Procedures for Estimating 

Earthquake Ground Motions
PROCEDURES FOR ESTIMATING 

EARTHQUAKE GROUND MOTIONS
High-altitude view of the San Francisco Bay region showing surface traces of the Hayward and Calaveras faults. The Hayward fault was the 

source of two large earthquakes in 1836 and 1868 that caused surface rupture along as much as 64 km of its trace. The Calaveras fault, with 

a length of approximately 160 km, is one of the largest in northern California. The San Andreas fault passes offshore near Mussel Rock 

(arrow at bottom of photograph). Fault systems such as these must be critically studied when evaluating the seismic hazards and risk in an 

urban area.
Procedures for Estimating 

Earthquake Ground Motions

By WALTER W. HAYS

GEOLOGICAL SURVEY PROFESSIONAL PAPER 1114

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1980
UNITED STATES DEPARTMENT OF THE INTERIOR 

CECIL D. ANDRUS, Secretary

GEOLOGICAL SURVEY 

H. William Menard, Director

Library of Congress Cataloging in Publication Data

Hays, Walter W.

Procedures for estimating earthquake ground motions.

(Geological Survey professional paper ; 1114)

Bibliography: p. 69-77.

Supt.ofDocs.no.: 119.16:1114

1. Earthquakes-United States. 2. Seismology United States. 3. Earthquake

resistant design. I. Title. II. Series: United States. Geological Survey.

Professional paper ; 1114. 

QE539.H39 363.3'495 79-607183

For sale by the Superintendent of Documents, U.S. Government Printing Office

Washington, D.C. 20402

Stock Number 024-001-03276-7
CONTENTS

Page

Glossary ____________________________VII

Abstract ______________________________ 1

Introduction______________________________ 2

Determine seismicity ______________________ 3

Sources of information _____________________ 5

Summary of United States earthquake history _______ 5 

Identify seismotectonic features._________________ 9

Summary of United States earthquakes ___________ 12

Western United States ___________________ 12

Eastern United States ___________________ 17

Determine regional seismic attenuation _ _______ _____ 19

Define the characteristics of ground shaking expected at the site 21

The seismogram___________________________ 23

Types of information derived from the seismogram _____ 25 

Peak ground acceleration.___________________ 28

Peak ground velocity and displacement ___________ 31 

Duration ______________________________ 33

Page

Define the characteristics of ground shaking—Continued

Spectra _______________________________ 34 

Knowledge gained from nuclear explosion groundmotion studies________-_ —— ————— ———— 37

Intensity ___________________ ———— — —— ——— 41

Probabilistic estimates of peak ground acceleration ___ 42 

Effective peak ground acceleration ____—————————— 43

Define design response spectra for site —__ —————— _______ 43

Summary of procedures for siting of nuclear powerplants __ 44 

Site-independent response spectra__—————— ———— _ 46 

Site-dependent response spectra __—————— —— —— _ 51 

Design time histories _____——— ——— __ —— ———— 54

Determine local ground response _ __ __ _—————————— 56

Summary of Uniform Building Code procedures __________ 63

Define uncertainties of the ground-motion design values ———_ 66 

Seismic design trends for the future___________---——— 68

References cited —____ ——— —————— ———— —--————— 69

ILLUSTRATIONS

FRONTISPIECE. High-altitude view of the San Francisco Bay region showing surface traces of the Hayward and Calaveras faults.

Page

FIGURE 1. Flow diagram illustrating steps in estimating ground motions for design of earthquake-resistant structures —— 4 

2-5. Maps showing:

2. Location of past destructive earthquakes in the United States____________________________ 6

3. Areas of the conterminous United States where regional seismicity studies have been made—— ——— __— 7

4. Seismic source zones within the conterminous United States ____________ ——————— —— ----— 8

5. Principal faults in the vicinity of Fremont, Calif ____________— — ——— __ ———— -_ — ——— ——— 11

6. Chart for correlating fault rupture length and earthquake magnitude _______————__ —————— -- —— ——— 12 

7-15. Maps showing:

7. Major tectonic features along the Pacific-North American plate boundary in Alaska —— — ——— ———— 12

8. Epicenters of earthquakes in Alaska between 1962 and 1969 __________— ——————— ——— ———— 13

9. Major faults in southern Alaska _____________———————— —————— _ ——— ——— ——— --— 14

10. Major faults in California and Nevada and locations of past surface ruptures___________ — ———— —— 15

11. Wasatch fault zone.________________________________—-- ————— — ——— ——— 17

12. Major tectonic features and historic earthquake activity in the Mississippi Valley area __ — ——— _——— 18

13. Historic seismicity in South Carolina area______—__ — ———— __ ——— __ ——— ——— — ——— ———— 19

14. Isoseismal contours for 1971 San Fernando, Calif., earthquake ______ — ——— ——— — ______———— 20

15. Isoseismal contours for 1906 San Francisco and 1811 New Madrid earthquakes _ ———— — ——— ————— 21 

16-20. Graphs showing:

16. Empirical intensity attenuation curves proposed for the southern Appalachian seismic zone and the

central Mississippi Valley _______________________--_____-———————— —— _____ 22

17. Average value of maximum acceleration in relation to distance from fault for earthquakes of various

magnitudes, Western United States _____________________— —— ——————— __ ——— ——— 22

18. Schnabel and Seed acceleration-attenuation curves modified for use in the Eastern United States ———— 23

19. Acceleration-attenuation relations derived from worldwide earthquakes and the San Fernando earthquake, 1971 ______________________________________________________ 24

20. Frequency-dependent attenuation of horizontal ground motions, southern Nevada and Colorado __ ——— — 26

21. Schematic diagram of elements that affect ground motion _________________________________ 26

22. Accelerogram of the 1940 Imperial Valley, Calif, earthquake recorded at El Centre, Calif_______________ 27

V
VI CONTENTS

Page

FIGURE 23. S. 16° E. accelerogram recorded at Pacoima Dam and the velocity and displacement seismograms derived from it;

1971 San Fernando, Calif., earthquake _________________________________________ 28

24. Graphic illustration of determination of Richter magnitude--_________________————————————— 28

25. Graph showing range of horizontal peak acceleration as a function of distance and magnitude for rock sites in the

Western United States ____________________________________________________ 31

26. Graph showing relation between peak horizontal ground velocity and distance from source of energy release for

magnitude 6.5 earthquakes-__________________________———____ ———— - —————— — 34

27. Bracketed duration values for the S. 16° E. accelerogram recorded at Pacoima Dam from the 1971 San Fernando earthquake and graph showing bracketed duration as a function of magnitude and fault rupture 

length ______________________________________________________________ 35

28. Graph of integral definition of duration of shaking for a site on rock and a site underlain by alluvium — ————— 36

29. Graph of Fourier amplitude spectrum derived from the accelerogram recorded at El Centre from the 1940 Imperial Valley, Calif, earthquake —_____________________________ — _______————- 36 

30-35. Schematic illustrations of:

30. Far-field displacement spectrum and some of the information about the source that can be derived from

it—_____________________________________________________________________—_ 37

31. Narrow-band-pass filtering involved in deriving a response spectrum _——__ ——————————— ————— 38

32. Response spectra derived from the 1940 Imperial Valley, Calif, earthquake accelerogram ————————— 39

33. Time-dependent response envelope derived from the 1940 Imperial Valley, Calif, earthquake accelerogram 39

34. Source effects on the spectral composition of ground motion________———————————————————— 39

35. Transmission path effects on the spectral composition of ground motion, 1971 San Fernando earthquake-- 39 

36. Map showing Nevada Test Site and vicinity ______________________________________———— 40 

37-41. Graphs showing:

37. Response spectra for 1940 Imperial Valley, Calif, earthquake and Cannikin nuclear explosion— —— ——— 40

38. Response spectra for two sites equidistant from energy source but on different travel paths _________ 40

39. Variability of ground motion recorded at two sites in Tonopah, Nev _________ _____ ____ ___ 40

40. Intensity and acceleration relations _________________________________________ 41

41. Mean values and standard-deviation error bars of peak ground acceleration, peak ground velocity, and

peak ground displacement as a function of Modified Mercalli intensity, Western United States ——— 42

42. Map showing levels of peak horizontal ground acceleration expected at the 90-percent probability level at rock

sites in the United States within a 50-year period _______________________________ 43

43. Acceleration, velocity, and displacement seismograms from the 1966 Parkfield, Calif., earthquake recorded at

station Cholame-Shannon No. 2 __________________________________—————____——— 44 

44-56. Graphs showing:

44. Variation in ground-motion response spectra and peak ground acceleration values for the same value of

Modified Mercalli intensity, San Fernando, Calif, earthquake _________________—___ 47

45. Site-independent velocity and acceleration response spectra _______________________———— 47

46. Schematic illustration of technique for developing site-independent response spectra ————_____——— 49

47. "Standard" site-independent horizontal response spectra _________________———————_————_ 50

48. Site-independent horizontal response spectra scaled to 1.0 g__——____— ______————____——— 51

49. Site-independent vertical response spectra.________________—________ ————— ——— ——— 52

50. Comparison of site-independent, horizontal response spectra produced by three different procedures —— 53

51. Site-dependent mean and mean-plus-one-standard-deviation response spectra for four site classifications __ 54

52. Comparison of site-dependent mean and mean-plus-one-standard-deviation response spectra with AEC

Regulatory Guide 1.60 spectrum _____________________________________———— 55

53. Effect of strain level on shear modulus and damping __———__ __—————__ _———————————— 56

54. Comparison of smooth response spectra for three soil columns-_____—————________ ——— ——————— 57

55. Average acceleration response spectra for four site classifications _____ ————— __ —————— —— ———— 57

56. Site transfer function for two sites in the Glendale, Calif, area derived from aftershocks of the 1971 San

Fernando earthquake ___________________________________———————————— 58

57. Map showing location of seismograph stations and thickness of alluvium in Las Vegas Valley and graphs

showing variation of horizontal velocity response spectra for two stations and their site transfer function —— 59

58. Contour maps showing the radial component of relative ground response in the period band 3.33-4.50 s and thickness of alluvium, Las Vegas Valley _____ ____ ____________ ____-____———————————— 60

59. Variation of ground motion with depth, Beatty, Nev _______________——______———————————— 60

60. Parametric curves for amplification of SH waves _________—————_____————————————————————— 61 

61-64. Graphs showing:

61. Example of site transfer function, elastic response ___________________—————__———— 62

62. Normalized rock response spectrum, 5-percent damping __________——______———————————— 62

63. Parametric curves for high-strain amplification of SH waves and three depths of unconsolidated

materials ________________________________________________________ 63

64. Effect of peak acceleration level on amplification_____————___——————__———————————— 63

65. Map showing United States seismic risk zones._________________________________________ 64

66. Map showing preliminary design regionalization proposed for 1976 Uniform Building Code _____________ 65

67. Graph showing soil-structure interaction factor proposed for 1976 Uniform Building Code __——————— ————— _ 66
VII

TABLES

Pape

TABLE 1. Property damage and lives lost in notable United States earthquakes ___ ________—————————————— 6

2. Summary of earthquake recurrence relations in the United States _____ ___—————————————————— 7

3. Relative seismicity of regions of the United States __ _ _____ ______ __ ___ ___________ _______ 8

4. Seismicity parameters for seismic source zones___________________________— ——————————— — 9

5. Criteria for recognizing an active fault _______________________________________———— 10

6. Classification of fault activity____________________________________________________ 11

7. Classification of selected faults relative to Fremont, Calif___________________________————————— 11

8. Relative intensity values and ground character, central California ______————__ —————— — ———————— 19 

9-13. Distance attenuation exponents derived from horizontal component PSRV spectra:

9. Northern Utah area _^____________________________________—————————————— 24

10. Southern Nevada area _____________________________-_____———————————— 25

11. California__________________________________________________________ 25

12. Piceance Creek Basin, Colo______________________________——————————————————— 25

13. San Juan Basin, N. Mex ________________________________________————————— 25

14. Magnitudes and seismic moments of southern California earthquakes — ———————————————— ———————— 28

15. Values of peak horizontal ground acceleration recorded in past earthquakes and used for estimating horizontal

ground motions in earthquake-resistant design ______________— ——————— — —————————— 29

16. Values of peak horizontal ground velocity and displacement derived from accelerograms of past earthquakes and

used for estimating horizontal ground motions in earthquake-resistant design ___ —————————— ——————— 32

17. Characteristics of the data samples used in selected studies of the correlation of Modified Mercalli intensity and

peak ground acceleration______________________________————————————————————— 41

18. Horizontal ground accelerations for the operating basis earthquake and safe shutdown earthquake for nuclear

powerplant sites in the United States _______________________———————————————————— 46

19. Earthquake accelerograms used to derive site-independent spectra __________———————— ——————— 48

20. Relative values of maximum ground acceleration, velocity, and displacement; "standard earthquake' ——————— 50

21. Horizontal design response spectra and relative values of spectrum amplification factors for control points _———— 50

22. Vertical design response spectra and relative values of spectrum amplification factors for control points ————— 52

23. Uncertainties in physical parameters that affect ground motion____-_________——— ——————————— — 67

GLOSSARY

Absorption. A process whereby the energy of a seismic wave is converted into heating of the medium through which the wave passes.

AcceFerogram. The record from an accelerometer showing acceleration as a function of time.

Accelerometer. An instrument for measuring acceleration.

Acceptable risk. A specification of the acceptable number of 

fatalities due to earthquake hazards, or an equivalent statement 

in terms of loss in buildings.

Acoustic impedance. Seismic wave velocity multiplied by density 

of the medium.

Active fault. A fault is active if, because of its present tectonic 

setting, it can undergo movement from time to time in the immediate geologic future.

Aftershocks. Minor seismic tremors that may follow an underground nuclear detonation or the secondary tremors after the main 

shock of an earthquake.

Alluvium. A general term for loosely compacted particles of rock, 

sand, clay and so forth deposited by streams in relatively recent 

geologic times.

Amplification. Modification of the input bedrock ground motion by 

the overlying unconsolidated materials. Amplification causes the 

amplitude of the surface ground motion to be increased in some 

range of frequencies and decreased in others. Amplification is a 

function of the shear-wave velocity and damping of the unconsolidated materials, its thickness and geometry, and the strain level of 

the input rock motion.

Amplitude. Maximum deviation from mean or center line of wave.

Amplitude spectrum. Amplitude versus frequency relation such 

as is computed in a Fourier analysis. See Fourier transform.

 Anisotrophic mass. A material having different properties in different directions at any given point.

Anisotropy. Variation of a physical property depending on the 

orientation along which it is measured.

Anomaly. A deviation from uniformity or normality.

Asthenosphere. The layer or shell of the earth below the lithosphere; roughly equivalent to the upper mantle.

Attenuation. (1) a decrease of signal amplitude during transmission, (2) a reduction in amplitude or energy with or without change 

of waveform, or (3) the decrease in seismic signal strength with 

distance which depends not only on geometrical spreading but also 

may be related to physical characteristics of the transmitting 

medium causing absorption and scattering.

Bandpass. Describing a range of frequencies (bandwidth) in which 

transmission is nearly complete while signals at frequencies outside these limits are attenuated substantially.

Bar. Equals 1 atmosphere: A unit of pressure, 0.01 kilopascal.

Basement. The igneous, metamorphic, or highly folded rock underlying sedimentary units.

Bedrock. An solid rock exposed at the surface or underlying soil; 

has shear-wave velocity greater than 765 m/s at small (0.0001 

percent) strains. See Firm soil and Soft soil.

Body wave. Waves propagated in the interior of a body, that is, 

compression and shear waves, the P- and S-waves of seismology.

Body-wave magnitude, m,,. See Magnitude.

Bulk modulus. The ratio of the change in average stress to the 

change in unit volume.

Capable fault. A fault that has the potential to undergo future 

surface displacement. A fault is capable if: (1) it has had late
VIII CONTENTS

Quaternary or more recent movement, or (2) macroseimic activity 

has been associated with it, or (3) it has a demonstrated structural 

relation to a known capable fault such that movement of the one 

may cause movement of the other, especially during the lifetime of 

the project under consideration.

Compression wave. A wave in which an element of the medium 

changes volume without rotation.

Converted wave. A wave which is converted from longitudinal to 

transverse, or vice versa, upon reflection or refraction at oblique 

incidence from an interface.

Convolution. The change of wave shape as a result of passing a 

signal through a linear filter.

Corner frequency. A spectrum's corner frequency is that frequency where the high- and low-frequency trends intersect. The 

location of the corner frequency,^, is related to the radius, r, of the 

equivalent circular fault through the relation r = 

2ff/r where ft is the shear-wave velocity at the source.

Covariance. A statistical regression analysis technique that allows 

one to analyze subsets of data having a common characteristic 

property.

Critical angle. Angle of incidence, 6C , for which the refracted ray 

grazes the surface of contact between two media in which the seismic velocities are v, and v2 .

Crust. The outermost portion of the earth, averaging about 30 km, 

that overlies the Mohorovicic discontinuity.

Design earthquake. The largest earthquake that has such a high 

probability of occurrence based on studies of historic seismicity 

and structural geology that it is appropriate to design a structure 

to withstand it. Ground shaking of the design earthquake might be 

exceeded, but the probability of this happening is considered to be 

small.

Design spectra. Spectra appropriate for earthquake-resistant design purposes. Design spectra are typically smooth curves that 

have been modified from a family of spectra of historic earthquakes 

to take account of features peculiar to a geographic region and a 

particular site. Design spectra do not include the effect of soilstructure interaction.

Design time history. One of a family of time histories which produces a response spectrum that envelopes the smooth design 

spectrum, for a selected value of damping, at all periods.

Earthquake hazards. The probability that natural events accompanying an earthquake such as ground shaking, ground failure, 

surface faulting, tectonic deformation, and inundation, which may 

cause damage and loss of life, will occur at a site during a specified 

exposure time. See Earthquake risk.

Earthquake risk. The probability that social or economic consequences of earthquakes, expressed in dollars or casualties, will 

equal or exceed specified values at a site during a specified exposure time.

Earthquake waves. Elastic waves propagating in the earth, set in 

motion by a sudden change such as faulting of a portion of the 

earth.

Effective peak acceleration. The peak ground acceleration after 

the ground-motion record has been filtered to remove the very high 

frequencies that have little influence upon structural response.

Effective peak velocity. The peak ground velocity after the ground 

motion record has been filtered to remove high frequencies.

Epicenter. The point on the Earth's surface vertically above the 

point where the first rupture and the first earthquake motion occur.

Exceedance probability. The probability (for example, 10 percent) 

over some period of time that an earthquake will generate a level 

of ground shaking greater than some specified level.

Exposure time. The period of time (for example, 50 years) that a 

structure is exposed to the earthquake threat. The exposure time is

sometimes chosen to be equal to the design lifetime of the structure.

Failure. A condition in which movement caused by shearing stresses in a structure or soil mass is of sufficient magnitude to destroy 

or seriously damage it.

Fault. A fracture or fracture zone along which displacement of the 

two sides relative to one another has occurred parallel to the fracture. See Active, Capable, Normal, Thrust and Strike-slip 

faults.

Filter. That part of a system which discriminates against some of 

ths information entering it. The discrimination is usually on the 

basis of frequency, although other bases such as wavelength may 

be used. Linear filtering is called convolution.

Finite element analysis. An analysis which uses an assembly of 

finite elements which are connected at a finite number of nodal 

points to represent a structure or a soil continum.

Firm soil. A general term for soil characterized by a shear wave 

velocity of 600 to 765 m/s. See Soft soil, Bedrock.

Focal depth. The vertical distance between the hypocenter and the 

epicenter in an earthquake.

Focus. The point within the earth which marks the origin of the 

elastic waves of an earthquake.

Forced vibration. Vibration that occurs if the response is imposed 

by the excitation. If the excitation is periodic and continuing, the 

oscillation is steady-state.

Fourier spectrum. See Amplitude spectrum, Phase response, 

and Fourier transform.

Fourier transform. The mathematical formulas that convert a 

time function (waveform, seismogram, etc.) G(t) into a function of 

frequency S(f) and vice versa.

Free field. The regions of the medium that are not influenced by 

manmade structures, or a medium that contains no such structures. It also refers to that region in which boundary effects do not 

significantly influence the behavior of the medium.

Free vibration. Vibration that occurs in the absence of forced 

vibration.

Frequency. Number of cycles occurring in unit time. Hertz (hz) is 

the unit of frequency.

Gaussian distribution. Equals normal distribution (bell-shaped 

curve): A quantity or set of values so distributed about a mean 

value, m, that the probability, e(Aa), of a value lying within an 

interval, Aa, centered at the point, a, is:

e(Aa) =

277X7 2(72

where cr is the standard error of estimate.

Geometrical damping. That component of damping due to the radial spreading of energy with distance from a given source.

Geophone. Sensing device used to measure electronically the rate 

of travel of sound or force waves transmitted through the earth 

from a known source.

Geophysics. The study of the physical characteristics and properties of the earth.

Geotechnical. Related to soil mechanics.

Grain size. A term relating to the size of mineral particles that 

make up a soil deposit.

Ground response, ground motion, seismic response. A general 

term, includes all aspects of ground motion, namely, particle acceleration, velocity, or displacement; stress and strain from a nuclear 

explosion, an earthquake, or another energy source.

Group velocity. The velocity with which most of the energy in a 

wave train travels. In dispersive media where velocity varies with 

frequency, the wave train changes shape as it progresses so that 

individual wave crests appear to travel at a different velocity (the 

phase velocity) than the overall energy as approximately enclosed 

by the envelope of the wave train.
CONTENTS IX

Half-space. A mathematical model bounded only by one plane surface; that is, the model is so large in other dimensions that only the 

one boundary affects the results. Properties within the model are 

assumed to be homogeneous and usually isotropic.

Hertz. A unit of frequency; cycles per second (cps).

Holocene. The past 10,000 years of geologic time.

Hydrostatic pressure. The pressure in a liquid under static conditions; the product of the unit weight of the liquid (water =1 kg/L) 

and the difference in elevation between the given point and the 

ground water elevation.

Hypocenter. The location in space where the slip responsible for an 

earthquake occurs; the focus of an earthquake.

Hysteresis loop. (1) the stress-strain path of a material under cyclic loading conditions, or (2) a trace of the lag in the return of an 

elastically deformed specimen to its original shape after the load 

has been released.

Incident angle. The angle which a ray path makes with a perpendicular to an interface.

In situ strength. The in-place strength of a soil deposit.

Intensity. A numerical index describing the effects of an earthquake on the earth's surface, on man, and on structures built by 

him. The scale in common use in the United States today is the 

Modified Mercalli scale of 1931 with intensity values indicated by 

Roman numerals from I to XII. The narrative descriptions of each 

intensity value are:

I. Not felt or, except rarely under especially favorable circumstances. Under certain conditions, at and outside the boundary of the area in which a great shock is felt: sometimes, 

birds, animals, reported uneasy or disturbed; sometimes 

dizziness or nausea experienced; sometimes trees, structures, liquids, bodies of water, may sway; doors may swing, 

very slowly.

II. Felt indoors by few, especially on upper floors, or by sensitive, 

or nervous persons. Also, as in grade I, but often more 

noticeably: sometimes hanging objects may swing, especially when delicately suspended; sometimes trees, structures, liquids, bodies of water, may sway, doors may swing, 

very slowly; sometimes birds, animals, reported uneasy or 

disturbed; sometimes dizziness or nausea experienced.

III. Felt indoors by several, motion usually rapid vibration. Sometimes not recognized to be an earthquake at first. Duration 

estimated in some cases. Vibration like that due to passing 

of light, or lightly loaded trucks, or heavy trucks some distance away. Hanging objects may swing slightly. 

Movements may be appreciable on upper levels of tall structures. Rocked standing motor cars slightly.

IV. Felt indoors by many, outdoors by few. Awakened few, especially light sleepers. Frightened no one, unless apprehensive from previous experience. Vibration like that due to 

passing of heavy or heavily loaded trucks. Sensation like 

heavy body striking building or falling of heavy objects inside. Rattling of dishes, windows, doors; glassware and 

crockery clink and clash. Creaking of walls, frame, especially in the upper range of this grade. Hanging objects 

swung, in numerous instances. Disturbed liquids in open 

vessels slightly. Rocked standing motor cars noticeably.

V. Felt indoors by practically all, outdoors by many or most; outdoors direction estimated. Awakened many, or most. 

Frightened few—slight excitement, a few ran outdoors. 

Buildings trembled throughout. Broke dishes, glassware, to 

some extent. Cracked windows—in some cases, but not generally. Overturned vases, small or unstable objects, in many 

instances, with occasional fall. Hanging objects, doors, 

swing generally or considerably. Knocked pictures against 

wall, or swung them out of place. Opened, or closed, doors,

shutters, abruptly. Pendulum clocks stopped, started or ran 

fast, or slow. Moved small objects, furnishings, the later to 

slight extent. Spilled liquids in small amounts from wellfilled open containers. Trees, bushes, shaken slightly.

VI. Felt by all, indoors- and outdoors. Frightened many, excitement general, some alarm, many ran outdoors. Awakened 

all. Persons made to move unsteadily. Trees, bushes, shaken 

slightly to moderately. Liquid set in strong motion. Small 

bells rang—church, chapel, school, etc. Damage slight in 

poorly built buildings. Fall of plaster in small amount. 

Cracked plaster somewhat, especially fine cracks in chimneys in some instances. Broke dishes, glassware, in considerable quantity, also some windows. Fall of knick-knacks, 

books, pictures. Overturned furniture in many instances. 

Moved furnishings of moderately heavy kind.

VII. Frightened all; general alarm, all ran outdoors. Some, or 

many, found it difficult to stand. Noticed by persons driving 

motor cars. Trees and bushes shaken moderately to 

strongly. Waves on ponds, lakes, and running water. Water 

turbid from mud stirred up. Incaving to some extent of sand 

or gravel stream banks. Rang large church bells, etc. Suspended objects made to quiver. Damage negligible in buildings of good design and construction, slight to moderate in 

well-built ordinary buildings, considerable in poorly built or 

badly designed buildings, adobe houses, old walls (especially 

where laid up without mortar), spires, etc. Cracked chimneys to considerable extent, walls to some extent. Fall of 

plaster in considerable to large amount, also some stucco. 

Broke numerous windows, furniture to some extent. Shook 

down loosened brickwork and tiles. Broke weak chimneys at 

the roof-line (sometimes damaging roofs). Fall of cornices 

from towers and high buildings. Dislodged bricks and 

stones. Overturned heavy furniture, with damage from 

breaking. Damage considerable to concrete irrigation 

ditches.

VIII. Fright general; alarm approaches panic. Disturbed persons 

driving motor cars. Trees shaken strongly—branches, 

trunks, broken off, especially palm trees. Ejected sand and 

mud in small amounts. Changes: temporary, permanent; in 

flow of springs and wells; dry wells renewed flow; in temperature of spring and well waters. Damage slight in structures 

(brick) built especially to withstand earthquakes. Considerable in ordinary substantial buildings, partial collapse: 

racked, tumbled down, wooden houses in some cases; threw 

out panel walls in frame structures, broke off decayed piling. Fall of walls. Cracked, broke, solid stone walls seriously. Wet ground to some extent, also ground on steep 

slopes. Twisting, fall, of chimneys, columns, monuments, 

also factory stacks, towers. Moved conspicuously, overturned, very heavy furniture.

IX. Panic general. Cracked ground conspicuously. Damage considerable in (masonry) structures built especially to withstand earthquakes: Threw out of plumb some wood-frame 

houses built especially to withstand earthquakes; great in 

substantial (masonry) buildings, some collapse in large 

part; or wholly shifted frame buildings off foundations, 

racked frames; serious to reservoirs; underground pipes 

sometimes broken.

X. Cracked ground, especially when loose and wet, up to widths 

of several inches; fissures up to a yard in width ran parallel 

to canal and stream banks. Landslides considerable from 

river banks and steep coasts. Shifted sand and mud horizontally oh beaches and flat land. Changed level of water in 

wells. Threw water on banks of canals, lakes, rivers, etc. 

Damage serious to dams, dikes, embankments. Severe to
X CONTENTS

well-built wooden structures and bridges, some destroyed. 

Developed dangerous cracks in excellent brick walls. Destroyed most masonry and frame structures, also their foundations. Bent railroad rails slightly. Tore apart, or crushed 

endwise, pipe lines buried in earth. Open cracks and broad 

wavy folds in cement pavements and asphalt road surfaces.

XI. Disturbances in ground many and widespread, varying with 

ground material. Broad fissures, earth slumps, and land 

slips in soft, wet ground. Ejected water in large amounts 

charged with sand and mud. Caused sea-waves ("tidal" 

waves) of significant magnitude. Damage severe to woodframe structures, especially near shock centers. Great to 

dams, dikes, embankments often for long distances. Few, if 

any (masonry) structures remained standing. Destroyed 

large well-built bridges by the wrecking of supporting piers, 

or pillars. Affected yielding wooden bridges less. Bent railroad rails greatly, and thrust them endwise. Put pipe lines 

buried in earth completely out of service.

XII. Damage total—practically all works of construction damaged 

greatly or destroyed. Disturbances in ground great and varied, numerous shearing cracks. Landslides, falls of rock of 

significant character, slumping of river banks, etc., numerous and extensive. Wrenched loose, tore off, large rock 

masses. Fault slips in firm rock, with notable horizontal and 

vertical offset displacements. Water channels, surface and 

underground, disturbed and modified greatly. Dammed 

lakes, produced waterfalls, deflected rivers, etc. Waves seen 

on ground surfaces. Distorted lines of sight and level. Threw 

objects upward into the air. 

Interface. The common surface separating two different geologic

media in contact.

Internal friction. The resisting shear strength considered to be due 

to the interlocking of the soil grains and the resistance to sliding 

between the grains.

Isotropic. Having the same physical properties regardless of the 

direction in which they are measured. Strictly applies only to an 

arbitrarily small neighborhood surrounding a point and to single 

properties.

Lame's constants. See Modulus.

Least squares fit. An analytic function which approximates a set of 

data with a curve such that the sum of the squares of the distances 

from the observed points to the curve is a minimum. 

Linear system. A system whose output is linearly related to its 

input. If a linear system is excited by a an input sine wave of 

frequency /I, the output will contain only the frequency /i; the 

amplitude and phase may be changed.

Linear viscoelastic medium. A medium for which the functional 

relation between stress and strain can be expressed as a linear 

relation between stress, strain and their nth order temporal derivatives.

Liquefaction Temporary transformation of unconsolidated materials into a fluid mass during an earthquake. 

Lithology. The description of rock composition and texture. 

Lithosphere. The crust and upper mantle of the earth._ __ 

Loading. The force on an object or structure or element of a structure.

Longitudinal wave. Equals compression wave; equals P-wave. 

Love wave. A seismic surface wave which propagates in a surface 

layer. The vibration is transverse to the direction of propagation 

with no vertical motion.

Low-cut filter. Equals high pass filter: A filter that transmits frequencies above a given cutoff frequency and substantially attenuates lower frequencies.

Low-pass filter. Equals high-cut filter: A filter that transmits frequencies below a given cutoff frequency and substantially attenuates all others. The earth acts like a low-pass filter.

Magnitude. A quantity that is characteristic of the total energy 

released by an earthquake, as contrasted to intensity, which subjectively describes earthquake effects at a particular place. Professor C. F. Richter devised the logarithmic magnitude scale in 

current use to define local magnitude (ML ) in terms of the motion 

that would be measured by a standard type of seismograph located 

100 km from the epicenter of an earthquake. Several other magnitude scales are in use, for example, body-wave magnitude (mh ) 

and surface-wave magnitude (Ms) which utilize body waves and 

surface waves. The scale is open ended, but the largest known 

earthquake magnitudes (Afs) are near 8.9.

Major principal stress. (See Principal stress) The largest (with 

regard to sign) principal stress.

Mantle. The part of the earth's interior between the core and the 

crust. The upper surface of the mantle is the Mohorovicic discontinuity.

Meizoseismal zone. Zone of intense shaking in the near field of an 

earthquake. The radial width of this zone increases with magnitude.

Mesosphere. The lower mantle. It is not involved in the earth's 

tectonic processes.

Microtremor. A weak tremor.

Minor principal stress. (See Principal stress). The smallest (with 

regard to sign) principal stress.

Model. A concept from which one can deduce effects that can then 

be compared to observations; this concept assists in understanding 

the significance of the observations. The model may be conceptual, 

physical , or mathematical.

Modulus. A measure of the elastic properties of a material. Moduli 

for isotropic bodies include:

1. Bulk modulus, k. The stress-strain ratio under simple hydrostatic pressure: the bulk modulus can be expressed in terms of 

other moduli as:

k=E/3(l-2a) .

