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Predictive Model for Important 

Ground Motion Parameters 

Associated with Large and 

Great Earthquakes

U.S. GEOLOGICAL SURVEY BULLETIN 1838

Predictive Model for Important 

Ground Motion Parameters 

Associated with Large and 

Great Earthquakes

By J. F. EVERNDEN and J. M. THOMSON

Presentation of data and model for prediction of seismic 

intensities and various other damage parameters resulting 

from earthquakes throughout the conterminous 

United States and the world

U.S. GEOLOGICAL SURVEY BULLETIN 1838
DEPARTMENT OF THE INTERIOR 

DONALD PAUL MODEL, Secretary

U.S. GEOLOGICAL SURVEY 

Dallas L Peck, Director

UNITED STATES GOVERNMENT PRINTING OFFICE: 1988

For sale by the Books and Open-File Reports Section, 

U.S. Geological Survey, Federal Center, 

Box 25425, Denver, CO 80225

Library of Congress Cataloging in Publication Data

Evernden, J.F., 1922-

Predictive model for important ground motion parameters associated with large

and great earthquakes. 

(U.S. Geological Survey bulletin ; 1838) 

Supt.ofDocs.no.: I 19.3;1838 

1. Earthquake prediction Mathematical models. I. Thomson, Jean Marie.

II. Title. III. Series.

QE75.B9 no.1838a 557.3s 87-600483 

[QE538.8] [551.2'2]
CONTENTS

Abstract 1

Introduction 1

Part I: Data and analysis required for development of the model 1

Introduction 1

Prediction of seismic intensity 2

Correlation of strong motion parameters and intensity 3

Maximum acceleration versus intensity 4

RMS acceleration versus intensity 4

Maximum velocity versus intensity 5

Maximum displacement versus intensity 5

RMS displacement versus intensity 5

Pseudovelocity versus intensity 5

Correlation of ground failure and intensity 7

Part II: Model for predicting ground motion and damage parameters of earthquakes 13

Step 1. Select from figures 12A-J the one having the k and pseudodepth (C) 

values appropriate to the earthquake to be modeled 14

Step 2. Decide on length of rupture of earthquake to be modeled 16

Step 3. Read intensity on saturated alluvium at desired locality 18

Step 4. Determine distances to various types of ground failure 18

Step 5. Calculate intensity(ies) for proper ground condition(s) 19

Step 6A. Determine ground motion parameter of interest by using 

least-squares estimates of correlations with intensity, or Step 6B. 

Determine ground motion parameter of interest by using slope value of 2 

and passing through (Xbar, Ybar) 19

Step 7. Calculate expected value of pseudovelocity versus frequency 21

Step 8. Derive estimates of expected level of damage to buildings of various

types 21 

Final remarks 22 

References cited 27

FIGURES

1. Maximum acceleration versus intensity for the 1971 San Fernando 

earthquake

A. Full bandwidth, all stations 6

B. Full bandwidth, buildings of six stories or less on alluvium 

C. Full bandwidth, stations on hard rock 6 

D. Band 1, all stations 6

E. Band 1, buildings of six stories or less on alluvium 6 

F. Band 1, stations on hard rock 6 

G. Band 2, all stations 7

H. Band 2, buildings of six stories or less on alluvium 7 

/. Band 2, stations on hard rock 7 

/. Band 3, all stations 7

Contents III
K. Band 4, all stations 7

2. RMS acceleration versus intensity for the 1971 San Fernando earthquake 

A. Full bandwidth 8 

B. Band 1 8 

C. Band 2 8 

D. Band 3 8 

E. Band 4 8

3. Maximum velocity versus intensity for the 1971 San Fernando earthquake 

A. Full bandwidth 9 

B. Band 1 9 

C. Band 2 9 

ZX Band 3 9

4. Maximum displacement versus intensity for the 1971 San Fernando earthquake

A. Full bandwidth, all stations 10

B. Full bandwidth, buildings of six stories or less on alluvium 10

C. Full bandwidth, stations on hard rock 10

D. Band 1, all stations 10

E. Band 1, buildings of six stories or less on alluvium 10

F. Band 1, stations on hard rock 10

5. RMS displacement versus intensity for the 1971 San Fernando earthquake 

A. Full bandwidth 11 

B. Band 1 11

6. Predicted Rossi-Forel intensities for a repeat of the Fort Tejon earthquake of 

1857 11

7. Predicted pseudovelocity for a repeat of the Fort Tejon earthquake of 1857 

A. 0.5 Hz 12 

B. IHz 12 

C, 5 Hz 12 

D. 10 Hz 12 

E. Interpreted relationship between intensity and pseudovelocity 12

8. Observed maximum distances of coherent slides and predicted intensities versus magnitude and rupture length for earthquakes in western California 

A. Rossi-Forel intensities 13 

B. Modified Mercalli intensities 13

9. Observed maximum distances of lateral spreads and flows and predicted 

intensities versus magnitude and rupture length for earthquakes in western 

California

A. Rossi-Forel intensities 13

B. Modified Mercalli intensities 13

10. Observed maximum distances of disrupted slides or falls and predicted intensities versus magnitude and rupture length for earthquakes in western California

A. Rossi-Forel intensities 14

B. Modified Mercalli intensities 14

11. Approximate pattern of &-value distribution throughout the conterminous 

United States 15

12. Predicted Modified Mercalli intensity patterns for earthquakes where the 

ground condition is saturated alluvium 

A. k= 1.875, C=25 16 

B. fc=1.75, C=25 16 

C. k=1.15, C=20 16 

D. k= 1.625, C=25 16 

E. fc=1.50, C=60 17

IV Contents
F. A:=1.50, C=30 17 

G. fc=1.25, C=30 17 

//. fc=1.25, C=40 17

/. fc=1.00, C=30 17

/. fc=1.00,C=40 17

13. Predicted limit of ground failure in regions of different k values 

A. Lateral spreads, flows, and coherent slides 19 

B, Disrupted slides and falls 19

14. Relationships between Rossi-Forel and Modified Mercalli intensities and specific ground motion parameters (best-fit least-squares curves) 

A. Maximum acceleration, all stations 20 

B. RMS acceleration, all stations 20 

C. RMS acceleration, stations on alluvium 20 

D. RMS acceleration, stations on hard rock 20 

E. Maximum velocity, all stations 21 

F, Maximum displacement, all stations 21 

G. RMS displacement, all stations 21

15. Relationships between Rossi-Forel and Modified Mercalli intensities and specific ground motion parameters (curves have slope of 2) 

A. Maximum acceleration, all stations 22 

B. RMS acceleration, all stations 22 

C. Maximum velocity, all stations 22 

D. Maximum displacement, all stations 22 

E. RMS displacement, all stations 23

16. Interpreted relationship between intensity and pseudovelocity 23

17. Rossi-Forel and Modified Mercalli intensities versus mean percentage of loss 

to buildings of various types 23

18. Predicted Modified Mercalli intensities for a repeat of the Fort Tejon earthquake of 1857 24 

19/4. RMS acceleration (all bands) versus intensity and acceleration units used on

figures 19C and 19D 25

19B. Maximum velocity (all bands) versus intensity and velocity units used in figure 19£ 25

19C. Predicted values of maximum acceleration (full bandwidth) on ground condition L for a repeat of the Fort Tejon earthquake of 1857 25 

19D. Predicted values of RMS acceleration (band 2) on ground condition L for a

repeat of the Fort Tejon earthquake of 1857 25 

19E. Predicted values of maximum velocity (full bandwidth) on ground condition L

for a repeat of the Fort Tejon earthquake of 1857 25

20. Predicted percentages of loss as a result of a repeat of the Fort Tejon earthquake of 1857

A. Pre-1940 wood-frame buildings on ground condition J 26 

B. Post-1940 wood-frame buildings on ground condition J 26 

C. Post-1940 wood-frame buildings on ground condition L 26

TABLES

1. Correlation of relative shaking units in terms of expected intensity relative to 

intensity on saturated alluvium 2

2. Correlation of map units on geologic map of California with relative shaking 

units 15

Contents

Predictive Model for Important Ground Motion 

Parameters Associated with Large and Great 

Earthquakes

ByJ.F. Evernden ancfJ.M. Thomson

Abstract

This paper presents all requisite empirical data, figures, and graphs required to design a mathematical model 

for predicting seismic intensities and several other parameters of ground motion pertinent to risk analysis for all 

potentially damaging earthquakes throughout the conterminous United States. If (1) the requisite correlations of intensity and damage for building types throughout the world 

and (2) the pattern of k (attenuation) values throughout the 

world are established, the model's use can be extended 

worldwide.

INTRODUCTION

Many organizations, both public and private, are 

interested in estimating a wide variety of ground-motionrelated effects associated with large and great earthquakes, such as types of ground failure, amplitudes of 

various types of ground motion, and expected losses to 

buildings of various types. Although data are adequate to 

build a first-generation predictive model for many parameters of interest, no such model has been generally 

available. This paper presents such a model. Detailed 

changes of interrelationships of parameters (possibly on a 

regional basis), as well as addition of new parameters, will 

probably be appropriate subsequent to testing of the 

model, but general use and evaluation of a model such as 

that proposed here seem timely. Various models purporting to perform some of the tasks of the proposed model 

are in use, but none has been subjected to close scrutiny 

and independent evaluation. Publication of this paper 

should encourage open discussion of these currently used 

but private models and hopefully lead to a new model 

incorporating the best features of all models now in use.

The model proposed is here applied to the conterminous United States but is immediately applicable to any 

part of the world by means of the additional analysis and 

data acquisition described in Part II of this paper.

Part I presents pertinent data relative to the parameters studied (that is, gives the data establishing the

quantitative relationships within the model). Part II 

presents the predictive model and all pertinent figures 

assembled in a logical sequence for analysis. Text and 

figures illustrating regional predictions for some parameters requiring further discussion are included at the end. 

All illustrations in this paper have been produced by 

computer from BASIC programs and data files and can 

be supplied by the authors at a scale useful for plotting 

data and making measurements. All programs are in HP 

BASIC, and all files are available on SVi-'m floppy disk in 

either HP or IBM format. All material is available on 

request from the authors.

PART I: DATA AND ANALYSIS REQUIRED 

FOR DEVELOPMENT OF THE MODEL

Introduction

The aim of this paper is to develop a scheme, based 

on observations, to predict all ground motion parameters 

of current interest relative to large and great earthquakes. 

There are two possible approaches. The first is to predict 

each parameter independently of others, somewhat like 

U.S. Geological Survey Professional Paper 1360 (Ziony, 

1985), in which the authors did not correlate several of the 

predicted parameters with others. The second is to demonstrate, if possible, close correlation of all of these 

parameters and thus provide the basis for a model that 

effectively operates by predicting a single parameter while 

using scaling laws for other parameters. Such a model has 

several attractive features, not the least of which would be 

the demonstration of the integrated and physically coherent character of the several ground motion parameters 

and the earthquake shaking process.

We now proceed to demonstrate that a model such 

as the one sketched in the second approach is indeed 

possible. As might be expected from earlier papers, we 

will choose seismic intensity, either Rossi-Forel intensity 

(RFI) or Modified Mercalli intensity (MMI), as the 

directly predicted quantity. Figures based on both RFI

Data and Analysis Required for Development of the Model
and MMI will be included, as some intensity scales used 

throughout the world correlate more directly with one 

than with the other.

