higher than for western earthquakes of the same seismic moment, which would affect the high-frequency spectral content, but we believe

that most of the differences in ground motion can be accounted for by

differences in attenuation, caused in turn by differences in absorption

between the EUS and the WUS. One of the major effects of the lower

attenuation in the EUS is to enrich the high-frequency parts of the ground motion spectra at the larger distances.

- 30 - 100 L

co f 5.0 3: lo-, ..a f 1.0 0 CO f 0.5

E lo 2

lo 3 1 t i I I I I 100 lo' 102 103 Epicentral distance (km)

FIG. 11. Variation of amplitude ratio with epicentral distance for three frequencies. QE was chosen as 660; W as 330.

- 31 - STRONG GROUND MOTION CHARACTERISTICS IN THE

CONTERMINOUS UNITED STATES

We have demonstrated a regional difference in attenuation (as well as velocity) between the BUS and WUS. We then discussed the implications of this regionalization of both the attenuative property and the propagation velocities of seismic waves upon strong ground motion attenuation in the near field. Some inferences concerning apparent differences in strong ground motion characteristics in the conterminous United States may now be made.

These differences can be quantified in terms of differences in frequency content, amplitude, and duration of the motion as follows:

• The potential for damage from ground motions in the far field, compared to the near field, is greater in the EXJS than in the WUS. This implies a relatively larger energy content. This also implies

larger accelerations, larger velocities, longer durations, or all three.

• For periods of 0.1 to 10 s, the EUS is a more efficient propagator of surface waves than the WUS. This implies relatively longer durations and larger short- and long-period motions in the EUS. • There may be fewer complexities and lower water content (Mitchell, 1979) in the transmission path in the EUS. This could explain in part

the lower damping inferred in the EXJS. It might imply less scattering

of waves, making the EUS a relatively more efficient propagator of the higher-frequency motions.

• Since there are more-competent rocks at depth in the EUS, earthquake foci may be deeper. This might imply lower attenuation of ground motion, compared to the WUS, at distances less than several focal depths. (Typical focal depths of EUS earthquakes are to 20 km, with

the majority between and 15. This is similar to the WUS.) This

would not explain differences in attenuation at greater distances.

• Source parameters for earthquakes of the same 'size' may be different in the EXJS from those in the WUS. The higher competency of the rock

and lack of major well-developed fault zones might imply higher stress drops and smaller source dimensions in the EUS.

- 32 - INFERRING EUS ATTENUATIONS: FOUR POSSIBLE METHODS

Given the paucity of strong ground motion data and the availability of intensity data for the EXJS, there are very few options for approaching the

existing attenuation problems of that region. One possible approach is to

develop a model for the attenuation of site intensity based upon the EUS

intensity data, then to use existing EUS strong ground motion data, in

conjunction with data from the WUS, to convert the site intensity into a

ground motion parameter. The ground motion parameters chosen for this analysis are peak ground acceleration (PGA), peak ground velocity (PGV), and several spectral ordinates at frequencies ranging from 0.5 to 25 Hz. Ideally, we would have a time history of the ground motion, made at the site for the earthquake of

interest. Equally well, we could have its Fourier amplitude and phase spectra. But such data do not yet exist for the EUS. The best we can hope for, then, is to have knowledge of peak or sustained maximum acceleration, peak or sustained maximum velocity, their dominant frequencies, and their

durations. In recent years, we have gotten better at predicting accelerations and velocities, but we cannot yet accurately predict displacements.

Frequencies and durations will have to come from theoretical modeling and from data for other parts of the world; establishing these values are among the

more challenging research topics in contemporary strong-motion seismology. The attenuation function for the ground motion parameters of interest is

usually written in the form

ln(GMP) = c1 + 2M + c3 ln R + c4R (4)

where c1 through c4 are constants, is either the epicentral or hypocentral distance, and M is an earthquake magnitude. The GMP can be either

PGA, PGV, or peak spectral amplitude (PSA). Functional relationships such as Eq. 4 are not sensitive to site-specific factors (compared to seismicity);

therefore, attenuation functions are often considered to be applicable on a regional scale. McGuire (1976a) prepared a summary of various attenuation functions, and in the appendix we have reproduced his list to aid the user in

finding a suitable function and to provide a basis for comparing newly proposed attenuation relationships.

- 33 - In general, there seems to be no method free of theoretical deficiencies for using intensity data from California to estimate ground motion in the EEJS. One problem is that, in estimating one random variable (z) from another W, introduction of a third random variable (y), used as an intermediary, results in both bias in the mean estimate of z and a larger uncertainty in the estimate of z than would be the case if z were to be estimated directly from x. In the case of estimating ground motion, the procedure of estimating site intensity from epicentral intensity, then estimating ground motion amplitudes from site intensity, results in amplitudes that are less dependent on earthquake size and distance than would be the case if ground motion could be estimated directly. Inclusion of a magnitude or distance term in the correlations of GMP to site intensity (I S),

GMP = f(I s, R) (5) or

G14P = f (Is#, M (6) tends to increase the dependence of GMP on M and R (i.e., it affects the relationships in the correct manner). Such correlations are preferred to relationships of the type GMP = f(IS). However, inclusion of M or R does not ensure that unbiased estimates will be made. In fact, no intermediate parameter can do that, unless it is perfectly correlated with the first parameter (in this case, I or with the last (GMP) . A second problem arises in combining Es. (5) and 6 based on WUS data, with intensity estimates for the EUS. Even if the relative contributions of body and surface waves are the same, and even if source properties are the same, we expect different ground motion spectra for the two regions, for the same Iand the same R or M. If Eq. (5) is used, we assume explicitly that ground motions are identical for the same I and R in the WUS and in the EUS. However, since we observe different intensity attenuations in the two areas, the body-wave spectra as well as the surface-wave spectra must be different. Likewise, if the GMP is estimated using Eq. 6 we assume explicitly that ground motions are identical for the same I and M in the two areas. However, because of different attenuations, we can again expect differences in both the body-wave spectra and the surface-wave spectra.