2. Shear modulus. Equals rigidity modulus, equals Lame's constant, /u,: The stress-strain ratio for simple shear. The shear 

modulus can also be expressed in terms of other moduli and

Poisson's ratio a as:

E

2(l+cr)

3. Young's modulus, E. The stress-strain ration when a rod is 

pulled or compressed.

4. Lame's constant X. If a cube is stretched in the up-direction by 

a tensile stress, S, is giving an upward strain, s, and S' is the 

lateral tensile stress needed to prevent lateral contraction, 

then:

K=S'/s .

This constant can also be expressed in terms of Young's 

modulus, E, and Poisson's ratio, cr:

E a

(l + o-) (l-2o-)

The velocities of P- and S-waves, Vp and Vs, can be expressed 

in terms of the moduli and the density, p:

Vs =

Modulus of elasticity. The ratio of stress to strain for a material
CONTENTS XI

under given loading conditions; numerically equal to the slope of 

the tangent of a stress-strain curve.

Mohorovicic (M) discontinuity. Seismic discontinuity which separates the earth's crust and mantle.

Moment. The seismic moment M0 =fjulA contains information on 

the rigidity (/A) in the source region, average dislocation (u), and 

area (A) of faulting. It determines the amplitude of the long-period 

level of the spectrum of ground motion.

Monotonic loading. Continuously increasing load in one direction.

Natural frequency. Property of the elastic system in free vibration. Free vibration occurs naturally at a discrete frequency when 

an elastic system vibrates under the action of forces inherent in 

the system itself and in the absence of external impressed forces.

Normal fault. Vertical movement along a sloping fault surface in 

which the block above the fault has moved downward relative to 

the block below. The Wasatch fault in Utah is an example.

Normal stress. That stress component normal to a given plane.

Operating basis earthquake (OBE). A design earthquake used by 

the U.S. Nuclear Regulatory Commission in nuclear power plant 

siting: the largest earthquake that reasonably could be expected to 

affect the plant site during the operating life of the plant. The 

powerplant is designed to withstand the OBE and still operate 

without undue risk to the health and safety of the public. See Safe 

shutdown earthquake.

Oscillation. The variation, usually with time, of the magnitude of a 

quantity with respect to a specified reference when the magnitude 

is alternately greater and smaller than the reference.

Overburden. The generic term applied to uppermost layers of the 

geologic structure, usually unconsolidated materials having low 

seismic velocity overlying rock.

P-wave. (See also Compression or Body wave). Body wave in 

which the direction of the particle motion is the same as the direction of wave propagation. P-wave velocity is commonly measured 

in geophysical refraction surveys to define the contact between the 

competent rock layers (high-velocity materials) and the overlying 

unconsolidated materials (low-velocity materials).

Particle acceleration. The time rate of change of particle velocity.

Particle displacement. The difference between the initial position 

of a soil particle and any later position.

Particle velocity. The time rate of change of particle displacement.

Period. The time interval occupied by one cycle.

Permeability. A measure of the ease with which a fluid can pass 

through the pore spaces of a formation.

Phase. The angle of lag or lead (or the displacement) of a sine wave 

with respect to a reference; the stage in the course of a rotation or 

oscillation to which it has advanced, considered in relation to a 

reference or assumed instant of starting.

Phase response. A graph of phase shift versus frequency illustrates the phase response characteristics of a system. The 

amplitude-frequency response of a filter to the shape of pulses put 

through it will be different for different phase characteristics; this 

response leads to phase distortion.

Phase velocity. The velocity with which any given phase (such as a 

wave of single frequency) travels; it may differ from group velocity because of dispersion.

Plane strain (biaxial! A measure of strain that takes place in two 

directions while remaining zero in the third dimension.

Plastic range. The stress range in which a material will not fail 

when subjected to the action of a force, but will not recover completely, so that a permanent deformation results when the force is 

removed.

Plate tectonics. A theory introduced in 1967 and subsequently refined that considers the earth's crust and upper mantle to be made 

up of more than 15 relatively undistorted plates about 60 km thick 

which move relative to one another. The plates spread from the

mid-oceanic ridges where, by means of the upflow of magma, new 

lithospheric material is continually added. On the opposite margins of the plates, there are usually deep submarine trenches. At 

these trenches, the plates converge from opposite directions (for 

example, the Nazca and South American plates along the Andes 

Mountains), and one plate is consumed or subducted beneath the 

other into the deeper parts of the earth. Earthquake belts or zones 

mark plate boundaries, the zones along which the lithospheric 

plates collide, diverge, and slide past one another. The San Andreas fault zone is an example of a boundary between the North 

American and Pacific plates.

Poisson's ratio. The ratio of the transverse contraction to the longitudinal extension when a rod is stretched. The ratio of the velocities of P- and S-waves, Vp and Vs, can be expressed in terms of 

Poisson's ratio, a:

Pore water pressure. Pressure or stress transmitted through the 

pore water filling the voids of the soil.

Power spectrum. A graph of power spectral density versus frequency. The power spectrum is the square of the amplitudefrequency response.

Principal stress. Stresses acting normal to three mutually perpendicular planes intersecting at a point in a body, on each of which 

the shearing stresses are zero.

Probability of occurrence. The annual rate of occurrence of a 

hazard.

Pulse. A waveform whose duration is short compared to the time 

scale of interest and whose initial and final values are the same 

(usually zero).

Q. Q, the reciprocal of the specific dissipation function, is an index of 

the dissipative nature of the earth's transmission path on propagating seismic waves. Q is essentially independent of frequency 

or wavelength for a wide range of frequencies. Empirically determined values of Q range from 50 to 500 for crustal materials in 

various regions of the United States. Also called quality factor.

Rayleigh wave. A type of seismic surface wave which propagates 

along the surface. Particle motion is elliptical and retrograde in 

the vertical plane containing the direction of propagation, and its 

amplitude decreases exponentially with depth.

Raypath. A line everywhere perpendicular to wavefronts in isotropic media. The path which a seismic body wave takes.

Reflection. The energy or wave from a seismic source which has 

been reflected (returned) from an acoustic impedance contrast or 

series of contrasts within the earth.

Reflection coefficient. The ratio of the amplitude of a reflected 

wave to that of the incident wave. For normal incidence on an 

interface which separates media of densities PI and p2 and velocities Vi and V2 , the reflection coefficient for a plane wave is:

p2V2 - p1Vl

Region. A geographical area surrounding and including the site 

sufficiently large to contain all the features related to a physical 

phenomenon or to a particular earthquake hazard.

Relative density. The ratio of (1) the difference between the void 

ratio of a cohesionless soil in the loosest state and any given void 

ratio, to (2) the difference between its void ratios in the loosest and 

in the densest state.

Resonance. The reinforced response of one of the natural modes of 

vibration of a body when excited at a frequency close to the natural 

frequency of vibration.

Resonant frequency. A frequency at which resonance occurs.
XII CONTENTS

Response. The motion in a system resulting from an excitation 

under specified conditions.

Response spectrum. The peak response of a series of simple harmonic oscillators of different natural period when subjected mathematically to a particular earthquake ground motion. The response spectrum may be plotted as a curve onr tripartite 

logarithmic graph paper showing the variation of the peak spectral 

acceleration, displacement, and velocity of the oscillators as a 

function of vibration period and damping.

Return period. The average period of time or recurrence interval 

between events causing ground shaking exceeding a particular 

level at a site; the reciprocal of annual probability of exceedance. A 

return period of 475 years means that, on the average, a particular 

level of ground motion will be exceeded once in 475 years.

Risk. See Earthquake risk.

Rock. See Bedrock.

Rupture velocity. The velocity at which the fault rupture propagates along its length. The rupture velocity is usually some fraction of the shear wave velocity and in the range 1.5 to 4.5 km/s for 

most earthquakes. It affects the effective stress.

S-wave (Shear wave). Body wave in which the particle motion is at 

right angles to the direction of wave propagation. SH and SV 

denotes planes of polarization of wave. S-wave velocity may be 

measured by in-hole geophysical procedures to determine the 

dynamic shear moduli of the materials through which the wave 

passes.

Safe shutdown earthquake (SSE). A design earthquake used by 

the U.S. Nuclear Regulatory Commission in nuclear powerplant 

siting: the largest possible earthquake at the site, considering the 

regional and local geology and seismology and specified characteristics of local and subsurface material. Important nuclear power 

plant structures, systems, and components are designed to remain 

intact during the SSE. See Operating basis earthquake.

Saturated soil. Soil with zero air voids. A soil which has its interstices or void space filled with water to the point where runoff 

occurs.

Seismic source zones. Areas of spatially homogeneous earthquake 

activity.

Seismic wave. An elastic wave generated by an earthquake or explosion which causes only a temporary displacement of the 

medium, the recovery of which is accompanied by ground 

vibrations.

Seismogram. A record of ground motion or of the vibrations of a 

structure caused by a disturbance, such as an underground nuclear 

detonation or an earthquake. See Accelerogram.

Seismograph. A system for amplifying and recording the signals 

from seismometers.

Seismometer. The instrument used to transform seismic wave 

enegry into an electrical voltage. Most seismometers are velocity 

detectors their outputs being proportional to the velocity of the 

inertial mass with respect to the seismometer's case (which is proportional to the velocity of the earth motion.) Below the natural 

frequency, the response of most geophones decreases linearly with 

frequency so that they operate as accelerometers.

Seismotectonic province. A geographic area characterized by 

similarity of geologic structure and earthquake characteristics.

Sensitivity. The smallest change in a quantity that a detector can 

detect.

Shear modulus (Rigidity). The ratio between shear stress and 

shear strain in simple shear.

Shear wave. Equals S-wave equals transverse wave: A body wave 

in which the particle motion is perpendicular to the direction of 

propagation.

Shear wave velocity. See Modulus.

Simple shear. The state of stress at the point where only shearing 

stresses act on any two perpendicular planes.

Site vicinity. The geographical region within about 10-km radius of 

the center of the site.

Snell's law. When a wave crosses a boundary, the wave changes 

direction such that the sine of the angle of incidence divided by the 

velocity in the first medium equals the sine of the angle of refraction divided by the velocity in the second medium.

Soft soil. A general description for soil which has a shear wave 

velocity less than 600 m/s. See Firm soil, Bedrock.

Sonic log. A record of the seismic velocity (or of interval time) as a 

function of depth.

Specific dissipation. See Q.

Standard deviation. The standard deviation, &, of n measurements of a quantity xt , with respect to the mean, X, is:

-J— f (xt -Xf

N-l «=i

Standing wave. A wave produced by simultaneous transmission in 

opposite directions of two similar waves. It may result in fixed 

points of zero amplitudes called nodes.

Station. A ground position at which a geophysical instrument or 

seismograph is set up for an observation.

Steady-state vibration. Vibration in a system where the velocity 

of each particle is a continuing periodic quantity.

Stochastic. Random; value determined entirely by chance.

Strain. The change in length per unit of length in a given direction 

which a body subjected to deformation undergoes.

Strain dependent property. A property exhibited by soil wherein 

the magnitude of a physical property depends on the magnitude of 

the induced strain.

Stratigraphy. The order of succession of the different sedimentary 

rock formations in a region.

Strength of earthquake. In current usage, it is often expressed in 

terms of the peak ground acceleration recorded or predicted for a 

particular earthquake, expressed usually ing units, where 1 g is 

an acceleration equal to that of gravity, or 980 cm/s2 .

Stress drop. Acr=cr0 —cr, where CTO is the initial stress before the 

earthquake and o-j is the stress after the earthquake. For the 1971 

San Fernando, Calif, earthquake, the average initial stress is estimated to have been about 100 bars and the stress drop to have 

been about 60 bars. Stress drop controls the high-frequency 

spectral content of earthquake ground motions.

Stress (effective). In modeling an earthquake, the effective stress is 

defined as cr=cr0 —oy where CTO is the stress before the earthquake 

and (Tf is the frictional stress acting to resist the fault slip.

Strike-slip fault. A fault in which movement is principally horizontal. The San Andreas fault is strike-slip.

Strong motion. Ground motion of sufficient amplitude to be of engineering interest in the evaluation of damage due to earthquakes 

or nuclear explosions.

Structural features. Features such as faults and folds which are 

produced in rock by movements after deposition, and commonly 

after consolidation, of the constituent sediment.

Surface waves. Seismic energy which travels along or near the 

surface. Rayleigh and Love waves.

Surface wave magnitude. MA . See Magnitude.

Tectonic province. As defined by the U.S. Nuclear Regulatory 

Commission, it is a region of the North American continent 

characterized by the uniformity of the geologic structures contained therein.

Tectonic structure. As defined by the U.S. Nuclear Regulatory 

Commission, it is a large dislocation or distortion within the 

earth's crust whose extent is greater than several kilometers.

Tectonics. A branch of geology dealing with the broad architecture 

of the upper part of the earth's crust in terms of the origin and
CONTENTS XIII

historical evolution of regional structural or deformational features.

Thrust fault. An inclined fracture along which the rocks above the 

fracture have apparently moved up with respect to those beneath. 

The 1964 Alaska and 1971 San Fernando earthquakes occurred on 

thrust faults.

Time-distance curve. Equals T-X curve: A plot of the arrival time 

of refracted events against the source-receiver distance.

Time dependent. Describing an operation in which the physical 

parameters vary with time.

Transfer function. Filter characteristics in the frequency domain 

as represented by the amplitude-versus-frequency and phase 

angle-versus-frequency curves. Contains the same information as 

the impulse response in the time domain and is convertible into 

the impulse response through the Fourier transform.

Transform. To convert information from one form into another, as 

with the Fourier transform.

Transverse wave. See Shear wave.

Upper-bound earthquake. The hypothetical earthquake that is 

considered to be the most severe reasonably possible on the basis of 

comprehensive studies of historic seismicity and structural geology.

Vibration. An oscillation. The motion of a mechanical system.

Viscoelastic. Having a stress-strain relation that includes terms 

proportional to both the strain and the rate of strain. Leads to 

frequency-dependent attenuation for seismic waves. Materials 

with this property are also called Voigt solids.

Viscoelastic medium. A stress-strain relation in which the stress 

is a function of both strain and strain rate, although not necessarily proportional to both.

Viscosity. The cohesive force between particles of a fluid that 

causes the fluid to offer resistance to a relative sliding motion 

between particles; internal fluid friction.

Viscous damping. The dissipation of energy that occurs when a 

particle in a vibrating system is resisted by a force that has a 

magnitude proportional to the speed of the particle and a direction 

opposite to the direction of the particle.

Void ratio. The proportion of void space in a given soil mass.

Voigt solid. See Viscoelastic.

Waveform. A plot of voltage, current, seismic displacement, etc., as 

a function of time.

Wave guide. A geologic situation which permits surface waves.

Wave length. Normal distance between two wave fronts with periodic characteristics and a phase difference of one complete cycle.

Wavelet. A seismic pulse usually consisting of 1% to 2 cycles.

Wavenumber. The number of wave cycles per unit distance; reciprocal of wavelength.

White noise. Random energy containing all frequency components 

in equal proportions.

Young's modulus. E. The ratio of unit stress to unit strain within 

the elastic range of a material under a given loading condition, 

numerically equal to the slope of the tangent of a stress-strain 

curve.

PROCEDURES FOR ESTIMATING EARTHQUAKE GROUND MOTIONS

By WALTER W. HAYS

ABSTRACT

This paper is a comprehensive review of the current procedures 

used for specifying earthquake ground motion for many applications 

in the United States. These applications include: siting and design of 

nuclear powerplants, hospitals, dams, schools, oil pipeline systems, 

waste storage facilities and military facilities; city and land-use 

planning; disaster planning; building codes; and evaluation of insurance needs for indemnification of losses from natural hazards. The 

seismic design problem varies considerably in the United States because of the markedly different seismicity in the east and west. In 

the Western United States, particularly in California and Nevada, 

the seismicity is very high. More large- and moderate-sized earthquakes have occurred in these two states than in any other part of 

the conterminous United States. Tectonic surface ruptures related to 

historic (0-200 years before present) and Holocene (0-10,000 years 

before present) earthquakes are common. In addition, the active 

plate boundary represented by the 1,000-km-long San Andreas fault 

system makes part of the Western United States very different from 

other seismically active parts of the country. By contrast, the Central 

and Southeastern United States have almost none of the characteristics exhibited in the Western United States. Seismicity is low, largeto moderate-sized earthquakes occurred only in 1811, 1812, and 

1886, and no evidence of tectonic surface ruptures related to historic 

or Holocene earthquakes has been found. Also, no currently active 

plate boundaries of any kind are known there.

Setting the seismic design parameters for a site requires consideration of a large body of geologic, geophysical, seismological, and 

geotechnical information. For the region surrounding the site, statistical and deterministic models are developed from this information to 

characterize the geologic province where the earthquake occurs, the 

earthquake source and wave propagation path, and the local ground 

response.

Knowledge of the physical parameters that affect the characteristics of ground motion and their range of values has been gained from: 

observational and instrumental data from earthquakes, nuclear explosions and aftershock sequences, regional seismicity networks, 

geologic mapping, trenching of fault zones, analytical models, 

geophysical measurements, and laboratory measurements. Although 

each source of data has contributed to the knowledge about ground 

motion, all these data have not been incorporated into earthquakeresistant design procedures. For example, current procedures do not 

use stress drop or seismic moment. Also, conservatism is introduced 

in the current procedures because the various physical processes that 

occur during an earthquake are not completely understood, and 

statistical distributions for many empirical relations used to estimate earthquake ground motions are not well defined.

Seven basic steps are followed in specifying the characteristics of 

the ground motion needed for earthquake-resistant design. They are:

1. to determine the seismicity of the geographic region where 

the application is planned,

2. to identify the seismotectonic features,

3. to estimate the regional seismic attenuation,

4. to estimate the ground shaking parameters (for example, 

peak acceleration or Modified Mercalli intensity) at the 

site,

5. to define the ground-motion response spectra for the site,

6. to determine the local amplification effects and to modify the 

design response spectra for the site as necessary, and

7. to estimate the uncertainty in the ground-motion design 

values.

Each step requires careful evaluation of the best available data. For 

some applications, the available data may be inadequate for precise 

specification of the earthquake ground motion. In these cases, an 

effort is generally made to use ground motion values that, based on 

experience and the uncertainty in the data, are considered to be 

conservative. Examples of conservatism include: using a rare event 

as the maximum possible earthquake because the location and magnitude of potential earthquakes are uncertain, using upper-bound 

values for the peak ground acceleration expected at a site because of 

uncertainties in the regional seismic attenuation function and the 

local ground response, and using upper-bound values for the design 

response spectrum because the details of ground-motion spectra can 

vary widely for a given value of peak ground acceleration or Modified 

Mercalli intensity. The controversy that exists today in earthquakeresistant design is largely a debate over whether the geologic, 

geophysical, seismological, and geotechnical data are adequate for 

the specific design application under consideration and whether the 

judgments about conservative ground-motion estimates are reasonable.

The ideal data base, which is not yet available for all geographic 

regions of the United States, should contain the following information for the region surrounding the site:

1. Seismicity

A complete historical record and location map of all reported

earthquakes in the region; 

Information about the source parameters such as epicenter,

focal depth, source mechanism and dimensions, magnitude,

stress drop, effective stress, seismic moment, and rupture

velocity) of each historic earthquake; 

Earthquake-recurrence relations for the region and for

specific seismic source zones in the region.

2. Seismotectonic features

Maps showing the seismotectonic provinces and capable 

faults;

Information about the earthquake potential of each seismotectonic province including information about the 

geometry, amount, sense of movement, and temporal history of each fault and the correlation with historical and 

instrumental earthquake epicenters;

Correlation of historic earthquakes with tectonic models to 

estimate the upper-bound magnitude (or seismic moment) 

that should be associated with specific tectonic features.

1
PROCEDURES FOR ESTIMATING EARTHQUAKE GROUND MOTIONS

3. Seismic attenuation

Isoseismal maps of significant historic earthquakes that occurred in the region;

Strong ground-motion records of historic earthquakes;

Scaling relations and their statistical distribution for 

ground-motion parameters as a function of distance.

4. Characteristics of historic ground shaking

Isoseismal maps of all significant historic earthquakes that 

have affected the site;

Ensembles of strong ground-motion records of earthquakes 

that occurred either in the region of interest or in other 

regions that have similar source-path-site characteristics 

adequate for "calibrating" the near-field, the regional 

seismic wave attenuation characteristics, and the local 

ground response.

5. Earthquake spectra

Ensembles of spectra (Fourier, power spectral density, and 

response) adequate for "calibrating" the near-field, the 

transmission path, and the local ground response.

6. Local amplification effects

Seismic-wave transmission characteristics (amplification or 

damping) of the unconsolidated materials overlying bedrock and their correlation with physical properties, including seismic shear wave velocities, bulk densities, shear 

moduli, strain levels, water content, and geometry; 

Strong ground motion records at surface and subsurface locations for a wide range of strain levels.

Very limited empirical data exist for the near field of earthquakes. 

Also, analytical models are presently considered to be inadequate for 

specifying the details of the ground motion in a manner that is acceptable in current earthquake-resistant design. In the near field, 

ground-motion parameters are strongly influenced by the dynamics 

of the fault rupture, a physical process that is not well understood at 

the present time.

The strong-motion accelerograph network is the source of 

ground-motion date used in earthquake-resistant design. About 200 

of the approximately 500 digitized records currently available are 

basement or free-field records, principally from the 1971 San Fernando, California earthquake. Only a few records have been obtained in the near field distance range in which earthquakes have 

caused significant damage. Relatively few records have been obtained at surface and subsurface sites underlain by rock and unconsolidated materials having varied physical characteristics. Also, only 

accelerograms from small earthquakes have been recorded in the 

Eastern United States.

Better estimates of earthquake ground motion will require improved data. Regional seismicity and strong-motion accelerograph 

networks must be expanded in order to obtain adequate data for 

"calibrating" large regions of the United States in terms of their 

earthquake source mechanisms, regional seismic attenuation, and 

local ground response. Better geologic and geophysical data and 

analyses are needed to define the earthquake potential and upperbound magnitude in different geographic regions and to establish the 

dynamics of faulting and recurrence intervals for specific faults. 

Knowledge about the origin of intraplate earthquakes, which seem 

to have different causes than the earthquakes that occur along plate 

boundaries, is needed to assess more accurately the earthquake potential of low-seismicity regions such as the Eastern United States.

INTRODUCTION

This paper is a part of ongoing investigations by the 

U.S. Geological Survey to better understand the 

causative mechanisms and physical effects of earthquakes in order to contribute to tha reduction of earthquake hazards in the United States. This paper provides a comprehensive summary of current procedures 

that use geologic, geophysical, seismological, and 

geotechnical data for estimating ground-motion 

characteristics of earthquakes for sites of interest in 

the United States. These procedures are used in many 

applications, including siting of nuclear power plants 

(U.S. Atomic Energy Commission, 1971 and 1973 a, b; 

American Society of Civil Engineers, 1976); construction of hospitals (Veterans Administration, 1973); construction of dams (Peak, 1973); seismic design of oil 

pipeline systems (Page and others, 1972; Newmark 

and Hall, 1973); construction of schools (State of 

California, 1933); construction of military facilities 

(Department of Army, Navy and Air Force, 1973); city 

and land-use planning (California Council on Intergovernmental Relations, 1972 and 1973; WoodwardNcNeill and Associates, 1973; Nichols and 

Buchanan-Banks, 1974); city lifeline engineering 

(American Society of Civil Engineers, 1974); regional 

earthquake zonation (Borcherdt, 1975; Espinosa, 

1977); earthquake ground shaking hazard maps 

(Algermissen, 1969; Algermissen and Perkins, 1976); 

disaster planning (Office of Emergency Preparedness, 

1972, Algermissen and others, 1972, 1973; Hopper and 

others, 1975, Rogers and others, 1976); insurance 

against natural hazards (Baker, 1971); building codes 

(Wiggins and Moran, 1971; Applied Technology Council, 1976), and management of hazardous wastes 

(Healy and others, 1968;Wyss and Molnar, 1972).

A great deal of important research is being performed through the earthquake research programs of 

the U.S. Geological Survey (USGS) and the National 

Science Foundation (National Science Foundation and 

U.S. Geological Survey, 1976; Hamilton, 1978). These 

programs are complementary and represent a balanced 

study of six elements: (1) fundamental earthquake 

studies, (2) earthquake prediction, (3) induced seismicity, (4) earthquake hazards assessment, (5) engineering, and (6) research for utilization. Academic and 

private-sector workers are involved in these studies 

along with USGS personnel.

The information contained in this paper is developed 

for the geologist or engineer who needs to know how to 

estimate the earthquake ground motion for a site. It 

represents several scientific disciplines and is a subset 

of the comprehensive body of knowledge now available. 

This subset of information provides a framework for a 

technical understanding of the empirical procedures 

currently used to estimate ground motion.

Simplifications and generalizations are made to 

some degree in the paper to enable the geologist or 

engineer to have a broad understanding of the technical concepts without having to know all of the details.
DETERMINE SEISMICITY

Extensive references are provided to give additional 

information when needed. Also, a glossary of of standard nomenclature, terminology, and definitions is 

provided to aid understanding. Some subjects, such as 

the causative mechanisms of U.S. earthquakes, are obviously too complex to be covered completely; therefore, only the most important facts related to the problem of estimating earthquake ground-motion are emphasized. Earthquake-resistant design is a dynamic 

field; therefore, the procedures discussed in this paper 

should be expected to change as progress in fundamental research is made. 1

A number of investigators (for example, Barosh, 

1969; Lomenick, 1970; Werner, 1970; Shannon and 

Wilson, Inc., and Agbabian Associates, 1972, 1975; 

Algermissen, 1973; Hoffman, 1974; Trifunac, 1973b; 

Hays and others, 1975b; Krinitzsky and Chang, 1975; 

Werner, 1975, Gates, 1976; Guzman and Jennings, 

1976; American Society of Civil Engineers, 1976; and 

McGuire, 1977a) have published procedures for estimating earthquake ground motions. On the basis of 

accumulated knowledge and experience in geology, 

geophysics, seismology, and geotechnical engineering, 

a general procedure, such as shown in figure 1, provides a reasonable basis for specifying the groundmotion parameters needed for earthquake-resistant 

design.

Empirical correlations are widely used today in 

earthquake resistant design. These correlations are 

frequently based on statistical analysis of the best 

available data, but, in many cases, they are based on 

interpreted trends or projected upper bounds in the 

data. Thus, all the empirical correlations do not have 

well-defined statistical distributions. The relations 

most frequently used are:

1. Earthquake recurrence relations (Algermissen, 1969; Algermissen and Perkins, 1976);

2. Magnitude and Modified Mercalli intensity 

(Gutenberg and Richter, 1942);

3. Peak ground acceleration and Modified Mercalli intensity (Neumann, 1954; Gutenberg 

and Richter, 1956; Trifunac and Brady, 

1975c; O'Brien and others, 1977);

4. Magnitude and length of fault rupture 

(Bonilla, 1970; Wallace, 1970; Housner, 

1970; Mark, 1977);

5. Peak acceleration, distance, and magnitude 

(Housner, 1965; Schnabel and Seed, 1973; 

Donovan, 1973; Boore and others, 1978);

6. Modified Mercalli intensity and distance (Nut- 

______tli, 1972; Brazee, 1976; Young, 1976);

'Note added in press. The October 15, 1979, Imperial Valley, Calif., earthquake is an 

example of a significant opportunity to increase our knowledge. This ML 6.6 earthquake was 

well recorded, especially near the fault, and will provide a basis for improving present 

procedures used in earthquake-resistant design.

7. Duration of shaking and magnitude (Housner, 

1965; Page and others, 1972; Bolt, 1973; 

Trifunac and Westermo, 1977);

8. Peak velocity and distance (Esteva and 

Rosenblueth, 1964; Seed, Murarka, Lysmer, 

and Idriss, 1976);

9. Site-independent response spectra (Housner, 

1959; Newmark and Hall, 1969; U.S. 

Atomic Energy Commission, 1973; N. M. 

Newmark Consulting Engineering Services, 

1973; and J. A. Blume and Associates, Engineers, 1973); 

10. Site-dependent response spectra (Seed, Ugas,

and Lysmer, 1976).

Deterministic models have been developed by a 

number of investigators (for example, Brune, 1970; 

Schnabel, Lysmer and Seed, 1972) to simulate numerically the various physical processes that occur in an 

earthquake. With the exception of the local groundresponse models, deterministic models generally have 

not been adopted in current earthquake-resistant design.

Probabilistic methods have recently emerged as a 

useful way to estimate ground motion. It will take a 

number of years, however, to evaluate their full range 

of usefulness and to incorporate them into earthquake-resistant design.

The steps in a general procedure for estimating 

earthquake ground motion for earthquake-resistant 

design are discussed below.

DETERMINE SEISMICITY

The objective of this step is to use the historic seismicity record to define earthquake recurrence relations 

applicable for the region of interest, to provide a basis 

for correlating earthquake epicenters and tectonic 

structure, and to define seismic source zones. From the 

seismicity record, one attempts to establish:

1. The date of occurrence of each past event;

2. Epicentral intensity and, for post-1933 events, 

magnitude;

3. Epicenter and hypocenter locations;

4. Epicentral maps showing the epicenters of all reported earthquakes centered within an 80-km 

radius of the site and all earthquakes with 

Modified Mercalli intensity greater than or 

equal to V within a 320-km radius;

5. The aftershock zone of historic earthquakes;

6. Correlation of epicenter locations and tectonic 

structure;

7. The frequency of occurrence for earthquakes of

various magnitudes or epicentral intensities. 

Evaluation of the seismicity of a region requires the
PROCEDURES FOR ESTIMATING EARTHQUAKE GROUND MOTIONS

USER PROVIDES SITE AND 

STRUCTURE INFORMATION

IS STRUCTURE 

CRITICALLY 

IMPORTANT?

ESTIMATE LOCAL SOIL AMPLIFICATION EFFECTS

MODIFY RESPONSE SPECTRA FOR SITE 

(IF NECESSARY)

ESTIMATE UNCERTAINTY IN 

SEISMIC DESIGN PARAMETERS

DOES CRITICAL

NATURE OF

STRUCTURE REQUIRE

ADDITIONAL

ANALYSIS? USER PROVIDES 

ANALYSIS 

CRITERIA

PERFORM DETAILED

SITE AND STRUCTURE

ANALYSIS

USER DOCUMENTS ANALYSES, 

ALTERNATIVES, AND RECOMMENDATIONS

FIGURE 1.—Steps in estimating ground motion for design of earthquake-resistant structures.
DETERMINE SEISMICITY

compilation and evaluation of an earthquake catalog 

(Stepp, 1972; Gardner and Knopoff, 1974; Kagen and 

Knopoff, 1976). This task is complex because the design application (for example, a dam, hospital, or nuclear power plant) under consideration may require a 

fairly precise specification of the frequency of occurrence of large earthquakes on a local scale whereas the 

catalogs of instrumentally recorded earthquakes and 

felt earthquakes generally do not cover a time interval 

long enough to allow valid extrapolations of future 

earthquake activity except on a broad regional scale. 

It has been clearly demonstrated by Evernden (1970) 

and others that the earthquake recurrence law follows 

the empirical linear relation

\ogN(M)=a-bM,

where N(M) is the number of earthquakes occurring 

within a region in a given time period with a magnitude greater than or equal to M. The constants a and 

b are determined from least squares analysis. The 

seismicity index a is dependent upon the size of the 

geographic area, the level of activity, and the length of 

the time period considered. The seismic severity index 

b is usually in the range -0.8 to -1.0 for most parts of 

the world and appears to be related to the nature of the 

tectonic activity causing the earthquakes. A similar 

empirical linear relation holds for Modified Mercalli 

intensity.

SOURCES OF INFORMATION

There are numerous sources of seismicity data. The 

most complete single source of seismicity data is 

Earthquake History of the United States (Coffman and 

Von Hake, 1973) which is published by NOAA (National Oceanic and Atmospheric Administration). In 

addition, detailed information is given in the annual 

publication, U.S. Earthquakes, formerly published by 

U.S. Department of Commerce but now published 

jointly by NOAA and USGS. This publication contains 

reproductions of important accelerograms, isoseismal 

maps, and other important data.

A catalog of some 6,000 U.S. earthquakes is contained in Hays and others (1975b). This catalog includes earthquakes through 1970 that have been assigned Modified Mercalli intensities of IV or greater. 

Information about the seismicity in individual states is 

usually available through the State Survey or a state 

university. For example, information on the seismicity 

of Nevada can be obtained from the University of 

Nevada, Reno, and from publications such as Rogers, 

Perkins, and McKeown (1976) and Ryall (1977). Information on the seismicity of Utah is available from the 

University of Utah at Salt Lake City. Townley and 

Alien (1939) cataloged preinstrumental data in

California, whereas information on the instrumental 

seismicity of California can be obtained from California Institute of Technology's Seismological Laboratory, 

University of California, Berkeley's Seismic Station, 

and the California Division of Mines and Geology. Information on Alaska's seismicity is contained in the 

publication by Meyers (1976). Recently, an earthquake 

information center was established at Memphis State 

University, Tennessee.