Prediction of Seismic Intensity

Several papers in the literature describe our procedures for calculating Rossi-Forel and Modified Mercalli 

intensities throughout the various attenuation regions of 

the United States (Evernden, 1975, 1983; Evernden and 

others, 1981; Evernden and Thomson, 1985). These 

papers illustrate the sensitivity of the intensity pattern to 

the regional attenuation characteristics and the agreement 

of the predictions and observations in all of the attenuation regions of the conterminous United States and eastern Asia. This scenario for predicting intensities has been 

elaborately described in the literature mentioned above 

and will not be given again. Suffice it to say that incorporation of signal persistence into the analytical model 

allows accurate prediction of intensities over a magnitude 

range from M 5.5 to at least M 8.25 (the largest historical 

earthquakes in the United States).

Maps of predicted intensities will be based on either 

saturated alluvium (J) or water table at a depth of 30 ft or 

greater (L). A few comments on these designations are in 

order. A problem in making predictions in California and 

elsewhere is the convention of classing all alluvial deposits 

as a single unit on many maps, including the 1:250,000- 

scale regional geologic maps of the State of California.

Digitization of such maps for use as our ground 

condition data base required that we treat grossly diverse 

materials as being of a single behavioral type. The way in 

which this problem was handled initially was to consider 

all of these materials as having the properties of very 

loose, medium to fine alluvium, so that the material was 

sensitive to the level of the water table. Thus, we used J 

(see table 1) as characteristic of saturated alluvium (water 

table at or near the surface) and L when the water table 

in alluvium was at a depth of 30 ft or greater. This decision 

was made with the realization that many of the areas 

classed as alluvium on the State map either were not 

alluvium or were of markedly compacted or very coarse 

alluvium, such as terraces and alluvial fans (that is, 

material with properties involving much greater strength 

than loose alluvium even when saturated). Treatment of 

these areas as being of L character involved assuming 

either a lowered water table or materials of greater 

coherence than loose alluvium. In the San Francisco Bay 

area, we long ago adopted the alluvial units established by 

Helley and others (1979) and the scaling of relative 

ground motion on these materials as suggested by the 

instrumental measurements of R.D. Borcherdt (written 

communication, 1983). We do not make corrections for

Table 1. Correlation of relative shaking units in terms of 

expected intensity relative to intensity on saturated alluvium

Relative intensity

Ground-condition unit compared to saturated

alluvium (J)

Derived from geologic map of California:

A

B..................................

r

D .................................

E

F..................................

G .................................

H .................................

I ..................................

J (saturated alluvium). ................

Alluvial units based on depth to water table: 

J1 .................................

L2

*0 ft < water table < 100 ft. 

230 ft < water table.

-2 5

-2.5

-2.2

-1.8

-1.7

-1.5

-1.0

-2.7

-2.7

0

0

-1.00

depth to water table in the areas of the stronger alluvial 

units defined by Helley and his co-authors. Thus, whenever we have been able to improve on the State map, we 

have done so. In southern California, such correction for 

local alluvial properties has not been incorporated in our 

model as yet, so we continue to make a correction for 

depth to water table, realizing that, in most cases, there 

may be little sensitivity to water table because ground 

condition characteristics are such as to imply the lower 

intensities that we associate with lowered water table in 

loose alluvium. Thus, when Tinsley and Fumal (1985) 

reported little or no sensitivity to depth of water table, we 

believe that they were dealing with materials that never 

display the high intensities associated with loose alluvium. 

Therefore, we feel that there is no disagreement between 

their results and our mode of analysis.

Only in very sensitive materials is ground motion 

sensitive to depth to water table. In many so-called 

"alluvial" deposits, ground motion response is at most 

equivalent to our L condition. That loosely consolidated 

alluvium does indeed display sensitivity to depth to water 

table was clearly illustrated by the behavior of the materials around San Jose, Calif., in 1906 (San Francisco 

earthquake) and 1927 (Monterey Bay earthquake) 

(Evernden and others, 1981).

It was pointed out by Evernden and others (1981) 

and Evernden (1983) that refinements of the attenuation 

parameter k in increments of 0.125 (k= 1.875 and 1.625 in 

addition to £=1.75 and 1.50) are frequently useful and 

logical in perfecting understanding of observed patterns 

of intensity. In most cases, however, 0.25 steps in the 

attenuation parameter are found to be adequate.

2 Model for Ground Motion Parameters Associated with Large Earthquakes
Correlation of Strong Motion Parameters and 

Intensity

Evernden and others (1981) presented many examples of the close correlation of predicted and observed 

intensity patterns for earthquakes throughout the United 

States. Data compiled by Evernden and Thomson (1985) 

illustrated the correlation of intensity values and observed 

strong motion parameters. Further illustration of this 

latter correlation is presented here as the basis for establishing the requisite set of empirical relationships for our 

predictive model. The data that we use in our figures are 

restricted to those obtained at the time of the 1971 San 

Fernando earthquake (see Evernden and Thomson (1985) 

for source of intensity values used).

In this paper, we consider only those ground motion 

parameters of general interest that is, maximum acceleration, root-mean-square (RMS) acceleration, maximum 

velocity, maximum displacement, and RMS displacement. 

Other parameters have been investigated, and the relevant 

data are available in the programs and files mentioned 

earlier. We consider the studied parameters in terms of 

the full available bandpass (0.1-25 Hz) (SM) and the four 

partial bandpasses used previously 0.1 to 0.5 Hz (Bl), 

0.5 to 3 Hz (B2), 3 to 10 Hz (B3), and 10 to 25 Hz (B4). 

All analysis is based on the higher of the two orthogonal 

components of horizontal ground motion as recorded by 

strong motion instruments at the time of the 1971 San 

Fernando earthquake.

Two types of calculations are made and illustrated 

in figures 1 through 5. The first type is conventional least 

squares, which assumes, as Evernden and Thomson 

(1985) did, detailed knowledge of the value of the strong 

motion parameter and possible error in the intensity value 

only. These calculations lead to the dashed lines on all 

figures, which are to be compared with the solid lines that 

follow a relation of the type:

ground motion parameter=«4X2RFI

where A is a constant. The so-called slope value on 

each figure is the number equivalent to the 2 in the 

equation above that leads to the best least-squares fit of 

the two sets of data (that is, log(ground motion parameter) = log (A ) + intensity X log (slope)). The sigslope 

parameter is the standard deviation of the slope value. 

Simulations obtained by using random numbers of the 

type of model used for these calculations indicate, as 

expected, that the number of data points for all stations 

is adequate to provide an excellent estimate of the slope 

and standard deviation (under the assumption that all 

data come from the same population that is, same 

intensity versus ground motion parameter relationship). 

If there is error in the calculated relationship because of 

insufficient data to fulfill the conditions of statistical 

theory, it is always in the direction of calculating too

steep a functional relationship (too high a slope value). 

For figures based on data from all stations, the implied 

potential error is always minor.

The other relationship used for calculations (the 

dotted lines) is the assumption that both parameters 

may be in comparable error, so that the parameter 

minimized is the sum of the perpendicular distances of 

data from the best-fit relationship. The slope2 value on 

each figure is the slope value for this model, while the 

C.C. parameter is a measure of the fit of the data to the 

model; the better the fit, the closer C.C. is to 1.0. This 

second mode of analysis always leads to slope values 

that are flatter than those for the least-squares analysis, 

an expected result. In comparison studies of these two 

statistical models based on random numbers, the empirically imposed slope of the randomized data always lay 

between the dashed and dotted lines. For figures using 

all data, this relationship is of little relevance, as both 

lines are very close together. For some figures to be 

discussed below, marked disagreement of the dashed 

and dotted lines is expressive of inadequate data of too 

great a scatter to solidly establish the actual functional 

relationship for the figure. All lines (solid, dashed, and 

dotted) are constrained to pass through the "center of 

mass" of the studied population (Xbar, Ybar). As was 

the case in Evernden and Thomson's (1985) paper and 

for the reasons therein stated, the Pacoima Reservoir 

datum, although shown in all figures (upper margin of 

figures at RFI 7), is ignored in all statistical analyses.

It may be important to note that nearly all data 

used come from instruments in the basements or first 

stories of multistory buildings (all upper story observations are ignored). In other words, there are virtually no 

true free-field data available for the San Fernando 

earthquake. Whether data such as those used are critically perturbed from free-field values is uncertain. We 

assume that, on the average, they are not. We will 

assume in the following discussion that the conventional 

least-squares model is the more reasonable interpretation of the San Fernando earthquake strong motion 

data, although there does exist the possibility that the 

location of essentially all instruments in buildings may 

lead to marked failure of the assumptions of the leastsquares model (that is, ground motion parameters as 

observed, although precise, are not accurate measures 

of the free-field values of such parameters and are thus 

not accurate in the sense- supposed in the statistical 

model).

Most of the figures to be shown are based on all 

data in the basements or first stories of buildings on all 

types of ground, the adjustment of intensity for ground 

condition being as given in all previous papers except 

for one small change. That change is the use of a 

correction factor of -2.5 rather than the previous 

 3.0 for intensity (RFI) for granitic and metamorphic

Data and Analysis Required for Development of the Model 3
rocks relative to saturated alluvium. Several figures will 

indicate -2,5 to be in distinctly better agreement with 

observations than 3.0 is. This correction to our previously used value of -3.0 is included in table 1 (that is, 

,4=-2.5).

Figures 1 through 5 present data for several 

strong motion parameters versus Rossi-Forel and Modified Mercalli intensities for the full available bandwidth 

or for one of the four selected frequency bands. Most of 

the figures are based on data for all ground conditions 

and all sites, with the slight qualification that half of the 

data between intensities 6.8 and 7.2 is eliminated, there 

being an excessive number of data within this intensity 

range. Investigation of the impact of twofold decimation 

of data in this narrow intensity range on interpreted 

relationships indicated there to be no detectable effect. 

Further decimation did affect the calculated functional 

relationship between intensity and the pertinent strong 

motion parameter. As noted above, no upper story 

observations were used in any of our analyses.

As pointed out by Evernden and Thomson (1985) 

and as stressed repeatedly (see, for example, the paper 

by Evernden and others, 1981), RFI values are predictable when a twofold change in RMS acceleration is 

assumed to be equivalent to a one-unit change in RFI. 

MMI values do not so scale. Therefore, RFI values 

vary linearly across the tops of figures 1 through 5, 

while the MMI values along the bottoms of these figures show a nonuniform distribution. All calculations of 

functional relationships between intensity and strong 

motion parameters are based on RFI values. However, 

variations with MMI can be derived from the figures.

Maximum Acceleration versus Intensity

The several components of figure 1 present data 

relative to maximum acceleration and intensity. Figure L4 

is for the full bandwidth (full bandwidth is designated by 

SM on all pertinent figures); figures IB and 1C are for 

subsets of the data of figure L4, figure IB being for sites 

on alluvium and buildings of six stories or less and figure 

1C being for sites on granitic or metamorphic rocks. The 

calculated slope and sigslope values suggest that the 

observations obey a slightly steeper relationship than 

(constantX2RFI). The difference between the 2 curve 

(solid line) and the least-squares (L/S) line (dashed line) 

leads to a difference of a factor of two in predicted 

maximum acceleration at RFI IX. In Part II of this paper, 

we will present summary plots of calculated L/S curves 

(fig. 14) and slope2 curves (fig. 15), which allow a user of 

the model to employ the set of predicted relationships that 

he deems most appropriate.

Figures IB (alluvium) and 1C (hard rock) have 

slopes of 4.40±1.29 and 2.01±0.323, respectively, that are

statistically indistinguishable at high confidence from the 

slope for all data (2.63±0.242). The item of most interest 

on each of these plots is the position of the (mean RFI, 

mean log(maximum acceleration)), or (Xbar, Ybar), 

point. The alluvium intensity values were adjusted for 

depth to water table, and an adjustment of -2.5 was used 

for the hard rock sites relative to saturated alluvium. The 

near identity of the Xbar, Ybar values on the two figures 

indicates that the intensity adjustment parameters used 

agree with the strong motion observations.