- 34 - Finally, a third correlation may be considered:

GMP = f(Isil M R . (7)

Using this equation requires the assumption that ground motions are identical for the same Isr M, and R in the WUS and the EUS. Because of differences in attenuation, we would expect I in the WUS to be equal to that in the EUS for the same M and R only if an anomalously large intensity (and ground motion) were observed in the WUS for that M and R. Reasons for such an anomaly might be local soil amplification, focusing effects, etc. Clearly, we would expect the shear-wave spectra for the two ground motions to be different, and quite likely the surface-wave motions would be different as well. Not accounted for in these comparisons are differences in source properties: EUS earthquakes are often thought to be associated with higher static stress drops and smaller source dimensions than events with equivalent energy release in the WUS. Also, the relative contributions of surface waves, particularly of modes higher than the first, are quite likely larger in the EUS. The excitation of higher-mode surface waves is essentially the same for the EUS and the WUS. Furthermore, the propagation of the higher-mode surface waves is controlled by the physical properties of the granitic layer of the earth's crust, and the alluvial sediments on the surface do not have the prominent effect on both the excitation and the propagation of these higher-mode surface waves. It is, however, observed that the Q of the crustal layers is much higher in the EUS than that in the WUS. Both of these differences contribute further to differences in ground motion spectra. As part of the Site Specific Spectra Project (SSSP) of the Systematic

Evaluation Program (SEP), the Lawrence Livermore National Laboratory (LLNL), with its subcontractor, the TERA corporation, has developed four possible methods for inferring strong ground motion attenuations for the EUS through the appropriate application of attenuation data from the WUS (U.S. Nuclear Regulatory Commission, 1980). The first three methods were derived from • The MM intensity-attenuation relation. • An empirical formula relating source MM intensity to body-wave

magnitude. • An empirical relation between site MM intensity and PGA.

- 35 - The fourth method depends on an entirely different procedure for constructing

attenuation curves (Nuttli, 1979). Nuttli's approach was (1) to determine the excitation (near-field acceleration), 2 to estimate wave frequency as a

function of mb for the peak accelerations, using empirical data, then 3 to use empirical attenuation relations to determine the absorption coefficient as

a function of frequency for the central United States. These steps, combined with the application of a theoretical seismic source scaling relation, allowed

Nuttli to estimate maximum horizontal acceleration as a function of m b and

epicentral distance for the central United States. This method, used to

predict maximum horizontal accelerations and ground velocities for coastal California and the WUS, has produced results in good agreement with observations (Nuttli, 1979).

Method 1. One method, suggested by Trifunac in a personal communication, simply relates site intensity to ground acceleration, ground velocity, and/or the response spectrum, as obtained from existing strong ground motion records. Thus, we have

GMP = f(I (8) s

For the EUS sites near the earthquake source zone, this may be a perfectly

satisfactory method, at least as good as anything else we have. However, it essentially ignores the problem of attenuation. method 2 The second method relates site intensity to epicentral intensity

I0 and distance, utilizing data from WUS and EUS sites experiencing the same site intensity at the same epicentral distance. Thus,

GMP = f(Is R)

and

ln(GMP) = c1 + 2Is + c3 ln R (9)

36 - In this case, the site intensity is given by

Is C 1 + 2R + C 3 ln R Io

where

I0 C 4 + 5 mb

The c and C are empirical constants. This method, which can be called

"distance weighting," requires that the magnitude of the WUS earthquake be

larger than that of the ECJS earthquake. In that case, we would expect the WUS

time history to consist of lower wave frequencies for two reasons: Larger- magnitude earthquakes tend to be richer in low-frequency motion, and the absorption of the high-frequency waves is greater in the WUS than in the EXJS. We would also expect to see lower peak accelerations for the WS strong-motion time histories than for those from the EUS, even though the site intensities are the same. The durations for the WUS and EUS time histories should be about the same, as they are controlled by dispersion, which would be similar at the same epicentral distance. The shapes of the response spectra would be different.

Method 3 The third method, called "magnitude weighting," uses the same intensity and the same magnitude of WUS and EUS earthquakes, but different epicentral distances. Thus, we have

GMP = f(Isr M)

and

ln(GMP) = cf + 21Is + c31ML (10)

Here, site intensity is given by

I C 1 + 2 IR + C3 1 In R I

37 - where

I0 C4 + 5 1 b

The local magnitude ML is given by

ML = 6 + 7 Mb

All the c 1, C , and C are empirical constants. For this method, the frequencies of the peak accelerations and velocities should be more nearly equal, because the magnitude is the same for both earthquakes and because the WUS site is at a smaller distance. This smaller epicentral distance tends to compensate for the higher absorption in the WUS. But the duration of the WUS time history will be less than that of the EUS, because dispersion becomes more important at greater distances.

Method 4 The fourth method, proposed by Nuttli 1979), uses theoretical modeling, an mb scaling law for accelerations and velocities, observed values of absorption coefficients for WUS and EUS higher-mode surface waves, and the observed attenuation of maximum sustained horizontal and vertical accelerations and velocities for the 1971 San Fernando earthquake. This method also assumes (with some justification from observations in other parts of the world) that the near-field extrapolation of the far-field L motion is the same for earthquakes with the same mb in both the WUS and the EUS. Nuttli 1979) assumed a theoretical attenuation curve for L waves (higher-mode surface waves) with an absorption coefficient y of 00135 km-1 as

GMP(R) = C8 k-5/6 exp (- yR) (11) where C8 is the amplitude at 1-km distance. Nuttli 1979, p. 36) has shown the goodness of fit of the 1971 San Fernando (California) earthquake data to Eq. (11) for the sustained maximum 3 cycles) horizontal and vertical acceleration versus the epicentral distance R. Eq. (11) seems to fit equally well for the sustained maximum vertical and horizontal velocity data of the

- 38 - San Fernando earthquake, with the absorption coefficient y = .010 km- 1 A frequency-dependence of y is seen by Nuttli 1979). of these four methods, which one is best? In the absense of actual data, one cannot give an unqualified answer. In the following, we shall discuss the promise of these methods.