The seismicity of the Eastern United States has been 

discussed by several investigators (for example, McClain and Meyers, 1970; Bollinger, 1972, 1973; Chinnery and Rogers, 1973; Sbar and Sykes, 1973; Hadley 

and Devine, 1974; Nuttli, 1974; Long, 1974; Young, 

1976, and McGuire, 1977b).

The Bulletin of the Seismological Society of America 

contains data about recent earthquakes in the "Seismological Notes" of each issue.

Current data are frequently available through the 

National Earthquake Information Service, USGS, 

Golden, Colo. (for example, Stover and others, 1976).

The earthquake history of the United States will be 

discussed below to illustrate the problem of seismicity 

on a national scale. Regional earthquake recurrence 

relations, "b values," upper-bound magnitudes, and 

seismic source zones can be readily compared on this 

scale.

SUMMARY OF 

UNITED STATES EARTHQUAKE HISTORY

Although the zone of greatest seismicity in the 

United States is along the Pacific Coast in Alaska and 

in California, the central and eastern parts of the 

United States have also experienced seismic activity 

(fig. 2). Earthquakes have occurred in the St. Lawrence 

River region on many occasions from 1650 to 1928, in 

the Boston vicinity in 1755, in the central Mississippi 

Valley at New Madrid, Mo., in 1811-1812, in Charleston, S.C., in 1886, and at Hebgen Lake, Mont., in 1959.

Historical earthquakes that have caused notable 

damage and loss of life are listed in table 1. Property 

damage in the United States due to earthquakes occurring since 1865 approaches $2 billion. The loss of life in 

the United States has been relatively light, considering the number of destructive earthquakes that have 

occurred. Since 1964, the United States has experienced one great earthquake (the 1964 Alaska earthquake). The Alaska earthquake had a magnitude of 8.4 

and caused $500 million in property damage, 131 

deaths, and hundreds of injuries. The San Fernando 

earthquake had a magnitude of 6.6. It released about 

one-thousandth as much energy as the Alaska earthquake, but it caused the same amount of property
PROCEDURES FOR ESTIMATING EARTHQUAKE GROUND MOTIONS

St. Lawrence River region, 

1663, 1870

Helena, 1935 

'Manhattan area, 

•7325

^Hebgen Lake, 

Mont., 1959

Giles Coun 

-Va..«?37 Charleston^ 

Mo., 1895 JF 1952 \<- 

Santa BarbaraTv Riverside Co., 1918

LongBeaT73^*H7et-"f'

San Juan* -Imperial Valley.

30 ,.

FIGURE 2.—Location of past destructive earthquakes in the United States.

TABLE 1.—Property damage and lives lost in notable United States 

earthquakes

[From Office of Emergency Preparedness, v. 3 (1972), p. 80-82]

Year

1811-12-

1865 _

1868 _

1872 _

1886 __

1892 ___

1898

1906 ___

1915 __

1925 ___

1933 _

1935 —

1940 ___

1946 ___

1949 ___

1952 ___

1954 ___

1954 —

1955 _

1957 —

1957 __

1958 _

1959 _

1960 ___

1964 ___

1965 ___

1971 ___

Locality

_ New Madrid, Mo.

II W^ TIG A/al 10V (^al I'f*

Charleston, S.C.

Mare Island, Calif.

Imperial Valley, Calif.

- -Eureka, Calif.

--Wilkes-Barre, Pa.

-Oakland, Calif.

Lituya Bay, Alaska

Prince William Sound,

Alaska

San Fernando, Calif.

Magnitude

7.5 (est.) 

8.3 (est.)

8.3 (est.)

8.3 (est.)

6.3

6.0

7.0

7.1

7.7

n q

— —

8.4

6.6

Damage 

(million 

dollars)

~0~4

.4

00 fl

o

1.4

500.0

6.0

8.0

40.0

4.0

C. f\

oc n

oc n

60.0

9 1

1.0

1.0

q n

1.0

11~6

on n

500.0

19 ^

ncq o

Lives 

lost

—— -

Of)

97

60

700

6

1 °.

115

4

0

17°.

8

1

1

5

98

61

131 

7

65

damage and half as many deaths because the San Fernando earthquake occurred on the edge of a large metropolitan area, whereas the Alaska earthquake occurred in a sparsely populated region.

One indication of the seriousness of the earthquake 

problem in the United States is the fact that earthquakes were felt in 34 states in 1973. All or parts of 39 

states lie in regions classified as having major and 

moderate seismic risk. Within these 39 states, more 

than 70 million people are exposed to earthquake 

hazards.

The focal depths of earthquakes vary widely 

throughout the United States. Earthquakes in California occur at relatively shallow depths, (=£16 km), 

whereas large earthquakes in the Puget Sound, Washington, area occur primarily at depths of 50-60 km. 

Earlier, scientists thought that earthquakes in the 

central United States (for example, New Madrid area) 

occurred at depths of 50-60 km, but recent studies 

have shown that they occur at depths of 5-20 km. A 

shallow depth of 5-10 km is also indicated for earthquakes in the Charleston, S.C. area.

The historical seismicity record in the United States 

is not more than 400 years long and quite variable 

regionally. Earthquake recurrence relations have been 

derived from this relatively short record. (Algermissen,
DETERMINE SEISMICITY

1969). Figure 3 shows the regions studied by Algermissen in 1969 to determine earthquake recurrence relations, expressing the number of earthquakes, N, occurring in a given region in a given time period with 

intensity greater than or equal to Modified Mercalli 

intensity I. These recurrence relations are summarized 

in table 2. These data, integrated with Alaska seismicity data, provide the relative ranking of regional seismicity shown in table 3.

In 1976, Algermissen and Perkins defined 71 regions 

(fig. 4) within the conterminus United States as seismic source zones. Each zone was defined on the basis of 

the historic seismicity and the distribution and activity 

of faults. Table 4 lists the seismicity parameters deTABLE 2.—Summary of earthquake recurrence relations in the United States

[From Algermissen (1969), fig. 3. N, number of earthquakes of intensity 7]

Area

Nos. from 

fig. 3 States

1 California

2 Nevada

3 Puget Sound, Wash ___ _

4 Montana, Idaho, Utah, 

Arizona (Intermountain Seismic Belt)

5 Wyoming, Colorado, 

New Mexico

6 Oklahoma, North 

Texas

7 Nebraska, Kansas, 

Oklahoma

8A, Mississippi and St. 

B Lawrence Valleys

9 East Coast

Recurrence relation

.___ _ log7V=3.92-0.547

— ___ log 7V=3.98-0.56 /

. __ ___log7V=3.45-0.627

._______log7V=3.41-0.567

. ____ log N =3.66- 0.68 7

_ log7V=2.10-0.557

Inp N— 1 QQ-0 4Q T

._______log7V=2.71-0.57

._______log7V=3.02-0.587

Earthquakes/100 yrs/ 

100,000 km2 for 

Modified Mercalli 

intensity

V

300

68.0 

64.4 

32.8 

13.3 

13.0

24.2 

12.8

VI

84.6

16.3 

17.7 

6.85 

3.73 

4.20

7.65 

3.39

VII

23.8

3.92 

4.99 

1.42 

1.07 

1.35

2.42 

.88

VIII

6.72

.94 

1.35 

.31 

.30 

.45

.76 

.23

FIGURE 3.—Geographic areas of the conterminous United States where regional seismicity studies have been made (modified from 

Algermissen, 1969). Numbered areas are described in table 2. Shading depicts boundaries of regions.
PROCEDURES FOR ESTIMATING EARTHQUAKE GROUND MOTIONS

TABLE 3.—Relative seismicity of regions of the United States

Area

Equivalent magnitude-4

earthquakes/year/

1,000 km2

Normalized to 

Pacific West

S.E. Alaska

(lat 54°-63° N.)

(long 144°-156° W.) _____15 

Pacific West

(west of long 114° W.) ___ .20 

Rocky Mountains (long

106°-114°W.) ________ .04 

Central Plains

(long 92°-106° W.) ______ .006 

Eastern United States

(east of long 92° W.)_____ .017

75

1.0

.20

.03

.08

termined for each source zone. On the basis of current 

knowledge, future earthquakes are considered equally 

likely to occur anywhere in a source zone.

Estimating the upper-bound magnitude for various 

geographic regions of the United States is a difficult 

problem (Smith, 1976). The nature of the problem varies for different areas, as discussed below, and its solution depends upon comprehensive studies of the available geologic and seismological data:

Area of high seismicity, several major shocks, 

and a fairly long (>100 years) historical record of earthquakes.—The number of major 

(M>8) shocks may be insufficient to obtain a 

reliable average rate of occurrence, but the 

average rate of occurrence can probably be 

estimated reasonably well from a plot of log 

N=a—bM. California and Alaska are examples of such an area.

Area of high seismicity, some moderate shocks, 

no known major shocks, fairly long (>100 

years) historical record of earthquakes.—The 

crustal rocks may not be able to support high 

levels of strain and thus strain accumulation 

is relieved through moderate magnitude 

(6-7) shocks. The rate of occurence of 

moderate and small shocks can probably be 

estimated accurately from the historic record. 

Unless geologic evidence indicates the possibility of large shocks, it is probably justified 

to assume that no large shocks will occur. 

The Puget Sound area and the Intermountain

125° 120° 115° 110° 105° 100° 95° 90° 85° 80° 75° 70° 65°

FIGURE 4 —Seismic source zones within the conterminous United States (from Algermissen and Perkins, 1976). Zone numbers correspond to

those in table 4.
IDENTIFY SEISMOTECTONIC FEATURES 9

TABLE 4. — Seismicity parameters for seismic source zones

[Zone numbers shown in fig. 4]

Zone

No.

1 __

2 —

3

4. _

5 -.

6 —

7 —

8

9 —

10 —

11 ___

12

13 —

14

15

16 —

17 —

18 —

19 —

20

21

22 —

23 —

24___

25 —

26 —

27 —

28___

29___

30 ___

31

32 —

33___

34___

35 —

36___

37 —

38___

39 —

40 —

41

42___

43___

44 —

45 —

46 —

47 —

48 —

49 —

50___

51 —

52 —

53___

54 —

55 _

56 __

57 —

58___

59 —

60___

61

62 —

63___

64 __

65 —

66 —

67 —

68 —

69___

70 —

71

Number of Modified 

Mercalli maximum

Seismic 

severity

intensity V's/100 yrs index b

—245.2

— 110.0

_ 27.2

___ 75.1

___ 14.9

— 44.4

—299.6

73

—208.0

— 125.0

— 80.1

— 43.0

— 99.4

— 34.9

— 0.0

— 33.9

_ .223.0

— 2.8

—613.6

— 14.8

— 79.8

_ 80.1

— 12.7

— 6.0

— 8.5

_ 137.1

— 99.9

— 35.3

— 90.4

___ 10.5

84.6

_ 17.0

_ 126.8

— 71.0

— 23.0

_ 15.3

__ 15.6

— 31.1

_ 21.5

— 2.7

__ 27.6

__ 11.1

— 23.0

— 13.8

— 6.7

— 2.7

___ 2.7

— 14.7

— 10.3

— 4.6

_ _ 7.4

— 13.0

— 9.3

— 21.2

— 1.7

— 5.7

_ _ 7.8

.6

_ _ 16.0

___ 16.0

— 84.5

— 22.0

— 22.1

___ 54.4

— 19.9

— 13.0

— 7.8

— 69.1

— 117.6

— 33.5

21.7

-0.50

-.40 up to IX

then zero -.45

-.45

-.50

-.45

-.53

-.49

-.40

-.51

— 53

-.43 up to XI

then zero -.45

-.45

-.53

-.50

-.45

-.50

-.52

-.29

-.59

-.76

Not applicable

-do-.59

-.72

-.67

-.32

-.36

-.26

-.63

-.56

-.56

-.56

-.56

-.54

-.31

-.54

-.54

-.40

Not applicable -.40

Not applicable

-do———— -.31

-.40

-.40

-.54

Not applicable

-do— —— ___ -.53

-.40 '

-.24

-.55

Not applicable -.53

-.55

-.50

-.50

-.50

-.50

-.50

-.64

-.59

-.33

-.59

-.59

-.67

-.59

-.65

-.49

Maximum

intensity

X

XII

XI

XI

X

XI

VIII

VI

XI

VIII

VIII

XII

XI

XI

VIII

X

XI

X

X

VIII

VII

VI

V

V

VII

VI

VII

IX

X

VII

VII

VI

IX

VII

VIII

VII

VIII

VII

VII

VI

V

VI

V

V

VIK

VI

VI

VII

V

V

VI

VI

VIII

VII

V

VI

VII

VII

VIII

VIII

X

VIII

VIII

VIII

X

VIII

VII

VIII

IX

VIII

X

Corresponding 

maximum

magnitude

7.3

8.5

7.9

7.9

7.3

7.9

6.1

4.9

7.9

6.1

6.1

8.5

7.9

7.9

6.1

7.3

7.9

7.3

7.3

7.1

5.5

4.9

4.3

4.3

5.5

4.9

5.5

6.7

7.3

5.5

5.5

4.9

6.7

5.5

6.1

5.5

6.1

5.5

5.5

4.9

4.9

4.9

4.3

4.3

6.1

4.9

4.9

5.5

4.3

4.3

4.9

4.9

6.1

5.5

4.3

4.9

5.5

5.5

6.1

6.1

7.3

6.1

6.1

6.1

7.3

6.1

5.5

6.1

6.7

6.1

7.3

Seismic Belt are examples of this type of 

area.

3. Area of moderate seismicity and occasional or 

single occurrence of a moderate or large 

shock.—Unless the seismic history is long, it 

is difficult to estimate the rate of occurrence 

of moderate or major shocks in such an area 

with high reliability. The lower Mississippi 

Valley is an example of this type of area.

4. Area of low seismicity with no known moderate 

shocks.—Unless geologic information is 

available, no reliable method for estimating 

future seismicity is presently available for 

these areas. Special studies utilizing temporary seismograph stations to investigate the 

occurrence of microearthquakes may provide 

important research information, but the relation between the level of microearthquake 

activity and the occurrence of large (or even 

intermediate) earthquakes is not clear. The 

Atlantic and Gulf Coastal Plains geologic 

provinces are examples of this type of area. 

Probably the most useful data for estimating the 

upper-bound magnitude in a region and recurrence 

rates of moderate to large earthquakes are the lengths 

of rupture in recent and prehistoric faulting. Length of 

rupture seems to be closely related to the magnitude of 

the earthquake (Wallace, 1970; Bonilla, 1970; Mark, 

1977). Also, dating of the times of occurrence and the 

time intervals between fault ruptures is useful for establishing recurrence rates. Present data are 

inadequate to resolve all the questions that have now 

arisen about the upper-bound magnitude for most regions of the United States.

IDENTIFY SEISMOTECTONIC FEATURES

The location and characteristics of faults and other 

tectonic structures in the region surrounding the site 

are essential information along with the historical 

seismicity for estimating the upper-bound magnitude 

and the locations of potential earthquakes. An analysis 

of faulting and tectonic activity in a region can be complex and time consuming, requiring data from three 

sources: (1) geologic data on faults and the ages of rock 

formations they displace, (2) seismological data on the 

areal distribution of seismicity in relation to known 

faults and tectonic structures, and (3) historical accounts which provide evidence that a fault has ruptured at the surface or that earthquakes might reasonably be associated with a particular fault.

Faults that are active, such as the San Andreas and 

Hayward faults in California, usually exhibit clear 

geologic, seismological, and historical evidence of re-
10 PROCEDURES FOR ESTIMATING EARTHQUAKE GROUND MOTIONS

cent and recurrent fault movement. In many cases, 

however, the information is not definitive and the fault 

tends to fall in the borderline category between active 

and inactive. Specific criteria (Cluff and others, 1972) 

for recognizing an active fault are given in table 5.

One rationale for classifying fault activity (table 6) 

uses the available geologic, seismological, and historical data to specify four fault-activity classifications: active, potentially active, activity uncertain, and inactive. To quantify fault activity requires researching the 

scientific literature concerning specific faults, the instrumentally recorded seismicity of the region, and 

historical accounts of past earthquakes and their aftershock sequence. The dimensions of fault rupture can 

often be estimated from the distribution of aftershocks. 

Trenching may also be required. Data and maps may 

be obtained from many sources, including the United 

States Geological survey, state geological surveys, 

local universities, and private consulting firms.

Faults are considered to be significant if they fall 

into one of the following categories: (1) faults crossing 

the site that are capable of rupturing during the life of 

the engineered structure, and (2) faults located either 

near the site or some distance from the site that are 

capable of generating large damaging earthquakes.

Specification of faulting potential in the vicinity of 

the site is of particular importance, but subject to controversy. The fault is defined as a fracture along which 

differential slippage of adjacent earth materials has 

occurred. Surface faulting is differential ground displacement at or near the surface caused directly by

TABLE 5.—Criteria for recognizing an active fault

[from Cluff and others (1972)]

Data source Specific criteria

Geologic Active fault indicated by young geomorphic features 

such as: fault scarps, triangular facets, fault rifts, 

fault slice ridges, shutter ridges, offset streams, enclosed depressions, fault valleys, fault troughs, 

sidehill ridges, fault saddles; ground features such 

as: open fissures, mole tracks and furrows, rejuvenated streams, folding or warping of young deposits, 

ramps, ground-water barriers in recent alluvium, 

echelon faults in alluvium, and fault paths on 

young surfaces. Usually a combination of these features is generated by fault movements at the surface. Erosional features are not indicative of active 

faults, but they may be associated with some active 

faults. Stratigraphic offset of Quaternary deposits 

by faulting is indicative of an active fault.

Seismological Earthquakes and microearthquakes, when well located instrumentally, may indicate an active fault. 

Absence of known earthquakes, however, does not 

ensure that a fault is inactive.

Historical Historical manuscripts, news accounts, personal 

diaries, and books may describe past earthquakes, 

surface faulting, landsliding, fissuring or other related phenomena. Usually for a large earthquake, 

there will be several accounts in the historical record. Evidence of fault creep or geodetic movements 

may be indicated.

fault movement. Current criteria suggest that a fault 

should be considered capable of permanent surface displacement if it is characterized by one or more of the 

following:

1. Movement at or near the ground surface occurred at least once during the past 35,000 

years or more than once during the past 

500,000 years.

2. Instrumentally determined seismicity is directly related to the fault.

3. A relation to another active fault exists such 

that movement on one active fault can be 

reasonably expected to be accompanied by 

movement on the other active fault. 

The controversy arises from the current lack of understanding of the geologic processes that lead to the accumulation of strain and the sudden fracture of rocks 

in the earth's crust. Also, in seismically quiet regions 

like the Eastern United States, no seismic source zones 

can be identified with historic surface faulting.

Cluff and others (1972), Krinitzsky (1975), American 

Nuclear Society (1975), and Slemmons and McKinney 

(1977) have published information and guidelines to 

aid in the evaluation of faults. The key factors in the 

assessment of a fault's potential for producing an 

earthquake are:

1. fault length,

2. magnitude and nature of displacement,

3. geologic history of displacements, especially the 

age of latest movements, and

4. the relation of the fault to regional tectonic features.

An example will illustrate the procedure for evaluating fault activity. Figure 5 depicts the principal faults 

in the San Francisco Bay region in the vicinity of the 

city of Fremont, Calif. Because of their location, the 

Hayward, Mission, Silver Creek, and Chabot faults 

have the potential for producing significant ground 

motions at the Fremont site. The San Andreas fault, 

despite being a greater distance away, is also important because it is capable of producing very large 

earthquakes. Table 7 illustrates the evaluation.

Housner (1970) developed an empirical relation for 

correlating fault rupture length and earthquake magnitude (fig. 6). The rupture lengths for the San Andreas, Hayward, and Calaveras faults are plotted on 

the figure as a guide. The relation shows that (1) faults 

with rupture lengths of 32-40 km generally produce 

magnitude 5 to 7 earthquakes, (2) faults with rupture 

lengths of 40-113 km generally produce magnitude 7 

to 7.5 earthquakes, and (3) faults with rupture lengths 

of 300 km or more generally produce earthquakes of 

magnitude 8 or greater. Exceptions to the general 

trend occur, for example, some magnitude-8 earth-
IDENTIFY SEISMOTECTONIC FEATURES 11

TABLE 6.—Classification of fault activity

[From Cluff and others (1972)]

Active

Potentially 

active

Uncertain 

activity Inactive

Historical

Geologic

Seismological

-Surface faulting and

associated strong

earthquakes. 

Tectonic fault creep

or geodetic

indications of

movement.

-Generally young deposits 

have been displaced 

or cut by faulting.

Fresh geomprphic features 

characteristic of 

active fault zones 

present along fault 

trace.

Physical ground-water 

barriers in geologically 

young deposits.

-Earthquake epicenters are 

assigned to individual 

faults with a high 

degree of confidence.

No reliable report 

of historic surface 

faulting.

Geomorphic features

characteristic of

active fault zones

subdued, eroded,

and discontinuous. 

Faults are not known

to cut or displace

the most recent

alluvial deposits,

but may be found in

older alluvial deposits. 

Water barrier may be found

in older materials. 

Geologic setting in

which the geomorphic

relation to active

or potentially active

faults suggests similar

levels of activity.

Alinement of some earthquake 

epicenters along fault 

trace, but locations 

have a low degree of 

confidence.

No historic activity.

Available information 

does not satisfy 

enough criteria to 

establish fault 

activity.

If the fault is near 

the site, additional 

studies are necessary.

Geomorphic features 

characteristic of 

active fault zones 

are not present, 

and geologic 

evidence is available to indicate 

that the fault has 

not moved in the 

recent past.

Not recognized as a 

source of 

earthquakes.

CHABOT FAULT

BOLINGER FAULT

PLEASANTON FAUL

\ \SILVERCREEK 

N Jfc- FAULT

*

FIGURE 5.—Principal faults in the vicinity of Fremont, Calif, 

(modified from Cluff and others, 1972).

TABLE 7.—Classification of selected faults relative toFremont, Calif.

[From Cluff and others, (1972)]

Fault

Classification 

of activity Criteria

Hayward

Mission

-Active

-Potentially active

Silver Creek _-Tentatively active

Chabot-_- 

Calaveras _.

Pleasanton 

Bolinger _

-Potentially active 

.Active

._-Active

-Potentially active 

near junction with 

Calaveras. 

Tentatively inactive 

away from Calaveras junction.

Parks ____-Potentially active

San Andreas _-Active

Historical faulting.

Geologic setting and microearthquake epicenters.

No geomorphic features, no 

ground water barrier, no 

earthquake epicenters.

Geologic setting.

Geomorphic features, historical faulting, and 

strong earthquakes.

Documented tectonic fault 

creep.

Geologic setting, no 

characteristic geomorphic features.

Ground-water barrier in 

Tertiary-Quaternary 

gravels.

Geomorphic features, historic faulting, and 

strong earthquakes.
12 PROCEDURES FOR ESTIMATING EARTHQUAKE GROUND MOTIONS

IUUU

500

100 

50

10 

5

1.0 

0.5

n 1

_ i

-

-

-

\

-

-

i

i

L=1f

/

v

I

Cft

2X10~ 2 i

Mr

1

1

L=2.2

LAVER/

^r

i

1

SAN/

5X10" 5 e

HAYWAI

Sv

h

^NDREAi

2M/ v

7

i

^

/:

5

-

\

-

\

-

Tt>UU 

800

160 

80

16 

8

1.6 

0.8

23456789

FIGURE 6.—Empirical relationship of fault rupture length and 

earthquake magnitude (modified from Housner, 1970).

quakes have had fault rupture lengths that are less 

than 300 km long. Housner did not specify the statistical distribution for his empirical relation. Mark (1977), 

however, showed that a = 0.93 for the least squares fit 

to the magnitude and fault rupture length relation, 

and he argued that this relation is more physically 

meaningful than fault rupture length as a function of 

magnitude.

SUMMARY OF UNITED STATES EARTHQUAKES

The exact mechanisms that produce tectonic earthquakes in various parts of the United States are still in 

doubt. The most extensively favored theory is that tectonic earthquakes are caused by slip along geologic 

faults. The correlation of earthquakes with fault slip is 

clear in the Western United States, but it is not very 

clear in the Central and Eastern United States. The 

seismicity patterns of the Western and Eastern United 

States are quite different, and the causative mechanisms are not well understood at the present time.

A number of physical factors are different in the 

Eastern and Western United States and may be the 

cause, in part at least, of the difference in seismicity. 

The area east of the Rocky Mountains is generally 

characterized by low heat flow, a thick crust in which 

east-northeast compressive stress is typical, and

Cenozoic epeirogenic uplift. The area west of the Rockies is characterized by high heat flow, a thin crust, and 

extensive late Cenozoic volcanism. The attenuation of 

seismic waves is also appreciably lower east of the 

Rocky Mountains than it is to the west (Nuttli, 1973a, 

b; Nuttli and Zollweg, 1974), suggesting a distinctly 

different crustal structure. The basic premise is that 

basement structures and crustal blocks are adjusting 

to epeirogenic forces and continued movements along 

old fracture lines developed at different times in the 

geologic past to produce the present seismicity.

WESTERN UNITED STATES

The complex tectonic pattern of eastern and southcentral Alaska is created by the interaction of the 

Pacific and North American plates (Packer and others, 

1975). Interaction between two crustal plates either 

creates, destroys, or preserves crustal material. Crust 

is created at oceanic ridges, destroyed at trenches and 

collision-type mountain belts, and preserved along 

transform and strike-slip faults. Because of the present 

plate interaction in Alaska, two types of boundaries 

occur (fig. 7). An active subduction zone, which extends

FIGURE 7.—Major tectonic features along the Pacific-North American plate boundary in Alaska (modified from Packer and others, 

1975).
IDENTIFY SEISMOTECTONIC FEATURES 13

from the Aleutian Islands to the vicinity of Mount 

McKinley, is denned by a line of volcanoes and a Benioff zone (Davies and Berg, 1973). In the east, a topographic trench is denned in the Gulf of Alaska.

The eastern boundary of the subduction zone is a 

series of faults that roughly define a transform fault 

system. This system is believed to be a westward extension of the Queen Charlotte Islands fault (Tobin and 

Sykes, 1968). The exact characteristics of the faults 

that connect the Alaska subduction zone with the 

Queen Charlotte Islands transform fault are poorly defined and are still a major unsolved problem.

The geology and seismicity of Alaska are complex 

and still not well known in many areas. For this reason, many hypotheses (for example, Plafker, 1965, 

1967; Grantz, 1966; Gedney, 1970; Page, 1972; Van 

Wormer and others, 1974; Brogan and others, 1975) 

have been proposed to explain the origin of Alaska and 

its tectonic development and seismicity (fig. 8). At least 

24 active faults have been identified in Alaska (Brogan 

and others, 1975). The dominant fault in the southen 

area is the Denali fault system (fig. 9). This system 

consists of relatively straight, right-slip segments that

combine to create a 2,200-km-long arcuate fault that 

curves 30° and extends from Chatham Strait to Bristol 

Bay. The fault system is generally considered to be an 

extension of the Queen Charlotte Islands transform 

fault. Estimates of total right-lateral displacement on 

the Denali fault range from 80 to 250 km.

Evaluation of the seismicity of California and 

Nevada shows that fault slips are the causative mechanism (Alien and others, 1965; Albee and Smith, 1966; 

Ryall and others, 1966; Bonilla, 1967, 1970; Wallace, 

1970; Alien, 1975). Seismicity data show that the 

earthquakes occur primarily at relatively shallow 

depths (=sl6 km) in the crust. Tectonic surface ruptures 

related to historic (0-300 years before the present) and 

Holocene (0-10,000 years before the present) earthquakes are common.

The well-known San Andreas fault (fig. 10) is a 

transform fault zone, or system; it is the boundary between the Pacific and North American plates. The 

Pacific plate carries a small piece of North America 

with it as it moves northward at a rate of about 3.2 

cm/year along the right-lateral strike-slip San Andreas 

fault.

FIGURE 8.—Epicenters of earthquakes in Alaska between 1962 and 1969 (U.S. Dept. Commerce, 1970).
14 PROCEDURES FOR ESTIMATING EARTHQUAKE GROUND MOTIONS

100 200 300 KILOMETERS 

I______I______I

EXPLANATION

Observed fault 

Inferred fault

Epicenter of 1964 

Alaska earthquake

l

55° 150"

FIGURE 9.—Major faults in southern Alaska.

A distinctive alinement of seismic activity occurs in 

southern California. This zone of activity branches 

from the main trend of the San Andreas fault zone in 

the vicinity of the Garlock fault (fig. 10) and trends 

northward into western Nevada, marking the eastern 

flank of the Sierrra Nevada. Garfunkel (1974) suggested that right-slip motion between the Pacific and 

North American plates on the San Andreas fault has 

produced a region of crustal extension in the Gulf of 

California and the Salton trough. When the Pacific 

plate encountered the Mojave block, rotation and 

internal deformation of the block and bending of the 

San Andreas system occurred. This resistance and 

bending was accommodated by distortion of the block 

and by left-slip on the Garlock fault and other westtrending faults as well as thrusting in the Transverse

Ranges. i

The characteristics of some of the California and 

Nevada fault systems are summarized below:

1. The San Andreas fault zone is the largest fault 

system in California. The right-lateral 

strike-slip system is approximately 1,000 

km long and up to 80 km wide. Several destructive earthquakes have occurred along 

the fault, for example, near San Francisco in 

1836 and 1838 and near Fort Tejon in central California in 1857. The magnitude-8.3 

San Francisco earthquake of April 18, 1906 

caused a surface rupture of about 432 km. 

Creep occurs along sections of the fault (Nason, 1973), but some sections of the fault in 

both northern and southern California appear to be locked at the present time and 

may be the zones of future earthquakes.

2. The Hay ward fault was the source of two large 

earthquakes in 1836 and 1868. The 1836 

earthquake caused a surface rupture of 64
IDENTIFY SEISMOTECTONIC FEATURES 15

OREGON

r - 

i

IDAHO

50\

|/97 RAINBOW MOUNTAINSTILLWATER EARTH

QUAKE FAULTING DIXIE VALLEY

\ ^""FAULT SCARP

( August 23, 1954 f ^December 16J954

July 1954 f &I 1C J" 4iF u

FAIRVIEWPEAK f Dumber 16, 1954 

FAULT SCARP

PLEASANT VALLEY 

FAULT SCARP

1915

NEVADA

1934 m^ EXCELSIOR MOUNTAIN 

FAULTING

SAN FRANCISCO

CALI FOR N IA

SACRAMENTO

I UTAH

_ LAS VEGAS • o;

ARIZONA

EXPLANATION

—— Recently active fault

Surface rupture 

Two recorded ruptures

SAN DIEGO)

50 

I

100 

I

150 KILOMETERS

FIGURE 10.—Major faults in California and Nevada and locations of past surface ruptures.

km, and the 1868 earthquake caused a rupture of 32 km. 

3. The Calaveras fault system, with a length of

approximately 160 km, is one of the largest 

in northern California. It is primarily a 

right-lateral strike-slip fault with a vertical
16 PROCEDURES FOR ESTIMATING EARTHQUAKE GROUND MOTIONS

component responsible for upward movement on the west side. The vertical component is estimated to be about 90.4 m. Creep 

presently occurrs along the fault near Hoilister (Rogers and Nason, 1971; rMayerRosa, 1973).

4. The 240-km-long Garlock fault in southern 

California has a left-lateral movement and 

separates the Mojave Desert province from 

the Sierra Nevada and Basin and Range 

provinces. Only small historic earthquakes 

have been attributed to this fault system.

5. The Sierra Nevada fault zone was the source 

of the 1872 Owens Valley earthquake which 

had an estimated magnitude of 8.3. Many 

people consider this earthquake to be the 

largest in California.

6. The White Wolf fault zone was the source of 

the 1952 magnitude-7.7 Kern County 

earthquake. The fault motion was mainly 

dip-slip and produced a surface rupture of 

about 52 km.

7. The Imperial fault, a southern extension of the 

San Andreas fault system, was the source of 

the magnitude-7.0 1940 Imperial Valley 

earthquake. The surface rupture was about 

64 km.

8. The 1971 San Fernando earthquake caused a 

19-km surface rupture on a segment of the 

Sierra Madre fault system. The epicenter 

was about 4.8 km north of the San Gabriel 

fault system. Faulting was associated with 

the Transverse Ranges structural province, 

a region noted for its relatively young tectonic deformation, and it is the first example 

of surface faulting within that province.