Figures ID through IF and 1G through 17 give 

maximum acceleration in bands 1 and 2, respectively, 

versus intensity; figures ID and 1G are for all data, 

figures IE and 1H are for alluvium, and figures IF and II 

are for hard rock. As figure L4 does, figures ID and 1G 

indicate a slope value somewhat greater than 2. The other 

figures indicate no statistically different slopes for all sites 

or for alluvium or hard rock sites and again support the 

case for a hard rock intensity adjustment value of -2.5.

Figures I/ and IK give maximum acceleration in 

bands 3 and 4, respectively, versus intensity. The data for 

band 3 (3 -10 Hz) give a slope estimate indistinguishable 

from that for band 2. However, the data for band 4 

suggest that the rate of dieoff of maximum acceleration 

between 10 and 25 Hz is markedly greater than that 

between 0.5 and 10 Hz (bands 2 and 3), the implication 

being that the rate of attenuation of these higher frequencies is markedly greater with distance. The alluvium and 

hard rock data for both bands 3 and 4 suggest a hard rock 

adjustment factor of 2.5.

RMS Acceleration versus Intensity

Figures 2A through 2E give RMS acceleration in 

the five spectral windows investigated versus intensity 

when data from all sites are plotted. Time windows of 10 

s were used for SM and bands 2 through 4, while a time 

window of 20 s was used for band 1. The five slope values 

(2.30±0.164 for full bandwidth, 2.86±0.20 for band 1, 

2.24±0.128 for band 2, 2.74±0.298 for band 3, and 

5.62±1.28 for band 4) indicate slope values either indistinguishable from or slightly greater than 2 for bands 1 

through 3 and, for maximum acceleration, indicate a 

much greater slope value for band 4. It is interesting to 

note that the calculated slope value for band 2, the band 

deemed by Evernden and Thomson (1985) to be that most 

closely approaching the frequency band controlling intensity values, is indistinguishable from the value of 2.0 used 

in the model for predicting seismic intensities (Evernden 

and others, 1981). As was the case for maximum acceleration, the data for alluvium and hard rock do not lead to 

statistically different estimates of slope and intercept 

(that is, they imply essentially identical Xbar, Ybar values 

for each population).

4 Model for Ground Motion Parameters Associated with Large Earthquakes
Maximum Velocity versus Intensity

Figures 3L4 through 3D give data for maximum 

velocity at all stations for full bandwidth and bands 1 

through 3, values being so low in band 4 that they are not 

calculated. The slope for the full bandwidth 

(2.24±0.108) is as close to the intensity model value of 2 

as any parameter investigated and leads to predicted 

values of maximum velocity at all intensities that are only 

very slightly different from those predicted by the 2 curve.

As with the acceleration data, the alluvium and hard 

rock analyses indicate that the hard rock intensity adjustment relative to saturated alluvium is best set at -2.5.

Maximum Displacement versus Intensity

Finally, there are several figures at low frequencies 

relative to displacement. Figures 4/4 through 4F show 

maximum displacement versus intensity. The first three 

(figs. 4/4, 4B, 4C) are full bandwidth analysis of all sites, 

alluvium sites, and hard rock sites, respectively. The final 

three (figs. 4D, 4E, 4F) are for band 1 at the same sites. 

Not surprisingly, the slope and Xbar, Ybar values for full 

bandwidth and band 1 analysis of data from all sites are 

identical, the slope value being, as are most other parameters, somewhat greater than 2 (2.67±0.194 and 

2.78±0.216) (figs. 4/1, 4Z)). The identity of calculated 

displacements for full bandwidth and band 1 implies that 

there is no purpose in analyzing displacement for the 

higher frequency bands. The paired figures 4B and 4C 

and 4E and 4F again exhibit identical Xbar, Ybar values, 

illustrating for the last time the appropriateness of the 

hard rock adjustment value of -2.5. relative to saturated 

alluvium. It is somewhat surprising that the value of this 

adjustment parameter seems independent of strong 

motion parameter and bandwidth. Although the slope 

values for alluvium and hard rock may be somewhat 

different, this fact certainly cannot be demonstrated from 

the San Fernando data. The values for full bandwidth are 

distinctly different, but the sigslope values are so high that 

the slope differences are of questionable significance, 

particularly in light of the similarity of band 1 slope and 

sigslope values on figures 4E and 4F.

RMS Displacement versus Intensity

Figures 5A and 5B are for RMS displacement versus 

intensity for full bandwidth and band 1 data, respectively, 

at all sites. Again, note the essential identity of predicted 

parameter values as a function of intensity on both 

figures, both slope values and sigslope values suggesting 

falloff rates with intensity somewhat greater than 2. As we 

suggested (Evernden and Thomson, 1985), the fact that 

the rates of dieoff of band 1 strong motion values with

decreasing intensity are greater than those for bands 2 

and 3 may well be simply expressing the role of the elastic 

near-field terms at longer periods (the range of effective 

influence of these near-field terms scaling in wavelengths 

of the period of wave under consideration).

Summary figures of the data in figures 1 through 5 

for use in the prediction scenario of this paper will be 

presented in Part II.

Pseudovelocity versus Intensity

Joyner and Fumal (1985) presented empirically 

established patterns of pseudovelocity versus earthquake 

magnitude and distance for California earthquakes but 

did not correlate their values explicitly with observed or 

predicted intensity values. We shall do exactly that. Our 

approach is to compare the pattern of predicted intensity 

for a particular modeled earthquake with the predicted 

patterns of pseudovelocity for the same modeled earthquake. We choose as the modeled earthquake a repeat of 

the Fort Tejon earthquake of 1857. Figure 6 gives the 

pattern of Rossi-Forel intensities predicted for this earthquake by the program described by Evernden and 

Thomson (1985) and by earlier papers. The assumed 

ground condition for this map is saturated alluvium (J). 

Joyner and Fumal said that their predictions are appropriate to "soil," a designation whose correlation with the 

ground conditions used in papers by Evernden and coauthors is unknown. We will let the investigation establish 

the correlation.

Figures 1A through ID present the patterns of 5 

percent damped pseudovelocity according to Joyner and 

Fumal's formulas at frequencies of 0.5, 1, 5, and 10 Hz. 

The units used on these figures are such that a one-unit 

change in value (for example, from 8 to 9 or from h to i) 

implies a twofold change in velocity (9 designates velocities from 80 to 113 cm/s, and j designates velocities from 

113 to 160 cm/s). Thus, the plotted pseudovelocity units 

scale as do the predicted Rossi-Forel intensities (increase 

of one full RFI unit for a twofold change in predicted 

RMS acceleration in the intensity bandpass). Comparing 

figures 1A through ID with figure 6 indicates nearly 

exactly matched scaling of intensity and pseudovelocity 

units at frequencies of 1 Hz and higher. The continued 

increase of pseudovelocity values near the fault for the 

0.5-Hz map (fig. 7A), a phenomenon observed by Joyner 

and Fumal (1985) in the strong motion data of the 

Imperial Valley earthquake of 1979, is not observed in 

intensity data, the suggestion being that 0.5 Hz has little 

to do with influencing intensity values. The patterns for 1 

and 5 Hz (figs. IB, 1C) agree closely with the intensity 

data, even near the fault. Figure IE presents the scaling of 

pseudovelocity with intensity on "soil" as implied by 

figures 7/4, IB, 1C, and ID. Also shown on figure IE is

Data and Analysis Required for Development of the Model 5
Rossl-Fore) Intensities 

3456789 10

-3

Slope* 2.63 

Slgslope - .242 

Slope?- 1.69 

C.C. - .723

Sol Id Llnei Y - R * 2*RFI 

DashesiL'S(RFI> 

Dots:Perp. Distance 

I I I I I I

2343 

Modified Nercal

6 7 8 S IB 

I Intensities

Rossl-Forel Intensities 

3456789 18

-3

Slope- 4.40 / 

Stgslope - 1.29 / 

Slopo2- 1.72 

C.C. - .573

L/L

Solid Llnei Y - R * 2~RFI 

DashessLxSCRFI) 

Dots:Perp. Distance

23 4 5678910 

Modified Merc*llI Intensities

A. Full bandwidth. Data for all stations except those having Rossi-Forel intensities between 6.8 and 7.2, where decimation is by a factor of 2.B. Full bandwidth. Data for stations on alluvium in buildings of six stories or less.

Rossl-ForeI Intensities 

3456789 IB

- I I I 

Slope- 2.01 

Stgslope - .323 

SlopeS- 1.46 

C.C. - .728

!"

o

8.

-3

Solid Line: Y - R * 2"RFI

Dashes:L/S(RFI)

DotsiPerp. Distance

j__L

23 4 5 6 769 10 

Modified Mercalll Intensities

Rossl-Forel Intensities 

3456789 10

T -2

Slope- 2.92 

Slgs lope - .196 

Slopes- 2.27 

C.C. - .858

'Solid Line: Y - H * 2*RFI 

Dashes IL'SCRFI) 

Dots:Perp. Distance 

I i III

23 4 5 6 789 10 

Modified Mercalll Intensities

C. Full bandwidth. Data for stations on hard rock. D. Band 1 (0.1-0.5 Hz). Data for all stations except those 

having Rossi-Forel intensities between 6.8 and 7.2, where 

decimation is by a factor of 2.

Rossl-Forel Intensities 

23456789 10

-3

Slope- 3.39 

Stgslope ° .714 

Slope2- 2.01 / 

C.C. - .731 °/

ilId Line: Y - R * 2~RFI 

Dashes:L/SCRFI) 

Dots:Perp. Distance

23 4 5 6 7 B 9 10 

Modified Mercalll Intensities

Rossi-Forel Intensities 

23456769 10

i T i i y/

Slope- 4.56 '/

Sigslope - .918 /J»

Slope2- 3.37 //

C.C. - .866 ./

.S/Ild Line: Y > f\ * 2"RFI 

DashesiLxS(RFI) 

DotsiPerp. Distance 

I I lit

23 4 5 6 789 10 

Modified Mercalll Intensities

E Band 1 (0.1-0.5 Hz). Data for stations in buildings of F. Band 1 (0.1-0.5 Hz). Data for stations on hard rock, 

six stories or less on alluvium.

Figure 1. Maximum acceleration versus intensity for the 1971 San Fernando earthquake. Horizontal component of 

motion. Ground condition correction of intensities. Lines and parameters are as described in the text.

Model for Ground Motion Parameters Associated with Large Earthquakes
Rosa1-Forel Intensities 

23456789 IB

-3

Slop*- 2.49 

Slgctope ,163 

Slope2- 1.B4 

_C.C. - .813

Sol Id Lln.i Y - fl * 2*RFI 

DashesiLxS(RFI) 

Dots:Perp. Distance 

I____I I III

Z 3 4 5 6 7 0 9 10 

Modified Meroalll Intensities

£ Band 2 (0.5-3 Hz). Data for all stations except those 

having Rossi-Forel intensities between 6.8 and 7.2, where 

decimation is by a factor of 2.

Rosa I-Fore I Intensities 

3456789 IB

Slope- 3.23 

Slgslope - .666 

SlopeZ- 1.93

Sol Id Llnei Y - R » 2*RFI 

Dashes:L/S<RFI) 

Dot«:Perp. Distance 

I I I I I I I

23 4 5 6 7 8 9 10 

Modified Moroalll Intensities

H. Band 2 (0.5-3 Hz). Data for stations on alluvium in 

buildings of six stories or less.