EXAMPLES AND DISCUSSION

The intensity attenuation relationships for several well-known earthquakes in the East are shown in Fig. 12. These events are the 1886 Charleston earthquake, with an MM intensity (MMI) of X; the 1897 Giles County event (MMI = VII to VIII); the 1944 Cornwall event (MMI = VIII); the 1968 southern Illinois earthquake (MI = VII); and the 1969 West Virginia earthquake (MMI = V). As seen in Fig. 12, all five attenuation relationships have a characteristic functional form, which can be expressed as

IS = A A2R - A 3 log R , where R is the epicentral distance in km and the constants A are empirically determined parameters. The values of these constants for the fiv events being discussed are shown in Table .

TABLE 1. Values for the constants A.. I

Earthquake A1 A2 A 3

Charleston 1886) 12.87 0.0052 2.88 Cornwall 1944) 9.69 0.0052 1.58 Giles County 1897) 7.85 0.0038 0.79 S. Illinois 1968) 7.35 0.0046 0.72 West Virginia 1969) 6.50 0.00093 1.06

- 39 - x 1 - 1866 Charleston 2 - 1897 Giles County (VII-VIII) 3 - 1944 Cornwall (Vill) Ix 4 - 1968 S. Illinois (VIO - 1969 W. Virginia (V)

Vill

VII 3

VI 2 4

V -5

I V, 1 77 N 5 100 Epicentral distance (km)

FIG. 12. The intensity attenuation relationships for five historical events in the EUS.

- 40 - The attenuation relationships for PGA, derived for an earthquake with Mb 6.5 using the four different methods described in the previous section, are illustrated in Fig. 13. Shown in Fig. 13 are the computed values of the horizontal PGA for an earthquake of magnitude mb 6.5. Let us now discuss three different ranges of epicentral distance, or better, distance from the earthquake fault. Again, we shall refer to the set of observations out to 25 km as being in the near field; those from 25 to 200 km as in the intermediate field; and those beyond 200 km as in the far field. For the near-field distances, differences in attenuation between the EUS and WUS are insignificant. In this case, methods 1 2 and 3 should give equally good results, if certain conditions are satisfied. These conditions include: same mb' same focal depth, same stress drop, and same length of faulting. Variations of the last three quantities, particularly the focal depth, can cause order-of-magnitude changes in peak acceleration, velocity, and displacement for the same mb' Thus, the observed scatter in data at near-field distances is not necessarily due to poor quality data, it may be due to actual differences in the earthquake source process. In both the WUS and the EUS, very shallow earthquakes <5 km deep) excite anomalously large high-frequency, fundamental-mode surface waves. This motion attenuates extremely rapidly, so it is critical only at near-field distances. Method 4 should not be used for near-field estimates of peak acceleration and velocity, as it assumes a point source and a focal depth greater than km; either or both of these conditions may be violated. In modeling or estimating near-field ground motion, it is important to ask if the maximum-magnitude earthquake can occur at a very shallow focal depth. Our physical intuition says the answer should be no, that there should be different maximum-magnitude earthquakes for very shallow and normal depths. if this were not so, it would be necessary to design for enormously large accelerations and velocities in the near-field region. For the intermediate-field distances, we believe that methods 3 and 4 will give the best values of ground acceleration and velocity. To determine response spectra, duration must be known. In method 3 the duration of WUS time histories cannot be used for EUS sites; the duration must be lengthened without changing the frequencies of the ground acceleration and velocity. Variations in focal depth and length of faulting are not so critical at the intermediate-field distances. Overall, we would expect the best estimates of EUS ground motion in this distance range.

- 41 - 103

C- E Method 1

0 CU 102 Method 3 Method 2

P

0 lo, Method 4 0

100 I I till I I I I I 100 lo, 102 Epicentral distance (km)

FIG. 13. A comparison of the results of the four attenuation models, for an event with mb = 65.

- 42 - Absorption becomes very important for the far-field distances. Even in the ECJS, the absorption will suppress the high-frequency waves, allowing those

of 2 Hz and less to dominate. The shape of the response spectrum will be noticeably different from that obtained from time histories recorded at

intermediate-field distances. We expect that method 4 will give the best estimate of ground motion in the far-field region.

For methods 3 and 4 we need to know the magnitudes of the earthquakes on

a scale which allows them to be directly compared at frequencies of Hz and

greater. The m b scale appears to be perfectly suited for this, but there

are problems. First, the ML scale is commonly used for WUS earthquakes.

Furthermore, m b values for WUS earthquakes as determined by the USGS are notoriously poor, because they are usually based on P-wave amplitudes at distances of less than 2500 km. At these short distances, two problems must be faced: the large variation of P-wave amplitude due to variations in

upper-mantle structure and the known difficulties with the Gutenberg-Richter calibration function. (The latter problem can be reduced by using the

Veith-Clawson calibration function, which is used by DARPA but not by the

USGS.) For the larger WUS earthquakes (m b > 5.5), there are sufficient

P-wave observations at distances greater than 2500 km to overcome these problems. But some seismologists who have studied the amplitudes of P waves from underground nuclear explosions at the Nevada Test Site conclude that anomalous upper-mantle structure there causes m b values for WUS events to be underestimated by about 03 m b units (a factor of two in ground motion). If this is the case, one should assume that an earthquake of ML = 5.0 in the

WUS corresponds to one of about m b 4.9 in the US for waves of frequency near Hz. If it is not the case, an ML of about 5.0 for a WUS earthquake would be comparable to an m b of about 46 for an EUS earthquake. We don't know which is correct. The very limited strong-motion data from the New Madrid region would suggest the latter, but this could well be disproved by the next intermediate to large earthquake in that region.