9. The San Jacinto fault zone is one of the most 

seismically active in California (Thatcher 

and others, 1975). Thirteen large earthquakes have occurred since 1890 along the 

240-km-long fault. The 1899 earthquake 

south of Hemet, Calif., ruptured the ground 

surface for 19 km.

10. The Pleasant Valley fault scarp in Nevada 

was associated with a magnitude-7.6 earthquake in 1915. The surface rupture along 

the normal fault system was 32-64 km.

11. The Dixie Valley fault scarp in Nevada is an 

example of a normal fault system. It was 

associated with the 1954 magnitude-6.8 

earthquake which produced 61 km of surface rupture.

12. The magnitude-7.3 Cedar Mountain, Nevada, 

earthquake of 1932 produced surface rupture of approximately 61 km along the normal fault system.

13. The magnitude-6.5 Excelsior Mountain, 

Nevada, earthquake of 1934 produced 1.5 

km of surface rupture.

Ryall (1977) pointed out that active faulting in 

California is confined fairly well to single belts such as 

the San Andreas fault zone, but it is fairly evenly distributed over the entire western Basin and Range province in Nevada. He argued that neither the historic 

seismicity nor the distribution of active faults is by 

itself sufficient to determine the earthquake potential 

in Nevada and that the seismic cycle in Nevada corresponding to the rerupture time of major faults is of the 

order of several thousands of years.

The Puget Sound area of Washington is another zone 

of seismic activity along the Pacific Coast. The earthquake-related fault breaks have not been clearly identified in the area and the exact cause of seismicity has 

not been determined (Crossen, 1972; Rasmussen and 

others, 1975). According to Walper (1976), the seismicity may be related to a triple junction at the north end 

of the Juan de Fuca Ridge (fig. 7). Spreading motion is 

transmitted there to the Explorer Ridge which joins 

with another segment of the transform boundary regime represented by the Queen Charlotte IslandsFairweather fault zone. The Puget Sound area has an 

anomalously thick crust compared to the rest of the 

Western United States (Warren and Healy, 1973) and 

may be an extension of Vancouver Island, which also 

has an anomalously thick crust (Berry, 1973). Thus, 

one hypothesis to explain the seismicity of the area is 

that the block of thick crust is a continental fragment 

caught up in a plate-boundary regime, moving independently to cause seismicity.

The Intermountain Seismic Belt (Smith and Sbar 

1974) is a zone of earthquake activity 1,300 km long 

and 100 km wide that extends southward from the 

south end of the Rocky Mountain front in western 

Montana, through Yellowstone, Wyoming, and eastern 

Idaho and then south-southwest through Utah into 

Arizona (see fig. 3, zone number 4). This seismic belt 

encompasses the Yellowstone mantle plume (Wilson, 

1973) and is also coincident with the Cenozoic fault 

zones of the northern Rocky Mountains. Smith and 

Sbar (1974) interpreted the belt as a boundary between 

the northern rocky Mountain and the Great Basin subplates of the North American plate because it closely 

follows the boundary between major physiographic and 

structural provinces.

The Wasatch fault (fig. 11) is the dominant fault in a 

system of generally north-south-trending active faults 

in the Intermountain Seismic Belt. It is a normal fault, 

down to the west, that extends for 370 km from Gunni-
IDENTIFY SEISMOTECTONIC FEATURES 17

FIGURE 11.—Wasatch fault zone.

son, Utah, to Malad City, Idaho. More than 30 m of 

vertical displacement of late Pleistocene and Holocene 

materials has occurred in places along the Wasatch 

fault zone (Cluff and others, 1975). Only minor seismicity has been associated with the fault during the last 

140 years. A 50- to 105-m-wide zone of damaged 

streets, curbs, houses, and buildings occurs in Salt 

Lake City along the fault trend. Approximately 85 percent of Utah's population lives within 8 km of the 

Wasatch fault zone. The only historical earthquake in 

Utah that produced ground displacement was the 1934 

magnitude-6.6 Hansel Valley earthquake. It occurred 

north of the Great Salt Lake.

EASTERN UNITED STATES

The earthquakes of the Mississippi Valley are associated with continuing tectonic activity at the upper 

end of the Mississippi embayment (fig. 12), a part of the 

Gulf Coastal Plain. The embayment is a structural 

trough that was formed in Paleozoic basement rock and 

subsequently filled with marine deposits. It is generally thought that down warping of the underlying 

Paleozoic basement rock is continuing today. Faults 

are thought to be present in the basement rocks in the

embayment area but have not been conclusively identified.

With the possible exception of the 1811-12 New 

Madrid earthquake, surface rupture has not been associated with historic or Holocene earthquakes in the 

Mississippi Valley area or any other area in the Eastern United States.

Several fault systems have been identified in the 

Mississippi Valley area. The best-known faults include: the New Madrid fault zone, the Kentucky River 

fault zone, the Mount Carmel fault, the Rough Creek 

fault zone, the Wabash fault zone, the Cottage Grove 

fault zone, the Saint Genevieve-Rattlesnake Ferry 

fault zone, and the Bowling Green fault zone. Some of 

these faults are shown in figure 10. None of these faults 

has exhibited either displacement or concentrated 

seismic activity in historical time.

The New Madrid fault zone, source of the 1811-1812 

earthquakes and several thousand aftershocks, is postulated to be a combination of normal fault zones 

trending northeastward from the northernmost extent 

of the Mississippi embayment to the east-westtrending Rough Creek fault zone. This zone has been 

inferred to exist beneath Cretaceous deposits in the 

embayment area. Fuller (1912) established his "epicentral line" on the basis of evidence of maximum 

ground surface disturbance from the 1811-1812 earthquakes. Some investigators have suggested that the 

New Madrid fault zone can be traced across the 

Mississippi river flood plain in the vicinity of New 

Madrid, Mo.; others believe that the fault zone may 

extend as far north as Vincennes, Ind., or include the 

Wabash fault zone. The critical fact is that the causative faults in the region of the Central United States 

where the largest historic earthquakes occurred are 

still not well identified today.

The present seismicity in the New Madrid region has 

been determined by a regional seismic network 

(Stauder and others, 1976). The most significant finding is the identification of linear trends of seismic activity. These trends are 30-100 km long and are offset 

from or parallel to one another. The greatest number of 

earthquake foci lie very close to the surface of the Precambrian rocks. Seismic activity is episodic, occurring 

in turn along some trends, then along others. When a 

particular linear segment is active, hypocenters are 

usually distributed along the whole segment. These 

phenomena suggest that the linear trends act as continuous seismic features and are not dependent on 

forces acting at distant plate boundaries. Since 1963, 

one earthquake having body-wave magnitude (mb ) 

greater than or equal to 4.75 has occurred about every 

2 years.

Kane and Hildenbrand (1977) reported on the good
18 PROCEDURES FOR ESTIMATING EARTHQUAKE GROUND MOTIONS

ST. LOUIS • I

/

f/

EXPLANATION 

O V 

O VI

O"

O 

O

IXXII

Maximum intensity 

and probable epicenter of earthquake

• City

9 Disturbance

Normal fault 

"-»• Thrust fault

50

I

100I

150 KILOMETERS

FIGURE 12.—Major tectonic features and historic earthquake activity in the Mississippi Valley area.

correlation of the Mississippi embayment seismicity 

with a zone of subdued magnetic field having sharply 

defined parallel boundaries striking N. 45° E. The zone 

is about 100 km wide. The principal seismicity of the 

Mississippi embayment, including the 1811-1812 

earthquake sequence, is located along the axis of the 

zone in a configuration similar to spreading ridges. The 

magnetic field data suggest that the zone is caused by a 

structural depression of 1-2 km relief below the Precambrian basement, which lies at an average depth of 

2-4 km.

The general alinement of earthquakes and the axis 

of high seismic transmissibility extending from southern Illinois to the St. Lawrence Valley in Ontario and 

Quebec was noted by Woolard in 1958. He suggested 

that the alinement might be related to unloading of the 

Pleistocene ice cap. Sykes (1972) pointed out that surface faulting had not been observed for any of the 

earthquakes in the St. Lawrence Valley and that 

understanding of the tectonic mechanism was limited. 

In addition, Sbar and Sykes (1973) noted that large 

seismic gaps occur in the postulated seismicity trend 

and argued against the continuity of the southern

Illinois-St. Lawrence trend. These questions are still 

unresolved.

The earthquakes of the Appalachian region are associated with the Piedmont and the Appalachian 

Mountains, particularly the belt of thrust faults and 

folds. The seismicity pattern has been suggested to correlate with areas of high stress along preexisting fault 

zones that formed during continental collision (Rankin, 1975).

Colton (1970) suggested that the 1886 Charleston, 

S.C., earthquake was caused by movement on a late 

Precambrian or early Paleozoic aulacogen (a faultbounded trough or graben) in the Carolina area of the 

Appalachians. The trends of historic epicenters (fig. 13) 

in this area (Bollinger, 1972, 1973) are not conclusive 

as to the mechanism. The seismic network in the 

Charleston area (Tarr and King, 1974) is providing 

evidence that the current seismicity is concentrated in 

discrete source zones, with the largest shocks being 

7-14 km deep. The fault-plane solutions suggest 

northeast-southwest compression.

The mechanism for the New England earthquakes is 

controversial. No clear evidence of Holocene faulting is
DETERMINE REGIONAL SEISMIC ATTENUATION 19

J911

1929,1930,1931.1956

•1945 ^1799

- EXPLANATION

Epicentral 

oarea of 1886 

earthquake and its 

aftershock sequence

91914

Epicenter of other 

earthquake' and 

year of occurence

Charleston-Summerville 

area

0 40 80 KILOMETERS 

I I I I I

FIGURE 13.—Historic seismicity in South Carolina area (from Bollinger, 1972).

associated with the seismicity. Coney (1972) and 

Morgan (1973) suggested that the present seismicity is 

in response to the continuing adjustment of the crust to 

the horizontal drift of the North American plate and 

epeirogenic warping. They suggested that North 

America was over the Azores hot spot or plume before 

rifting took place to open the Atlantic Ocean. Sbar and 

Sykes (1973) suggested that the locations of earthquakes in Eastern North America are controlled by 

unhealed faults or fault zones in the presence of a high 

deviatoric stress and that the orientation of these 

faults with respect to the stress field may be a major 

factor in determining when an earthquake occurs in 

this area.

There are presently many gaps in knowledge about 

the causative mechanisms for earthquakes in various 

regions of the United States. Progress in understanding has been slow. Expanded regional seismicity networks and greatly improved knowledge of the 

3-dimensional geologic structure over broad geographic areas are needed before the earthquake potential in 

various regions throughout the United States can be 

specified precisely.

DETERMINE REGIONAL SEISMIC 

ATTENUATION

One of the most important factors in specifying 

earthquake ground-motion precisely is knowledge of 

how seismic waves attenuate from the source in various geographic regions of the United States. Research

on seismic attenuation has proceeded slowly because 

the physical parameters of the crust and upper mantle 

causing attenuation are difficult to quantify. Also, the 

present strong-ground-motion data are geographically 

limited, and few empirical data exist to define the effects of path parameters, such as: (1) the natural 

anisotropy and inhomogeneity of the earth; (2) loss 

mechanisms (geometrical spreading, absorption and 

scattering); (3) reflection, refraction, diffraction, and 

wave-mode conversion; and (4) wave interference.

It will be a long time before adequate strongground-motion data are available for all parts of the 

United States; therefore, attenuation functions for 

areas outside California will have to be based on 

Modified Mercalli intensity data, which have deficiencies. One significant deficiency of these relations is the 

lack of knowledge about the statistical distribution. A 

number of investigators (for example, Button, 1887; 

Lawson, 1908; Fuller, 1912; Gordon and others, 1970; 

Coulter and others, 1973; Evernden, 1975; Howell and 

Schultz, 1975; Trifunac and Brady, 1975c; Gupta and 

Nuttli, 1976; Brazee, 1976; Borcherdt and Gibbs, 1976; 

O'Brien and others, 1977; and Espinosa,* 1977) have 

evaluated the intensity data of individual earthquakes 

or a set of earthquakes. These investigations have produced results, some of which are now being applied in 

earthquake-resistant design.

A detailed isoseismal map from a past earthquake is 

the best basis for deriving an intensity attenuation 

function for a region when ground-motion data are unavailable. The critical data contained on an isoseismal 

map are the values of maximum Modified Mercalli intensity reported at various locations. These values are 

transformed into an iso-intensity contour map. The 

contours can be deceiving, however, because isoseismal 

maps typically represent intensity values reported at 

sites underlain by alluvium or unconsolidated materials. Because these sites generally undergo more intense ground motion than sites underlain by rock, attenuation functions derived from an isoseismal map, 

without regard for the local site geology, may overestimate the ground motion level at the site of interest. 

Data showing the effect of site geology in central 

California on intensity increments are listed in table 8

TABLE 8.—Relative intensity values and ground character, central 

California

[From Evernden and others (1973)]

Ground character Relative intensity increments

Granite __________——————————————————————~3 

Jurassic to Eocene sedimentary rocks ——————————————-2 

Oligocene, Miocene, and Pliocene sedimentary rocks —————-1 

Late Pliocene sedimentary rocks.——————————————————-1 

Quaternary sediments (not saturated) ———————————————V£ 

Saturated or near-saturated alluvium or bay fill ——————— ^h.
20 PROCEDURES FOR ESTIMATING EARTHQUAKE GROUND MOTIONS

(Evernden and others, 1973). The reports by Hopper 

and others (1975) and Rogers and others (1976) also 

contain information about the effects of the surficial 

geology on intensity for the Puget Sound, Wash, and 

Salt Lake City, Utah areas.

Figure 14 shows the Modified Mercalli intensity 

isoseismal map for the 1971 San Fernando, Calif, 

earthquake. The area of very heavy ground shaking 

was 768 km2 . The total Los Angeles metropolitan area 

affected was about 1,536 km2 and a total populaton of 

about 7 million was exposed to the shaking.

Isoseismal maps for the 1906 San Francisco and the 

1811 New Madrid earthquakes are compared in figure 

15. The very large difference in felt areas for these two 

earthquakes is characteristic of the difference in seismic wave attenuation in the Eastern and Western 

United States (Nuttli, 1971; 1973b).

Evernden (1975) used the difference in seismic attenuation rates in the Eastern and Western United 

States as a basis for assessing the size of earthquakes. 

Using a predictive model for intensity that incorporated regional variation in seismic attenuation, 

Evernden concluded that the 1906 San Francisco 

earthquake was more than 100 times larger than the 

1811-1812 New Madrid and 1886 Charleston earthquakes. He suggested that the lengths of the fault 

breaks for the New Madrid and Charleston earthquakes were on the order of 10-20 km, considerably 

smaller than had been assumed in the past. He also 

suggested that the 1872 Owens Valley, Calif, earthquake was not so large as originally thought.

Gupta and Nuttli (1976) derived the relation:

! UTAH

San Diego^ 

0 100 200 KILOMETERS

I I I I I

MEXICO

_____I

FIGURE 14.—Isoseismal contours for 1971 San Fernando, Calif., 

earthquake

=/ +3.7-0.001R-2.7 log R for R>20 km

where I(R) is MM intensity atR, epicentral distance in 

kilometers. This relation is applicable for the Central 

United States in the area between the Rocky 

Mountains and the Appalachians. This empirical attenuation law is consistent with intensity data from 

past earthquakes in the Mississippi Valley and model 

studies (Herrmann and Nuttli, 1975a, b).

A number of intensity attenuation relations have 

been proposed for use in the Eastern United States (for 

example, see Cornell and Merz, 1974; M&H Engineering and Memphis State University, 1974; and Young, 

1976). Two attenuation relations proposed for use respectively in the southern Appalachian seismic zone 

and in the central Mississippi Valley are shown in 

figure 16. Both sets of curves are for firm ground conditions.

The most accurate procedure for defining the seismic 

attenuation function of an area is to use observed 

strong-motion accelerogram data to derive a family of 

empirical acceleration-attenuation curves. Such a family of mean acceleration attenuation curves (Schnabel 

and Seed, 1973) applicable for sites in the Western 

United States is shown in figure 17. Each site is assumed to be located on rock, material having a shearwave velocity of at least 760 m/s at low (0.0001 percent) 

strain levels. These curves are somewhat controversial 

in terms of whether or not they underestimate the peak 

acceleration inside 20 km, but they are still used at the 

present time in many applications. The statistical distribution for the Schnabel and Seed acceleration attenuation curves is unknown. Another set of peak acceleration attenuation curves proposed by Davenport 

(1972) is also shown in figure 17. These curves are 

based on regression analysis of the available strongmotion data sample and indicate substantially higher 

values of peak ground acceleration than the corresponding Schnabel and Seed attenuation curves. These 

empirical curves have not received wide use in the 

United States.

Algermissen and Perkins (1976) proposed that acceleration attenuation in the Eastern United States can 

be estimated by modifying the Schnabel and Seed 

curves as shown in figure 18. These empirical curves 

are identical with the Schnabel and Seed curves in the 

distance range 45-50 km and conform to the Nuttli 

(1973a) curves at greater distances. The statistical distribution is unknown for these proposed attenuation 

curves.

Donovan (1973) used two sets of data to derive 

acceleration-attenuation relations. He used data from 

515 worldwide earthquakes encompassing a wide 

range of magnitudes to derive a general relation (fig. 

19). The geometrical standard deviation for the mean
CHARACTERISTICS OF GROUND SHAKING 21

FIGURE 15.—Isoseismal contours for 1906 San Francisco and 1811 New Madrid earthquakes (modified from Nuttli, 1973b).

curve was 2.01. When he analyzed the peak acceleration data obtained from the 1971 San Fernando earthquake, he obtained a standard deviation of 1.62 (fig. 

19). The distribution of data relative to the mean regression line was shown to be log-normal.

Ground-motion data from California earthquakes, 

from nuclear explosions in Nevada, Colorada, and New 

Mexico, and from the aftershock sequence of the March 

1975 Pocatello Valley, Idaho earthquake have been 

analyzed to define preliminary frequency-dependent 

seismic attenuation relations (Johnson, 1973; 

McGuire, 1977a; and King and Hays, 1977). Values of 

the distance attenuation exponent, /3, were derived 

from pseudo relative velocity (PSRV) response spectra 

by least squares analysis (that is, PSRV=ARfi where R 

is the epicentral distance and A and /3 are constants 

derived in the least-squares analysis) and are listed in 

tables 9-13 along with values of a. These data indicate 

that seismic attenuation rates are about the same in 

southern Nevada and California, and that highfrequency (5-20 Hz) seismic energy attenuates more 

rapidly in Colorado and northern Utah than in 

California and southern Nevada (fig. 20.) Values of the 

geometrical standard error of estimate range from 1.58

to 1.78 for the highly "calibrated" transmission path of 

southern Nevada (Lynch, 1973) and from 1.61 to 2.22 

for the less well "calibrated" transmission path of Colorado (Foote and others, 1970). They range from 2.26 to 

2.73 when both distance and magnitude are considered.

DEFINE THE CHARACTERISTICS OF 

GROUND SHAKING EXPECTED AT THE SITE

After specifying the location and magnitude (or epicentral intensity) of each potential earthquake and an 

appropriate regional attenuation relation, the characteristics of ground shaking expected at the site can be 

determined. To implement this step requires consideration of the earthquake mechanism and basic wave 

propagation theory although current design procedures are primarily based on empirical procedures.

It is well known that the amplitude, temporal, and 

spectral characteristics of ground motion produced at a 

site by an earthquake are functions of the earthquake 

source mechanism, the epicentral distance, and the 

geometry and physical properties of the geologic structures traversed by the body waves and surface waves 

as they propagate from the source to the site (fig. 21). 

Seismograms recorded at all distances are complex, but
22 PROCEDURES FOR ESTIMATING EARTHQUAKE GROUND MOTIONS

SOUTHERN APPALACHIAN SEISMIC ZONE

1000

VI VII VIII IX XI IV

CENTRAL MISSISSIPPI VALLEY

MODIFIED MERCALLI INTENSITY

FIGURE 16.—Empirical intensity attenuation curves proposed for the Southern Appalachian seismic zone and the central Mississippi

Valley (after Young, 1976).

0,7

0.6

0.5

0.4

0.3

0.2

0.1

10 50 100

0.001

A=0.279e°-80m R- 1 -64 - 

er= 2.10 -

(R = focal distance, in ~ 

kilometers)

0.01 -

100 1000

DISTANCE FROM FAULT, IN KILOMETERS DISTANCE FROM EPICENTER, IN KILOMETERS

FIGURE 17.—Average value of peak acceleration A in relation to distance R from fault for earthquakes of various magnitudes M (proposed by 

Schnabel and Seed, 1973 (left) and Davenport, 1972 (right)). Dashed lines represent extrapolated values.
CHARACTERISTICS OF GROUND SHAKING 23

i i———i

. . Modified Schnabel-Seed curves 

Schnabel-Seed curves

DISTANCE, IN KILOMETERS

FIGURE 18.—Schnabel and Seed acceleration-attenuation curves 

modified for use in the Eastern United States (from Algermissen 

and Perkins, 1976).

they are especially complex in the near field (that is, 

source-to-source distances of a few fault rupture 

widths) where the seismic spectrum tends to be rather 

broad. In the near field, the ground motions are 

strongly influenced by the dynamics of the fault rupture, and site properties are less important than source 

properties in defining the characteristic features of the 

ground shaking.

The source of an earthquake is believed to involve a 

fracturing process in which rock in an environment of 

shear stress fails. This process may be idealized in 

terms of an elasto-dynamic crack in an elastic region. 

The failed region extends rapidly at its periphery to 

become the "fault surface." The loss of cohesion across 

the region of failure translates into a boundary condition in which the faces of the crack are free of shear 

stress. Assuming that the faces of the crack do not 

move apart, the rupture grows in a shear mode. A key 

to a physical understanding of the earthquake source 

problem, therefore, lies in understanding the physical 

processes that take place at the tip of the propagating 

crack.

Body (P, SH, and SV) and surface (Love and 

Rayleigh) seismic waves are generated by the complex 

physical processes which occur during and after the 

rupture along the fault surface. The body waves are 

characterized by high frequencies (2-10 Hz) and commonly produce the peak ground acceleration on the accelerogram. Rayleigh and Love waves travel and attenuate more slowly than body waves and have lower 

fundamental frequencies of vibration (for example, <1 

Hz).

The physics of the earthquake source is still not 

completely understood although a great deal of research is being concentrated on this problem. Brune 

(1970) and other scientists have shown on the basis of 

earthquake fault models that the earthquake source 

parameters, rupture velocity, effective stress, seismic 

moment, fault length, and stress drop, appear to have a 

predictable effect on the radiated seismic signal. In the 

far field (that is, source-to-station distances greater 

than about ten fault rupture widths), the highfrequency characteristics of the broad-band spectrum 

of the seismic signal are determined primarily by the 

dynamic stress drop. The low-frequency characteristics 

are determined by the seismic moment. The character 

of the radiated seismic signal is strongly dependent on 

the rupture velocity, which in turn is directly related to 

the effective stress available to accelerate the fault motion. In the near field, the effective stress primarily 

determines the high-frequency wave characteristics, 

and the permanent static displacement determines the 

low-frequency wave characteristics although wave 

scattering and attenuation can affect the spectral composition of the seismic signal at any distance. None of 

the source parameters, stress drop, seismic moment, 

and rupture velocity are used in current earthquakeresistant design.

The source parameters, focal depth, rupture velocity, 

elastic constants of the source medium, stress drop, the 

fault configuration at depth, and source multiplicity, 

are probably the ones whose influence on ground shaking is least understood at present. The effect of focal 

depth may be of practical importance for nuclear power 

plant siting and other applications because the spectral 

composition of strong ground motion is strongly influenced by energy partition between body and surface 

waves, which is in turn influenced by focal depth. The 

effects of the differences in focal depth in California 

(«s!6 km) and in the Puget Sound area (50-60 km) on 

ground motion are not clear.

Ground motion can be described in a wide variety of 

ways (for example: as a time history, as spectra, and as 

peak ground-motion parameters). Almost all these descriptive formats are used in at least one of the various 

applications that require characterization of earthquake ground motions. These formats will be described 

below.

THE SEISMOGRAM

The seismogram, whether written by a broad-band 

strong motion accelerograph system or on the shortand long-period seismographs of WWSSN (World-Wide
24 PROCEDURES FOR ESTIMATING EARTHQUAKE GROUND MOTIONS

1000

100

10

i l I

• MEAN+N 

^ • STANDARD \ 

*^f DEVIATION

i i i 1 1 

i-1.52

'HP"-

^•x ,• »\ MEAN + 2

% X !• \» ^STANDARD

• • . W . .V DEVIATIONS

, MEANSTANDARD 

^^^DEVIATION

' MEAN-2X

STANDARD 1> 

DEVIATIONS \ •

\

WORLDWIDE DATA

i i i i i i i 11 !• I«N I I I I

1000 -

100

10

A=516.500(R+25)-2 -04 

<r=1.62

MEAN +2 STANDARD DEVIATIONS

MEAN + 1 STANDARD DEVIATION -

MEAN -1 

STANDARD DEVIATION

MEAN -2 STANDARD DEVIATIONS

SAN FERNANDO DATA (1971)

' D ROCKLIKESITE

* SOIL SITE

• ' i'''————

10 100 1000 

DISTANCE FROM HYPOCENTER, IN KILOMETERS

10 100 

DISTANCE FROM ENERGY CENTER, IN KILOMETERS

FIGURE 19.—Acceleration-attenuation relations derived from worldwide earthquakes and from the San Fernando earthquake, 1971 (from

Donovan, 1973).

TABLE 9.—Distance attenuation exponents derived from horizontal 

component PSRV spectra, northern Utah area

[The form of the equation is PSRV=AR@. Data sample-48 PSRV spectra (5-percent 

damped) from four Pocatello, Idaho, aftershocks; magnitude (m,,) range from 2.9 to 

4.15, distance (R) range from 12 to 150 km. The six recording stations were located 

on alluvium. Data sample was inadequate to derive a reliable standard error of 

estimate]

Period

(s)

0.061 ________

.075

.082-——

. 101 ________

.123 ————

.150 _ _ _ _

.203 ________

.248———

.302 _______

.369————

.408 ________

.451 __ ____

Mean 

Distance 

exponent (/3)

-1 74

_____ ___-1.77

__——— -1.79

__ ___ -1.84

__——— -1.90

— 1 Q9

_ ___ .-1.87

— 1 8Q

————— -1.78

________ -1.72

__———-1.66

— ——— -1.65

Period

(s)

0 4QQ

.609—— ___

.744 ______

.822 ______

1.004 ______

1.498 ———

2.022 ______

9 4fiQ

3.333 ______

4.070 ______

4 Q79

6.072 ______

Mean 

distance 

exponent (/3)

_____ ___ 1.62

__________-1.57

________ __-1.56

__________-1.54

__________-1.43

__________ .99

__ _____ .94

__________ .96

-1.00

___ ____ -1.06

__________-l.ll

__________-1.12

Standard Seismograph Network), is a key element in 

seismological research. An ensemble of seismograms 

contains the basic information needed to characterize 

an earthquake and the ground motion that it produces. 

Figure 22 illustrates an accelerogram of the 1940 

Imperial Valley, Calif, earthquake recorded in El Centro, Calif, about 8 km from the surface trace of the 

fault. The peak horizontal ground acceleration was 

0.33 g. This accelerogram has been used as a basis for 

seismic design throughout the world. It was recorded at 

a site underlain by a thick soil column, containing from 

the surface down (1) about 30 m of stiff clay, with a 

shear-wave velocity of 198 m/s, (2) 274 m of shale with 

a shear-wave velocity of 852 m/s, (3) 610 m of shale 

with a shear-wave velocity of 1,040 m/s, and (4) rock 

with a shear-wave velocity of 2,432 m/s. Schnabel, 

Seed, and Lysmer (1972) showed that the peak ground 

acceleration would have been in the range of 0.5 g in-
CHARACTERISTICS OF GROUND SHAKING 25

TABLE 10.—Distance attenuation exponents derived from horizontal 

component PSRV spectra, southern Nevada area

[The form of the equation is PSRV=AR^. Data sample—796 PSRV spectra (5- 

percent damped) from 36 Pahute Mesa and Yucca Flat nuclear detonations; yield 

range less than 20 to 1,200 kilotons; distance (R ) range from 10 to 200 km. The 103 

recording sites were located on rock and alluvium of various thickness with alluvium sites predominating. From Lynch (1973)]

Period

(s)

0.050

.055

.061

.067

.075

.082

.091

.101

.111

.123

.136

.150

.166

.183

.203

.224

.248

.274

.302

.334

Mean 

distance 

exponent (/3)

—— -1.33

—— -1.36

—— -1.38

—— -1.39

—— -1.43

-1.47

-—-1.51

—— -1.54

—— -1.57

—— -1.57

- — -1.56

-—-1.56

- — -1.54

_ _ -1.53

—— -1.51

- — -1.49

—— -1.49

-—-1.47

- — -1.44

-—-1.41

Standard 

error of 

estimate (o-)

1.75

1.74

1.73

1.70

1.69

1.69

1.68

1.67

1.67

1.68

1.71

1.71

1.69

1.68

1.67

1.66

1.66

1.64

1.63

1.60

Period

(s)

0.369

.408

.451

.499

.551

.609

.673

.744

.822

.908

1.004

1.110

1.226

1.355

1.498

1.655

1.829

2.022

2.234

2.469

Mean 

distance 

exponent (J3)

- — -1.38

—— -1.36

_— -L34

-—-1.31

__ -1.30

__ -1.26

__ -1.24

_ _ -1.24

-—-1.23

— _-1.20

—— -1.17

—— -1.15

—— -1.14

— --1.13

_ _-1.13

_ _ -1.13

-—-1.13

_ _-1.12

—— -1.12

—— -1.08

Standard 

error of 

estimate (o-)

1.60

1.59

1.59

1.58

1.59

1.61

1.63

1.64

1.63

1.63

1.64

1.66

1.67

1.69

1.68

1.69

1.72

1.74

1.75

1.78

TABLE 11.—Distance attenuation exponents derived from horizontal 

component PSRV spectra, California

[(From Johnson, (1973) The form of the equation is PSRV=ARftlQam*. Data sample—41 

PSRV spectra (5-percent damped); 37 California and 4 non-California earthquake records; magnitude range from 5.3 to 7.7; distance (R) range 6.3 to 149.8 km. California 

earthquakes in sample: Long Beach (1933), Southern California (1933), Lower California 

(1934), Northwest California (1938, 1941, 1951), Imperial Valley (1940), Northern 

California (1952, 1967), Kern County (1952), Humboldt County (1954), Santa Clara 

County (1954), Wheeler Ridge (1954), El Centre (1956), San Francisco (1957), Hollister 

(1961), Parkfield (1966), Borrego Mountain (1968), San Fernando (1971). Other earthquakes in sample: Helena, Mont. (1935), Western Washington (19491, Puget Sound, 

Wash. (1965). All the recording stations except four were located on alluvium. Values of 

the standard error of estimate are a function of distance and magnitude (m/,)]

Period

(s)

0.055

.075

.101

.136

.183

.248

.334

Mean 

distance 

exponent (/3)

____-1.40

—— -1.52

__ -1.56

— _-1.59

—--1.53

__ -1.40

. — -1.30

Standard 

error of 

estimate (o-)

2.36

2.51

2.48

2.45

2.43

2.26

2.26

Period

(s)

0.451

.609

.822

1.004

1.355

1.829

2.469

Mean 

distance 

exponent (/3)

_ _ -1.26

- — -1.14

—— -1.06

—— -1.13

— _-1.16

_ _ -1.17

__ -1.14

Standard 

error of 

estimate (j3)

2.45

2.44

2.27

2.41

2.51

2.73

2.63

stead of 0.33 g if the stiff clay layer had been about 9 m 

thick instead of 30 m.

The accelerogram recorded at El Centro, Calif., in 

1940 has proved to be very valuable in earthquake resistant design. The value would be many times greater 

if an array of instruments underlain by various types 

of geologic materials had recorded the Imperial Valley 

earthquake.

Velocity and displacement seismograms are derived 

form the strong-motion accelerogram (Trifunac, 1970; 

Trifunac and others, 1971). These time histories, although subject to some small error because of the integration process, give useful information about the

Period

(s)

0.050

.055

.061

.067

.075

.082

.091

.101

.111

.123

.136

.150

.166

.183

0.203

.224

.248

.274

.302

.334

Mean 

distance 

exponent (J3)

-—-2.09

- — -2.08

__ -2.08

__ -2.05

__ -2.05

—— -2.03

—--2.02

__ -2.04

__ -2.04

-1.98

~ — -L94

__ -1.99

- — -2.01

__ -1.96

—— -1.90

—— -1.86

—— -1.81

—--1.81

Standard 

error of 

estimate (o-)

1

1

85

80

Period

(s)

Mean 

distance 

exponent (J3)

0.369 ____-!