Rosa I-Fore 1 Intensities 

3436789 18

-2

 3

Slope- 4.27 

Slgslope - .974 

SlopeS- 3.B6 o 

_C.C. - .849

Solid Llnei Y - fl » 2*RFI 

Dashas:L/S(RFI) 

Dots:Perp. Distance 

I I II I II

23 4 56789 10 

Modified Heroalll Intensities

Rossi-Forel Intensities 

3456789 IB

-3

Slope- 2.96 

Stgslope - .350 

Slope2- 1.66 

C.C. - .664

Sol Id Line: Y - R * 2"RFI 

DashesiL/S(RFI> 

DotsiPerp. Distance 

I l I I I l

23 4 56 789 IB 

Modified MaroalI I Intensities

/. Band 2 (0.5-3 Hz). Data for stations on hard rock. J. Band 3 (3-10 Hz). Data for all stations except those 

having Rossi-Forel intensities between 6.8 and 7.2, where 

decimation is by a factor of 2.

Rout-Fore! Intensities 

3456789 IB

 I I I I T 7T

Slope- 6.88 /

-Slgslope - 1.56 /

SlopeZ- 1.68 /.

C.C. - .5B7 | '

Llnei Y - H * 2"RFI 

DashostL/S(RFI)

/

Dots:P«rp. Distance 

l I l ill

2345 

Modified Morea I

6 7 0 9 IB 

I Intensities

K. Band 4 (10-25 Hz). Data for all stations except those 

having Rossi-Forel intensities between 6.8 and 7.2, where 

decimation is by a factor of 2.

Figure 1. Continued.

the least-squares maximum velocity versus intensity curve 

for band 2 (fig. 3CJ. It can be seen that the maximum 

velocity curve for the bandwidth from 0.5 to 3 Hz lies 

between the three pseudovelocity curves for 0.5,1, and 5 

Hz and has nearly the same slope. As discussed earlier, 

the maximum velocity curve of figure 3C seems appropriate to all sites when predicted intensity is adjusted for 

ground condition. Therefore, in Part II, we will consider 

figure IE (to be repeated there for convenience as fig. 16) 

as the basis for predicting pseudovelocity; that is, we will 

predict intensity (taking account of ground condition) and 

then read from figure 16 the implied pseudovelocity at the 

frequency of interest.

Correlation of Ground Failure and Intensity

Wilson and Keefer (1985, figs. 164, 174) presented 

empirical data as well as suggested correlations of earthquake magnitude and maximum range of observation of

Data and Analysis Required for Development of the Model 7
Rossl-Forel Intensities 

3456789 IB

Solid Unei Y - R X 2*RFI 

DashesrU'SCRFI) 

Dots:Perp. Distance

23 4 5 6 7 8 9 IB 

Modified Mercall1 Intensities

Rossl-Forol Intensities 

23455763 10

~ -3

Slope- 2.86 

Slgslope - .200 

-Slope2- 2.1? 

C.C. = .843

/Solid Line: Y = R * 2*RFI 

Dashes:L/SCRFI) 

Dots:Perp. Distance

23 4 56 789 IB 

Modified Mercalll Intensities

A Full bandwidth. B. Band 1 (0.1-0.5 Hz).

Rossl-Forel Intensities 

3456789 10

Slope- 2.24 

Stgslopo - .128 

Slope2- 1.77 

C.C. = .828

Solid LI noi Y - H * 2~RFI

DashesiLXS(RFI)

Dots:Perp. Distance

23 4 56 789 10 

Modified Mercaltl Intensities

Rossl-Forel Intensities 

23456789 10

-2

-3

Slope- 2.74 

Slgslope - .298 

Slope2- 1.60 o 

C.C. - .663 8 

o 8%

Solid Llnei Y - R * 2-M?FI 

DashesiL/SCRFI) 

Dots:Perp. Distance

23 4 56 789 10 

Modified Mercalll Intensities

C. Band 2 (0.5-3 Hz). D. Band 3 (3-10 Hz).

Rossl-Forel Intensities 

3436789 10

Slope- 5.62 

Stgelope - 1.28 

Slope2- 1.80 8 

-C.C. - .550 «

ine: Y R * 2~RFI 

Dashes:L/SCRFI) /

Dots:Perp, Distance 

l i II ii

23 4 5 6 789 10 

Modified Mercal1 I Intensities

E Band 4 (10-25 Hz).

Figure 2. RMS acceleration versus intensity for the 1971 

San Fernando earthquake. Horizontal component of 

motion. Data for all stations except those having RossiForel intensities between 6.8 and 7.2, where decimation is 

by a factor of 2. Ground condition correction of intensities. 

Lines and parameters are as described in the text.

various types of ground failure (lateral flows and spreads) 

(that is, liquefaction), coherent slides, and disrupted slides 

or falls. They combined data from all possible sources 

with the intent of obtaining a statistically meaningful 

sampling. They attempted to make the case that the 

magnitude-distance relationship is independent of the 

attenuation characteristics of the region of the earthquake, even when the data for California earthquakes 

clearly disagreed with any of die three relationships 

suggested in their figure 174C. The relationships given in 

that figure (for lateral spreads and flows) were based on 

Arias intensities, on Youd and Perkins' (1978) interpretation of available data for liquefaction effects of less than

8 Model for Ground Motion Parameters Associated with Large Earthquakes
Rosel-Forel Intensities 

23*36789 IB

Slopo- 2.24 

51gsI ope - .108 

S1ope2- 1.87 

C.C. - .872

Solid Llnei Y R H 2~RFI 

DashesiL/S(RFI> 

DotsiPerp. Distance 

I____I I III

23 4 3 6 7 8 9 18 

Modified Mercalll Intensities

Rosel-Forel Intensities 

23456789 IB

Slope- 2.79 

Slgslope - .187 

Slope2" 2.15 

_C.C. - .848

/ Aolld Llnei Y - fl * 2*RFI 

/ ' DasheeiL'S(RFI) 

/ / DotsiPerp. Dletenee 

/ I I I I I I

23 4 56789 IB 

Modified Mercalll Intsnsltles

A. Full bandwidth. B. Band 1 (0.1-0.5 Hz).

Rose I-Fore I Intensities 

23436789 10

Slope- 2.61

Slgslope - .135 

Slope2- 1.88 . 

C.C. - .796

Solid Llnei Y - R » 2-RFI 

Dashes:L/S(RFI) 

DotsiPerp. Distance

23 4 36789 10 

Modified Mercalll Intensities

Rose 1-ForeI Intensities 

3496769 10

- e

Slops- 2.37 

Si gel ope - .208 

SlopeZ- 1.99 o o _ ._ 

C.C. - .701 O o^JR0-o

f

Sot id Llnei Y - fl » 2*RFI 

DashessL'S(RFI) 

DotsiPerp. Distance

23 4 S67B910 

Modified MercelH Intensities

C. Band 2 (0.5-3 Hz). D. Band 3 (3-10 Hz).

Figure 3. Maximum velocity versus intensity for the 1971 San Fernando earthquake. Horizontal 

component of motion. Data for all stations except those having Rossi-Forel intensities between 6.8 

and 7.2, where decimation is by a factor of 2. Ground condition correction of intensities. Lines and 

parameters are as described in the text.

10-cm movement, and on the maximum range to detectable liquefaction effects as interpreted by Wilson and 

Keefer. The curves based on Arias intensities cannot be 

used, as they disagree with observations at high magnitudes, the Arias curves displaying no tendency to saturate 

with increasing magnitude. Also, the magnitudeliquefaction-distance relationship for these curves at lower 

magnitudes does not agree with intensity predictions. The 

other two relationships shown by Wilson and Keefer were 

investigated relative to predicted intensities for California 

earthquakes. Both relationships, when investigated relative to earthquakes of varying size, showed physically 

uninterpretable relationships in that the implied correlation of ground motion parameter and intensity varied 

grossly as a function of earthquake size, extending to

lower and lower intensity with increasing magnitude. 

Since, as we discussed above and in our earlier paper 

(Evernden and Thomson, 1985), predicted intensities 

show strong correlation with ground motion parameters 

as measured by strong motion seismometers, failure of 

interpreted ground failure parameters to agree even 

approximately with predicted intensities is surprising, to 

say the least.

When it is noted that the California data used by 

Wilson and Keefer disagree with their suggested empirical 

relationships of distance and magnitude, investigation of 

the California data versus predicted intensities for California earthquakes is suggested. Figures &4, SB, 9/4, 9B, 

Id4, and 105 give the results of such an investigation. 

Figures 8/4, 9A, and 10/4 give predicted Rossi-Forel

Data and Analysis Required for Development of the Model 9
Rossl-Forel Intensities 

3456789 10

Slope- 2.67 

Slgslope - .134 

Slopo2- 1.96 

.C.C. - .813

'Solid L1ne« Y - H * 2*RFI 

Dashes:L/S(RFI> 

DotsiPerp. Distance

23 4 56789 IB 

Modified Mercall1 Intensities

3 4 5 6 7

Slope- 3.48 

Slgslope - .630 

Slope2- 1.86 

_C.C. - .680

/

Sfclld Llnej Y - R » 2*RFI 

DeshesiL/'SCRFI) 

DotsiPerp. Distance

2 3 4.5 6.7 89 IB 

Modified Mercallt Intensities

A. Full bandwidth. Data for all stations except those having Rossi-Forel intensities between 6.8 and 7.2, where decimation is by a factor of 2.B. Full bandwidth. Data for stations in buildings of six 

stories or less on alluvium.

Rossl-Forel Intensities 

3456789 IB

Slope- 4.53 

Slgslope " 1.00 

Slope2- 3.21 / /, 

- .842 ,/

TT

rlId Linei Y - H * 2*RFI 

Dashes«LXS(RFI) 

DotstPerp. Distance

23 4 5 6 789 10 

Modified Mercalli Intensities

C. Full bandwidth. Data for stations on hard rock.

Rossi-Forel Intensities 

3456789 10

Slope- 2.78 

Slgslope = .216 

Slope2" 1.99 

.C.C. - .803

/*iol Id Line: Y = fl »

DashesiLxStRFI) 

DotsrPerp. Distance

23 4 S £ 7 8 9 18 

Modified MercallI Intensities

Z7. Band 1 (0.1-0.5 Hz). Data for all stations except those 

having Rossi-Forel intensities between 6.8 and 7.2, where 

decimation is by a factor of 2.

Rossl-Forel Intensities 

345S78918

Slope- 3.84 

Slgslope - 1.07 / 

Slope2- 1.77 o/ 

L.C.C. - .627

f\ Id Llnei Y - H « 2~RFI 

DashesiLXS(RFI)

/

DotsiPerp. Distance 

I I I I II

23 4 5 6 789 10 

Modified MercalU Intensities

Rossl Fore) Intensities 

23456789 10

I I I I y , I

Slope- 4.58 '/

Slgslope - .989 //

SlopeS- 3.24 /,«

,C.C. - .846 ./

J/S

So/lid Line: Y - R »

Dashes tL/'SCRFI) 

// DotsiPerp. Distance 

I/ / I I I I II

2 3 4 5 67 89 10 

Modified Mercalli Intensities

E Band 1 (0.1-0.5 Hz). Data for stations in buildings of 

six stories or less on alluvium.

F. Band 1 (0.1-0.5 Hz). Data for stations on hard rock.

Figure 4. Maximum displacement versus intensity data for the 1971 San Fernando earthquake. Horizontal component of 

motion. Ground condition correction of intensities. Lines and parameters are as described in the text.