Finally, we wish to say a word concerning the range of m b values for which method 4 is applicable. The assumed scaling law (that log a is proportional to 0.5m b and log v is proportional to 1.0m b) is valid if the corner frequency is less than Hz. This occurs only for earthquakes of m b greater than approximately 45 to 5. At the upper end, we know that the m b scale saturates near mb = 73. Thus, the attenuation curves should not be

- 43 - scaled upward beyond about mb 7.0. But the range of mbi s between 5.0 and 70 encompasses most earthquakes of interest insofar as damage to structures is concerned. In a personal communication, 0. W. Nuttli has offered an independent evaluation of methods 3 and 4 He points out that the results of method 3 depend on the delineation of the seismic source zones, on the estimation of the maximum-magnitude earthquake for each region, and on the determination of the magnitude-recurrence relation for each source zone. For most of the central and eastern United States, we do not yet have as good a knowledge of these parameters as we might like. Continued research effort must be devoted to these problems, so that there will be less variation in the experts' opinions on these points. As it is, the differing opinions of the experts result in rather wide confidence limits on PGA, PGV, site MMI, and response spectrum. A narrowing of these confidence limits by a better understanding of the seismicity of the EUS should have high priority. Nuttli's comparison of the results of the two methods for PGA as a function of epicentral distance appears in Table 2 He remarks that,

TABLE 2 Peak ground accelerations (in cm/s 2) calculated for three body-wave magnitudes, using methods 3 and 4 (from 0. W. Nuttli, personal communication).

Epicentral distance, km

mb Method 10 20 30 50 100 200

6.5 3 500 350 280 200 130 65 4 300 200 100 45

5.5 3 170 110 85 62 39 22 4 250 130 95 60 30 10

4.5 3 52 40 30 21 13 4 80 38 28 17 7

- 44 - considering the complete independence of the two approaches and their dependence on different sets and kinds of empirical data, the agreement in an absolute sense between the acceleration values is remarkable. It indicates that we have a good knowledge of the excitation and attenuation of maximum acceleration values as a function of mb and epicentral distance in the EXJS. Nuttli concludes that method 3 is a realistic and practical means of assessing the seismic hazard in the ES. The procedure itself appears sound. What is required is further research on certain aspects of the seismicity to reduce the uncertainty in the calculated ground motion parameters.

- 45 - ESTIMATES OF THE EPICENTRAL GROUND MOTION IN THE CENTRAL

AND EASTERN UNITED STATES

In this section, seismic ground motion from earthquakes in the central United States, recorded at regional distances, is used as a basis for estimates of the strong ground motion that could be expected from future earthquakes in the same region. We have the problem of extrapolating far-field data into the near field. However, as in some cases, far-field values extrapolated back to near-field distances are similar for earthquakes of the same magnitude throughout the world, but these near-field extrapolations may not correspond to the actual near-field motions. Because observed near-field values for the same magnitude earthquakes show up to an order-of-magnitude difference due to differences in focal depth, stress drop,

source time function, etc., we do not have one unique method to be used for back-extrapolating the data into the near field.

Large earthquakes are much less frequent in the EUS than in California; nevertheless, they do occur. In addition, earthquakes in the East affect a much larger area than earthquakes of similar magnitude in California. Because of this difference in damage and felt areas, one cannot directly use the data from California to make predictions for the EUS. Furthermore, since few strong-motion data exist for eastern earthquakes, the ground motion parameters must be inferred. (The few data that do exist are for earthquakes with m b Is of 43, 45, 5.0, and 53; most are for distances greater than 100 km.) A variety of approaches are available. We investigate one such method, which uses as its basis the data from the 1968 southern Illinois earthquake and the

1811-1812 New Madrid earthquake, both of which were studied by Nuttli (1973a, b, c) to make estimates of the ground motion in the epicentral region of the

1968 earthquake and for possible future earthquakes similar to the 1811-1812 series.

Our method comprises the following steps: We derived a relation that correlates vertical velocity with peak horizontal acceleration.

- 46 - • We then back-extrapolated available measurements (Fig. 10) of vertical velocity for the 1968 earthquake into the near field. We thus have estimated PGA as a function of epicentral distance for the 1968 earthquake. • Finally, we translated this curve to the right (on a plot of PGA vs epicentral distance) to yield a relation between acceleration and distance for the 1811-1812 series.