1.83

1.84

1

1

82

93

2.02

2.03

2.09

2 13

2.08

2.01

1.98

1.97

2.00

2.13

2.07

2.04

__ -1.74 2.08

__ -1.72 2.11

1

1

1

1

1

1

1

2

408

451

499

551

609

673

744

822

908

004

110

226

355

498

655

829

022

2.234

2 469

__ -1

___ -1

___ -1

___ -1

___ -1

___ -1

___ -1

___ -1

——— -1

_ —— -!

——— -1

——— -1

___ -1

_ __ -1

___ -1

___ -1

68

67

66

63

63

63

64

58

55

54

56

54

60

54

49

54

48

__ -1*66

—— -1

__ -1

51

51

Standard 

error of

estimate (o-)

2

2

2

2

2

17

17

22

17

12

2.02

1

1

1

1

1

86

80

71

68

68

1.64

1

1

1

1

1

1

1

1

61

70

.71

74

81

73

.76

.79

TABLE 12.—Distance attenuation exponents derived from horizontal 

component PSRV spectra, Piceance Creek Basin, Colo.

[The form of the equation isPSRV=ARP. Data sample 59PSRV spectra (5-percent damped) 

from the Rulison event; yield 40 kilotons; distance (R) range from 6.2 to 296 km. The 

recording stations were located on rock or thin (1-10 m) alluvium and were primarily in 

the Piceance Creek Basin. From Foote and others (1970)]

TABLE 13.—Distance attenuation exponents derived from horizontal 

components PSRV spectra, San Juan Basin, N. Mex.

[The form of the equation isPSRV=AR13. Data sample-46PSRV spectra (50-percent damping) from the Gasbuggy event; yield 26 kilotons; distance (R) range from 5 to 90 km. The 

recording stations were located on rock or thin (1-30 m) alluvium within the San Juan 

Basin. From Foote, Hays, and Klepinger (1969)]

Period

(s)

0.09 —

.12 —

.16 —

.22 —

9Q

.40 __.

Mean 

distance 

exponent (/3)

. _ -1.48

_ -1.66

.—-1.73

— -1.83

—— -1.84

—— -1.76

Standard 

error of 

estimate (o-)

2.04

2.00

1.82

2.04

2.09

2.04

Period

(s)

0.54 —

.74 —

1.00 —

1.33 —

1.82 —

2.44 ___

Mean 

distance 

exponent (J3)

—— -1.63

. — -1.70

— -1.54

—— -1.42

— -1.32

_ -1.27

Standard 

error of 

estimate (o-)

2.35

1.70

1.70

1.55

1.55

1.66

lower frequency spectral components. Figure 23 shows 

the S. 16° E. horizontal component accelerogram recorded at Pacoima Dam from the 1971 San Fernando, 

Calif, earthquake and the corresponding velocity and 

displacement seismograms derived from it. The peak 

horizontal acceleration was estimated to be 1.2 g, the 

largest value obtained to date. The corresponding peak 

velocity and the peak displacement were, respectively, 

115 cm/s and 43 cm.

TYPES OF INFORMATION DERIVED FROM THE 

SEISMOGRAM

Information about the seismic source parameters of 

an earthquake can be derived from the seismograph 

records. Examples in the literature include: Savage,
26 PROCEDURES FOR ESTIMATING EARTHQUAKE GROUND MOTIONS

SOUTHERN NEVADA

100.0

w 10.0 —

0.01

PICEANCE CREEK BASIN, COLORADO

100.0

K /

(5-percent 

damped spectra)

10.0

1.0

0.1

PERIOD

DISTANCE EXPONENT ( B )

STANDARD DEVIATION

0.05

2.09

1.85

0.1

2.04

2.03

0.5

1.63

2.17

1.0

1.56

1.64

2.5

1-51 

1.79

\/40ktat2.6km

/\

SPECTRAL VELOCITY =A-R

10.0

0.01

0.1 1.0 0.01

PERIOD, IN SECONDS

FIGURE 20.—Frequency-dependent attenuation of horizontal ground motions, southern Nevada and Colorado.

0.1 1.0 

PERIOD, IN SECONDS

10.0

LOVE WAVE

RECORDING SITE

S • WAVE

FIGURE 21.—Schematic diagram of elements that affect ground 

motion.

1966; Kanamori, 1970; Brune, 1970; Aki, 1972; Bolt, 

1972; Savage, 1972; Hanks and Wyss, 1972; Trifunac, 

1972a, b; Molnar, Tucker, and Brune, 1973; Randall, 

1973; Gibowicz, 1973, Thatcher and Hamilton, 1973; 

Thatcher and Hanks, 1973; Savage, 1974; Boore and 

Zoback, 1974; Johnson and McEvilly, 1974; Archambeau, 1975; Kelleher and Savino, 1975; Hanks, Hileman, and Thatcher, 1975; Knopoff and Mouton, 1975; 

Anderson and Fletcher, 1976; Herrmann, 1976; Bollinger, Langer, and Harding, 1976; Helmberger and 

Johnson, 1977; and Kanamori, 1977. These examples 

demonstrate that the following parameters, considered 

to be important in constructing a model of faulting and 

in estimating ground motion effects, can be obtained:

1. magnitude (Ms mb ML } of the earthquake;

2. the spatial dimensions of the fault which ruptured;

3. seismic energy released by the earthquake;

4. moment of the earthquake;

5. average displacement across the fault;

6. orientation of the fault;

7. sense of slip across the fault;

8. depth of the fault;

9. velocity with which rupture propagates on the 

fault;

10. the elastic constants of the medium in which 

the fault is located;

11. the stress drop across the fault;

12. the configuration of the fault plane at depth 

(that is, whether planar or warped); and
CHARACTERISTICS OF GROUND SHAKING 27

0.3

0.2

0.1

0

-0.1

-0.2

-0.3

-0.4

North-south component

East-west component

0.2

0.1

0

-0.1

-0.2

-0.3

Vertical component 0.3

0.2

0.1

0

-0.1

-0.2

-0.3

FIGURE 22.—Accelerogram of the 1940 Imperial Valley, Calif, earthquake recorded at El Centre, Calif.

13. complexity of energy release (that is, multiple

sources).

Information about the characteristics of the 

transmission path and the site can also be extracted 

from the seismogram or the spectra derived from it. 

The types of information available include:

1. values of Q (Knopoff, 1964; Berg and others, 

1971; Joyner and others, 1976; Bakun and 

others, 1976);

2. frequency-dependent filtering effects (Murphy, 

Weaver, and Davis, 1971; Hays and Murphy, 

1971; Hanks, 1976; King and Hays, 1977);

3. site transfer functions (Lastrico and others, 

1972; Hays, 1977a, b, 1978; Rogers and Hays, 

1978).

The magnitude of an earthquake is the most familiar 

number computed from a seismogram (Duda and Nuttli, 1974). It is based on a measure of seismic-trace 

amplitude in or near a particular frequency band, and 

it is independent of the observation point. ML , the original magnitude introduced in 1935 by Richter, is defined as the logarithm of the maximum recorded (trace)

amplitude written by a Wood-Anderson seismograph 

with specified constants (free period: 0.8 sec; maximum 

magnification: 2,800; damping factor: 0.8) when the 

seismograph is on firm ground at an epicentral distance of 100 km. Observations at distances other than 

100 km are corrected to the standard distance by using 

empirical curves, Figure 24 illustrates how the Richter 

magnitude is determined from a seismogram.

The body-wave (mb ) and surface-wave (Ms) magnitude scales, which are defined, respectively, in terms 

of 1- and 20-second-period seismic waves, are widely 

used. These three magnitude scales (ML , mb , and Ms) 

are interrelated by empirical formulas (see Duda and 

Nuttli, 1974).

Seismic moment, which characterizes the overall deformation at the source, is an interpretive quantity 

that some investigators (for example, Hanks and 

others, 1975; Geller, 1976, and Kanamori, 1977) consider to be better than magnitude for characterizing 

the earthquake's source strength. This is especially 

true for great earthquakes (M>8) because the rupture 

dimensions of the earthquake exceed the wavelengths
28 PROCEDURES FOR ESTIMATING EARTHQUAKE GROUND MOTIONS

1.5

1.0

0.5

0

-0.5

-1.0 

150

100

50

0

-50

-100 

50

-50

S. 16°E. component, 

ground acceleration

S. 16°E. component 

ground velocity

S. 16°E. component, 

ground displacement

10 15

TIME, IN SECONDS

FIGURE 23.—S. 16° E. accelerogram recorded at Pacoima Dam and 

the velocity and displacement seismograms derived from it; 1971 

San Fernando, Calif, earthquake.

of the seismic waves used in the magnitude determination. Although seismic moment is an interpretative 

quantity, its greatest advantage is that it can be interpreted simply in terms of the source mechanism; that 

is, the moment is proportional to the product of the 

fault area and the displacement across the fault.

The magnitudes and seismic moments derived for a 

number of southern California earthquakes are listed 

in table 14. Although additional research is needed to 

establish all the physical facts about seismic moment 

and its applicability in earthquake-resistant design, 

one of the most interesting results obtained to date is 

the remarkable linearity that exists between the logarithm of the seismic moment and the logarithm of the 

fault area (Thatcher and Hanks, 1973). This linearity 

suggests a constant average stress drop of about 10 

bars in earthquakes.

PEAK GROUND ACCELERATION

Current practice in design of earthquake-resistant 

structures is to use peak ground acceleration as a 

measure of the severity of ground motion even though 

peak acceleration may not be the best parameter to 

represent this characteristic of ground motion. Peak 

acceleration is used because of its familiarity and wide 

acceptance in the engineering community as a measTrace

amplitude = 23 mm

400 —

I

\ 300 - 

x

200 —

100- 

60-

40-^ 

20 —

-40

-30

— 20

— 4

— 2

0-5—1 

DISTANCE (km) I S-PTIME(s)

6-

4-

3-

2-

1-

0-

— 100

-50

-0.2

-0.1 

AMPLITUDE (mm)

MAGNITUDE SCALE

FIGURE 24.—Determination of Ric'hter magnitude. Using the 

maximum amplitude of the seismogram and the difference in 

arrival times of the P and S waves, the value of magnitude can be 

read from the nomogram.

ure of the lateral forces on high-frequency structural 

systems. For intermediate- and low-frequency systems, 

ground velocity and displacement data are more applicable.

Values of peak horizontal ground acceleration, tabulated in table 15, have been used by various investigators to develop empirical relations for estimating 

horizontal ground motions.

TABLE 14.—Magnitude and seismic moments of southern 

California earthquakes

[From Hanks (1976)]

Date

Jan. 9, 1857 1 _

March 26, 1872 1

July 22, 1899 1 _ March 11, 1933

May 19, 1940 _

July 21, 1952 _

April 9, 1968 _

Sept. 12, 1970 -

Feb. 9, 1971 ___

Geographic

locality

___ Fort Tejon

-_ Owens Valley

___ San Jacinto

__Long Beach

___ Imperial Valley

___ Kern County

_ Borrego Mountain

___ Lytle Creek

_ San Fernando

Magnitude

8 +

8 +

7±

6.3

7.1

7.7

6.4

5.4

6.4

Seismic moment

(1025 dyne-cm)

900

500

15

2

30

200

6

.1

10

'Noninstrumental magnitude assignment.
CHARACTERISTICS OF GROUND SHAKING 29

TABLE 15.—Values of peak horizontal ground acceleration recorded in past earthquakes and used for estimating horizontal ground motions in

earthquake-resistant design

[From Seed, Murarka, Lysmer, and Idriss 1976]

Earthquake Date Magnitude

Approximate 

source 

distance

(km)

Component 

of motion

Maximum 

Accleration

Soil 

depth 

(m)

Recording 

site

Rock sites

Helena, Mont _______ 10/31/35 6.0

Kern County, 

Calif ________________ 7/21/52 7.7

San Francisco, 

Calif ________________ 3/22/57 5.25

Lytle Creek, 

Calif __________________ 9/12/70 5.4

________ Do. ________

Parkfield, Calif ________ 6/27/66 5.6

Borrego Mtn., 

Calif ________________ 4/8/68 6.5

San Fernando, 

Calif ________________ 2/9/71 6.6

________ Do. ________

________ Do. ________

________ Do. ________

________ Do. ________

________ Do. ________

	Do. 

________ Do. ________

Lower California _____ 12/30/34 6.5

Imperial Valley, 

Calif ________________ 5/18/40 7.0

San Francisco, 

Calif __________________ 3/22/57 5.25

________ Do. ________

Parkfield, Calif __________ 6/27/66 5.6

________ Do. ______

San Fernando,

Calif __________________ 2/9/71 6.6

________ Do. ________

________ Do. ________

________ Do. ________

________ Do. ________

________ Do. ______

________ Do. ________

43

11

13

19

7

134

3-5 

21 

24 

26

30

31

30

40

North—South

East—West

North 21 East 

South 69 East

North 10 East 

South 80 East

South 25 West 

South 69 East 

North—South

East—West

North 65 West 

South 25 West

North 33 East 

North 57 West

South 16 East 

North 76 West 

North 21 East 

North 69 West 

North—South

East—West 

South 69 East 

South 21 West 

South 08 East 

South 82 West 

North—South

East—West 

North—South

East—West 

North 03 West 

North 87 East

0.146

.145

.156

.179

.083

.105

.197

.142

.164

.177

.269

.347

.041

.046

1.24

1.075

.367

.287

.164

.147

.188

.394

.217

.202

.180

.171

.089

.192

.176

.213

rock Carrol College, 

Helena.

do Taft, Calif.

do Golden Gate Park, 

San Francisco.

do Wrightwood, Calif.

do Devils Canyon,

San Bernardino, 

Calif.

do Temblor, Calif.

do SCE Power Plant, 

San Onofre, Calif.

do Pacoima Dam.

do Lake Hughes,

Sta. 12. 

do 3838 Lankershim

Blvd;, Los Angeles, 

do Lake Hughes,

Sta. 4. 

do Santa Felicia Dam

(outlet) 

do Griffith Park

Observatory, 

do Cal. Tech. Seismol.

Lab., Pasadena, 

do Santa Anita Dam.

Stiff soil sites

58 North—South 0.160 32 El Centra, Calif.

East—West .182

8 North^South .33 32 Do. 

East—West .21

16 North 09 West .043 45 Alexander Bldg.,

North 81 East .046 San Francisco.

17 South 09 East .085 64 State Bldg.,

South 81 West .056 San Francisco.

.1 North 65 East .489 48 Cholame-Shandon 2.

5 North 05 West .354 32 Cholame-Shandon 5.

21 North 21 East .315 19 Castaic, Old Ridge

North 69 West .270 Route. 

35 North—South .170 64 Hollywood Storage, 

East—West .211 P.E. Lot, Los

Angeles. 

39 North—South .136 14 3470 Wilshire Blvd.

Los Angeles. 

39 North 9 West .153 32 3550 Wilshire Blvd.,

Los Angeles. 

28 North 11 East .225 22 15250 Ventura Blvd.,

North 79 West .149 Los Angeles. 

28 South 12 West .243 22 14724 Ventura Blvd.,

Los Angeles.

39 North—South .161 13 3407 W. Sixth St., 

East—West .165 Los Angeles.
30 PROCEDURES FOR ESTIMATING EARTHQUAKE GROUND MOTIONS

TABLE 15.—Values of peak horizontal ground acceleration recorded in past earthquakes and used for estimating horizontal ground motion in

earthquake-resistant design—Continued

Earthquake Date Magnitude

Approximate 

source 

distance

(km)

Component 

of motion

Maximum

Accleration

fe)

Soil 

depth

(m)

Recording

site

Deep cohesionless soil sites

Western

Washington _______ 4/13/49 7.1 20 South 04 East 0.165

South 86 West .280 

Kern County, 

Calif ________________ 7/21/52 7.7 127 North—South .047

East—West .053

Eureka, Calif ________ 12/21/54 6.5 25 North 11 West .168

North 79 East .257

_____ Do. _____ 30 North 44 East .159

North 46 West .201 

Puget Sound,

Wash.___________ 4/29/65 6.5 58 South 04 East .137

South 86 West .198

Ferndale, Calif __________ 12/10/67 5.6 25 North 46 West .105

South 44 West .237 

San Fernando,

Calif ________________ 2/9/71 6.6 16 North—South .255

East—West .134

_____ Do. _____ 19 North—South .117

East—West .110

________ Do. ________ 37 North—South .095

East—West .109

____ Do. ___-__ 37 North—South .202

East—West .185

________ Do. ________ 30 North—South .141

East—West .212

Sites with soft-to-medium clay and sand

San Francisco, 

Calif ___________ 3/22/57 5.25 18 North 45 East 0.047

North 45 West .046 

Alaska ___________ 4/3/64 6.0 131 North 13 East .044

North 77 West .051

132 Highway Test Lab., 

Olympia, Wash.

112 Cal. Tech.,

Athenaeum,

Pasadena. 

80 Federal Bldg.,

Eureka. 

160 City Hall,

Ferndale.

134 Highway Test Lab., 

Olympia, Wash.

160 City Hall, 

Ferndale.

176 8244 Orion Blvd.,

Los Angeles. 

176 15107 Vanowen St.,

Los Angeles. 

112 Cal. Tech.,

Athenaeum,

Pasadena. 

112 Cal. Tech.,

Millikan Library,

Pasadena. 

148 Cal. Tech., Jet

Propulsion Lab.,

Pasadena.

91 So. Pacific Bldg., 

San Francisco. 

110 Elmendorf AFB, 

Anchorage.

In current design practice, it is common to assume 

that the maximum ground accelerations in the two 

horizontal directions are equal and that the maximum 

vertical acceleration is two-thirds or more of the 

maximum horizontal acceleration. The assumption of 

equality for the two horizontal components of ground 

motion is not always correct, so alternate approaches 

such as the spectrally maximized record (Shoja-Taheri 

and Bolt, 1977) may be needed in some design applications. The assumed ratio of % for peak vertical to peak 

horizontal ground acceleration has a probability of exceedance of 23 percent (Werner and Ts'ao, 1975).

A number of investigators, (for example, Housner, 

1965; Davenport, 1972; Boore and Page, 1972; Page 

and others, 1972; Schnabel and Seed, 1973; Dietrich, 

1973; Orphal and Lahoud, 1974; Trifunac and Brady, 

1975a; Seed, Murarka, Lysmer, and Idriss, 1976; 

Trifunac, 1976a; Hanks and Johnson, 1976; and Boore 

and others, 1978) have studied various aspects of peak 

ground acceleration. Some of these studies and their 

conclusions are summarized below:

1. Hanks and Johnson (1976) studied a set of

strong-motion accelerograms and showed 

that the causative processes that generate 

peak ground accelerations within approximately 10 km of the source are independent 

of magnitude (M) for 4.5<M*£7.1. This result 

is important because current design practice 

assumes that peak acceleration is strongly dependent on magnitude.

Trifunac and Brady (1975a), on the basis of regression analysis of the strong-motion data 

recorded in the Western United States from 

1933 to 1971, suggested that peak accelerations at the fault, for the frequency band 

0.07-25 Hz, probably do not exceed about 3-5 

g. They proposed that the maximum acceleration may be reached at a magnitude of 6.5- 

7.0. Both conclusions are controversial, mainly because of limited data and overemphasis 

of data from the San Fernando earthquake.

Seed, Murarka, Lysmer, and Idriss (1976) noted 

that peak amplitudes of ground acceleration 

measured at sites on rock in the Western
CHARACTERISTICS OF GROUND SHAKING 31

United States exhibit very little difference 

statistically from peak amplitudes measured 

at sites underlain by less than 48 m of stiff 

clay, sand, or gravel. At sites where rock is 

overlain by at least 80 m of cohensionless 

soil, the mean recorded peak acceleration is 

greater by factors of 3.5-4.0 than at rock sites 

for weak ground motions on the order of 0.003 

g. The effect is reversed for peak accelerations at rock sites between 0.1 and 0.7 g, and 

these peak accelerations tend to exceed those 

recorded at deep cohesionless soil sites by as 

much as 80 percent.

4. Dietrich (1973), using finite element techniques 

to model various earthquake sources, showed 

that peak ground acceleration is proportional 

to stress drop. Hence, the variability in peak 

ground acceleration is a function of the variability in stress drop. Data to quantify the 

variability of stress drop are scarce. Rogers, 

Perkins, and McKeown (1976) estimated on 

the basis of the available data that stress 

drop has a log-normal distribution with a 

mean stress drop of about 20 bars and a 

geometrical standard deviation of 3.7. 

The range of horizontal peak acceleration for sites on 

rock in the Western United States is shown in figure 

25. These curves are based on limited data, especially 

for source-to-site distances of less than 20 km, which 

causes disagreement about whether the "probable

Oroville, Calif, 

earthquake (ML=4.7)

DISTANCE FROM CAUSATIVE FAULT, IN KILOMETERS

FIGURE 25.—Range of horizontal peak acceleration as a function of 

distance and magnitude for rock sites in the Western United 

States (from Schnabel and Seed, 1973).

upper bound" is correct. For example, the 1975 

Oroville, California earthquake (ML =4.7) produced a 

peak ground acceleration of 0.7 g at a distance of 11.2 

km from the fault. The 1972 Stone Canyon, California 

earthquake (AfL =4.7) produced peak ground accelerations of 0.19, 0.63, and 0.16g at distances of 3, 6, and 7 

km, respectively. The 1971 San Fernando, California 

earthquake produced a peak acceleration of 1.2 g at 

Pacoima dam and also exceeded the bounds proposed 

by Schnabel and Seed (1973). The explanation for these 

observations is that they are "rare" points lying at the 

extremes of the distribution of the acceleration data 

sample or that the curves proposed by Schnabel and 

Seed depict peak ground accelerations that are too low, 

especially those close to the fault.

PEAK GROUND VELOCITY AND DISPLACEMENT

Ground motion can also be characterized by velocity 

and displacement time histories derived from an accelerogram and their peak values. Ground velocity and 

displacement values (table 16) seem to have a more 

determinant upper bound than ground acceleration. 

Displacement time histories and spectra are used in 

defining seismic moment, stress drop, and source dimensions and are also used in wave propagation 

studies. The amplitudes of ground displacement are 

propagated more coherently than amplitudes of ground 

velocity and acceleration because their low-frequency 

spectral composition is not very sensitive to scattering 

by small geologic inhomogeneities. Velocity and displacement time histories are needed, respectively, for 

modeling earthquake effects on intermediate- and 

low-frequency structural systems. Velocity time histories can be used in conjunction with the shear-wave 

velocity of the surficial materials to estimate the level 

of shear strain induced in the soil and rock through the 

relation

where

du = 1 du 

dx /3 dt

du^ is the shear strain level, du is the peak 

dx dx

ground velocity, and /8 is the shear- wave velocity of the 

material.

Various investigators (for example, Newmark and

Rosenbleuth, 1971; Page and others, 1972; Ambraseys,

1973; Trifunac and Brady, 1975a; Trifunac, 1976a;

Seed, Murarka, Lysmer, and Idriss, 1976; and Boore

and others, 1978) have evaluated peak velocity and

displacement in terms of distance and magnitude.

Some of the important conclusions of these studies are:

1. Trifunac and Brady (1975a) suggested that, at

the 90-percent confidence level, the peak

ground velocities and displacements at the
32 PROCEDURES FOR ESTIMATING EARTHQUAKE GROUND MOTIONS

TABLE 16.—Values of peak horizontal ground velocity and displacement derived from accelerograms of past earthquakes and used for

estimating horizontal ground motions in earthquake-resistant design

[From Seed, Ugas, and Lysmer (1976)]

Earthquake

Kern County, 

Calif ________________

San Francisco, 

Calif—— __ ________

Lytle Creek, 

Calif ___ __ ________

______ Do.

Parkfield, 

Calif _______________

Borrego Mountain, 

Calif _______________

San Fernando, 

Calif- ___ ____ ___ _

______ Do. ______

______ Do. ______

______ Do. ______

______ Do. ______

______ Do.

______ Do.

______ Do. ______

Approximate 

source 

distance 

Date Magnitude (km)

Rock sites

10/31/35 6.0 8

7/21/52 7.7 43

3/22/57 5.25 11

9/12/70 5.4 13

19 

6/27/66 5.6 7

4/8/68 6.5 134

2/9/71 6.6 3-5

21 

24 

26 

30 

31 

30 

40

Component 

of motion

North— South 

East— West

North 21 East 

South 69 East

North 10 East 

South 80 East

South 25 West 

South 69 East 

North— South 

East— West

North 65 West 

South 25 West

North 33 East 

North 57 West

South 16 East 

North 76 West 

North 21 East 

North 69 West 

North— South 

East— West 

South 69 East 

South 21 West 

South 08 East 

South 82 West 

North— South 

East— West 

North — South 

East— West 

North 03 West 

North 87 East

Maximum 

velocity

(cm/a)

7.3 

13.3

15.7 

17.7

4.9 

4.6

9.6

8.9

14.5 

22.5

3.7 

4.2

115.5 

57.7 

14.7 

12.4 

12.3 

15.0 

9.9 

6.2 

9.9 

6.2 

20.5 

14.5 

5.8 

11.6 

5.3 

6.7

Maximum 

displacement (cm)

1.4 

3.7

6.7 

9.2

2.3

.8

1.03 

2.21

4.7 

5.5

1.6 

2.9

37.7 

10.8 

1.8 

8.9 

4.9 

5.4 

7.0 

4.6 

7.0 

4.6 

7.3 

5.5 

1.6 

5.0 

3.2 

5.9

Recording

site

Carroll College, 

Helena.

Taft, Calif.

Golden Gate Park, 

San Francisco.

Wrightwood, 

Calif. 

Devils Canyon, 

San Bernardino, 

Calif.

Temblor, Calif.

SCE Power Plant, 

San Onofre, Calif.

Pacoima Dam.

Lake Hughes, 

Sta. 12. 

3838 Lankershim Blvd., 

Los Angeles. 

Lake Hughes, 

Sta. 4. 

Santa Felicia Dam, 

(outlet). 

Griffith Park 

Observatory 

Cal. Tech. Seismol. 

Lab., Pasadena. 

Santa Anita Dam.

Stiff soil sites

San Fernando, 

Calif _______________

— ___ Do. ______

______ Do. ______

______ Do.

______ Do. ______

______ Do. ______

______ Do. ______

______ Do.

— ___ Do. ______

2/9/71 6.6 21

28 

28 

35

39 

39 

39 

39

67

North 21 East 

North 69 West 

North 11 East 

North 79 West 

South 12 West 

North 78 West 

North— South 

East-West

North— South 

East— West 

North— South 

East— West 

North— South 

East— West 

North— South 

East— West 

North 65 East 

South 25 East

16.5 

27.2 

28.2 

23.5 

31.5 

17.8 

16.5 

21.1

22.3 

18.5 

18.0 

22.1 

18.3 

16.5 

14.7 

16.1 

4.1 

5.0

4.2 

9.3 

13.4 

10.3 

18.3 

9.5 

8.0 

14.7

11.4 

11.6 

10.3 

12.9 

9.0 

10.3 

9.9 

9.1 

2.6 

3.4

Castaic, Old 

Ridge Route. 

15250 Ventura Blvd., 

Los Angeles. 

14724 Ventura Blvd. 

Los Angeles. 

Hollywood Storage, 

P.E. Lot, Los 

Angeles. 

3470 Wilshire Blvd., 

Los Angeles. 

3710 Wilshire Blvd., 

Los Angeles. 

3407 W. Sixth St., 

Los Angeles. 

3345 Wilshire Blvd., 

Los Angeles. 

2516 Via Tejon.

Sites underlain by deep cohesionless soil

Puget Sound, 

Wash _______________

San Fernando, 

Calif _____ —— ________

______ Do. ______

4/29/65 6.5 58

2/9/71 6.6 16

19

South 04 East 

South 86 West

North— South 

East— West 

North— South 

East— West

8.0 

12.7

30.0 

23.9 

31.5

28.8

2.7 

3.8

14.9 

13.8 

17.5 

15.3

Highway Test Lab., 

Olympia, Wash.

8244 Orion Blvd., 

Los Angeles. 

15107 Vanowen St., 

Los Angeles.
CHARACTERISTICS OF GROUND SHAKING 33

TABLE 16.—Values of peak horizontal ground velocity and displacement derived from accelerograms of past earthquakes and used for 

estimating horizontal ground motions in earthquake-resistant design—Continued

Approximate 

source 

distance 

Earthquake Date Magnitude (km)

Do. _ __ 39

______ Do. ______ 37

__ . Do. _ _ 30

Component 

of motion

North South

East— West 

North South

East— West 

North South

East— West

Maximum 

velocity 

(cm/s)

7 9

14.3 

9.8

16.3 

9 0

13.4

Maximum 

displace- Recording 

ment (cm) site

3.0 Cal. Tech.,

7.3 Athenaeum, 

Pasadena.

0 7 na l Tpr>h

6.9 Millikan Library, 

Pasadena. 

2.9 Cal. Tech. Jet

5.0 Propulsion Lab., 

Pasadena.

fault for the frequency band 0.07-25 Hz 

probably do not exceed 400-700 cm/s and 

200-400 cm.

2. Seed, Murarka, Lysmer, and Idriss (1976) proposed that the average maxima of strong motion velocity and displacement may be 

reached for magnitude 6.5-7.0 earthquakes; 

however, the validity of their suggestion has 

yet to be proved. They proposed the attenuation relation shown in figure 26 for moderate 

earthquakes.

DURATION

Duration of shaking has been shown to be one of the 

most important parameters of ground motion for causing damage. Some earthquakes (For example, Parkfield, Calif., 1966, and Stone Canyon, Calif., 1972) have 

produced short, high-frequency accelerograms, but 

they have not caused structural damage, even though 

the peak ground accelerations were on the order of 0.5 

g. In other earthquakes that produced damage, the 

peak ground acceleration level was less, but the duration of shaking for a wide range of frequencies was 

greater. The 1966 Parkfield, Calif., and 1967 Koyna 

Dam, India, earthquakes both produced peak groundaccelerations and velocities as large or larger than 

those produced by the 1940 Imperial Valley, Calif, 

earthquake. The Imperial Valley earthquake caused 

more damage than either of the other two earthquakes 

although towns were about the same distance from 

each earthquake's epicenter, mainly because the duration of ground shaking was several times greater in the 

Imperial Valley earthquake.

Duration of shaking also plays an important causative role in liquefaction, a physical process that can 

also lead to damage. In the 1964 Alaska earthquake, 

for example, soil liquefaction developed about 90 seconds after the ground shaking began, but it has been 

postulated that it would not have occurred if the 

ground shaking had lasted only 45 seconds (Seed and 

Idriss, 1971).

Since 1964, a number of investigators (for example, 

Esteva and Rosenblueth, 1964; Housner, 1965; Husid,

1967; Rogers, 1972; Page and others, 1972; Bolt, 1973; 

Hays and others, 1973; Perez, 1973; Housner, 1975; 

Hays, 1975a; Trifunac and Brady, 1975b; Dobry and 

others, 1977; Trifunac and Westermo, high-frequency 

accelerograms, but they have not caused structural 

damage, even though the peak ground accelerations 

were on the order of 0.5 g. In other earthquakes that 

produced damage, the peak ground 1977; and Hays and 

others, 1978) have studied duration of ground shaking. 

The studies by Trifunac and Brady (1975b) and 

Trifunac and Westermo (1977) were the most comprehensive in scope, but all the studies have provided 

evidence that three interrelated parameters (1) the 

amplitude, (2) the length of time that the ground 

shakes, and (3) the dominant frequency at which it 

shakes, are the parameters that cause structural damage.

Bracketed duration, a measure used frequently in 

the engineering community, is the time during which 

the acceleration level equals or exceeds some 

amplitude threshold such as 5 percent g. This parameter is illustrated in figure 27 for the accelerogram recorded at Pacoima Dam during the 1971 San Fernando, 

Calif, earthquake. The general trend of increasing 

bracketed duration with increase in magnitude is also 

shown in figure 27.

Trifunac and Brady (1975b) used a definition proposed by Husid (1967) to calculate the duration of 

strong earthquake ground motion. Their definition was 

based on 90 pecent of the integral of the squared time 

history, for example:

a (t)dt, v (t)dt, d (t)dt.