10 Model for Ground Motion Parameters Associated with Large Earthquakes
Rose I-For*1 Intensities 

3456789 10

Slope- 2.73 

SI gelope .217 

SlopeZ- 1.92 

C.C. - .730 

8 o

olid Llnei Y - R « 2"RFI 

DksheciLXS(RFI) 

DotsiPerp. Distance 

I I I l I I

8345

Modified Mer-CBl

6 7 8 9 10 

I Inten«ltle«

Rosel-Forel Intensities 

3456789 IB

'Slope- 2.80 

Slgslope - .24S 

SlopeZ- 1.88 

C.C. - .763 °

.Solid Line: Y - R * 2*RFI 

' DashestL/SCRFI) 

DotsiPerp. Distance

B

23 4 56789 10 

Modified Hero) 1 I Intensities

Figure 5. RMS displacement versus intensity data for the 1971 San Fernando earthquake. A, Full 

bandwidth. B, Band 1 (0.1-0.5 Hz). Data for all stations except those having Rossi-Forel intensities 

between 6.8 and 7.2, where decimation is by a factor of 2. Ground condition correction of 

intensities. Lines and parameters are as described in the text.

123 121 120 119 lie 117

Figure 6. Predicted Rossi-Forel intensities for a repeat of 

the Fort Tejon earthquake of 1857. Uniform ground condition of saturated alluvium (J). Minimum intensity is V. Arabic numbers indicate the lower half of an intensity value (9 

is the lower half of IX), and letters indicate the upper half (j 

is the upper half of IX). Asterisks indicate the lower half of 

X.

intensities, and figures 85, 95, and 105 give predicted 

Modified Mercalli intensities (as measured on saturated 

alluvium) (see table 1) perpendicular to the fault strike 

for earthquakes of varying length, surface wave magnitude M, and moment Mo in regions where fc=1.75 (that 

is, western California). It is apparent immediately that 

there is remarkable agreement between the data for 

California earthquakes (die Mammoth Lake earthquake 

not being used, since its epicenter is deep within the 

region of fc=1.5) and the predicted intensities for California earthquakes.

It seems certain that the merging of data from 

earthquakes of different regions into a composite curve

led both Wilson and Keefer (1985) and Youd and Perkins 

(1978) into a misinterpretation of their data. The data for 

coherent slides and for lateral spreads and flows (figs. &4, 

9A) follow very closely the RFI curve for the intensity 

VII-VIII boundary (MMI VI-VH-Vs) (figs. SB, 95), 

while the data for disrupted slides and falls in figure 1CL4 

follow closely the RFI VI-VII boundary beyond M 5.5 

(approximately MMI V-VI) (fig. 105). We conclude that, 

when properly interpreted, the observed data for ground 

failure phenomena agree very closely with intensity values 

and are thus predictable on the basis of predicted RossiForel or Modified Mercalli intensities. The pertinent 

curves for use within our predictive model will be given in 

Part II of this paper (figs. 13/i, 135).

As we pointed out above and in our earlier paper 

(Evernden and Thomson, 1985), intensity values correlate 

closely with strong motion parameters in the bandpasses 

from 0.5 to 3 Hz and from 3 to 10 Hz but not with 

bandpasses from 0.1 to 0.5 Hz and from 10 to 25 Hz. 

Correlation of ground failure with intensity then implies 

that ground failure is linked to strong ground motion in 

part or all of the frequency range from 0.5 to 10 Hz.

Discussion of the apparently highly discordant 

datum at magnitude 6.4 (2L=20 km) in figures 8 and 9 is 

important, as this datum illustrates clearly the danger in 

attempting one-parameter interpretation of multiparameter data. These data are for the 1966 Parkfield, Calif., 

earthquake, an earthquake with a demonstrable break of 

20 to 30 km and a surface-wave magnitude M of about 

6.4. Why are the data from this event in such marked 

disagreement with the other California data? Fortunately, 

there is a clear explanation, supported by unequivocal 

seismological observations (Lindh and Boore, 1981). By 

great good luck, short-period seismometers in the immediate vicinity of this earthquake clearly recorded that

Data and Analysis Required for Development of the Model 11
34 34

122 121 126 119 11B 117

33 33

A. 0.5 Hz, 5 percent damping.

122 121 120 119 lie

B. 1 Hz, 5 percent damping.

11?

117

122 121 128 119

C. 5 Hz, 5 percent damping.

tie 117

36

122 121 120 119

D. 10 Hz, 5 percent damping.

us 117

Rossi-Forel Intensities 

23456783 10

o 2

1

-1

I I I I I

 MRXVel-B2 HI 1

- PSEUDOVel-.S Hz 

= PSETUDOVol-l Hz

-2

I =

23 4 5678910 

Modified Mercalli Intensities

E Interpreted relationship between intensity and pseudovelocity (5 percent damping).

Figure 7. Predicted pseudovelocity (in centimeters per 

second) for a repeat of the Fort Tejon earthquake of 1857 

(following Joyner and Fumal, 1985). Ground condition is 

"soil." Arabic numbers indicate the lower half of an intensity value (9 is the lower half of IX), and letters indicate the 

upper half (j is the upper half of IX). Asterisks indicate the 

lower half of X.

rupture for this earthquake began to the north and 

propagated southward with radiation of very low amplitude high-frequency waves for nearly the entire length of 

the rupture. Only the southerly 3 km of rupture resulted 

in radiation of "normal" amplitudes of high-frequency 

waves. Thus, seismic energy at frequencies relevant to 

ground failure (and other intensity-sensitive parameters) 

was nearly entirely radiated by the southern 3 km of 

rupture. As Evernden and others (1981) pointed out, the 

intensity pattern for this earthquake is consistent with a 

3-km rupture at the southern end of the observed rupture,

12 Model for Ground Motion Parameters Associated with Large Earthquakes
I0ea

1B3 ica

IB 2L(Kn.) 188

Figure 8. Observed maximum distances (distances from rupture) of coherent slides (pentagons) 

and (A) predicted Rossi-Forel intensities and (B) predicted Modified Mercalli intensities versus 

magnitude and rupture length (2Z.) for earthquakes (solid lines) in western California (k="\.75, 

£=25). Ground condition is saturated alluvium. See figure 12 for explanation of dashed line 

Mo. Observations taken from Wilson and Keefer (1985).

1080

100

1000

18

28

23'

18 2L(Km) 188 1000 10 2L(Kn) 188

23 ieaa

B

Figure 9. Observed maximum distances (distances from rupture) of lateral spreads and flows 

(pentagons) and (A) predicted Rossi-Forel intensities and (B) predicted Modified Mercalli intensities 

versus magnitude and rupture length (2Z.) for earthquakes (solid lines) in western California (/r=1.75, 

O=25). Ground condition is saturated alluvium. See figure 12 for explanation of dashed line Mo. 

Observations taken from Wilson and Keefer (1985).

while the surface-wave amplitudes indicate a rupture 

length of 20 to 30 km. Within the earthquake model 

described in detail by Evernden and others (1986) and 

discussed by Evernden and Thomson (1985), the physical 

explanation for such behavior is slow rupture for the first 

many kilometers of break and normal rates of rupture 

(UR VS} for only the final 3 km, where UR is the rupture 

velocity and Vs is the shear-wave velocity in rocks adjacent 

to the fault. Since, as noted above, figures 8 through 10 

indicate correlation of ground failure with intensityrelevant frequencies (0.5 to 3 or 10 Hz), it is clear that the 

Parkfield datum on figures 8 and 9 should be moved to a 

rupture length of 3 km, a position that would show 

agreement with all of the other California data. It must

always be kept in mind that the seismological world is 

never one dimensional, and efforts to so treat it will often 

lead to serious misinterpretation.

PART II: MODEL FOR PREDICTING GROUND 

MOTION AND DAMAGE PARAMETERS OF 

EARTHQUAKES

Given the correlations of strong motion and ground 

failure parameters with intensity discussed in Part I, the 

correlations of structural damage and intensity presented 

by Evernden and Thomson (1985) and the model given by 

Evernden and others (1981) for predicting seismic intensities throughout the several different geotectonic regions 

of the United States (and thus of the world), we are now

Model for Predicting Ground Motion and Damage Parameters of Earthquakes 13
laea

100 tee 

25'

13 2L(K») 100 IB 2L(K«> 10B

23

B

Figure 10. Observed maximum distances (distances from rupture) of disrupted slides or falls 

(pentagons) and (A) predicted Rossi-Forel intensities and (B) predicted Modified Mercalli intensities 

versus magnitude and rupture length (2Z.) for earthquakes (solid lines) in western California (/r=1.75, 

£=25). Ground condition is saturated alluvium. See figure 12 for explanation of dashed line Mo. 

Observations taken from Wilson and Keefer (1985).

in a position to develop a generally applicable model for 

predicting all of the above parameters for earthquakes 

throughout the United States and the world. Detailed 

confirmation or modification of the model must await 

testing against observations from regions other than western California.

For application of the model in any specific area, 

one must have established the appropriate rate of decrease 

of intensity with distance. This rate can be found either by 

studying intensity maps for previous earthquakes of the 

area or by establishing, by using any of several geophysical 

parameters, the geotectonic equivalence of the area of 

interest and a region of known attenuation characteristics 

(Evernden, 1983). Such study finally leads to selection of 

the appropriate k (or attenuation) value (Evernden and 

others, 1981; Evernden, 1983). Figure 11 presents the 

pattern of k values found for the conterminous United 

States by studying intensity maps of U.S. earthquakes 

(Evernden and others, 1981), while Evernden (1983) 

presented a comparable map for eastern Asia.

If the selection of k value is determined by study of 

local intensity patterns, it will be necessary to establish 

the correlation of the local intensity scale with MMI or 

RFI values. Even if the selection of k value is reached by 

other means, it will still be necessary to establish the 

correlation of the local intensity scale with RFI or MMI in 

order to be able to use the following figures, expressed as 

they are in terms of RFI and MMI. In regions where 

building types differ markedly in character from those 

used to define RFI and MMI units, new definitions of 

those units may need to be established in terms of local 

structure types, including percentage of damage versus 

intensity versus structural type. Massive confusion results 

if intensity is defined in terms of percentage of damage to

structures without regard for structural type and (or) 

quality of construction. This failure to modify definitions 

of intensity units as structural types are modified (as, say, 

the earthquake resistance of structures is improved, as it 

has been in California in recent decades) is already 

leading to great confusion in interpreting the intensity 

maps of recent earthquakes.

Finally, it will be necessary to establish the physical 

equivalence of local geologic units to those used in 

California in order to be able to use table 1 for adjusting 

intensities predicted for saturated alluvium to those predicted for other rock types. Table 2, repeated from papers 

by Evernden and others (1981) and Evernden and 

Thomson (1985), presents the correlation of the geologic 

units of the State geologic map of California and our 

shaking units. The codification of the rock units on the 

State map follows general rules and thus should be 

understandable to most geologists.

When these tasks have been completed for the 

region of interest, the application of the model is straightforward.

Step 1. Select from figures 12/4-Jthe one 

having the /rand pseudodepth (C) values 

appropriate to the earthquake to be modeled

If a U.S. earthquake is being modeled, find the k 

value by inspection of figure 11. If an earthquake elsewhere is being modeled, establish the geotectonic equivalence of the area of interest and a portion of the United 

States, and then use figure 11. Evernden (1983) presented 

a figure that was similar to figure 11 of this paper but that 

applied to eastern Asia (the People's Republic of China 

and surrounding areas).

14 Model for Ground Motion Parameters Associated with Large Earthquakes
Figure 11. Approximate pattern of /r-value distribution throughout the conterminous United States.