APPROACH AND RESULTS

The method used here is similar to the approach used by Nuttli (1973a, b, c) to establish the ground motion for large central U.S. earthquakes. His key assumption was that a one-to-one correspondence exists between peak ground velocity and MMI. By back-extrapolating the observed ground motion from the 1968 southern Illinois earthquake into the near field, Nuttli obtained a normal-depth, point-source estimation of the ground motion, which, in turn, was used as a reference value for determining magnitudes of earthquakes for which only intensity data are available. Nuttli's approach was modified to account for factors that will be discussed in detail below. He used a different law than we use to back-extrapolate, and he used velocity rather than acceleration to correlate intensities of the small and large earthquakes. There is little theoretical justification for back-extrapolating far-field data into the near field, if one Yishes to estimate peak ground motion in the near field. The maximum motion in the far-field is typically associated with longer-period surface waves, whereas in the near field it is associated with much shorter period body waves. Nuttli (1973b, c)used the attenuation equations

A = KA-a (sinA) 1/2 exp (-yA) (12) where A is the epicentral distance and y is the coefficient of anelastic attenuation. The constant a is equal to 13 for the Airy phase and 12 for normal dispersed surface waves. The period and type of the waves with which the maximum ground motion is associated changes with epicentral distance, whereas Nuttli's back-extrapolation is for waves of a given period. To apply his method to determine peak values, one would have to consider a wide range

- 47 - of wave frequencies, and take into account how the frequency of the peak motion changes with epicentral distance. Nuttli's 1979) later work supplants the need for such calculations. The basis we use for back-extrapolation is empirical. With the use of abundant data on ground motions obtained from various underground nuclear explosions (see, for example, Murphy and Lahoud, 1969; Loux, 1970), we relate near-field data to far-field data, using the relationship,

log(GMP) = K + log (distance) (13) where GMP is either the PGA, PGV, or displacement. In Fig. 14, the peak accelerations from the 1973 Rio Blanco event are plotted as measured at various recording stations. A similar illustration was presented earlier in Fig. 8, where a relationship similar to Eq. 13) was shown to fit the peak particle velocity measured from the 1968 Buggy event. For earthquakes, Orphal and Lahoud 1974) observed that all the available data (sparse though they are) also fit this form of Eq. 13). As a specific example, we saw in Fig. 9 that the measured vertical velocity from the 1971 San Fernando earthquake fit Eq. 13) very well. (Near the epicenter, where the effects of focal depth and source dimension become important, Eq. 13) might not be applicable.) The 1971 San Fernando earthquake is probably at the upper limit of magnitude of earthquakes that can be treated as point sources, and extrapolated back to 10 km. Figure 9 shows the relationship between the vertical velocity as computed from the strong-motion accelerograms and the averaged value of the far-field peak velocities. This relationship suggests that it is feasible to use far-field data to deduce meaningful estimates of near-field ground motion. In the very near field, problems often arise because the diffuse nature of the source of seismic energy and the lack of near-field data makes it difficult to determine the proper form of the distance parameter in Eq. 13). As described earlier, nonlinear effects of soils become much more important in the near field, particularly in regard to peak acceleration. The San Fernando earthquake data seem to show that these effects are seen only in the very near field. This discussion leads us to believe that, having the far-field data from a central U.S. earthquake, we may then be able to make reasonable estimates of the near-field ground motion from that earthquake.

- 48 - 0 0 lo, 0

L) C 40 A2 OA

lo'

PGA = 18613- 0

lo 3 lo 2 lo-' 100 Peak acceleration (g)

FIG. 14. Measured peak accelerations from the Rio Blanco event as a function of distance. The line is a least squares fit.

- 49 - The choice to use acceleration as the basis for the correlation between the smaller 1968 earthquake and the larger 1811-1812 earthquakes is based primarily on the fact that stress, and therefore damage, in a structure is not a function of the PGV, but of the relative velocity between the structure and the ground. The study by Newmark et al. 1973) showed that the relative velocity response spectra can be scaled from PGV in the frequency range of 0.5 to 2 Hz. For frequencies greater than 2 Hz, the response spectra should be scaled relative to the ground acceleration. Most of the structures involved in both the 1811-1812 series and the 1968 southern Illinois earthquake were stiff one- or two-story structures. These structures typically have fundamental periods in the range of to 20 Hz. We can correlate the peak acceleration at the edge of the MMI = VII isoseismal for the 1968 southern Illinois earthquake with the peak acceleration at the edge of the same isoseismal for the much larger 1811-1812 series of earthquakes. Thus, wth the average value of acceleration known at one point, one can use Eq. 13) to get estimates of the average peak acceleration for some future large earthquake, provided that the parameter is known. Nuttli (1973a, b, c; 1979) has published estimates of peak sustained values of the vertical component of the velocity observed at seismograph stations throughout the Midwest from the 1968 Illinois earthquake. We should reemphasize that these data were obtained from the standard seismographs typically used in the WSSN. Our approach to obtaining estimates of the 'average' peak acceleration in the near field of the 1968 earthquake was as follows: First, we developed a correlation between peak vertical velocity and peak horizontal acceleration (naturally, only western data is involved), using only rock sites corresponding to conditions at the seismographic stations. A least squares fit to the data resulted in

log (horizontal acceleration) 1.52 087 log (vertical velocity) (14)

- 5 - Thus, the extrapolated near-field velocity estimates can now be converted to horizontal acceleration. This conversion is made only over a limited range where the data are most applicable. We choose to do this at the edge of the MMI = VII isoseismal, which is at an epicentral range of about 22 km. Here, the vertical velocity is about 5 cm/s, which corresponds to a horizontal 2 acceleration of about 134 cm1s We might note that we were able to correlate the peak vertical and peak horizontal velocities as well. This correlation,

log (horizontal velocity) 0.269 + 1.05 log (vertical velocity) (15)

is also useful. At 22 km, for example, we estimate the peak horizontal velocity as 9 cm/s. With the use of this correlation, it is also possible to correlate the peak horizontal acceleration with the peak horizontal velocity:

log (horizontal acceleration) = 127 087 log (horizontal velocity) (16)

Equation 16) gives a peak horizontal acceleration value of 125 cm/s2 at 22km a somewhat lower acceleration value than that obtained with Eq. 12), but a reasonable estimate nonetheless. Although it is difficult to generalize an analysis based only on a limited range of data, our experiences indicate that the WUS data can be extrapolated into the far-field in accordance with Eq. 13). we showed in Fig. 10 that the vertical velocities, plotted as a function of epicentral distance from earthquakes of magnitude 45 to 5.8 in the WUS, and the vertical velocities observed from the 1968 southern Illinois earthquake fit one straight line with a slope of 1.62. Thus, our second step was to assume for central U.S. earthquakes

log (vertical velocity) = 288 1.62 log R (for mb = .5) (17)

5 - It is noted that as the magnitude increases, the frequency of the peak ground acceleration decreases and should also decrease. This correlation enables us to back-extrapolate from the far-field data to obtain near-field ground motion.