They correlated the integral (fig. 28) of the squared 

acceleration (a), velocity (v), and displacement (d) time 

histories with recording site conditions, magnitude, 

and epicentral distance and concluded:

1. The average duration for a "soft" alluvium site 

is 5-6 seconds longer than for an intermediate site and 10-12 seconds longer than 

for rock sites.
34 PROCEDURES FOR ESTIMATING EARTHQUAKE GROUND MOTIONS

200

SITES 

A Rock 

O Stiff soil 

• Deep soil

D Probable maximum value 

suggested by Atnbraseys 

(1973)

10 100 

DISTANCE FROM ZONE OF ENERGY RELEASE, IN KILOMETERS

1000

FIGURE 26.—Relation between peak horizontal ground velocity and distance from source of energy release for magnitude 6.5 earthquakes

(from Seed, Murarka, Lysmer, and Idriss, 1976).

2. The average duration increases by 2 seconds for 

acceleration and about 5 seconds for displacement for each unit increase in earthquake magnitude.

3. The average duration increases about 1-1.5 

seconds for every 10 km increase in epicentral distance. ;

Trifunac and Westermo (1977) extended the procedure for denning duration. Instead of deriving the integral of the square^ seismogram, they calculated the 

integrals for 10-15 squared band-pass filtered time 

histories of the original seismogram. Duration derived 

in terms of filtered time histories exhibits the same 

trends as stated above, but the variability is less. 

Frequency-dependent characteristics of ground motion 

(For example, amplification) can be identified in the 

band-pass filtering process and eliminated from consideration in the analysis.

SPECTRA

Fourier techniques are the standard for spectral 

analysis of ground motion data. A Fourier spectrum 

resolves the ground-motion time history into an infinite series of simple harmonic functions in the frequency 

domain. The resulting transformation provides both an 

amplitude and a phase spectrum that are uniquely related to the seismogram.

Four amplitude spectra (fig. 29) are used frequently 

in engineering seismology. Examples of uses include: 

(1) analysis of ground-motion data (Hudson, 1962; 

Hays and others, 1975a); (2) source-mechanism studies 

(Savage, 1966; Brune, 1970; Trifunac, 1972b); (3) seismic attenuation studies (Hays, 1969; Trifunac, 1967b); 

(4) site amplification studies (Duke and Hradilek, 

1973; Rorcherdt and Gibbs, 1976); and (5) soilstructure interaction (Liu and Fagel, 1973; Grouse and 

Jennings, 1975). The application proposed by Brune in
CHARACTERISTICS OF GROUND SHAKING 35

1.24

5S>

-. 0.62

z 

o

i < tu_l 

tu

« -0.62

<

-1.24

San Fernando earthquake,

Pacoima Dam, 

S. 16°E. component

0 5 SECONDS

I l I I I I

Bracketed duration measure

, wf1" Wifl^W^^MMMfc* i

Duration >0.050 = 12.2s

50

^ 40

•E 30

QC

tu

< 

UJ 

QC 

O 

CO

3 20

z

UJ

FAULT RUPTURE LENGTH, IN KILOMETERS 

10 20 30 70 140 260 500

10

I l I I I

A Duration >0.05 g

+ Values proposed by Housner (1965)

——Bracketed duration, D >0.050

— -Bracketed duration, D >0.1 g

APugetSound, 1949 

Almperial Valley, 1940

San Fernando, 1971 — * (Castaic[_ ^ ^ ^_ _

A,San Fernando, 1971 (Pacoima Dam)

x

APugetSound, 1965

A Kern County, 1952

JjV'^San Francisco, 1957

5.5 6.5 7 

MAGNITUDE

7.5 8.5

FIGURE 27.—Bracketed duration values for the S. 16° E. accelerogram recorded at Pacoima Dam from the 1971 San Fernando 

earthquake (top; from Hays, 1975a), and bracketed duration as a 

function of magnitude and fault rupture length (bottom; modified 

from Bolt 1973).

1970 to deduce source parameters from the far-field 

displacement spectrum has stimulated much important research in seismology. The displacement 

spectrum, after being corrected for instrument response and path propagation, has a flat low-frequency 

level (fig. 30), which is used to define the stress drop

and seismic moment. It is also has a corner frequency 

(the frequency where the high- and low-frequency 

trends interact) that is related to the radius r of the 

equivalent circular fault causing the earthquake.

In engineering seismology the spectral characteristics of ground motion are normally displayed as response spectra, a form preferred by structural engineers for the study of building response. Structures 

respond as oscillating systems with fairly well defined 

periods of vibration, and their response to ground motion is strongly dependent on its spectral composition 

and duration. Simple systems such as viscous-damped 

pendulum or mass-spring systems have been successfully used to model structural elements (Blume and 

others, 1961). When such a model is excited by ground 

motion from an earthquake, it will respond by vibrating. The vibratory motion is described by the well 

known differential equation

x+2(on hx+a>n 2x = -a(t)

where x is the relative displacement between the mass 

and ground, 'x and* are the velocity and acceleration of 

the mass relative to the ground, h is the fraction of 

critical viscous damping, o>,, is the undamped natural 

frequency of vibration of the system, and a(t) is the 

ground acceleration.

The Fourier amplitude spectrum has a close relation 

to the undamped velocity response spectrum (Hudson, 

1962). These two spectral respresentations, although 

fundamentally different, are essentially interchangeable in seismic data analyses.

The response spectrum technique, proposed by Benioff (1934) and Biot (1943), is a method for determining the maximum amplitudes of response of an ensemble of simple damped, harmonic oscillators (a narrowband filter) when excited by a given ground-motion 

time history (fig. 31). The various response spectra are: 

(1) pseudo absolute acceleration (PSAA), (2) pseudo 

relative velocity (PSRV), (3) absolute acceleration 

(AA), (4) relative velocity (RV), and (5) relative displacement (RD). Each response characterization has a 

physical meaning. PSAA is a measure of the maximum 

elastic spring force per unit of mass. RD represents the 

maximum value of the relative displacement of the 

simple system during vibratory motion. PSRV gives an 

approximate index of the greatest velocity, relative to 

its base, of the center of mass of the resonant simple 

structure. PSRV can also be related to the maximum 

energy absorbed in the spring. For low damping, the 

PSRV spectrum provides an upper bound to the 

Fourier amplitude spectrum (Jenschke,1970).

Response spectra for four values of damping (0, 2, 5, 

and 10 percent of critical) derived from the horizontal 

component accelerogram recorded at El Centro from
36 PROCEDURES FOR ESTIMATING EARTHQUAKE GROUND MOTIONS

STATION UNDERLAIN BY ROCK

0 CC

O LU -" tLU LJJ

> s

o10-J

RADIAL VELOCITY

-5.3cm/s

10

100 n

TIME, IN SECONDS

"° LU

V///////////////////////M 

DURATION = 6 SECONDS

10 J

100-,

STATION UNDERLAIN BY 100 M OF ALLUVIUM

RADIAL 

VELOCITY 11.2cm/s

10

TIME, IN SECONDS

DURATION = 10 SECONDS

FIGURE 28.—Example of integral definition of duration of shaking for a site on rock and a site underlain by alluvium (from Hays and others,

1978).

1000.0

100.0

10.0

1.0

0.1

0.01 I I I I

0.01

i1 r i i

I I I I i i i i

ill)

0.1 1.0

FREQUENCY, IN HERTZ

10.0 100.0

FIGURE 29.—Example of a Fourier amplitude spectrum derived from the accelerogram recorded at El Centro from the 1940 Imperial

Valley, Calif., earthquake.

the 1940 Imperial Valley, Calif., earthquake are shown 

in figure 32. Response spectra are typically plotted on 

tripartite log-log paper. From such a plot, the spectral

velocity, acceleration, and displacement can be determined simultaneously along with estimates of the peak 

ground acceleration and ground displacement. For
CHARACTERISTICS OF GROUND SHAKING 37

BASIC RELATIONS

a = corner frequency = 2.34^ , where/?= shear-wave 

velocity and r is the radius of the circular source

M0 = seismic moment =ju Tr2 D, where 0 = average 

offset on fault and At = rigidity = —A err3

ACT = stress drop = 27.4 /i/?0 0 /r 3

Low-frequency trend (zero slope)

Slope of high-frequency 

trend is proportioned 

frequency "^

LOG FREQUENCY

FIGURE 30.—Schematic illustration of far-field displacement 

spectrum and some of the information about the source that can be 

derived from it.

example, the peak value of horizontal ground acceleration is approximately equal to the value that the 

spectral acceleration approaches at very high frequencies (zero period), and the peak value of horizontal 

ground displacement is approximately the value which 

the spectral displacement approaches at very low frequencies (infinite period).

Another spectral representation, the time-dependent 

response envelope (Trifunac, 1971; Perez, 1973; Hays 

and others, 1973), is shown in figure 33. The example 

shown is for the 1940 Imperial Valley earthquake accelerogram recorded at El Centre, Calif. It demonstrates the increased information content over the 

standard response spectrum. This spectral representation is not widely used in earthquake-resistant design 

at the present time.

Response spectra are widely used in engineering 

seismology research to define the frequency-dependent 

effects caused by parameters of the earthquake source 

and the transmission path. It is well known, for example, that the dominant spectral composition of ground 

motion shifts to the long-period end of the spectrum 

with an increase in earthquake energy release. Figure 

34 illustrates the shift of corner frequency for two 

PSRV spectra representing, respectively, the San Fernando earthquake (M=6.6) and an aftershock (M=3.2). 

Both events were recorded at the same recording site 

(Glendale Municipal Building, Glendale, Calif.) and

had essentially identical travel paths. The difference in 

spectral composition, therefore, primarily correlates 

with the difference in source parameters for the two 

events. It is also well known that the earth tends to act 

like a low-pass filter on propagating seismic waves. 

That is, the high-frequency spectral components are 

attenuated more rapidly than low-frequency components. This effect is shown schematically in figure 35 

for response spectra derived from accelerograms recorded during the 1971 San Fernando earthquake.

Frequency-dependent seismic-source scaling laws 

could be used in many design applications if they were 

available. Although the current practice of scaling 

ground-motion characteristics (for example, peak acceleration or response spectra values) in a linear manner to provide design ground-motion estimates is not 

satisfactory physically, the procedure has not been 

modified at the present time.

Frequency-dependent distance-scaling laws that 

characterize the low-pass filtering effect of the earth in 

various geographic regions of the United States could 

also be used if they were available. Very few 

frequency-dependent attenuation relations have been 

developed because of the lack of ground-motion data. 

The few relations that are available (King and Hays, 

1977) are preliminary estimates. Peak ground acceleration is attenuated to the site then used as the high 

frequency anchor for the site-independent response 

spectrum. For sites in the Eastern United States where 

only Modified Mercalli intensity data are available, intensity is attenuated to the site, converted to peak acceleration, and used to define the response spectrum. 

(Intensity and the design response spectra will be discussed in a later section.)

A more accurate procedure for a scaling groundmotion data with distance could be used if data were 

available. Given a ground-motion response spectrum 

M2 derived from a recorded accelerogram at epicentral 

distance R2 , the predicted spectrum M: of ground motion at distance R l is give by

where /3 is the distance scaling exponent (see tables 

9-13) for a particular period. A procedure such as this 

would accurately account for the known differences in 

regional attenuation.

KNOWLEDGE GAINED FROM NUCLEAR EXPLOSION 

GROUND-MOTION STUDIES

During the past decade, more than 300 underground 

nuclear detonations have been conducted at the 

Nevada Test Site mainly on Yucca Flat or Pahute
38 PROCEDURES FOR ESTIMATING EARTHQUAKE GROUND MOTIONS

100.0 c

0.1

OUTPUT (RESPONSE 

TIME HISTORIES)

1.0 10.0 

FREQUENCY, IN HERTZ

100.0

40

20

0 

20

40

FREQUENCY = 0.33 hem

—

-

—

/

V ^

A ^

w

—

—

10 15 20 25 

TIME, IN SECONDS

10 15

INPUT TO RESPONSE SPECTRUM FILTER SYSTEM 

(GROUND-MOTION TIME HISTORY)

0 5 10 15

TIME, IN SECONDS 

FIGURE 31.—The narrow-band-pass filtering involved in deriving a response spectrum.

Mesa (fig. 36), located northwest of Las Vegas, Nev. 

These detonations ranged in yield from about 1 to 

1,200 kilotons (Springer and Kinneman, 1971, 1975). 

More than 4,000 velocity and acceleration seismograms were recorded on paper and tape. These seismograms were recorded at 600 different recording sites, 

which were selected for either research purposes or 

safety documentation. The source-to-station distances 

ranged from 0.4 to 600 km. The stations are underlain 

by rock of various types and unconsolidated materials 

of various thicknesses.

Eleven nuclear detonations have been conducted 

outside the Nevada Test Site. These detonations were 

as follows: Faultless and Shoal in central Nevada;

Longshot, Milrow, and Cannikin on Amchitka Island, 

Alaska; Rulison and Rio Blanco in Colorado; Gnome 

and Gasbuggy in New Mexico; and Salmon and Sterling in Mississippi.

Ground-motion data recorded from some of the important nuclear detonations have been published (for 

example, Environmental Research Corporation, 1968, 

1969, 1970a, b, c, 1974a; Hays and others, 1969; West, 

1971; West and Christie, 1971). Comprehensive studies 

of the ground motion and structural response data 

have been performed and are summarized in reports by 

Environmental Research Corporation (1974b) and 

URS/John A. Blume, Engineers (1975). Research on 

nuclear explosion ground-motion data has established:
CHARACTERISTICS OF GROUND SHAKING

kO.08

A .

Q-, M

kO.18 k0.5||k1.0 I 1k"5.orrk10.0

0.08 0.18 0.5 1.0 5.0 10.0 

FREQUENCY, IN HERTZ

100

50

20

10

5

Schematic ensemble of single-degree-of-freedom systems

1

0.05 0.1 0.2

127.0

50.8

25.4

12.7

5.1

0.5 1 2 5 

FREQUENCY, IN HERTZ

10 20 50

>7 Story 3-7 Story 1-2 Story

Natural frequency range of building

FIGURE 32.—Example of response spectra derived from the 1940 

Imperial Valley, Calif., earthquake accelerogram. M and k represent the mass and spring constant of the equivalent mechanical system. Damping factor 0, 2, 5, and 10%.

VELOCITY, 

IN CENTIMETERS 

PER SECOND

100.0 TNORTH-SOUTH COMPONENT

10.0 20.0 

TIME, IN SECONDS

30.0

FIGURE 33.—Diagram showing time-dependent response envelope 

derived from the 1940 Imperial Valley, Calif., earthquake accelerogram.

1. The similarity of ground-motion response 

spectra of explosions and earthquakes (fig. 

37) over the period range from 0.01 to 5 seconds.

2. The approximate log-normal distribution of nuclear explosion ground-motion spectral values at a fixed period (Lynch, 1969, 1973).

3. The wide range (up to a factor of 10) in levels of 

ground motion that can occur because of dif100.0

39

RADIAL COMPONENT

10.0

0.1

0.01

I I

: SAN FERNANDO 

\ EARTHQUAKE

_ 2/9/71 M = 6.6

0.001

0.01

- SAN FERNANDO 

\AFTERSHOCK 

" 4/29/71 M = 3.2

0.1 1.0 

PERIOD,INSECONDS

10.0

FIGURE 34.—Example of earthquake source effects on the spectral 

composition of ground motion.

100.0 r

10.0

0.1 1.0 10.0

PERIOD, INSECONDS

FIGURE 35.—Example of transmission path effects on the spectral 

composition of ground motion, 1971 San Fernando earthquake.
40 PROCEDURES FOR ESTIMATING EARTHQUAKE GROUND MOTIONS

FIGURE 36.—Nevada Test Site and vicinity.

100.0 t=

10.0

mperial Valley (1940 

orth-south componen*

0.1

0.01 10.0

PERIOD, IN SECONDS

FIGURE 37.—Response spectra obtained from 1940 Imperial Valley, 

Calif., earthquake and Cannikin nuclear explosion. Recording stations were located within 10 km of source.

ferences in the transmission paths to two 

sites (fig. 38) (Weetman and others, 1970) or 

because of variations in the physical properties of the local geology (fig. 39) within a

100.0

10.0

1.0

0.1

. I ! 1 I Illf

5 percent damped

BEATTY-'

..I I

0.1 1.0

PERIOD, IN SECONDS

FIGURE 38.—Response spectra for two sites equidistant from energy 

source but on different travel paths.

STATION 

CHURCH 183m- .STATION

= 1 .7g/cm3

P2 =2.1 g/cm 3

:10.0

1.0 10.0 

FREQUENCY, IN HERTZ

100.0

FIGURE 39.—Variability of ground motion recorded at two sites in 

Tonopah, Nev.
CHARACTERISTICS OF GROUND SHAKING 41

small geographic ara (Murphy, Lynch and 

O'Brien, 1971; Hays, 1972a, 1978).

4. The high degree of repeatability of site transfer 

functions for strain levels varying from 10'5 

to 10-3 (Rogers and Hays, 1978; Hays and 

others, 1979).

5. The high degree of confidence with which a nuclear explosion can be used to "calibrate" the 

seismic attenuation and local ground response for a region where ground-motion 

data are limited (Foote and others, 1970; 

Hays, 1975b).

Newmark (1974) has reported on two little-known 

facts about nuclear explosion ground motions. The 

quantity ad-v2 (where a is peak acceleration, u is peak 

velocity, and d is peak displacement) has a median 

value of 5 to 6, and the ratio of the peak ground velocity 

to the peak ground acceleration is 122 cm for 1 g acceleration (except for very close distances to a nuclear 

explosion). Both of these values are essentially the 

same as those for earthquake ground motions.

INTENSITY

In earthquake-resistant design, the accepted practice is to express the Modified Mercalli intensity at the 

site in terms of peak ground acceleration in order to 

scale the design response spectra. This step, which 

must be performed with care, is needed because no procedure exists for scaling spectra directly in terms of 

intensity. To perform the conversion, one of the empirical intensity-to-acceleration relations shown in table 

17 is used. Figure 40 shows two of the empirical relations (Neumann, 1954; Gutenberg and Richter, 1956)

MODI 

INT

FIED MERCALLI 

ENSITY SCALE GROUND ACCELERATION, IN0

1

II

III

IV

V

VI

VII

VIII

IX

X

0.005 ——

0.01 ——

0.05 —— 

0.1 ——

0.5 ——

1.0 ——

0.005 —— 

0.01 ——

0.05 —— 

0.1 ——

0.5 ——

1.0 ——

Gutenberg and Richter (1956) Neumann (1954)

FIGURE 40.—Intensity and acceleration relations proposed by 

Neumann (1954) and Gutenberg and Richter (1956).

TABLE 17.—Characteristics of the data samples used in selected studies of the correlation of Modified Mercalli intensity and peak ground

acceleration

[Modified from O'Brien, Murphy, Lahoud (1977)]

Study

Gutenberg and

Richter, 1942, 

1956

Hershberger, 1956 ______

Coulter, Waldron

and Devine 

1973

Trifunac and

Brady, 1975c

Number and location 

location 

of earthquakes

_ _ 61, Western

United States. 

— ________10, do.

___________60, do.

— __—_____, do.

(Not based 

entirely on 

observed data)

______ ____57, do.

Number of 

recordings

167

10

108

187

Range of 

Modified Mercalli 

intensity

III- VIII

V-VIII

II- VIII

IV-X

IV-X

Distance 

range (km)

3-450

25 and 160 

(distance 

dependent)

Short distance

3-250

Acceleration 

range (cm/s2 )

1-300

40-300

1-300

6-3000

(Dependent on 

site geology 

and local 

amplification) 

7-1150
42 PROCEDURES FOR ESTIMATING EARTHQUAKE GROUND MOTIONS

that have been used to convert intensity values into 

ground acceleration values. This conversion, depending on the empirical relation used, can lead to a range 

of answers-that differ by more than an order of magnitude and significantly affect the seismic design. The 

reason for the variability is that Modified Mercalli intensity values are a function of other variables besides 

peak ground acceleration.

Using data from the Western United States, 

Trifunac and Brady (1975c) proposed empirical relations between Modified Mercalli intensity IMM and: (1) 

peak horizontal (Ah ) and vertical (Av ) ground acceleration; (2) peak horizontal (Vh ) and vertical (Vu ) ground 

velocity; and (3) peak horizontal (Dh ) and vertical (Dr) 

ground displacement. These relations are:

log Ah = 

log AP = 

log Vh = 

log Vv = 

log DA = 

log A =

-0.014+0.30 IMM

-0.18+0.30 IMM

-0.63+0.25 IMM

-1.10+0.28 IMM

-0.53 + 0.19 IMM

-1.13+0.24/M,

The units of acceleration, velocity, and displacement 

are, respectively, centimeters per second per second, 

centimeters per second, and centimeters. The range of 

IMM is from IV to X. The average trends and the 

standard-deviation error bars for these relations are 

shown in figure 41.

Murphy and O'Brien (1977) derived statistical correlations between horizontal and vertical ground acceleration and Modified Mercalli intensity using a 

worldwide data sample. The basic relations and the 

geometrical standard deviation (o-) are:

log A* - 0.24/„„„ + 0.26 a- = 2.19 

log Av = 0.28 Imm - 0.40 o- = 2.53

PROBABILISTIC ESTIMATES OF PEAK GROUND 

ACCELERATION

The ground shaking hazard map of the United States 

(fig. 42) published in 1976 by Algermissen and Perkins 

provides a basis for estimating peak ground acceleration for a site. Unlike past maps (for example, Algermissen, 1969) that were based on a mapping of 

Modified Mercalli intensity, the new map depicts the 

90-percent probable peak horizontal ground acceleration expected at a site located on rock within a 50-year 

period of time. Their map was based on knowledge of: 

(1) the regional geology, (2) the earthquake history, 

and (3) the Schnabel and Seed (1973) and the "modified 

Schnabel and Seed" acceleration attenuation functions 

(see preceding section).

A 90-percent probability of not being exceeded in a 

50-year time interval is equivalent to a mean return 

period (recurrence interval) of 475 years, or an annual 

risk of 0.002 events per year. It should be emphasized 

that the earthquake causing the extreme level of 

ground motion may occur once or twice, or may not 

occur at all in 475 years; on the average, a particular 

level of ground motion will be exceeded once in 475 

years.

The Algermissen and Perkins map has only limited 

value for some design applications. For example, the 

nuclear power plant has a design requirement for peak 

rock accelerations with a 1,000,000 year return period. 

Such a map has not been constructed because of the 

short seismicity record and the lack of precise knowl1000

w 100

10 -

1

il

100

10

I I I \ I I \ o Vertical component

Horizontal component

I II III IV V VI VII VIM IX X XI XII

8 c

V *

c

100

^ 10 •

I II III IV V VI VII VIII IX X XI XII I II 111 IV V VI VII VIII IX X XI XII

MODIFIED MERCALLI INTENSITY

FIGURE 41.—Mean values and standard-deviation error bars of peak ground acceleration, peak ground velocity, and peak ground displacement as a function of Modified Mercalli intensity, Western United States (modified from Trifunac and Brady, 1975c).
DESIGN RESPONSE SPECTRA FOR SITE 43

Contour showing expected peak horzontal ground 

acceleration expressed as a percentage of gravity 

Numbers within closed contours are expected maxima. 

~ Maximum acceleration within the 60-percent contour 

along the San Andreas and Garlock faults in California 

is 80-percent of g, using the attenuation curves of 

Schnabel and Seed. 1973 0 500 KILOMETERS 

I I I I I I

10S

FIGURE 42.—Levels of peak horizontal ground acceleration expected at rock sites in the United States (from Algermissen and Perkins, 1976). 

The contoured acceleration values represent the 90-percent probability level; in other words, there is a 10-percent chance that these 

values will be exceeded within a 50-year period.

edge about regional seismic attenuation in various 

geographic provinces of the United States.

EFFECTIVE PEAK GROUND ACCELERATION

An effective peak ground acceleration value (Pfossel 

and Slosson, 1974) is sometimes selected for earthquake-resistant design instead of the actual value of 

peak acceleration. The effective peak acceleration can 

be thought of as the peak ground acceleration after the 

accelerogram has been filtered to remove the very high 

frequencies that have little influence on structural response. This choice is made when the peak ground acceleration is associated with one or more highfrequency spikes of short duration or when the total 

duration of the accelerogram is short. The accelerogram produced by the 1966 Parkfield, Calif., earthquake is one example (fig. 43) where the peak ground 

acceleration of about 0.5 g was caused by a single 

high-frequency spike. In this case, the effective peak 

acceleration was about 0.1 g. The accelerogram recorded at Pacoima Dam (fig. 27) from the 1971 San

Fernando earthquake has been assigned an effective 

peak acceleration of 0.7-0.8 g by some investigators 

(for example, Bolt, 1972) because the peak ground acceleration of 1.2 g was caused by a high frequency 

spike. At the present time, the use of effective peak 

acceleration in seismic design is controversial owing to 

inconsistent practice and vagueness in the definition of 

the characteristics of the filter used to obtain the effective peak acceleration value from an accelerogram. A 

similar concept holds for effective peak velocity, but it 

is not yet well established.

DEFINE DESIGN RESPONSE SPECTRA FOR SITE

Once the characteristics of ground shaking at the 

site have been established, elastic response spectra can 

be defined. Response spectra are defined by using siteindependent or site-dependent procedures. These procedures were developed primarily for the siting of nuclear powerplants and will be discussed in some detail 

below after a summary of siting procedures for nuclear 

powerplants.
44 PROCEDURES FOR ESTIMATING EARTHQUAKE GROUND MOTIONS

0.5

-0.5 

50

-50

0

-10

-20

-30

-40

N. 65° E. COMPONENT

VELOCITY

UVA A

DISPLACEMENT

5 SECONDS

FIGURE 43.—Acceleration, velocity, and displacement seismograms 

from the 1966 Parkfield, Calif, earthquake recorded at station 

Cholame-Shannon No. 2.

SUMMARY OF PROCEDURES FOR SITING 

OF NUCLEAR POWER PLANTS

The U.S. Atomic Energy Commission proposed seismological and geologic criteria in 1971 and 1973; and, 

under its new name, the U.S. Nuclear Regulatory 

Commission, proposed a standard review plan in 1975 

for determining design earthquakes at a proposed nuclear power plant site. These criteria significantly affect power plant siting and all other engineering applications that require characterization of the earthquake 

ground motion.

The procedure can be summarized as follows. The 

parameters of two design earthquakes, the safe shutdown earthquake and the operating basis earthquake, 

are estimated on the basis of integrated geologic, 

geophysical, and geotechnical investigations which include:

1. Determination of the lithologic, stratigraphic, 

and structural geology of the site and surrounding region.

2. Identification of tectonic structures underlying 

the site and surrounding region.

3. Determination of physical evidence concerning 

behavior of the surficial unconsolidated materials and the substrata during past earthquakes.

4. Determination of the static and dynamic properties of the materials underlying the site.

5. Determination of the historical seismicity.

6. Correlation of epicenters or regions of highest 

Modified Mercalli intensity for historically 

reported earthquakes with tectonic structures, any part of which is located within 322 

km (200 miles) of the site. Epicenters or regions of highest intensity that cannot be reasonably correlated with tectonic structures 

are identified with tectonic provinces.

7. Determination of the capability of each fault or 

part of a fault system located within 322 km 

of the site.

8. Estimation of the maximum magnitude earthquake consistent with each active fa^lt in the 

region.

The current procedures for defining the seismic input 

and site response of a nuclear power plant are based 

primarily on empirical data. For sites in the Eastern 

United States, the historic earthquake that caused the 

largest Modified Mercalli intensity in the tectonic 

province containing the site is generally used to define 

the seismic parameters of the safe shutdown earthquake (SSE). If this earthquake occurred in the tectonic province containing the site, the SSE is assumed 

to occur near the site and to reproduce its epicentral 

intensity I0 at the site. The epicentral intensity is converted into a peak ground acceleration value using 

empirical correlations between Modified Mercalli intensity and peak ground acceleration. This value of 

peak ground acceleration (or alternately a value of effective peak ground acceleration) is used to define the 

anchor of the high-frequency end of a smooth, broadband response spectrum. This design spectrum is a 

function of damping and has a shape and amplitude 

level that are based on the mean-plus-one-sigma level 

of ground motion spectra from a number of past earthquakes. A design time history may also be derived with 

the constraint that it produces a response spectrum 

which envelops the smooth, broad-band design response spectrum. The operating basis earthquake 

(OBE) is also defined and typically has seismic design 

values that are one-half those of the SSE. When the 

historic earthquake producing the largest intensity in 

the tectonic province lies outside the tectonic province 

containing the site, the SSE is assumed to occur on the 

province boundary at the closest point to the site. The 

epicentral intensity is attenuated to the site using empirical relations between Modified Mercalli intensity 

and epicentral distance that are applicable for the tectonic province. This value of Modified Mercalli intensity is then converted into peak ground acceleration 

and used to define the high-frequency anchor of the 

design response spectrum.
DESIGN RESPONSE SPECTRA FOR SITE 45

For sites in the Western United States where the 

tectonic faults and structures are comparatively easier 

to identify than in the Eastern United States, the procedure is similar. All the tectonic structures near the 

site are evaluated. The largest earthquake that has 

occurred anywhere on each of the nearby faults is determined and assumed to reoccur on that part of the 

capable fault that is closest to the site. Thus, the 

maximum epicentral intensity I0 and the minimum 

epicentral distanced are defined, and epicentral intensity is attenuated to the site using applicable attenuation relations and converted into a peak ground acceleration. Alternately, empirical relations that relate 

magnitude and fault rupture length can be used to 

define the upper-bound magnitude. This value can be 

converted into a value of peak ground-acceleration and 

attenuated to the site using peak ground-acceleration 

curves inferred or derived from strong ground motion 

data.

Definition of the seismic input and site response is a 

controversial process. The controversy is caused in part 

by the debate about whether the available geologic, 

geophysical, seismological, and geotechnical data are 

adequate to specify the seismic input and site response 

precisely. Controversy also centers on whether the 

judgments about conservatism in the seismic design 

specifications are reasonable in view of the uncertainties in the data and whether a given earthquakeresistant design will provide an adequate margin of 

safety in a future earthquake.

Perhaps the most controversial part of defining the 

seismic input is the question of how intense the peak 

ground acceleration should be, especially for the less 

seismic regions of the United States. The controversy is 

fed, at present, by the fact that:

1. peak ground acceleration is not a simple function of Modified Mercalli intensity,

2. peak ground acceleration observed in an earthquake can vary by an order of magnitude at 

any given distance from the source, and

3. peak ground acceleration within 10 km of the 

causative fault is independent of magnitude 

for 4.5=s M=s 7.1 and is a function of the 

dynamic stress drop and the local distribution of stress.

Several factors are intentionally incorporated into 

the design process to introduce conservatism in the 

seismic input for a nuclear power plant. They are:

1. selecting a low-probability, extreme event and 

moving it to the closest epicentral distance to 

the site,

2. using smooth, broad-band, mean-plus-onesigma response spectra, independent of the 

epicentral distance from the site,

3. using "worst-case" seismic attenuation functions,

4. requiring that the design time histories produce spectra that envelop the smooth, 

broad-band, mean-plus-one-sigma response 

spectra.

5. assuming that the two horizontal-component 

design time histories have equal values of 

peak ground acceleration; also, that the vertical component has peak values that are % 

or more of the peak values of the horizontal 

components, and

6. modifying the smooth, broad-band, mean-plusone-sigma response spectra to account for 

specific local ground response characteristics.

The safe shutdown earthquake is assumed to represent the maximum possible level of earthquake ground 

shaking at the site. The SSE may or may not have 

occurred at the site during historic times, but it is defined on the basis of a detailed investigation of the 

regional and local geology, the regional seismicity, and 

the characteristics of the underlying soil materials. For 

the SSE, the facility should be designed so that all 

systems necessary to protect the health and safety of 

the public will remain functional both during and after 

the earthquake. Although structures and their internal components may suffer severe damage from the 

SSE, the design must allow for a safe and orderly shutdown after an earthquake. The lower bound for the 

peak horizontal ground acceleration induced at the site 

by the SSE is 0.1 g. The second level, the operating 

basis earthquake is assumed to represent the 

maximum level of ground shaking that can be expected 

to occur at the site during the 40-year operating life of 

the nuclear power plant. This earthquake probably has 

occurred in the vicinity of the site during historic 

times. It is also based on a detailed investigation of the 

regional and local geology, the regional seismicity, and 

the characteristics of the underlying soil materials. For 

the OBE, the facility should be designed so that those 

features of the plant necessary for continued operation 

without undue risk to the public will remain funtional. 

The maximum horizontal ground acceleration of the 

OBE must be at least one-half of the SSE, with a 

lower-bound peak acceleration level of 0.05 g. Table 18 

lists the horizontal ground accelerations of the OBE 

and SSE for a number of nuclear power plant sites.