Figure 11 is divided into areas characterized by k 

values of 1.75, 1.50, 1.25, and 1.00 (k value increases in 

increments of 0.25). This set of k values is generally 

adequate. However, Evernden (1983) found, in his study 

of Chinese earthquakes, that use of A: values at increments 

of 0.125 was useful. Also, investigation of some California 

earthquakes (Evernden and others, 1981) suggested that k 

values such as 1.875 and 1.625 occasionally appeared to 

achieve marginally better fits to observations than did 

£=1.75. Therefore, figures having such k values are 

included.

Figures 12^4 through 12/ are labeled to facilitate 

the proper selection for a particular case. A few additional 

comments may be useful.

In general, it should be adequate to use only the k 

values of 1.75,1.50,1.25, and 1.00. Thus, figures 12.4 and 

12D are to be used only when specifically indicated or 

when investigating the influence of a slight change in k 

value.

The two C values of 25 and 20 for western California earthquakes (figs. 1ZB, 12CJ are intended for use with 

strike-slip earthquakes (for example, on the San Andreas 

fault) and thrust earthquakes (for example, the San 

Fernando earthquake), respectively.

All significant earthquakes in the Seattle area of 

Washington (fig. 12E, £=1.50) have been at depths of 40 

km or greater. Evernden and others (1981) showed that a 

C value of 60 yielded predicted intensities in agreement 

with observations for the 1949 Seattle earthquake. Therefore, figure 12E is for a C value of 60. The effect of a C 

value of 25 (focal depth of 10 km or so) would be to 

predict markedly higher intensities in the epicentral area. 

Figure 12F can be used to consider a shallower earthquake in the Seattle area.

Table 2. Correlation of map units on geologic map of 

California with relative shaking units

Geologic map units

Relative

shaking

unit

Granitic and metamoiphic rocks ..................... A

(Kjfv, gr, bi, ub, JT, m, mV, PpV, Cv, Dv, pS, pSv,

pCc, pCgr, pC, epC, XI) 

Paleozoic sedimentary rocks. ........................ B

(Ms, PP, Pm, C, CP, CM, D, S, pSs, O, E) 

Early Mesozoic sedimentary rocks.................... C

(Jk, Ju, JmE, Tr, Kjf) 

Cretaceous through Eocene sedimentary rocks .......... D

(Ec, E, Epc, Ep, K, Ku, KE) 

Undivided Tertiary sedimentary rocks................. E

(QTc, Tc, TE, Tm) 

Oligocene through middle Pliocene sedimentary rocks.... F

(PmEc, PmE, Me, Muc, Mu, Mmc, ME, £e, £) 

"Pliocene-Pleistocene" sedimentary rocks .............. G

(Qc, OP, PC, Puc, Pu) 

Tertiary volcanic rocks ............................. H

(Pv, Mv, Olv, Ev, QTv, TV) 

Quaternary volcanic rocks .......................... I

(Qrv, Qpv) 

Quaternary sedimentary deposits..................... J

(Qs, QaE, Qsc, Qf, Qb, Qst, QE, Qq, Qt, Qm)__________

Available analysis suggests that focal depths of 

earthquakes in the Basin and Range area (£=1.50) of the 

United States are very similar to those of earthquakes in 

western California. Therefore, figure 12F (£=1.50, 

C=30) is intended for use in these areas. An earthquake 

having a focal depth of 40 to 50 km could be rhodeled by 

using the Seattle figure (fig. 12E).

Again, available analysis indicates quite shallow 

focal depths for earthquakes in the eastern United States, 

in regions of both £=1.25 and £=1.0. Therefore, figures 

12G and 12H are for £ = 1.25 and C values of 30 and 40, 

respectively. Figures 127 and 127 are for £=1.00 and C 

values of 30 and 40.

Model for Predicting Ground Motion and Damage Parameters of Earthquakes 15
1000

180

1000

1 10 ZLCKw) 100 1000 

.VI . VII . VIII . IX , X

A. Western California earthquakes, where k= 1.875 and 

£=25.

B. San Francisco and Los Angeles earthquakes, where 

A= 1.75 and O25.

I |0 2L(Km) (00 

. VII . VIII , IX . X

1600 

.XI M ...,?.,.... .?..,..,.,,? ...,..,?,.,.....

C. Western California earthquakes, where /r=1.75 and 

C=20.

KMflX) 

M

. l | 2L<Km) ie 100 

V , VI . VII . VIII . IX ,

D. Western U.S. earthquakes, where k= 1.625 and O=25.

Figure 12. Predicted Modified Mercalli intensity patterns for earthquakes where the ground condition is saturated alluvium. 

Solid lines are distances perpendicular to the rupture for points between the two ends of the fault. Dashed lines are 

distances along the strike of the fault from the center of the rupture. 2L is the length of rupture, M is the surface wave 

magnitude Ms, and I(MAX) is the maximum intensity on saturated alluvium. The moment Mo of the earthquake can be 

found by starting from either M or 2L, moving vertically to the intersection with the dashed line labeled "Mo," and then 

moving horizontally to the right and reading Mo.

Figures 12A through 127 are drawn for Modified 

Mercalli intensities, as most practitioners use it, even 

though it is less physically interpretable than the RFI 

scale is. The predicted intensities in figure 12 are for 

saturated alluvium.

Step 2. Decide on length of rupture of 

earthquake to be modeled

Many would rather decide on the magnitude M 

(Ms) of the earthquake to be modeled rather than the

length of rupture. Figure 12 allows such a selection, but 

the current confusion in die literature about the correlation of magnitude Ms and length of rupture makes explicit 

analysis by using length of rupture a better procedure. At 

the very least, study figure 12 and note the drastic change 

in the relationship of magnitude versus length of rupture 

(2L) as the k value varies from 1.75 to 1.00. Thus, M=8 

is correlated with a 2L value of 400 km in regions of 

k=1.15 and with a 2L value of 3 km in regions where 

k= 1.00. This point was elaborately discussed by Evernden 

and others (1981).

16 Model for Ground Motion Parameters Associated with Large Earthquakes
leea

100

i

28

27

25"

23

.1 1 2L(Km> IB 100

I(MRX) IV . V . VI . V" . VI"

 ....,..,?.........?...,.....?.,...,.,.?..,.

£ Seattle earthquake's, where k= 1.50 and 0=60.

108001 I . I II.Ml I I I I I.Ill I I I MM. 28

18

27

.1 I 2L(Kra> 10

. VII , VIII . IX , X .XI

..........?.........?.. .......9.... ..

25"

24

1000

100

10

27

26

24

KMflX)

M '

23 .1 i 2L(Km> IB tea

V. VI . VII . VIII . IX . X

.?.........6 .........7.

F. Utah and Nevada earthquakes, where /r=1.50 and 

0=30. 26

KMflX) 

M

23

I 1 2L(Kra) |B 100

VI . VII . VIII . IX . X .XI 

I.........9.........T.........?.........?.

G. Atlantic coast-Mississippi embayment earthquakes, H. Atlantic coast-Mississippi embayment earthquakes, 

where A= 1.25 and C= 30. where A= 1.25 and C= 40.

100B0F

1000

I(hflX)

.01 .1 2L(Km) i

VI . VII . VIII . IX . X .

7-28

2?

25'

23

/. Eastern U.S. earthquakes, where /r=1.00 and C=3Q. 

Figure 12. Continued.

I(MRX)

.01 .1 2L(Km> | 11 

VI . VII .VIII . IX . X .XI

J. Eastern U.S. earthquakes, where /r=1.00 and 0=40.

Model for Predicting Ground Motion and Damage Parameters of Earthquakes 17
Step 3. Read intensity on saturated 

alluvium at desired locality

For strike-slip earthquakes, the "desired locality" is 

defined by rectangular coordinates based on the fault 

strike, the (0, 0) point of the coordinates being at the 

center of the modeled rupture. For thrust earthquakes, 

the center of coordinates should be about 6 km in the 

downdip direction from the center of the surface rupture. 

The desired locality can be either a single point, a series of 

specific localities, or an entire map area.

For regions characterized by k values of 1.25 and 

less, the intensity contours on uniform ground condition 

very closely approximate circles centered on the central 

point of the rupture. Therefore, all points at the same 

radial distance from the center are predicted to have the 

same intensity (uniform ground condition). So, determine 

the distance in kilometers of a desired locality from the 

center of rupture, find this distance along the vertical axis 

(labeled "Radius(Km)") of the appropriate figure, and 

read the predicted Modified Mercalli intensity for the 2L 

value (or M value) appropriate to the modeled earthquake. Thus, in figure 127, for a 2L value of 1 km and a 

radial distance of 200 km, read a predicted MMI value of 

VI.5 (that is, boundary between MMI VI and MMI VII). 

Also, read from the lower scales of the figure that such an 

earthquake would be of about Ms =7Vi, the maximum 

intensity expected on saturated alluvium being MMI IX. 

If one wishes to draw an intensity map for an earthquake 

in these k regions, read from the appropriate figure the 

distance to each of the intensity boundaries and draw 

circles of these radii centered on the middle of the 

hypothesized fault rupture.

For k values of 1.5, the intensity contours are no 

longer circles at short distances for large earthquakes. 

However, for earthquakes of Ms =7 or less in regions of 

&=1.50, the predicted intensity contours are so nearly 

circular that the assumption of circularity is legitimate. In 

regions where k=\.15 and for earthquakes of M=6.0 or 

less, the procedures described for k=1.25 or less can be 

used. In regions where fc=1.50 or greater and for larger 

earthquakes, slightly different procedures must be followed.

For fc=1.50 and greater, two types of distances 

(labeled "Radii") are given on figure 12. One is measured 

perpendicular to the modeled fault (solid lines), while the 

other is measured parallel to the modeled fault (dashed 

lines) along the strike of the fault, distances being measured from the central point of the fault. Strictly, the 

solid-line distances are perpendicular distances from the 

center of the fault. However, the intensity contours are so 

nearly parallel to the fault for the length of the fault that 

the solid-line distances can be applied to the entire region 

bounded by lines perpendicular to the fault and passing 

through the ends of the modeled break.

For regions beyond the fault line, two procedures 

giving nearly the same answers are possible:

1. Assume that the intensity contours beyond the ends 

of the fault are semicircles meeting tangentially the 

intensity contours determined above for the regions 

along the length of the rupture. For this procedure, 

measure the distance of a desired locality from the 

nearest end of the rupture and then use the solidline distances on the appropriate figure and at the 

appropriate 2L value for determining the predicted 

intensity on saturated alluvium.

2. Actually, procedure 1 slightly overpredicts intensity, 

as the intensity contours beyond the fault break are 

slightly flatter than circles; that is, the distance to a 

specific intensity value along the strike of the fault 

is less than the distance to that intensity contour 

perpendicular to the fault. A minor correction can 

be made if desired by using the dashed-line curves 

of the figures, remembering that the dashed-line 

distances are measured from the center of the rupture (not the end). For nearly all purposes, however, use of semicircular intensity contours in procedure 1 should be adequate.

The product of this step is either predicted Modified Mercalli intensities on saturated alluvium at a set 

of specified map points or a drawn contour map of 

predicted Modified Mercalli intensities on saturated 

alluvium. If one would rather have values in Rossi-Forel 

intensities, read, from any one of figures 1 through 5, 

the Rossi-Forel-Modified Mercalli equivalence and generate the desired table of RFI values or the desired RFI 

map.

From here on, one uses figures presenting the 

empirically determined correlations of Rossi-Forel and 

Modified Mercalli intensities with a wide variety of 

ground effects and damage scenarios. Some of the following steps can be used and some can be ignored in 

any given study.