Shown in Fig. 15 is a plot of the estimated peak horizontal acceleration obtained from Nuttli's data, as described above. Also shown is a least squares fit of the form of Eq. 13). The important parameter here is the attenuation coefficient B, which was found to be 1.62. To make estimates of the ground motion for some future large earthquake, we assume that Eq. (11 is valid. We determine the constant K and the attenuation coefficient as described above. The viability of our approach is based on obtaining a good estimate of B, which may vary with the tectonic region as well as with the frequency content of the generated ground motion. This latter functional dependence needs to be investigated in the future. As an example, we tabulate in Table 3 typical values obtained for the parameter B, for both acceleration and velocity, for several underground nuclear explosions and two earthquakes. For each of these events, there was considerable scatter in the original data, as shown, for example, in Figs. 9 and 10. In the epicentral region, this rule of back-extrapolation leads to peak accelerations in keeping with those observed in the WUS. For example, at the edge of the MMI = VII isoseismal line 20 km), the acceleration is about 0.15 g. At the median of the MMI = VII zone (about 1km), the g value is about 032 g. Considering (1) that these values are average values, 2 that the results from the San Fernando earthquake show recorded variations of a factor of two from the mean, and 3 that the damage from the 1968 earthquake was spotty, we can conclude that these estimates of acceleration compare favorably with the most complete recent correlation between intensity and acceleration, which produced a mean value of 013 g for the acceleration at mmi = vii amage levels (Trifunac and Brady, 1975). For the case at hand, we want to scale from the small 1968 earthquake to some future large earthquake in the same area; therefore, we assume the same value of B. (Strictly speaking, B is a weak function of earthquake magnitude.) An estimate of the constant K in Eq. 13) is obtained by assuming a one-to-one correspondence between the estimated PGA for the 1968 event at the MMI = VII isoseismal and that at the MI = VII isoseismal for the large earthquake, which we take to be the same as observed during the 1811-1812

- 52 - E .C 2 cb .0C 0 0 0 14D 0 (D Q U M 0

C 0 N

o -C

Median MM VH Median MM VI isoseismal, isoseismal, 0 -2 Illinois 1968 1811-1812 series

lo' 102 1 03 Epicentral distance (km)

FIG. 15. Estimated peak horizontal acceleration for the 1811-1812 New Madrid earthquake series, based on the 1968 southern Illinois event. The lower solid line is a least squares fit to the 1968 data, assuming that Eq. 14) is valid; the upper solid line, obtained by translation, can be used to project the ground motion of future earthquakes similar to the 1811-1812 series. Both lines have a slope of 1.62.

- 53 - TABLE 3 Attenuation coefficients for selected events.

Attenuation coefficient Name of Soil condition event Event type at recording sites Acceleration Velocity

Boxcar Explosion All rock -1.63 --

Ruilson Explosion Soil/rock -2.04 -1.92 Rio Blanco Explosion Soil/rock -2.29 -2.04

San Fernando Earthquake All rock -1.63 -1.65 Kern County Earthquake Soil/rock -1.65 --

series. Justifications for this assumption of correspondence and for the use of the MMI = VII isoseismals include:

e Mercalli intensity VII is established primarily on the basis of

chimney damage. Because chimneys are stiff, brittle structures, one would expect their damage to correlate well with peak acceleration.

* The lower MM intensities are established by using more subjective data and are therefore difficult to correlate with any ground motion parameter. e Very few data exist to establish meaningful relations between

intensity and acceleration for intensities greater than VII.

The upper solid line in Fig. 15, therefore, illustrates our estimate of the relationship between acceleration and epicentral distance for a future earthquake similar to the three major earthquakes of the 1811-1812 series. To verify our prediction of the level of strong ground motion at large epicentral distances, the available worldwide data were reviewed for those earthquakes that had significantly less attenuation than WS earthquakes. There are several such earthquakes with recorded ground motion data at large

- 54 - epicentral distances (see Kuriboyaski et al., 1972; Denham et al., 1973; Cloud and Perez, 1971). These data are also plotted in Fig. 15, along with data from the 1952 Kern County earthquake. It is seen from Fig. 15 that large accelerations can occur at large epicentral distances. In addition, the response spectra of these earthquakes have significant content at both high and low frequencies. Extensive chimney damage, as originally reported, suggests the ground motion from the 1811-1812 New Madrid earthquakes contained peak accelerations consistent with the data shown in Fig. 15.