To obtain information for evaluating the ground response in the site vicinity, a combination of borings, 

trenches, laboratory measurements, and geophysical 

methods are used (Shannon and Wilson and Agbabian 

Associates, 1972, 1975, 1976). The purpose is: (1) to 

determine the classification, lateral distribution, 

stratification, geologic structure, and physical prop-
46 PROCEDURES FOR ESTIMATING EARTHQUAKE GROUND MOTIONS

TABLE 18—Horizontal ground accelerations for the operating basis 

earthquake and safe shutdown earthquake for nuclear power plant 

sites in the United States

[From Johnson and Kennedy (1977)]

Site

Browns Ferry

Brunswick

Calvert Cliffs ______________

Connecticut Yankee

Davis-Besse

Dresden

Fermi

Fort St. Vrain ___ ___ __ ___

Indian Point

Kewaunee

Nine Mile Point

Oyster Creek

Peach Bottom

Quad Cities

Salem

Susquehanna

Three Mile Island

Turkey Point

Vermont Yankee - _ _ _ _ -

Zion

Diablo Canyon

Humboldt Bay

Rancho Seco

San Onofre

Trojan

WPPSS (Hanford) __________

State

Alabama

North Carolina

Maryland

Connecticut

Ohio

Illinois

Michigan

Colorado

New York

Wisconsin

New York

New Jersey

Pennsylvania

Illinois

New Jersey

Pennsylvania

do.

Florida

Vermont

Illinois

California

do.

do.

do.

Oregon

Washington

Operating

basis

earthquake

g level

0.10

.08

.08

.08

.10

.08

.05

.10

.06

.07

.11

.05

.12

.10

.08

.06

.03-.05

.07

.08

.33

.25

.33

.66

.15

.13

Safeshut down

earthquake

g level

0.20

.16

.15

.17

.15

.20

.15

.10

.15

.12

.11

.22

.12

.24

.20

.15

.12

.15

.14

.17

.66

.40

.66

.75

.25

.25

erties of the unconsolidated materials (soil) and rock 

underlying the site; (2) to obtain samples and cores for 

laboratory testing; and (3) to establish the elevation 

and variation of the ground-water table for foundation 

studies.

The response of geologic materials to ground shaking 

is governed primarily by: (1) shear wave velocity, (2) 

density, (3) shear modulus, (4) material damping properties, (5) Poisson's ratio, (6) bulk modulus, (7) static 

shear strength, and (8) dynamic shear strength. These 

physical properties are determined from laboratory 

and field tests and are used in conjunction with finiteelement and other computational models to calculate 

the ground response for the proposed site (Seed and 

Idriss, 1969; Joyner and Chen, 1975; Joyner, 1975).

The current procedures for specifiying the earthquake ground motion at a nuclear power plant site are 

based primarily on empirical models. Each empirical 

model is based on the collection and use of catalogs of 

seismograms, response spectra, and observational data 

(for example, intensity data) from past earthquakes. 

These data are used to derive earthquake recurrence 

relations, scaling laws, attenuation functions, and to 

confirm the adequacy of data analysis procedures. The 

deterministic method uses analytical models to simulate earthquake source mechanics, transmission path 

effects, and local ground response. In principle, analytical models can be applied any place in the world; the

only requirements are that the proper earthquake 

source, transmission path, and ground response models 

be selected. The analytical approach has not been acceptable in earthquake-resistant design in the past because the physical processes that occur in the source, 

path, and site are not well understood. At the present 

time only local soil conditions are modeled mathematically in earthquake-resistant design.

The data sample is particularly limited for siting of 

nuclear power plants in the Eastern and Central 

United States. In these regions, Modified Mercalli intensity data extracted from the historic earthquake 

record may be the only data available to define the 

design ground motion. In these cases, an attempt is 

made to select conservative values. Conservative values are introduced as follows:

1. The location and magnitude of likely earthquakes are uncertain because of the short 

historical seismicity record; therefore, a rare 

large-magnitude event located close to the 

site is selected.

2. The site intensity (as measured by peak ground 

acceleration or Modified Mercalli intensity) is 

uncertain due to lack of knowledge about regional seismic wave attenuation and the local 

ground response; therefore, an upper-bound 

value is selected.

3. The response spectrum that corresponds to a 

given site intensity exhibits scatter about a 

mean value and is uncertain because the details of earthquake ground can vary widely 

for a given measure of ground motion (fig. 

44); therefore, smooth, upper-bound spectral 

values are used.

SITE-INDEPENDENT RESPONSE SPECTRA

The site-independent procedure, one of two basic 

methods for specifying design response spectra for nuclear power plant sites, is based on the use of standard 

spectrum shapes. The standard spectrum shapes are 

considered to be independent of the characteristics of 

the site because the ensemble of seismograms from 

which the spectra were derived depict ground motions 

for a wide range of geologic and seismological conditions.

The site-independent method was first introduced by 

G. W. Housner in 1959. He derived smooth normalized 

acceleration and velocity response spectra (fig. 45) from 

the two horizontal components of ground acceleration 

recorded at four sites from four large earthquakes in 

the Western United States (table 19). The earthquakes 

were: (1) 1934 Imperial Valley, Calif. (M=6.5); (2) 

1940 Imperial Valley, Calif. (M=7.0); (3) 1952 Kern
DESIGN RESPONSE SPECTRA FOR SITE 47

! 200.0

100.0

10.0

———I——I——I—I I I I I |—————I——I——I I I I IT 

MODIFIED MERCALLI INTENSITY 

IS VII AT EACH SITE

Griffith Park(rock), peak

acceleration 0.18s1 

Glendale Municipal Building

(alluvium),peak acceleration

0.27 g

1.0 

0.01

i i i i i i i i i i i i i i i i i

0.1 1.0 10.0

PERIOD, IN SECONDS

FIGURE 44.—Variation in ground-motion response spectra and peak 

ground acceleration values for the same value of Modified Mercalli 

intensity. Spectra were derived from accelerograms of the San 

Fernando, Calif, earthquake (modified from Murphy and O'Brien, 

1977).

County, Calif. (Af =7.7); and (4) 1949 Puget Sound, 

Wash. (M =7.1). The epicentral distances ranged from 

8 to 56 km. The recording sites were underlain by rock, 

stiff soil, and deep cohesionless soil. These spectra are 

scaled by a factor based on the spectrum intensity 

rather than the peak ground-acceleration.

In 1969, Newmark and Hall proposed a new technique for estimating site-independent spectra. Their 

technique as based on the fact that the response 

spectrum over certain frequency ranges is related by 

an amplification factor (fig. 46) to the peak values of 

ground acceleration, velocity, and displacement. The 

amplification factors were statistically determined 

from response spectra derived from the accelerogram 

recorded at El Centre from the 1940 Imperial Valley, 

California earthquake (table 19) and are a function of 

the damping of the spectra. The factors correspond to 

about the 84th percentile of a log-normal distribution. 

In this method, the estimated values of peak ground 

acceleration, velocity, and displacement for the site are 

plotted on tripartite logarithmic paper. Using the 

amplification factors that correspond to the desired 

percentage of critical damping, the peak ground motion values are amplified to give a smooth design response spectrum for the site.

Newmark and Hall (1969) also proposed a "standard" earthquake response spectrum for use whenever 

adequate detail about the site ground-motion parameters was unavailable. These spectra (fig. 47) are based 

on peak ground motion values observed at El Centre 

from the 1940 Imperial Valley, California earthquake,

45.7

Damping factor

(percent)

0

Earthquake Scaling factor 

Imperial Valley, Calif., 1940 2.7

Imperial Valley, Calif., 1934 

Puget Sound, Wash., 1949 

Kern County, Calif., 1952

Damping factor 

(percent)

2.8

PERIOD, IN SECONDS

FIGURE 45.—Site-independent velocity and acceleration response 

spectra (modified from Housner, 1959).

but are about 50 percent more conservative that the El 

Centre values. The Imperial Valley accelerogram was 

recorded within 10 km of the fault, the bracketed (5 

percent) duration of strong motion was nearly 20 seconds, and the levels of peak horizontal ground acceleration, velocity, and displacement were, respectively, 

0.33 g, 34.8 cm/s, and 21.1 cm. The soil column at the 

El Centre site contained a 30-m-thick layer of stiff clay 

that amplified the input rock accelerations (Schnabel, 

Seed, and Lysmer, 1972). The proposed standard 

earthquake had peak ground motion values of 0.5 g, 

60.9 cm/s, and 45.7 cm, but it could be scaled to any 

peak ground acceleration level on the assumption that 

the three ground-motion parameters are proportional 

to each other regardless of the level of ground shaking. 

Thus, one would use peak ground velocity and displacement values of 121.8 cm/s and 91.4 cm for an 

earthquake having a peak ground acceleration of 1.0 g. 

The studies by Newmark and Hall (1969) also provided an empirical basis for defining vertical groundmotion spectra. They observed that the peak vertical 

ground-accelerations are about two-thirds of the peak
TABLE 19.—Earthquake accelerograms used to derive site-independent spectra

Earthquake and site characteristics

Earthquake

Helena, Mont

Imperial Valley,

Calif 

Puget Sound, Wash ____

Northwest California __ 

Kern County,

Calif 

Eureka, Calif ___ _______

Baja, Calif ___ __ __ ___

San Francisco,

Calif. 

Hollister, Calif - ______

Puget Sound, Wash ____ 

Parkfield, Calif ________

Peru

Borrego Mountain, _ _ 

Calif. 

Japan

San Fernando, Calif. _

Date

1934 

1935 

1940

1949

1951 

1952

1954

1956 

1957

1961

1965 

1966

1966 

1968

1968 

1971

Magnitude

6.5 

6.0 

7.0

7.1

5.8 

7.7

6.6

6.8 

5.25

5.6

6.5 

5.6

7.5 

6.5

7.8 

6.6

Peak 

acceleration

(g)

0.182 

.146 

.33

.28

.11 

.179

.06 

.06 

.257

.201 

.05 

.105

.18

.198 

.347 

.489

.354

.42 

.13

.23

1.24 

.26

.341 

.231

Recording 

site

El Centro 

Helena 

El Centro

Olympia

Ferndale 

Taft 

Hollywood 

Storage 

a. Basement 

b. P.E. lot 

Eureka

Ferndale 

El Centro 

Golden Gate 

Park 

Hollister

Olympia 

Temblor 

CholameShandon #2 

CholameShandon #5 

Lima 

El Centro

Hachinohe

Pacoima Dam 

Orion

Castaic 

Bank of 

California

Epicentral 

distance 

(km)

58 

8 

8

20

56 

56

119 

119 

25

30 

126 

11

40

58 

7 

0.1

5

160 

70

160

3-5 

22

19

28

Soil 

classification

Stiff 

Rock 

Stiff

Deep cohesionless 

do 

Rock

Stiff 

do 

Deep cohesionless 

do 

Stiff 

Rock

Deep cohesionless 

do. 

Rock 

Stiff

do

Stiff 

do

Deep cohesionless 

Rock 

Deep Cohesionless 

Stiff 

do

Depth to 

bedrock Housner 

(m) (1959)

32 X

32 X 

132 X

160 

X

64 

64 

160

160 

32

160 

134

48 

32

321? 

32

250±?

256

19 

22

New

and 

(19

X 
DESIGN RESPONSE SPECTRA FOR SITE 49

VELOCITY

AMPLIFICATION

FACTOR

SPECTRUM BOUNDS / pSRV t

PEAK 

~~

VELOCITY 

PEAK HORIZONTAL

GROUND MOTION

Uv,d)

PERIOD (LOG SCALE)

DAMPING 

(percent)

0

0.5

1

2

5

7

10

20

AMPLIFICATION FACTOR

ACCELERATION

6.4

5.8

5.2

4.3

2.6

1.9

1.5

1.2

VELOCITY

4.0

3.6

3.2

2.8

1.9

1.5

1.3

1.1

DISPLACEMENT

2.5

2.2

2.0

2.0

1.8

1.4

1.2

1.0

FIGURE 46.—Schematic illustration of technique for developing siteindependent response spectra (modified from Newmark and Hall, 

1969). The quantities a, v, and d refer to the peak ground acceleration, velocity, and displacement; PSAA, PSRV, and RD refer to the 

spectral acceleration, velocity, and displacement.

horizontal ground-accelerations when the fault 

movements are primarily horizontal, and that the vertical motions are approximately equivalent to the horizontal motions when the fault movements involve a 

large vertical component. Amplification factors are 

also applied to the estimated peak vertical groundmotion to obtain the design response spectra.

Values of maximum ground velocity and displacement are typically based on those of the standard 

earthquake when specific information about these parameters is unavailable. The standard earthquake has 

peak velocity and displacement values that are proportional to those obtained from the 1940 Imperial Valley, Calif., accelerogram (table 20) and are scaled proportionately up or down to correlate with the value of 

ground acceleration that specifies the SSE. The validity of this scaling procedure has been questioned, 

but no alternate techniques have been adopted.

The United States Atomic Energy Commission proposed guidelines in 1973 for developing improved siteindependent earthquake response spectra. These

guidelines, contained in AEC Regulatory Guide 1.60 

(1973b), were based on two independent studies of the 

statistical properties of response spectra (see table 19) 

of earthquake ground motions by N. M. Newmark Consulting Engineering Services (1973) and J. A. Blume 

and Associates, Engineers (1973). From the results of 

these two studies, a unified procedure (Newmark and 

others, 1973) was developed for defining siteindependent earthquake-response spectra that are applicable to most sites. The only exceptions are sites 

which are relatively close to the epicenter of a postulated earthquake or sites which have physical characteristics (for example, foundation deposits with welldefined frequency-filtering characteristics) that could 

significantly enhance the spectral characteristics of 

ground motion in a portion of the spectral band of 

interest.

The procedure proposed in Regulatory Guide 1.60 is 

very similar to the one proposed by Newmark and Hall 

(1969). Spectrum amplification factors (table 21) are 

based on a much larger number of earthquake 

ground-motion records than used by Newmark and 

Hall and represent the mean-plus-one-standarddeviation statistical level (84th percentile of a lognormal distribution). To define horizontal response 

spectra, the peak horizontal ground acceleration and 

displacement levels are established. The peak horizontal ground displacement is considered to be proportional to the peak horizontal ground acceleration 

and is fixed at 91.4 cm for an acceleration of 1.0 g. 

These two values are proportional to the values of 45.7 

cm and 0.5 g established for the "standard" earthquake. The bounds of each spectrum established by five 

line segments, similar to the Newmark and Hall procedure. The control points are designated by letters A, 

B, C, and D and have specified frequency ranges for all 

horizontal component spectra (fig. 48). The amplification factors (table 26) are a function of the percent of 

critical damping and are specified for each of the control points.

Vertical response spectra are constructed in a similar manner to horizontal response spectra (fig. 49), but 

three differences are incorporated into the procedure: 

The frequency for control point C is located at 3.5 Hz 

rather than at 2.5 Hz, (2) The amplification factors (table 22) are different, and (3) The value of peak horizontal acceleration is used as the initial reference value. 

In the frequency range 0.25-3.5 Hz, the ratio of vertical 

to horizontal spectral amplitudes varies between twothirds and one. The horizontal and vertical response 

spectra are identical in the frequency range 3.5-33 Hz. 

Beyond 33 Hz, the vertical spectral accelerations decrease from a value equal to the peak horizontal 

ground acceleration at 33 Hz to two-thirds of the horizontal ground acceleration at 50 Hz (control point, A').
50

1000

PROCEDURES FOR ESTIMATING EARTHQUAKE GROUND MOTIONS

PERIOD, IN SECONDS

0.2 0.1 0.05 0.02 0.01

0.1 0.2 0.5 1 2 5

FREQUENCY, IN HERTZ 

FIGURE 47.—"Standard" site-independent horizontal response spectra (modified from Newmark and Hall, 1969).

TABLE 20.—Relative values of maximum ground-acceleration, velocity, and displacement; "standard" earthquake

[From Newmark and Hall (1969)]

TABLE 21.—Horizontal design response spectra and relative values of 

spectrum amplification factors for control points

[From U.S. Atomic Energy Commission Regulatory Guide 1.60 (1973)]

Maximum values of ground motion

Condition

"Standard" relative 

values

Typical maxima 

Imperial Valley 

(1940) 

Horizontal

Vertical

Recommended minimum 

for any region: 

Horizontal

Vertical

Acceleration

<*>

0.5

.33

.22

.10

.07

Velocity 

(cm/s)

60.96

40.64 

27.94

12.70 

7.62

Displacement

(cm)

45.72

30.48 

20.32

10.16 

7.62

Percent of 

critical Acceleration Displacement

damping A(33 Hz) B(9 Hz) C(2.5 Hz) D(0.25 Hz)

0.5 1.0 4.96 5.95 3.20 

2.0 1.0 3.54 4.25 2.50 

5.0 1.0 2.61 3.13 2.05 

7.0 1.0 2.27 2.72 1.88 

10.0 ' 1.0 1.90 2.28 1.70

The horizontal site-independent response spectra 

(scaled to 0.1 gO proposed by Housner (1959), Newmark 

and Hall (1969), and U.S. Atomic Energy Comm. 

(1973b) are compared in figure 50. The differences be-
5.0

DESIGN RESPONSE SPECTRA FOR SITE 

PERIOD, IN SECONDS

2.0 1.0 0.5 0.2 0.1 0.05

51

0.02 0.01

1000

0.1

FREQUENCY, IN HERTZ

FIGURE 48.—Site-independent horizontal response spectra scaled to 1.0 g. See table 21 for amplification factors at 

control points A-D. Modified from U.S. Atomic Energy Comm. Regulatory Guide 1.60 (1973b).

tween the Newmark and Hall and the AEC Regulatory 

Guide 1.60 spectra are very small. The Housner 

spectrum, however, differs significantly from the other 

two design spectra. This difference is due to the probability level associated with each of the three approaches and the differences in the data samples. The 

Housner spectrum is an average derived from eight 

horizontal accelerograms; therefore, it would normally 

be exceeded 50 percent of the time. The Newmark and 

Hall and Regulatory Guide 1.60 spectra were derived 

from a much larger data sample and represent the 

mean-plus-one-standard-deviation probability level, or 

the 84th percentile; therefore, it should be exceeded 

about 16 percent of the time. In addition, the 

Newmark-Hall and Regulatory Guide 1.60 spectra

were based on ultimate strength design concepts instead of the design practice in effect during the time 

the Housner-type spectra were developed which 

utilized working stress concepts with allowable stresses being one-third less yield. A more accurate comparison is obtained when the Housner spectrum is increased by 50 percent. In this case, the agreement of all 

three spectra is good, especially in the 2-10 Hz range 

that is important in nuclear power plant design.

SITE-DEPENDENT RESPONSE SPECTRA

The current library of strong-motion accelerograms, 

although limited, contains representative samples of a 

wide variety of local site conditions (see tables 15, 16).
52 PROCEDURES FOR ESTIMATING EARTHQUAKE GROUND MOTIONS

PERIOD, IN SECONDS 

5.0 2.0 1.0 0.5 0.2 0.1 0.05 0.02

1000

FREQUENCY, IN HERTZ

FIGURE 49.—Site-independent vertical response spectra. See table 22 for amplification factors at control points A'-D. 

Modified from U.S. Atomic Energy Comm. Regulatory Guide 1.60 (1973).

TABLE 22.—Vertical design response spectra and relative values of 

spectrum amplification factors for control points

[From U.S. Atomic Energy Commission Regulatory Guide 1.60 U973b)]

Percent of 

critical 

damping

0.5 

2.0 

5.0 

7.0 

10.0

Acceleration

A'(50 Hz)

0.67 

.67 

.67 

.67 

.67

A(33 Hz)

1.0 

1.0

1.0 

1.0 

1.0

B(9 Hz)

4.96

3.54 

2.61 

2.27 

1.90

C(3.5 Hz)

5.67 

4.05 

2.98 

2.59

2.17

Displacement

D(0.25 Hz)

2.13 

1.67

1.37 

1.25 

1.13

In some cases, it is possible to select an ensemble of 

response spectra that were derived from seismograms 

whose local site conditions (Duke and Leeds, 1962;

Matthiesen and others, 1964; Woodward-Lundgren 

and Associates, 1973; Shannon & Wilson and Agbabian Associates, 1976; Gibbs and others, 1976) either 

match or are very similar to those of the proposed construction site. Spectra meeting this condition satisfy 

the seismic and geologi criteria proposed in 1971 by 

AEC for nuclear powerplant sites more easily. To date, 

site-dependent response spectra have not been used extensively in power plant siting because of the limitations of the ground-motion data sample.

The site-matched seismograms and response spectra 

should also match the source-mechanisms and the 

transmission-path characteristics of the designated de-
100

DESIGN RESPONSE SPECTRA FOR SITE

PERIOD, IN SECONDS 

10 1

53

0.01

Note:

Damping factor 5 percent; 

spectra normalized to zeroperiod acceleration of 0.1 a

0.01 0.1 1 10

FREQUENCY, IN HERTZ 

FIGURE 50.—Comparison of site-independent horizontal response spectra produced by three different procedures.

sign earthquake if possible. The ideal case is to have an 

ensemble of seismograms and response spectra that 

closely match the source-path-and-site parameters for 

the proposed construction site. The limits of the data 

sample usually prevent matching any of the parameters except those associated with the site.

Seed, Ugas, and Lysmer (1976) studied a selected set 

of 104 accelerograms (see table 6-9) to establish sitedependent response spectra for four site classifications. 

Their classifications were: (1) rock (28 records), (2) stiff 

soil (31 records), (3) deep cohesionless soil (30 records), 

and (4) soft to medium soil (15 records). In their study, 

ensemble average and mean-plus-one-standarddeviation response spectra were derived for each site 

classification. These spectra, normalized to 0.1 g at 

zero-period, are shown in figure 51.

Site-dependent spectra exhibit the following 

frequency-dependent effects. The spectra from sites

underlain by soft to medium soil and deep cohesionless 

soil have larger amplitudes than the spectra from sites 

underlain by rock and stiff soil for low frequencies (less 

than 1-3 Hz). For higher frequency responses (above 6 

Hz), the spectra from rock and stiff soil sites exhibit 

larger amplitudes than the spectra for deep and soft 

site conditions.

The mean-plus-one-standard-deviation sitedependent response spectra are compared in figure 52 

with the spectrum developed on the basis of AEC Regulatory Guide 1.60. This comparison shows that differences are most pronounced for frequencies below 2-3 

Hz. For sites underlain by stiff soil or deep cohesionless 

soil, higher frequency components of the sitedependent spectra differ from Regulatory Guide 1.60 

spectra by about 25 percent.

The use of site-matched seismograms to develop 

site-dependent design response spectra is superior to
54 PROCEDURES FOR ESTIMATING EARTHQUAKE GROUND MOTIONS

5 percent damped 

DEEP COHESIONLESS SOIL

5 percen* damped 

SOFT TO MEDIUM STIFF CLAY

Mean +1 standard deviation

5 percent damped 

STIFF CLAY

2.0 2.5 3.0 0 0.5 1.0 

PERIOD, IN SECONDS

1.5 2.0 2.5 3.0

FIGURE 51.—Site-dependent mean and mean-plus-one-standard-deviation response spectra for four site classifications (modified from Seed, 

Ugas, and Lysmer, 1976). Spectra are normalized by dividing by peak acceleration.

site-independent procedures. Unlike the siteindependent procedures, site-dependent procedures 

will generally produce ground-motion parameters that 

correspond closely with those expected on the basis of 

the seismological and geologic conditions at the site. 

The limiting factor, however, is that the source mechanisms, transmission-path characteristics, and local 

ground response may not be fully represented by the 

available data. Also, the ensemble of relevant seismograms may be inadequate to permit meaningful statistical evaluations of the variance in the data. For these 

reasons, care must be exercised to ensure that the most 

reasonable procedure for denning the design response 

spectrum is used.

DESIGN TIME HISTORIES

Time histories of particle acceleration, velocity, and 

displacement are the most accurate representations of

the seismic input. These representations are not 

needed for all earthquake-resistant design applications, but they are frequently used when analyzing the 

response of important structures such as nuclear power 

plants.

At the present time, no model is completely adequate 

for deterministically computing the acceleration time 

history of ground motion for arbitrary source-site 

configurations. Current design practice, therefore, 

requires design time histories to be developed in conjunction with the design response spectrum. The time 

histories are constrained to be compatible with the design spectrum for the site and to account for the peak 

ground shaking parameters, spectral intensity, and 

duration of shaking. Compatibility is defined to mean 

that the envelope of all the response spectra derived 

from the time histories lies above the smooth design 

response spectrum throughout the frequency range of 

interest.
100

DESIGN RESPONSE SPECTRA FOR SITE

PERIOD, IN SECONDS 

10 1

55

0.1 0.01

100

10

F 0.5

EXPLANATION

Ensemble average: 

.... Soft-medium soils 

, — Deep conesionless soils 

._ Stiff soil deposits 

_ _ Rock

Damping factor 5 percent; 

spectra normalized to 

zero-period accelera 

tion of 0.1 g

Damping factor 5 percent; 

..._ spectra normalized to 

'-. zero-period accelera 

'• tion of 0.1 g

EXPLANATION

Ensemble mean plus one 

standard deviation:

Soft-medium soils 

._ Deep cohesionlesssoils

—— Stiff soil deposits

—— Rock

Regulatory Guide 1.60

0.5

0.01

FREQUENCY, IN HERTZ

FIGURE 52.—Comparison of site-dependent mean and mean-plus-one-standard-deviation response spectra with

AEC Regulatory Guide 1.60 spectrum.
56 PROCEDURES FOR ESTIMATING EARTHQUAKE GROUND MOTIONS

Several techniques have been proposed for generating time histories (for example, Bycroft, 1960; Housner 

and Jennings, 1969; Rascon and Cornell, 1969; Lynch 

and others, 1970; Seed and Lysmer, 1972). These techniques can be categorized as follows:

1. Use of empirical data. Strong-motion accelerograms of past earthquakes, recorded either in 

the vicinity of the site or at other locations 

that have similar source-path-site characteristics, are used with appropriate modification to develop a design time history for the 

site of interest.

2. Use of calculational models. Because earthquake accelerograms recorded at moderate 

distances have the appearance of random 

time functions, calculational models have 

been developed that use white noise, filtered 

white noise, and stationary and nonstationary filtered white noise to generate design 

time histories.

The present lack of an adequate ensemble of strongmotion accelerograms is the major limitation in developing design time histories.

DETERMINE LOCAL GROUND RESPONSE

It has been recognized and widely documented since 

the early 1900's that the physical properties of the 

geologic materials underlying the recording site can 

significantly modify the amplitude level and spectral 

composition of the ground motion recorded there. 

Structures founded on unconsolidated materials are 

frequently damaged (Page, Blume, and Joyner, 1975; 

Steinbrugge and others, 1975) by ground shaking, and 

the damage distribution on many occasions has been 

recognized to be related to the site. Buildings of a certain class or type (that is, having a certain natural 

period) are often damaged from ground shaking when 

located on geologic materials having a similar characteristic site period, whereas buildings with a different 

natural period located on the same foundation materials are not damaged. The distribution of damage is 

explained by the fact that the local geologic materials 

amplify the ground motion input in a period range that 

coincides with the natural period of vibration for the 

damaged structure.

When the unconsolidated material underlying a recording site modifies the seismic input, the amplitude 

of the surface ground motion increases in a narrow 

range of frequencies and decreases for other frequencies. The amplitude of the amplified ground motion is a 

function of the shear wave velocity, the density and 

material damping, the thickness, water content, and 

where the surface or bedrock topography is irregular, 

the geometry of the unconsolidated deposits and underlying rock. The frequency range that is affected is a 

function of the thickness and physical properties of the 

unconsolidated materials (Seed and Idriss, 1969; Murphy, Weaver, and Davis, 1971; Joyner and Chen, 1975; 

Borcherdt and Gibbs, 1976; Hays, 1977a, 1978).

The amplification effect for surface waves is similar 

to that of body waves except that the thickness of the 

unconsolidated materials also affects the magnitude of 

amplification (Murphy and Davis, 1969; Drake and 

Mal, 1972; Hanks, 1976).

Local ground response is complicated by the fact that 

unconsolidated materials behave nonlinearly. Soils 

have a shear modulus and damping characteristics 

that are strain dependent (fig. 53). Soil nonlinearities 

and inelasticity may attenuate, rather than amplify, 

the surface ground motions relative to the rock ground 

motions under certain conditions.

The topography of the site has also been demonstrated to have an important frequency-dependent effect on ground motion (Bouchon, 1973; Trifunac, 

1973a; Rogers and others, 1973; Boore, 1973; Wong and 

others, 1977).

Figure 54 shows the variation in terms of smooth 

response spectra that would be expected if the same 

earthquake was recorded on stiff, medium, and soft soil 

columns (Smoots and others, 1969). These spectra show 

that the high-frequency components are usually 

damped out fairly rapidly by thick soft soils, reducing 

the level of peak ground acceleration.

i.o

0.8

° 0.6

a £ 0-4

0.2

EARTHQUAKES AND - 

NUCLEAR EXPLOSIONS

""^X. — FAILURES—

(SI ides,liquefaction; 

surface rupture)

LABORAfO'RYfESTS-

- Resonant column ——.——U X/////

I—Torsional column ' '

10°

SHEAR STRAIN, IN PERCENT

FIGURE 53.—Effect of strain level y on shear modulus and damping 

of soils (from Seed and Idriss, 1969).
100.0

DETERMINE LOCAL GROUND RESPONSE

PERIOD, IN SECONDS 

10 1.0

57

10.0

0.01 I /\ I

CRITICAL RESONANT PERIOD RANGES FOR SOIL SITES

\

FREQUENCY, IN HERTZ 

FIGURE 54.—Comparison of smooth response spectra for three soil columns (modified from Smoots and others, 1969).

From the present United States earthquake data 

sample, 104 horizontal-component accelerograms (see 

table 15) can be grouped in four broad site classifications: (1) rock or rocklike material having a shear 

wave velocity at low (0.0001 percent) strains of at least 

760 m/s, (2) stiff soil (firm soils less than about 45 m 

thick), (3) cohesionless soil (sandy soils exceeding 80 m 

in thickness), and (4) soft to medium-stiff clay. Seed, 

Ugas, and Lysmer 1976) analyzed the horizontal acceleration spectra representing these four site 

classifications and determined normalized average 

spectral response for each classification (fig. 55). 

Significant amplification relative to rock is indicated 

for sites underlain by soft-to-medium clay and sandsites for periods greater than 0.5 second.

Empirical data showing the effect of site geology on 

body waves have been obtained from the nuclear explosion safety program at the Nevada Test Site (Murphy, 

Weaver, and Davis, 1971; Hays, 1972a, b; Hays, 1978) 

and earthquake aftershocks (Murphy, Lynch, and O'Brien, 1971; Hays, 1977a). A classic example of bodywave amplification is illustrated by ground-motion

data recorded at Tonopah, Nev. (fig. 39). A pair of seismograph stations located 183 m apart and underlain

< 3

Total number of records analyzed: 104 Spectra for 5 percent damping

/Soft to medium clay and sand; 15 records

,Deep cohesionless soil (>80 m); 30 records 

.Stiff soil ( <45 m); 31 records 

/Rock; 28 records

0.5 1.0 1.5 2.0 

PERIOD, IN SECONDS

2.5 3.0

FIGURE 55.—Average acceleration response spectra for four site 

classifications (from Seed, Ugas, and Lysmer, 1976).
58 PROCEDURES FOR ESTIMATING EARTHQUAKE GROUND MOTIONS

respectively by dacite, an igneous rock, and 13.1 m of 

mine tailings (fill) have recorded input ground motions 

with a dynamic range of 10~5 -10~3 g from more than 

20 nuclear explosions located about 100 km away. The 

low acoustic-impedance contrast of the fill relative to 

rock causes the ground-motion spectral components at 

around 7 Hz to be amplified by a factor of six. The mean 

site transfer function is repeatable from event to event 

with a standard deviation (<r) of 1.30. The level of peak 

ground acceleration is also larger by a factor of about 

two at the station underlain by fill. The strain levels 

induced in the fill were low (10~5 to 10"4 ) because of the 

large source-to-recording site distances; therefore, the 

fill responds almost elastically to the input ground 

motions. A second example of body wave amplification 

was observed in the Glendale, Calif, area. Measurements of ground motion from the aftershocks of the 

1971 San Fernando earthquake were made at a 

number of locations in San Fernando Valley. Two stations in Glendale (fig. 56) exhibit significant relative 

ground response. The mean site transfer function is 

repeatable from event to event with a standard deviation (o-) of 1.50.