Step 4. Determine distances to various 

types of ground failure

Figures 13/4 and 13B give the predicted correlation 

of k value, magnitude Ms, and maximum expected distance of the various types of ground failure investigated by 

Wilson and Keefer (1985). Figure 13/4 is for lateral 

spreads and flows as well as for coherent slides. The 

curves are developed by noting the empirical correlation in 

figures &4, 8J5, 9/4, and 9B between these ground failure 

types and intensity of western California earthquakes 

(fc=1.75) and then drawing on figure 13/4 this intensity 

boundary as predicted in the several regions of different k 

values. The slightly erratic behavior of the predicted lines 

at low magnitude is a product of the digitized character of

18 Model for Ground Motion Parameters Associated with Large Earthquakes
1000 r

108

cc 

la

28

Z7

26

25

24

100B

180

Magnitude

23 Magnitude

Figure 13. Predicted limit of ground failure for (A) lateral spreads, flows, and coherent slides and (B) 

disrupted slides and falls in regions of different k values. Distances are measured perpendicular to the 

modeled fault, similar to those in figure 12. It should be remembered that occurrence of ground failure 

requires not only the requisite ground motion at the proper frequencies but also the proper terrain and 

soil deposits. Regions where /r=1.75 are characterized by high rates of uplift, steep slopes, and uplifted 

weak sediments. Regions where k= 1.00 are characterized by little or no uplift and gentle to flat slopes, 

and nearly all hills or valley walls are of hard rocks. Thus, this figure may well overpredict the extent of 

ground failure in regions of low k value, as it is based on the principle of equal probability of ground 

failure at the same intensity in all k regions.

the calculation procedures and is to be ignored. Figure 

13£, for disrupted slides, was developed in a similar way 

and is based on figures 1(M and 105.

Step 5. Calculate intensity(ies) for proper 

ground condition(s)

By using tables 1 and 2 and a table generated by the 

user correlating the geologic rock units of California with 

those of the region of interest, calculate the predicted 

intensities at all desired localities for the actual ground 

conditions at those sites. All intensity adjustments are 

negative; that is, all adjusted intensities are less than those 

predicted for saturated alluvium. In loose alluvium, take 

account of depth to water table, as table 1 indicates.

Step 6A. Determine ground motion

parameter of interest by using least-squares

estimates of correlations with intensity

OR

Step 6B. Determine ground motion

parameter of interest by using slope value of

2 and passing through (Xbar, Ybar)

As we noted in Part I, the least-squares estimates of 

the linear correlation of Rossi-Forel intensity and strong 

motion parameter are always slightly to markedly in 

excess of the slope value of 2 used in the model for predicting intensities. However, the differences for maximum 

velocity and RMS acceleration in the intensity bandpass 

(band 2) are so minor as to give clear support to the 

model. In these cases and in numerous others, it is not 

obvious that using the least-squares estimate of slope is 

superior to simply using a slope value of 2. Therefore, 

two sets of relationships between ground motion parameters and intensity are given; those based on the slope 

values are determined by least squares (figs. 144-14G 

and similar figures), and those based on a uniform slope 

value of 2 are determined with the constraint that the 

curve used must pass through the "center of gravity" of 

the population (Xbar, Ybar). These curves are given in 

figures 15A through 15E.

For most ground motion parameters, there was no 

clear evidence that the functional relationship between 

parameter and intensity was a function of ground condition. Therefore, most of the curves in figures 14 and 15 

are curves for all rock types.

Figures 14/4 and 15/4 are for maximum acceleration, curves being given for least-squares analysis of data 

for full bandwidth and for the four partial bandwidths. As 

can be seen, band 1 (0.1-0.5 Hz) shows very low maximum acceleration values, and bands 2 and 3 (0.5-10 Hz) 

show the highest narrow-band values; values for the full 

bandwidth are greater than those for any partial bandwidth, and all four of these curves have nearly identical 

slope values. The curve for band 4 (10-25 Hz) in figure 

14/1 displays a markedly different behavior, indicative of a

Model for Predicting Ground Motion and Damage Parameters of Earthquakes 19
Rossi-Forel Intensities 

23456789 10

-2

-3

-4 I I I I I

23 4 5678910 

Modified Mercalli Intensities

Figure 14A Relationships between Rossi-Forel and Modified Mercalli intensities and maximum acceleration. Data 

are for all stations (all rock types). Curves are best-fit leastsquares curves as described in text, curves for full bandwidth (SM) and bands 1 through 4 being given. Units of 

acceleration are fractions of g (980 Gal).

Rossi-Forel Intensities 

23456789 10

0 f=

-3 =

-4

-5 1 I II I._

23456 

Modified Mercalli

78910 

Intensities

Figure 14 C. Relationships between Rossi-Forel and Modified Mercalli intensities and RMS acceleration. Data are for 

stations on alluvium. Curves are best-fit least-squares 

curves as described in text, curves for full bandwidth (SM) 

and bands 1 through 4 being given. Units of acceleration 

are fractions of g (980 Gal). Time window is 10 s for full 

bandwidth and bands 2 through 4 and 20 s for band 1.

Rossi-Forel Intensities 

23456789 10

0 er

23456 

Mod i fled Mercal1i

7 8910 

Intens i 11es

Figure 14£. Relationships between Rossi-Forel and Modified Mercalli intensities and RMS acceleration. Data are for 

all stations (all rock types). Curves are best-fit least-squares 

curves as described in text, curves for full bandwidth (SM) 

and bands 1 through 4 being given. Units of acceleration 

are fractions of g (980 Gal). Time window is 10 s for full 

bandwidth and bands 2 through 4 and 20 s for band 1.

Rossi-Forel Intensities 

23456789 10

o 

u 

cr

cn_q z: J 

a:

<J.

j_/i

23 4 56 

Modified Mercalli

78910 

Intensities

Figure 14Z7. Relationships between Rossi-Forel and Modified Mercalli intensities and RMS acceleration. Data are for 

stations on hard rock. Curves are best-fit least-squares 

curves as described in text, curves for full bandwidth (SM) 

and bands 1 through 4 being given. Units of acceleration 

are fractions of g (980 Gal). Time window is 10s for full 

bandwidth and bands 2 through 4 and 20 s for band 1.

very high rate of falloff with intensity and thus with 

distance.

Figures 14/4 and 155 differ from figures 14/1 and 

15A only in the use of RMS acceleration rather than 

maximum acceleration. The relationships of the several 

curves for the various bands are as shown in figures 144 

and ISA. Figures 14C and 14D are also for RMS acceleration but for subsets of the available data, figure 14C 

being for sites on alluvium and figure 14D being for sites 

on hard rock. The curves for bands 2 and 3 are very 

similar in both figures, any differences being of questionable statistical significance (see earlier discussion). Band 

1 values appear to decrease more rapidly with intensity on

hard rock than they do on alluvium. This rapid decrease 

may simply be because a given intensity on hard rock is at 

a much shorter epicentral distance, and band 1 values on 

hard rock are thus able to more clearly display the role of 

the elastic near-field terms (see earlier discussion). At the 

same intensity, band 4 values are higher on hard rock 

(band 2 values being nearly identical), but, at the same 

range intensity (alluvium)=intensity (hard rock)-1-2.5 

 band 4 values are markedly greater on alluvium.

Figures 14£ and 15C are for maximum velocity 

versus intensity. Lack of clear evidence for different 

relationships instigated by rock type resulted in an absence 

of figures based on differing rock types. The fact that

20 Model for Ground Motion Parameters Associated with Large Earthquakes
Rossi-Forel Intensities 

23456789 10

Rossi-Forel Intensities 

23456789 10

u

* i vt 2

E 

U

1

0) 0 

X

a

w 1J

-2

I I

I I I I

0 2345678

Modified Mercalli Intensities

Figure 14£. Relationships between Rossi-Forel and Modified Mercalli intensities and maximum velocity. Data are for 

all stations (all rock types). Curves are best-fit least-squares 

curves as described in text, curves for full bandwidth (SM) 

and bands 1 through 3 being given. Units of velocity are 

centimeters per second.

23456 

Modified Mercal1i

7 8910 

Intens11 i es

Figure 14F. Relationships between Rossi-Forel and Modified Mercalli intensities and maximum displacement. Data 

are for all stations (all rock types). Curves are best-fit leastsquares curves as described in text, curves for full bandwidth (SM) and band 1 being given. Units of displacement 

are centimeters.

Rossi-Forel Intensities 

23456789 10

3 t=

a in 0

-2

I I

I I I I I

23 4 5678910 

Modified Mercalli Intensities

Figure 146. Relationships between Rossi-Forel and Modified Mercalli intensities and RMS displacement. Data are 

for all stations (all rock types). Curves are best-fit leastsquares curves as described in text, curves for full bandwidth (SM) and band 1 being given. Units of displacement 

are centimeters.

values for band 3 are an order of magnitude below those 

based on full bandwidth (and bands 1 and 2 at high 

intensity) made it irrelevant to include band 4 data on the 

figure.

Figures 14F and 15D are for maximum displacement, while figures 14G and 15E are for RMS displacement. The identity of the curves for full bandwidth and 

band 1 make it irrelevant to include curves for higher 

frequency bands. Note that maximum displacement at 

very high intensity is 200 to 300 cm, while RMS displacement (over a 20-s time window) is predicted to be 100 to 

200 cm.

For reasons stated by Evernden and Thomson 

(1985), we strongly recommend using figure 14 rather 

than figure 15.

Step 7. Calculate expected value of 

pseudovelocity versus frequency

Figure 16 (a repeat of fig. IE) presents the correlations of intensity and pseudovelocity (5 percent damping) as a function of frequency found by the investigation 

described in Part I. As for other parameters, correlation 

of this figure with predicted values of intensity (either RFI 

or MMI) can lead to predicted values of pseudovelocity at 

particular sites and ground conditions or to maps of 

pseudovelocity as a function of position around the modeled fault rupture. As we pointed out earlier, there was no 

detectable influence of rock type on the maximum velocity 

versus intensity relationships found in the study of the 

strong motion data of the 1971 San Fernando earthquake. 

Therefore, figure 16 is presumed applicable as a function 

of intensity independent of rock type.

Step 8. Derive estimates of expected level 

of damage to buildings of various types

Figure 17 is a redrafted version of a figure given by 

Evernden and Thomson (1985), the empirical bases for 

the curves of this figure being given in the same reference. 

The curves predict, on the basis of empirical studies, the 

expected level of damage to buildings of four distinctly 

different types:

1. Pre-1940 wood-frame construction in California.

2. Post-1940 wood-frame construction in California.

Model for Predicting Ground Motion and Damage Parameters of Earthquakes 21
Rossi Forel Intensities 

23456789 10

O) " H 

23 4 5678910 

Modified Mercalli Intensities

Figure 15A Relationships between Rossi-Forel and Modified Mercalli intensities and maximum acceleration. Data 

are for all stations (all rock types). Curves have a slope of 2 

and pass through Xbar, Ybar, as described in the text, 

curves for full bandwidth (SM) and bands 1 through 4 

being given. Units of acceleration are fractions of g (980 

Gal).

Rossi-Forel Intensities 

23456789 10

0 gcc 

£-3

-4

-5 I I I I I

23 4 5678910 

Modified Mercalli Intensities

Figure 15B. Relationships between Rossi-Forel and Modified Mercalli intensities and RMS acceleration. Data are for 

all stations (all rock types). Curves have a slope of,2 and 

pass through Xbar, Ybar, as described in the text, curves 

for full bandwidth (SM) and bands 1 through 4 being 

given. Units of acceleration are fractions of g (980 Gal). 

Time window is 10 s for full bandwidth and bands 2 

through 4 and 20 s for band 1.