COMPARISON WITH NUTTLI'S ANALYSIS

Nuttli (1973c) used the same basic data shown in Fig. 15 and arrived at much lower estimates of ground motion. For example, at the MMI = VII isoseismal, Nuttli's estimates of the acceleration (consistently converted) is about a factor of four lower. This difference comes about because, while Eq. (12), used by Nuttli, is appropriate to back-extrapolate a given surface-wave group into the near field, the peak ground motion there is not associated with the surface-wave groups having 1- to 3-s periods, but with body waves of much shorter period. Nuttli noted that the rule he used may not be valid in the strong motion region. To confirm the validity of his results, Nuttli compared the results of his extrapolation to the data compiled by Nicholls et al. (1971). Nuttli concluded that his estimate of a PGV of 12 in./s at the MMI VII isoseismal is consistent with the 2 in./s suggested by Nicholls et al. as the onset of minor change. The comparison made by Nuttli is open to question for two reasons. First, Nicholls et al. 1971) defined the 2-in./s level as the division between a safe zone (little risk of minor damage) and a zone of minor damage, which is defined as the formation of new fine cracks in either plaster or dry wall, or the opening of old cracks. This correlates better with NMI = VI than with MMI = VII. Nicholls et al. also delineated a major damage level of 76 in./s, where one might expect serious cracking for plaster or dry wall, fall of material, and possible structural damage. This definition more closely corresponds to MMI = VII and agrees with the results of Trifunac and Brady (1975). Second, Nuttli associated the peak motion with waves of period to 3 s and longer. However, the structures affected by the earthquake were

- 55 stiff, high-frequency types; hence, one would not expect a correlation between velocity and damage to be appropriate. On the other hand, ground motion from blasting compiled by Nicholls et al. 1971) is primarily in the high-frequency range of Hz and greater. This would cause significant amplification in the type of structures affected by the 1968 earthquake.

- 56 - APPENDIX: PUBLISHED ATTENUATION FUNCTIONS

The following tables, reproduced from McGuire 1976), are compilations of the attenuation functions available in 1976. They should be used to select the appropriate function for a given application, or as a basis of comparison when new functions are proposed.

- 57 - M 'o 4.) cu w C C) >

V) M 0 0

C Kr 0D c CD c + + a) to la .0 < u 0 _ _0 - - E E r- E -& CD4 4 w 10 w C71 cm C C w Ln M 4J 71 A W >, IT < - -4 .- > 41 C%) C%) 4i la to + 'o It Ln r_ C"EJ 0 4 C 4) CD C4 19 17 d, w m L. c 0 CL cn S- 4.0 w 11 11 I- 4J 11 C) 4) CU 0 W L- cm cn cli m 4) o, -C u -0 -i = w to to 11 11 go 3: 3r -

0 -C Q. S- -1 0E a cu S- a) a) u - u U- al u L X .,n > 'a- a) 0 a X: >1 41 4:n 45 cu S-.0 ES.. Tw cm SIm ., r- c 4i to 0 4) E C 4- 0) CD la 4J 4J 4a 4j S- a, cu 10CL 4 0

a) a) a) ci S- L) to o) c - 41 IC to a) 4i 410 41 E 'i la 42 .12 S- -0 a) u

1;S.- 12 'Z 45

MO Ca. w LLJ

'n Gi w a 4-1 a) 41 (A S- 'ow &_ la u .12 0)44 d) w 4 tA S- c 4-) 4j Ln 4J , Ln w = r_ - VI 4- a'a tn .- V) 4i o L.0 0 m -0 W a) 10 -; V) a) (V4J 4) Gi a) ra 4i w 4J 4i 4- = to Cl S- S- 0 S- fo o a(v 0 c 0 S- 0 ZD m Ln

u a - oe a) $.- w a) a) a) E 1, S- 4- to 0a) a) . S- Z; co co

58 10 'D PI a) C, -CT CP C C9 0 0 C 0 CD CD In M CL 1 C6 11 ,a 4j w (1) M 0) CTW M 9 Cn to CD > 4i 4i 4i 0) 0 0 0 to

CM ff! co C) cli C I I -z In cli cic cc Ci ci CI + I'l co cli CD + Cv + Ch %D + a) P + + cc: CD C) M r.- -!, 11: 2- C C) U) Lm C; C co ll L9 + C CD C) w C cc: a co -0,x Inenx r- w w Mr C a) C9 CD cli M 4 9 Le) la 0i In L2 It la M go la 10 M 10 'A >

>1

LA u u(L) L)d) UT 'TS- laUT I I I ua- tou CD >w M f C10 0 0 0 CM C :3 :3 0a 7 0r 0 C M 0 a 0 I- I 0 S- 0 10 tn S- 0 S- E CM 4J M.-4., M T; jS- C M 4.- 0'u -W to be to -NC M U.2 -W M ze S- MS- 10 ID to I- ea Im 06 " a) 0) 0) > In Cl- Cl.

u u S- >1 Ca >1 W M M M 4 4i 4i

to 4) E u -14 0 -fj to 10 C- 4J I 1= o S- - fa M 0 C) CD *4 4 4 J'X w 4j u uL. S- 4 CU go 00 41 9 U. 'C - CO 4J I u 4i 4JC 0 :, 4i r I 0 oul 0 wZ. S- fa uID 1

0 C; C; 1 4i to D a) 'o 'A la tol la I L- --_ u Cw CU, 0 3: 0) 41 I 0 L. cm S- 0 C I S- 4- V) W W W 'a a) '? S,. -Z LL. Af L L w 10 U - " CLJ CL 4i a 0 0 C In to C to go .0 M Q) Q- 00 I= In Le) V) 3c 31: In I cn I

a) u to > - > > 0 IN M 4- C C J, 4-3 (v 0 0 Z, 0 In C, C C Lj

59 -r Ln Mr r- P- kD C c; C C; 0 0 4- It Ii CL CL 0. 4j Ch to L- > f > 0) 4i 4J 4J 4., a) (V a 0 0 Le) =1 V) tn tF t;-

CQ Cj I 4i qrCO + r+l

CL x Cj C) Cl 09 1 cl + co %D+ CO Of C) c; C .1 >1 0 a) C, W CD U U (C> C) koC> CD1.0 C> +d) C MI Csi cli Le) fn a, In I- 4i CL CIL It It 11 %O cli - I (w a m tm cn III It 11 J-- L- > go > C.D L!)