Las Vegas Valley in southern Nevada is underlain 

by Cenozoic alluvium of widely varying thickness (Diment and others, 1961; Longwell and others, 1965). It 

has been recognized since 1970 (Davis and Lynch,

10.0

FREQUENCY, IN HERTZ

FIGURE 56.—Example of site transfer function for two sites in the 

Glendale, Calif, area derived from aftershocks of the 1971 San 

Fernando earthquake.

1970, Bennett, 1974) that the horizontal spatial variation of ground response in Las Vegas from nuclear explosions (epicentral distances of about 150 km) is 

significant. Peak ground-motion parameters differ by a 

factor of about four and response-spectra amplitudes by 

a factor of about ten (fig. 57). These differences are 

consistently observed at stations that are only a few 

kilometers apart in Las Vegas Valley. The standard 

deviation for the mean ground-response of any two 

sites is about 1.30. The consistency of the site transfer 

functions indicates that the relative ground response 

depends primarily on the local site geology, not on 

source or transmission path parameters. The strong 

frequency-dependent nature of the ground response, 

with substantial variability at long periods (>1 s) and 

essentially uniform response at short periods (0.1-0.5 

s), suggests that the principal effects are caused 

primarily by long-period surface waves propagating 

unevenly in the variable surface alluvium. The ground 

response derived from the radial component of spectral 

velocity for the long-period band 3.33-4.50 s correlates 

fairly well with the estimated thickness of the alluvium in Las Vegas Valley (fig. 58).

How ground motion varies with depth is not well 

known. One of the fairly recent studies (Murphy and 

West, 1974) used identical seismograph systems 

emplaced in tuff at the bottom of a 41-m drill hole at 

Beatty, Nevada and at the surface on alluvium. A large 

number of nuclear explosions were recorded on this 

array and established the repeatability of the site 

transfer function (fig. 59) for low-strain levels. The 

amplitudes of the spectral components, especially those 

in the 0.05-0.5 second range, decrease with depth. The 

most significant decrease occurs for periods in the 

vicinity of 0.3 second, the characteristic site period 

(that is, the period that corresponds to four times the 

thickness of the alluvium divided by its shear wave 

velocity). This experiment also demonstrated that the 

input ground motion at the base of the alluvium is 

essentially identical (except for the free-surface effect) 

to the ground motion observed at a surface site located 

on rock. The limited data available at present are 

inadequate to prove the common assumption of a 

broad-band spectrum at depth.

The present lack of data to show how ground-motion 

time histories and their response spectra change with 

depth is a major source of uncertainty in some earthquake-resistant design engineering applications such 

as waste isolation.

Although the procedure for predicting site amplification effects still has some elements of controversy, empirical data from past earthquakes and laboratory
DETERMINE LOCAL GROUND RESPONSE 59

100.0

10.0

100.0

0.1

0.01

0.01 1.0

PERIOD, IN SECONDS

10.0

10.0

0.01

0.01 0.1 1.0 

PERIOD, IN SECONDS

10.0

LAS VEGAS AREA

EXPLANATION

Contour showing depth of

alluvium, in meters 

Dashed where position uncertain

• • 

Seismograph stations

FIGURE 57.—Location of seismograph stations and thickness of alluvium in Las Vegas Valley and variation of horizontal velocity response 

spectra for two stations and their site transfer function. Ground motions are from nuclear explosions at the Nevada Test Site.
60 PROCEDURES FOR ESTIMATING EARTHQUAKE GROUND MOTIONS 

GROUND RESPONSE THICKNESS OF ALLUVIUM

Contour showing radial component of 

relative spectral velocity response 

in the period band 3.33-4.50 s

Seismograph station

•0.8-

Contour showing estimated thickness 

of alluvium, in kilometers

EXPLANATION

• 

Seismograph station

FIGURE 58.—Radial component of relative ground response in the period band 3.33-4.50 s and thickness of alluvium, Las Vegas Valley (from 

Murphy and Hewlett, 1975). Ground response is calculated relative to station 801.

100.0 I III

Site model

= 490 m/s I

= 1.8g/cm3 j!

1 = 10 T

$2 =1740 m/s

i i I I r

Site transfer function

10.0

FREQUENCY, IN HERTZ 

FIGURE 59.—Variation of ground motion with depth, Beatty, Nev.

studies (for example, Idriss and Seed, 1968; Espinosa 

and Algermissen, 1972; Seed and others, 1972; Hays 

and King, 1973; Warrick, 1974; Campbell and Duke, 

1974; Page, Boore, and Dieterich, 1975; Borcherdt and 

others, 1975; Seed, 1975; Joyner and Chen, 1975; Hays 

and others, 1979) suggest the following guidelines:

1. Spectral ratios (transfer functions) of the 

ground motion at sites underlain by unconsolidated materials and at sites underlain by 

rock may be as high as 10 to 1 for some 

periods when low-strain ground motions are 

involved. However, this ratio is generally 

thought to decrease substantially for intense 

high-strain ground motions, depending on 

the material properties.

2. Amplification is a sensitive function of the 

thickness of the unconsolidated materials 

overlying rock; increasing thickness generally lengthens the period at which amplification occurs.

3. The shorter period spectral components are 

usually damped out fairly rapidly by thick
DETERMINE LOCAL GROUND RESPONSE 61

soft materials. This effect tends to reduce the 

level of peak ground acceleration when the 

peak rock acceleration exceeds 0.1 g.

4. The top 30 m or so of a deposit of unconsolidated 

material frequently has the most critical effect upon amplification and should be investigated thoroughly to determine its dynamic 

properties.

5. Unconsolidated material below the topmost 30 

m generally does not need to be investigated 

for nonlinear behavior unless the specific 

material is especially sensitive to ground motion.

6. For long-duration high-strain ground motions, 

nonlinear effects become very important. The 

general effects of nonlinear behavior are to

decrease the amplification level (relative to 

what would have occurred for linear behavior) and to lengthen the characteristic site 

period.

For low-strain earthquake ground motions, unconsolidated materials can respond in a manner close to 

that which the theory of elastic wave propagation predicts. These effects represent realistic upper bounds of 

ground response. Parametric curves (fig. 60) published 

by Environmental Research Corporation (1974b) for 

amplification of incident, plane SH waves (Haskell, 

1960) show how the response characteristics of a lowvelocity material overlying rock change as the physical 

properties of the material and the angle of wave incidence change. The curves are plotted against the dimensionless parameter d/(3i • f where d is layer thickDIMENSIONLESS FREQUENCY

FIGURE 60.—Parametric curves for amplification of SH waves. A, f32 =2/3,, i=0, elastic response. B, /32 =4/3,, i=0°, elastic response. C, 

/32 =6/3,, f =0°, elastic response. D, /32 =2/3,, i = 30°, elastic response. E, /32 =4/3,, i = 30°, elastic response. F, /32 =6/3,, i=30°, elastic 

response. From Environmental Research Corporation (1974b).
62 PROCEDURES FOR ESTIMATING EARTHQUAKE GROUND MOTIONS

ness, /8i is shear wave velocity of the low- velocity layer, 

and f is frequency. For a fixed angle of incidence, the 

amplification factor depends only upon the acoustic 

impedance contrast and not upon the actual values of 

shear-wave velocity and density. Curves are given for 

two density contrasts (p2 /pi = 1.5 and 2.5), three 

shear- wave velocity contrasts (/82//3i=2, 4, and 6), and 

two angles of incidence, (i=Q° and 30°).

To use the parametric curves, one needs values of the 

ratio of shear wave velocities fr/fr and thickness d of 

the low- velocity material. The ratio dlftl provides the 

scale factor which converts the abscissa to frequency in 

hertz.

An example showing how the site transfer function 

is estimated is depicted in figure 61. If the density ratio 

is 1.35, the velocity ratio 7.5, and the angle of incidence 

30°, the amplification factor is interpolated from figure 

60F as follows:

A = p)8

A' p'

7-8 = (1.5) (6) 

A' (1.35) (7.5)

0rA'=

Thus, the amplification is a factor of 8.8. The resonant 

frequency is found from the relation (fig. 60 F):

or

183

so f is approximately 7 Hz for elastic response. 

10

10

FREQUENCY, IN HERTZ

FIGURE 61.—Example of site transfer function, elastic response, a, 

and a2 are P-wave velocities, /8, and /82 are S-wave velocities, and p, 

and p2 are densities.

Amplification above 10 Hz is not normally considered because high-frequency shear waves attenuate 

very rapidly.

The site transfer function for the case of multiple 

low-velocity layers can also be derived by using the 

Haskell (1960) matrix formulation or by other numerical methods. An estimate can be obtained by using 

figure 60 and combining the response calculated for 

each individual layer.

Site amplification modeling is especailly needed for 

the case of high-strain ground-motion loads. Because of 

the increased number of physical parameters and the 

present gaps in knowledge (Kanninen and others, 

1970) about inelastic behavior of solids, comprehensive 

parametric curves cannot be provided. The empirical 

procedures proposed for the 1976 Uniform Building 

Code (see next section) can be used to model the highstrain case and will give reasonable estimates of the 

effect. Also, some of the general curves (figs. 62-64) 

that have been published (Imbsen and Gates, 1973) 

permit estimates to be made for high-strain loading 

conditions. These curves were derived with the 

SHAKE program (Schnabel, Lysmer, and Seed, 1972).

Values of the peak horizontal rock acceleration and 

the thickness of the unconsolidated material are 

needed when estimating amplification effects for 

high-strain earthquake ground motion. The acceleration estimates can be derived from maps such as shown 

in figure 42 or by empirical "deconvolution" techniques 

(for example, Lysmer and others, 1971; Schnabel, Seed, 

and Lysmer, 1972; Papadakis and others, 1974). By 

multiplying the peak rock acceleration by the rock response factor (fig. 62), an estimate of the elasticresponse spectrum for rock is obtained. Amplification

FREQUENCY, IN HERTZ 

5.0 3.33 2.5 1.67 1.25 1.0 0.67 0.5 0.33 0.25

Peak acceleration levels

0.1 0.2 0.3 0.4 0.6 0.8 1.0 1.5 2.0 3.0 4.0 5.0

PERIOD, IN SECONDS

FIGURE 62.—Normalized rock response spectrum, 5-percent damping 

(modified from Imbsen and Gates, 1973).
DETERMINE LOCAL GROUND RESPONSE 63

effects relative to rock are determined by multiplying 

the appropriate curve of figure 63 and the estimated 

elastic-response spectrum for rock (fig. 62). This product gives the approximate amplification effects.

The peak rock acceleration that is transmitted to the 

soil column has a major effect on the amplification 

spectra. As the peak rock acceleration increases, the 

amplification level decreases and the predominant 

period of resonance lengthens (fig. 64).

The generalized parametric curves of figures 63-65 

may not provide the level of precision needed for predicting amplification effects at the site of interest. In 

this case, it might be desirable to utilize a finiteFREQUENCY, IN HERTZ 

5.0 3.33 2.5 1.67 1.25 1.0 0.67 0.5 0.33 0.25

Peak rock acceleration = 0.2 g

i i___i i j__i___i

0.1 0.2 0.3 0.4 0.6 0.8 1.0 1.5 2.0 3.0 4.0 5.0

PERIOD, IN SECONDS

FIGURE 63.—Parametric curves for high-strain amplification of SH 

waves and three depths of unconsolidated materials (modified from 

Imbsen and Gates, 1973).

FREQUENCY, IN HERTZ 

5.0 3.33 2.5 1.67 1.25 1.0 0.67 0.5 0.33 0.25

0.1 0.2 0.3 0.4 0.6 0.8 1.0 1.5 2.0 3.0 4.0 5.0 

PERIOD.IN SECONDS

FIGURE 64.—Effect of peak acceleration level on amplification 

(modified from Imbsen and Gates, 1973).

element program such as SHAKE (Schnabel, Lysmer, 

and Seed, 1972) or QUAD-4 (Idriss and others, 1973), 

or the technique proposed by Joyner (1975) to model 

the site in more detail. The degree of accuracy to which 

the physical properties of the rock and unconsolidated 

materials at the site are known is the primary consideration before deciding to use sophisticated calculational procedures.

Several new earthquake-design provisions, including a procedure for estimating the characteristic site 

period, were proposed for incorporation in the 1976 

Uniform Building Code (Freeman, 1975). These provisions will be discussed below.

SUMMARY OF UNIFORM BUILDING CODE PROCEDURES

The most widely used standard for earthquakeresistant design is the Structural Engineers Association of California (SEAOC) Code. The SEAOC Code, 

which was incorporated into the 1973 Uniform Building Code, contains the following commentary about 

aseismic design:

Basically, the problem is that the entire phenomenon, from the 

earthquake ground motion to the realistic response of structures to 

this ground motion, is very complex. Codes, of necessity, are generalized simplifications. Complex mathematical analyses have been 

made on simple and idealized structures subjected to past earthquake ground motions. These have been helpful in improving our 

understanding of the phenomenon. However, for purposes of design 

of the vast majority of structures, it is necessary to reduce this complex, dynamic problem to one of equivalent static lateral forces. 

These can be related to the dynamic characteristics of the structure. 

They provide the basic code criteria, applied with stresses within the 

elastic limit. However, in applying these simplified concepts, the 

structural engineer must do this with sound judgment that can only 

be developed with experience, observation, and study of the earthquake phenomenon. He must be especially aware of the nature of the 

response of the particular structure under design and he must evaluate the capabilities of that structure to perform satisfactorily beyond 

the elastic-code-stipulated stresses.

The SEAOC Code is a minimum standard to assure 

public safety. The requirements are intended to 

safeguard against major failures and loss of life. The 

aim of the code is to provide structures that will:

1. resist minor earthquakes with damage;

2. resist moderate earthquakes without structural 

damage, but with some nonstructural damage;

3. resist major earthquakes without collapse, but 

with some structural and nonstructural 

damage.

The basic formula used in the 1973 Uniform 

Building Code is

V=ZKCW

where

V is base shear or total lateral force to be resisted
64 PROCEDURES FOR ESTIMATING EARTHQUAKE GROUND MOTIONS

at the base of the structure,

Z is zone factor, based on the Algermissen (1969) 

U.S. seismic risk map (fig. 65) having four seismic risk zones. The numerical values of Z for the 

four zones are: Z = l for zone 3; Z=0.5 for zone 2; 

Z=0.25 for zone 1; and Z=0 for zone 0.

K is an arbitary factor that, in effect, is a safety 

factor adjustment based on an arbitrary 

classification of the type of construction. It recognizes that different degrees of hazard against 

collapse are inherent in different types of construction; K has no relation to the actual forces 

expected.

C is a coefficient related to the period of the structure. A plot of C against period represents a response spectrum and roughly parallels that derived from the 1940 Imperial Valley, Calif, 

earthquake accelerogram recorded in El Centro, 

Calif., and

W is the weight of the structure.

Several new design provisions were proposed for the 

1976 Uniform Building Code (Freeman, 1975; Nosse,

1975; Seed, 1975; and Donovan, 1975). The basic consideration is that, in general, structures shall be designed and constructed to resist minimum total lateral 

seismic forces assumed to act nonconcurrently in the 

direction of each of the main axes of the structure in 

accordance with the formula

V = ZIKCSW .

In this formula, Z is a zoning factor based on the preliminary design regionalization map (fig. 66) prepared 

by the Applied Technology Council (1976). K is a numerical factor determined by the type of framings,

0.067

C =

where T is the period of the building, and S is the 

soil-structure interaction factor or resonance coefficient, which is a function of the building period and the 

characteristic site period Ts . I is the importance factor 

for the building and W is the total dead load or weight 

of the building.

The values of Z, the seismic zoning factor, are defined as equal to 1 for locations in zone 4, % for locaEXPLANATION

ZONE o-No damage.

ZONE 1—Minor damage; distant earthquakes may cause 

damage to structures with fundamental periods 

greater than 1.0 second; corresponds to intensities 

V and VI of the Modified Mercalli scale

ZONE 2—Moderate damage; corresponds to intensity VII

of the Modified Mercalli scale.

ZONE 3—Major damage; corresponds to intensity VIII and 

higher of the Modified Mercalli scale.

This map is based on th 

the Modified Mercalli scal

own distribution of damaging earthquakes and 

intensities associated with these earthquakes.

115°

FIGURE 65.—United States seismic risk zones. Based on Modified Mercalli intensity scale and the distribution of damaging earthquakes 

(from Algermissen, 1969). The map of seismic risk zones in the 1979 Uniform Building Code is based on this map.
DETERMINE LOCAL GROUND RESPONSE 65

125° 120° 115° 110° 105° 100° 95'

EFFECTIVE 

CONTOUR ACCELERATION

115° 110° 105 100° 95° 90° 85° 80° 75°

FIGURE 66.—Preliminary design regionalization proposed for 1976 Uniform Building Code (from Applied Technology Council, 1976).

tions in zone 3, % for locations in zone 2, and 3/16 for 

locations in zone 1.

Values of S, the soil-structure interaction factor, 

range from 1 to 1.5 (fig. 67.) Both theory and empirical 

data suggest the S should have its lowest values when 

the ratio of the building period T to the characteristic 

site period Ts is either very low or very high. The 

maximum value occurs when TITS =1.

Determination of the characteristic site period Ts is 

an important new proposal. Studies of ground-motion 

characteristics and building damage from past earthquakes have shown that the characteristic period at 

which maximum damaging effects occur is approximately equal to the fundamental period of the soil deposit overlying rocklike formations. A rocklike formation may be considered as any earth or rock material in 

which the shear-wave velocity at small strains (0.0001 

percent) is about 760 m/s or greater. Shear-wave velocities of soils approach 760 m/s at depths of about 152 m; 

therefore, it is unnecessary to consider greater depths 

when determining the value of Ts . Values of Ts will 

vary from a minimum value of 0.5 s for shallow, stiff 

soil deposits to a maximum value of 2.5 s for deep, soft 

soil deposits (Seed, 1975).

An equivalent single-layer method was proposed for 

calculating the characteristic site period. The basic relation is

T 

J- s 

_ 

—

4H

where H is the depth of soil over bedrock, /8 is the 

average shear- wave velocity of the soil layer as measured under low-strain conditions in the field, and-R is a 

correction factor to allow for the reduction in shearwave velocity when the soil is excited by high-strain 

ground motion during an earthquake. It is necessary to 

specify the level of base rock excitation in order to assign values to.R. Values of.R have been established on 

the basis of the "effective peak acceleration" obtained 

from the design regionalization map (fig. 66) as follows:

1. zone 1: A magmtude-6 earthquake producing 

a peak effective acceleration of 0.1 g corresponds to a value of 0.9 for R.

2. zone 2: A magnitude-6 earthquake producing 

a peak effective acceleration of 0.2 g corresponds to a value of 0.8 for R. 

zone 3: A magnitude-7 earthquake producing 

a peak effective acceleration of 0.3 g corre3.
66 PROCEDURES FOR ESTIMATING EARTHQUAKE GROUND MOTIONS

0.5 1.0 1.5 2.0 2.5

BUILDING PERIOD 

SITE PERIOD

FIGURE 67.—Soil-structure interaction factor proposed for 1976 Uniform Building Code (from Seed, 1975).

spends to a value of 0.67 for R. 

4. zone 4: A magnitude-7 earthquake producing 

a peak effective acceleration of 0.4 g corresponds to a value of 0.67 for R.

As an example, consider a 12.2-m layer of sand with 

a shear wave velocity of 274 m/s overlying rock in Los 

Angeles (zone 4). For this example,

T -t s =

(4) (40)

(0.67) (900) = 0.27 seconds

This value is less than the minimum allowable value of 

0.5 s, so the value of Ts used in seismic design for this 

example would be 0.5 second.

For multilayered soil profiles, the equivalent singlelayer procedure can be used to compute an approximate value for Ts _ The basic relation for Ts ,

T *-K =

4H Rfi'

now let H be the total thickness of the unconsolidated 

material overlying bedrock and (3 the mean shear-wave 

velocity, weighted in proportion to the velocities and 

thicknesses of the individual layers as follows:

i = I

where )8, and Hi are the shear-wave velocity and thickness of each individual layer.

The importance factor / has also been proposed for 

incorporation in the Uniform Building Code formula 

for base shear to allow higher force levels to be assigned to structures housing certain facilities. The values of/ range from 1.0 to 1.5, with the highest value 

being assigned to essential facilities such as hospitals, 

communication centers, and fire stations where the acceptable level of risk from earthquakes is to be reduced.

The overall effect of all the new provisions is to provide for an increase in the design base shear.

The details about structural design in terms of the 

Uniform Building Codes are beyond the scope of this 

paper. References such as Degenkolb, Dean, and Wyllie (1971), Freeman (1975), Seed (1975), and Donovan 

(1975*) provide information on this subject for the interested reader.

DEFINE UNCERTAINTIES OF THE 

GROUND-MOTION DESIGN VALUES

Specification of the uncertainty model for the 

ground-motion design values is a complex task. The 

model depends upon the seismotectonic province where 

the earthquake occurs and the physical parameters 

controlling the source, path, and local ground-response 

effects (table 23). The complexity of the problem arises 

from two factors: (1) the statistical distribution of 

many of the physical paramenters is either unknown 

or poorly known and (2) the precise way to combine the 

uncertainties of the individual physical parameters of 

the system is not clear, even if the statistical distribution for each parameter were well known. An example 

of the second factor is illustrated by the problem of 

combining the uncertainty in magnitude and seismic 

moment, two parameters that affect the low-frequency 

ground motion characteristics and are related to the 

length of fault rupture.

At the present time, it is impossible to specify the exact 

location and magnitude of the earthquakes that will 

affect a site during the life of a structure. This difficulty is a consequence of the short incomplete seismicity record, the lack of regional seismicity networks to 

define current seismicity patterns, and the lack of 

adequate geologic data to define the earthquake potential of a 3-dimensional volume of rock. An example will 

illustrate the problem. Yucca Flat and Pahute Mesa, 

two areas on the Nevada Test Site, are probably the
UNCERTAINTIES OF THE GROUND-MOTION DESIGN VALUES 67

TABLE 23.—Uncertainties in physical parameters that affect ground

motion

Physical 

parameter

Effect on 

ground motion

Uncertainty and 

functional dependence

Seismicity Parameters

Seismic.____Zone controls location 

source zones of earthquakes.

Recurrence 

rates (6)

-Defines frequency 

of occurrences.

Upper-bound --Establishes groundmagnitude motion design levels.

Not known. Function of 

seismicity record, 

geologic, and tectonic 

history.

Average 6 = 0.45 in 

eastern U.S. where log 

N=a-bl; cr=f(N).

Not known. Function 

of completeness and 

length of seismicity 

record and geologic 

data on fault rupture.

Source Parameters

Epicenter___-Establishes location of 

design earthquake.

Focal depth___-Affects partition of

body-and surface-wave 

energy

Magnitude __ 

(mb ,ML ,Ms )

Seismic.--_ 

moment (M6

_Affects low frequencies 

and ground-motion 

scaling.

__Affects low frequencies, 

) especially for great 

earthquakes.

Stress drop 

(A<r)

Fault length

(L) 

Epicentral __

intensity (/„

..Affects high frequencies and peak 

acceleration.

_-Affects magnitude and

moment; duration. 

--Affects site accelera- 

) tion (AH and .A,).

Best location accuracy 

is 1 km; worst is 50 km. 

Function of regional 

velocity model and instrument locations.

Best location accuracy 

is 2 km; worst is 50 

km. Function of regional velocity model 

and instrument 

locations.

Best accuracy is 0.1 

unit; worst is > 1 

unit. Function of instruments and regional 

calibration.

logM0 ~3/2Ms until 

M0 s*102S dyne-cm. 

M0 = 21.9+3 logL with 

scatter a factor of 2. 

Function of instrument 

dynamic range.

ACT has a log-normal distribution.

Earthquakes exhibit 

a constant average 

stress drop of about 10 

bars 2<r= one order of 

magnitude. Function 

of moment determination.

M, = 1.235 +1.243 log L; 

CT=0.93.

log AH = 0.24 

IMM + 0.26; 

CT=2.19 

log A i- = 0.28 

IMM - 0.40; 

CT=2.53 

(worldwide data)

Path Parameters

Rate of atten- _ 

uation of 

seismic 

energy with 

distance.

-Establishes peak ground- Not well defined because 

motion values at site of limitations on data 

and frequency-de- sample. CT for peak acpendent signature. celeration vs distance 

relation is 2.01 for 

worldwide data and 

1.62 for San Fernando 

earthquake. CT for peak 

velocity vs distance 

is 1.5 for moderate 

U.S. earthquakes.

Local Ground Response

Soil/rock ____Affects amplitude of 

acoustic im- ground motion, 

pedance (p/3) 

contrasts.

Not well defined. Physical properties depend 

on geophysical and laboratory measurements.

TABLE 23.—Uncertainties in physical parameters that affect ground 

motion—Continued

Physical 

parameter

Effect on 

ground motion

Uncertainty and 

functional dependence

Local Ground Response—Continued

Soil thickness--Affects dominant freand geometry, quency, duration,

pseudo-ellipticity of 

wave particle motion, 

and damping.

Ground-motion data 

sample for each rock 

and soil classification is small. 

Not well defined. Depends on geophysical, 

geologic, borehole, and 

ground-motion data.

Strain level of Determines if ground 

input ground response is linear 

motion. or nonlinear.

Site transfer _ -Determines relative 

function. ground response 

between two sites.

Not well defined because of limitations 

of the ground-motion 

data sample, especially 

near the source. 

Repeatable with <r=1.30 

for nuclear explosions 

and 1.50 for earthquake aftershocks.

only areas in the United States that come close to fulfilling all three requirements listed above. More than 900 

man-years of geologic mapping and many deep drill 

holes have defined the 3-dimensional structure reasonably well. A regional seismicity network has defined 

the current seismicity patterns. Fairly good correlations have been made between current seismicity and 

specific active faults. Even with this information, assigning a magnitude to a given active fault on the basis 

of the assumption that 50-percent of its length is available to rupture gives a magnitude value with a standard deviation of almost 1 unit (see Mark, 1977).

A general model based on the use of mean values for 

a "lumped parameter" wave-progagation system provides some insight. The basic relation is given by

^ Total = (1 + -iTT" ) (^ source ~+~ ^ path + ^ site) 

system J\

where N is the size of the data sample, 

Sgource is the variance of the source, 

Spath is the variance of the transmission path. 

(Note: variance = S = log cr where cr is the geometrical 

standard deviation.)

The values of S can be approximated from values of cr 

reported in the literature. The distribution is assumed 

to be log-normal in each case, a reasonable assumption. 

The studies by N. M. Newmark Consulting Engineering Services (1973) and J. A. Blume and Associates, 

Engineers (1973) provide a value of 0.30 for Ssource (cr = 

1.35). Donovan (1973) studied a worldwide data sample 

of 515 peak acceleration values to derive a relation for 

peak acceleration and distance. The variance for this 

"general" transmission path is 0.70 (cr = 2.01). The 

studies of ground response by Murphy, Weaver, and 

Davis (1971) and Murphy, Lynch, and O'Brien (1971)
68 PROCEDURES FOR ESTIMATING EARTHQUAKE GROUND MOTIONS

show that the mean site amplification is repeatable for 

low-strain ground motions with a variance that ranges 

from 0.26 to 0.41 (corresponding values of cr are 1.30 

and 1.50). A reasonable value of the "general" site 

variance is 0.41. Combining these numbers after adjusting for the size of the data sample gives

S2Totai = 0.095 + 0.491 + 0.178

system

STotai = 0.87407 and

system

cr = log- 1 0.87407 = 2.40

Thus, an estimate of the geometrical standard deviation for mean ground motion estimates is about 2.40. 

However, one should remember that upper-bound values, not mean values, are used to define many 

ground-motion estimates. This practice suggests that 

the ground-motion estimates in some cases (for example, nuclear powerplants) may be at the one or twostandard deviation level relative to the mean value 

expected to occur at the site.

It is clear that the uncertainty in the seismic attenuation relation contributes most to the total uncertainty. One significant way to reduce the uncertainty 

(or the conservatism) in the ground-motion estimates 

is to "calibrate" the region's attenuation characteristics. As an example, consider the situation where the 

San Fernando Valley, California attenuation relation 

can be applied instead of the "general" relation. Donovan (1973) showed that the value of variance is 0.48 (cr 

= 1.62) for the San Fernando Valley. Substituting 0.48 

instead of 0.70 and retaining the other values gives a cr 

of 2.03 for the total system; therefore, the "calibrated" 

attenuation function provides a significant reduction 

in total uncertainty.

SEISMIC DESIGN TRENDS FOR THE FUTURE

There is little doubt that empirical procedures 

currently used for defining earthquake ground motion 

will be refined and extended in the future. However, 

greatly improved capability for specifying earthquake 

ground motion will require a significantly improved 

data base. Regional seismicity and strong-motion accelerograph networks must be expanded. Better 

geologic and geophysical data and analysis are needed 

to define the earthquake potential and upper-bound 

magnitude in different geographical regions and to establish the dynamics of faulting and recurrence intervals for specific faults. Knowledge of the origin of intraplate earthquakes, which seem to have different 

causes than the earthquakes that occur along plate 

boundaries, is needed in order to assess more accurately the earthquake potential of seismically quiet regions like the Eastern United States.

The quality of the data base is one of the most important factors leading to the capability for precise 

specification of earthquake ground motion. The "ideal" 

data base should contain complete information about 

the site and the region surrounding it, including a 

well-defined statistical distribution for each parameter 

and parametric relation used to make predictions of 

ground motion at the site. The basic components are:

1. Seismicity parameters

A complete record of all historic earthquakes;

Information about the source parameters (epicenter, focal depth, source mechanism and 

dimensions, magnitude, stress drop, effective 

stress, seismic moment, and rupture velocity) 

of each historic earthquake;

Definition of the current seismicity patterns;

Recurrence relations for the region and for 

well-defined seismic source zones in the region.

2. Seismotectonic features

Maps showing seismotectonic provinces and capable faults;

Information about the earthquake generating 

potential of each seismotectonic province, including: information about the geometry, 

amount, and sense of movement, the temporal history of each fault, and the correlation with historic instrumental earthquake 

epicenters;

Correlation of historic earthquakes with tectonic models to estimate the upper-bound 

magnitude of the earthquake likely to be associated with each tectonic feature.

3. Seismic attenuation function

Isoseismal maps of significant historic earthquakes occurring in the region;

The uncertainty of Modified Mercalli intensity 

distance-scaling relations;

Peak ground-motion distance-scaling relations 

for the region;

Frequency-dependent distance-scaling relations for the region.

4. Characteristics of ground shaking

Isoseismal maps of significant historic earthquakes that have affected the site; 

Ensembles of strong ground-motion records 

adequate for calibrating the near field, the 

regional seismic-wave transmission characteristics, and the local ground response for a 

wide range of earthquake source mechanisms.

5. Earthquake spectra

Ensembles of spectra (Fourier, power spectral 

density, and response) adequate for calibrat-
REFERENCES CITED 69

ing the near field, the transmission path, and 

the local ground response for a wide range of 

earthquake source mechanisms. 

6. Local ground response

Strong ground-motion records at surface and 

subsurface locations for a wide range of 

strain levels;

Seismic-wave transmission characteristics of a 

wide range of unconsolidated materials overlying rock for a wide range of strain levels; 

Information on the static and dynamic properties of the near-surface site materials, including: seismic shear-wave velocities, bulk 

densities, and water content.

The faulting mechanism, more than any other 

geologic parameter, requires a great deal of additional 

research. The direction, length, and type of faulting 

during an earthquake greatly affect the near- and farfield radiation patterns of the body and surface waves 

generated by the earthquake. As progress is made in 

understanding faulting, important questions can be 

answered, such as:

1. What are the important differences in the nearand far-field seismic-radiation patterns for 

different fault systems?

2. What is the best way to characterize the nearand far-field seismic radiation patterns in 

areas of the United States where surface 

faulting is uncommon (for example, New 

Madrid, Missouri and Charleston, South 

Carolina areas)?

Although the present empirically based procedures 

will remain in use for some time, improved procedures 

will evolve as advances in physical understanding and 

capability to model numerically occur. Improved procedures will incorporate the continually increasing 

knowledge in seismology and will improve the precision of earthquake ground-motion estimates. Some of 

the new approaches that are likely include:

1. Use of seismic moment as a measure of source 

strength instead of or in addition to magnitude,

2. Use of constant stress-drop source spectra 

scaled as a function of seismic moment instead of magnitude,

3. Interpretation of peak ground-motion parameters in terms of source spectra,

4. Interpretation of duration of strong ground motion in terms of length of fault rupture and 

rupture velocity,

5. Development of spectral values to correlate 

with specific values of the Modified Mercalli 

intensity scale,

6. Development of frequency-dependent seismic

attenuation laws for many different geographic regions of the United States. 

Earthquake-resistant design is fortunate to be a 

dynamic field in which many advances in basic 

knowledge are being made.

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