41

MI w fo 0 0) 4 - (U U U m to C7, a) U L. go > -0 >U C U. Ln m4-, V) la to A3 C', m (L) S.. T- S- .- - MI En a) .0 (L) L)E > a, 0) >CD 4i la =1 :3 C 0 0E 0 0 L) 0) 0 C E EF> S- C, S- 5I C7'- C cm E 4- (U 41 .3.f go -V> _le la -W> IV 4j to -IC to la S- -0 S- S- mL. W w w 'a *j 'o 41 CDaj 4 a)

U U w L. C a U U a) la la r_ 41 4i 41 10 E M fo 4- S- -0E 0 0 0 0 S- S- 'a w la 4i I 4J I S- S- a) u C m C I 4J0 4i U C a) Qj C .2 a C la L, L) (IJ 41 0 0 U Cl. CL > >1 C 4' el. cm I 11 LIU LLJ

S- GI 4i 0 i 1 41

U 41 au= S- V) =D 4i = . : No 0 -0 0 CLn 0 0 Ln S- C U 10 45 w 0 S- a) LO') L. 4J - C) J 41 41 4i LA I 0 4.) 4-j 4i r w D I a) I., (A CA :m ic

Ln Lr) ! LO 41 laC E0) u to -0 to (D a) S- laC > .0 41 0) >w > M 4 C.C IC a) 4' v) n a, 4 i 0) LA 4- 4J0 4.) OL 4.) m w Ln CC LM = = r, 0 cc L'i LLJ cm

60 C)

C C'! 0 C) 11 C it II M CZ) C71 6I to 4 C> fo > Im C) C CD CD C5 a) cm a)

LO m 0 t) 0 0 O O O 0 -C co (1) C a, Cl co m C7, (A - 7 7 -< Q to Zl LO S.- 'Lz r E 41 CQ C1.1 + 01i 1E r_ + + + co C m C) r- u to C cli co CO C X: M: c') x C> co CD r co C! "i C, ll C? CD CD Co C) 9 C) CD C -r + d) C .0 +w CD C < CD CA >, CD CD C) CD %D C= 0, C I ew-4j x x C9 o I. C9 C, I. .4 CCIJ> tA m co CD C) - C en 4 19 C7 w C +1 C; rE +1 CD S- C) Ila, II 0, It >

>1 4J 0

4n cm MI 0 el. 4 0i :01 I. r- 0a 4- -0 x a) w o (u 0 a w u 4J -Si W In 0 S- o 4- lj, > w -OC)II w0 CL) 0 0 E E cu cn 40a >1 >1 41 S 41 E 0 x :3 E :z CXI 4- (L) 0 (7l 0 41S- S- cu S- w S-u lxl to S'- 41 Imto a)S- .0 4i mt -I- ) - -W >CP 41 +j In cuL) a Em 4) 41 S- QjE cL a- 4, Q- 0- Cl. Ln 41

S- 10 10 10 41 4 la m S- 10 CD E 0 E 0 m E 0 tn Z! -0 S- -0 S- zl 4A 4 u 30 40 4i0 _ a r_ ..,2 CI..2 .2 0) CZ: 10 aj cu 41 .! .! CL 4J CL 41 CL 4i CL U.1 U.1 LLJ

v 4J Qj 4i 4i la UL. .to I C0 4-1 0=14 Im 0 to VI 0 c 10 - $- ; 0 VI 0 to 4) (L) 10 L.) 10 to a, 41 " w le Vl ID 1 4A la 4-) le L. z 31:CD 4) U.1 VI LAc CM U

4.1

a) 0Lj cr

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- 73 - _iR C o - 35 LRT NUM.-L R (A uP-7ro b DOC) 0 77) U.S. NUCLEAR RFGULATORY COMhISSION NUREG/CR-1655 BIBLIOGRAPHIC DATA SHEET UCRL-53004 L :TLE (-acld Vc,,urn- No. if_-z:- 2. (aae blaikJ

oil Rcr-innal Variation of Seismic Wave ACCE!-_ION No. on Atte the StL-rong Ground Motion frorl-, Eartli,nu- kes

7. AUTHOR (S) 5. DATE REFC,,' C-,;,-LETED VAC4 TH IYEAR D. H. Chung and D. L. Bernreuter July 1981

9 PERFORMING ORGANIZATION NAME AND MAILING ADDRESS fircluc- ZID Codej DATE REPORT ISSSUED MONTH YEAR Lawrence Livermore National Laboratory October 1981 P.O. Box 808 6. (I CAW# lo A) Livermore, California

S. (Le&ve bankl

12 SPONSORING ORGANIZATION NAME AND MAILING ADDRESS Inc!uo,- Zip Code) 10. PROJECTITASK/WORK UNIT NO. U.S. Nuclear Regulatory Commission Office of Nuclear Regulatory Research 11.CONTRACTNO. Washington, DC 20555 A0139

13 TYPE OF REPORT PERIOD COVE RED (Inclusive dates] Technical

.5 F.)PPLEMENTARY NOTES 14 Lve blank)

16 AE-STRACT 000 words or less)

Attenuation is caused by geometric spreading and absorption. Geometric spreading is almost independent of crustal geology and physiographic region, but absorption depends strongly on crustal geology and the state of the earth's upper mantle. Except for very high frequency waves, absorption does not affect ground motion at distances less than about 25 to 50 km. Thus, in the near-field zone, the attenuation in the eastern United States is similar to that in the western United States. Beyond the near field, differences in ground motion can best be accounted for by differences in attenuation caused by differences in absorption. The stress drop of eastern earthquakes may be higher than for western earthquakes of the same seismic moment, which would affect the high-frequency spectral content. But we believe this factor is of much less significance than differences in absorption in explaining the differences in ground motion between the East and the West. The characteristics of strong ground motions in the conterminous United States are discussed in light of these considerations, and estimates are made of the epicentral ground motions in the central and eastern United States.

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