Rossi-Forel Intensities 

23456789 10

« 2 \

E

o 0

X

a:

-2 I I I I I

23456 

Modified Mercal1i

7 8910 

Intens i t i es

Rosst-Forel Intensities 

23456789 10

E 1

v> i"

0-2

-3

RlI Bands 

Band 1

I I I

23 4 56789 10 

Modified Mercalli Intensities

Figure 15£. Relationships between Rossi-Forel and Modified Mercalli intensities and maximum velocity. Data are for 

all stations (all rock types). Curves have a slope of 2 and 

pass through Xbar, Ybar, as described in the text, curves 

for full bandwidth (SM) and bands 1 through 3 being 

given. Units of velocity are centimeters per second.

Figure 15D. Relationships between Rossi-Forel and Modified Mercalli intensities and maximum displacement. Data 

are for all stations (all rock types). Curves have a slope of 2 

and pass through Xbar, Ybar, as described in the text, 

curves for full bandwidth (SM) and band 1 being given. 

Units of displacement are centimeters.

3.

4.

This curve differs from the previous one in assuming the same level of damage at a greater intensity 

level (VIII.8 instead of VIII.O). As Evernden and 

Thomson (1985) discussed, this estimate of the protection achieved by the post-1940 code is probably 

too low.

Commercial unreinforced concrete construction. 

Residential unreinforced concrete construction.

FINAL REMARKS

All of the above relationships (steps 3-8) can be 

programmed for ease of analysis for a large set of

localities or for generation of maps. Many of these 

relationships have already been so programmed, and the 

programs are available on request. Figure 18, which is 

complementary to figure 6, gives predicted values of MMI 

for a repeat of the Fort Tejon earthquake of 1857, for 

which figure 6 gave RFI values. For those unfamiliar with 

the differences between these two scales, a study of 

figures 6 and 18 may be informative. Also, either of these 

maps can be converted to maps for other ground conditions by changing intensity units according to the unit 

designations in tables 1 and 2 and the RFI-MMI scalings 

indicated on figures 19A and 195 or similar figures, the

22 Model for Ground Motion Parameters Associated with Large Earthquakes
Rossi-Forel Intensities 

23456789 10

2 g=-

n g-1

-3

i r I I

Rll Bands 

Band 1

I I I

23 4 5678910 

Modified Mercal1i Intensities

Figure 15£. Relationships between Rossi-Forel and Modified Mercalli intensities and RMS displacement. Data are 

for all stations (all rock types). Curves have a slope of 2 

and pass through Xbar, Ybar, as described in the text, 

curves for full bandwidth (SM) and band 1 being given. 

Units of displacement are centimeters.

unit designations given in table 1 being in terms of 

Rossi-Forel intensities.

A few such maps are now presented to illustrate a 

point of particular significance the predicted levels of 

damages to California homes as the result of unavoidable 

large to great earthquakes in the future. We will not 

repeat the discussion given by Evernden and Thomson 

(1985). We will limit ourselves to presentation of maps 

illustrating the levels of damage predicted by the procedures described above. Figures 19/4 through 20C illustrate maps based on data of previous figures. Figures 19/4 

and 19B indicate along their right-hand margins the 

definitions of acceleration (fig. 19/4) and velocity (fig. 

195) units used on figures 19C through 19E. The unit 

definitions involve a twofold change in the parameter

Rossi-Forel Intensities 

23456789 10

o 2

~ 1

o 0

o

n

u-i

ui

o.

-2

 PS£UDOV«1-.S Hi 

3 __. PSEUDOVel-l Hi 

= PSEUDOVel-S Hz

 PSEUDO1

I I

23 4 56789 10 

Modified Mercalli Intensities

Figure 16. Interpreted relationship between intensity and 

pseudovelocity (5 percent damping). Ground condition is 

"soil" (Joyner and Fumal, 1985). See figure 7fand associated text.

value for a change of one in the map unit. It seemed 

irrelevant to define map units for acceleration and velocity 

values below 0.001 g and 1 cm/s, respectively. Each of the 

following three maps contains the mathematical equation 

expressing the unit relationships shown in figure 19/4 or 

195.

Figure 19C presents predicted values of maximum 

acceleration (full bandwidth) on material of ground condition L resulting from a repeat of the Fort Tejon earthquake of 1857. The values of acceleration and velocity for 

units 1 through 3 are so low that this figure and the 

following two figures indicate only unit values of four or 

greater (0.008-0.016 g and 8-16 cm/s). The asterisk and 

the dollar sign are to be understood as units 10 and 11, 

respectively. Figure 19C indicates a maximum predicted 

value of maximum acceleration slightly greater than g 

(actually, 1.18 g at RFI 8.8 on fig. 19/4 or low RFIIX). 

Figure 19/4 indicates predicted full bandwidth RMS acceleration under the same conditions to be 0.25 g.

Figure 19D, for RMS acceleration in band 2 (0.5-3 

Hz), indicates maximum predicted values of 0.028 to 

0.256 g for ground condition L or 0.512 to 0.024 on 

saturated alluvium or J ground condition (RFI 9.8, fig. 

19/4).

Figure 19E1 , for predicted maximum velocities (full 

bandwidth) resulting from a repeat of the Fort Tejon 

earthquake of 1857, indicates maximum velocity values of 

64 to 128 cm/s on ground condition L (RFI 8.8). From 

figure 195, one obtains a predicted maximum velocity on 

saturated alluvium (RFI 9.8) of 128 to 259 cm/s (unit 9) 

and on hard rock (RFI 7.3) of 64 to 128 cm/s (unit 7).

Figures 204, 205, and 20C illustrate levels of 

damage to wood-frame structures predicted by our proRossi-Forel Intensities 

23456789 10

100

10

0. i

T I

 Pre-1940 Hxr 

- ....._ Post-1940 W/F

 - UNRE-Commer.

 UNRE-Resident

23 4 5678910 

Modified Mercalll Intensities

Figure 17. Rossi-Forel and Modified Mercalli intensities 

versus mean percentage of loss to buildings of various 

types, all structural types being referenced against construction practice in California. Data sources as noted by 

Evernden and Thomson (1985). Pre-1940 W/F, pre-1940 

wood frame; post-1940 W/F, post-1940 wood frame; 

UNRE-Commer., commercial unreinforced concrete; 

UNRE-Resident., residential unreinforced concrete.

Final Remarks 23
33

122 121 120 113 118 117

Figure 18. Predicted Modified Mercalli intensities for a 

repeat of the Fort Tejon earthquake of 1857. Uniform 

ground condition of saturated alluvium (J). Minimum intensity is V. Arabic numerals indicate the lower half of an 

intensity value (9 is the lower half of IX), and letters indicate 

the upper half (j is the upper half of IX). Asterisks indicate 

the lower half of X. Compare with figure 6 to note differences between the Rossi-Forel and the Modified Mercalli 

intensity scales.

grams, the reference earthquake again being a repeat of 

the Fort Tejon earthquake of 1857. Since nearly all 

Californians live in wood-frame structures meeting the 

requirements of the post-1940 State building code, investigation of the probable damage to be experienced by such 

structures is pertinent. A repeat of the Fort Tejon earthquake will, according to some authorities, place many of 

these structures in southern California at severe risk. 

Figure 20/4 is the predicted percentage of loss to pre-1940 

wood-frame structures on saturated weak alluvium, a 

building type and a ground condition relevant today to 

only a few sites in southern California. Reference to the 

detailed ground condition maps for southern California 

given by Evernden and Thomson (1985) will illustrate this 

point. Thus, the 10+ percent loss shown bracketing the 

entire trace of the proposed rupture along the San 

Andreas fault is not expressive of reality, as the ground 

along this portion of the San Andreas is much firmer than 

that assumed for this map. Even on saturated alluvium, 

the predicted levels of damage in the greater Los Angeles 

area constitute a very low percentage of value. The major 

flaw in pre-1940 wood-frame construction in California 

was failure to fasten the buildings to a reinforced concrete 

perimeter foundation. This requirement is part of the 

post-1940 code. Assuming the relationship shown in 

figure 17 between percentage of loss and intensity, figure 

205 presents the predicted level of damage to post-1940 

wood-frame structures on saturated alluvium as a result 

of a Fort Tejon repeat. Note the marked reduction in 

predicted damage levels, which become inconsequential

throughout most of the Los Angeles area. Now, if post1940 construction is combined with the fact that nearly all 

structures in southern California are on ground of markedly better quality than saturated alluvium, we can generate a prediction such as that in figure 20C. This figure 

assumes post-1940 construction and a ground condition 

with an adjustment factor relative to saturated alluvium of 

-1 (firmer ground or water table at least 10 m below 

surface of loose alluvium). Note that maximum predicted 

percentages of loss are now only 2 along the fault rupture 

and that they are less than 1 to zero throughout essentially 

all of the built-up areas of southern California. We 

conclude that estimates of massive damage to residences 

and the associated vast disruption described by some as a 

result of this coming earthquake are in gross error. It may 

be useful to remember that the lives of San Franciscans 

would have been essentially undisturbed by the earthquake of 1906 if the only problem had been the shaking 

and associated damage. The disruption in that city was 

caused by the fire, the shaking having done remarkably 

little damage to the city. No significant structure experienced 5 percent structural damage; most suffered little or 

none (Freeman, 1932). We do not mean to imply that 

repeats of these past earthquakes will not be traumatic 

events or that there will not be severe problems of several 

sorts. We do believe, however, that expected levels of 

damage are being overestimated, to the detriment of 

proper emergency planning.

A subject requiring careful consideration by users 

and interpreters of intensity units is the current looseness 

in use of the Modified Mercalli intensity scale. All definitions of the Rossi-Forel and Modified Mercalli intensity 

units that incorporate structural damage due to shaking 

as part of the definition are based on structural styles 

current in the United States and a few European countries in the first quarter of this century or earlier. They are 

not based on current construction practice in California, 

and they never were directly usable in many countries of 

the world because of complete inconsistency between the 

structural styles assumed in the definitions and those 

actually followed in many countries. As Evernden and 

Thomson (1985) noted, cor/tinued application of old 

definitions of MMI units to communities built under 

codes far more restrictive than those assumed in the 

definitions is leading to publication of uninterpretable 

intensity maps and to consequent confusion (see Evernden and Thomson's (1985) discussion of the Coyote Lake 

and Imperial Valley earthquakes of 1979). In addition, 

using these old definitions to estimate expected levels of 

damage to modern California cities is leading to excessive 

estimates. Unless more care is taken, the entire science of 

damage estimation and ground motion estimation will be 

confused beyond resolution.

There are, of course, obvious ways to solve this 

developing problem of analysis and interpretation. If

24 Model for Ground Motion Parameters Associated with Large Earthquakes
Rossi-Forel Intensities 

23456789 10

u 

u

<r

£-3 

a

1-4

-5

E3 

B4 

I I I I I

Is

2 3 4 5 678910 

Modified Mercalli Intensities

Figure 19A RMS acceleration (all bands) versus intensity 

and acceleration units (right-hand scale) used on figures 

19£and 190. The acceleration units apply to either maximum or RMS acceleration.

.001*2MUn1t-l) TO .001*2MUntt) (g)

122 121 120

Figure 19(7. Predicted values of maximum acceleration 

(full bandwidth) on ground condition L for a repeat of the 

Fort Tejon earthquake of 1857. Map units are defined on 

the figure and indicated on figure 19/4. The asterisk and 

the dollar sign indicate units 10 and 11, respectively.

interested practioners resolve to promulgate a solution, 

the developing confusion can be arrested and eliminated. 

Group inertia much more than unavailability of a solution 

is the major factor preventing adoption of a generally 

accepted solution.

We will suggest two somewhat different routes to a 

definitive and permanent solution. Both depart from the 

premise that the original definitions must remain valid 

when applied to the structural types assumed in the 

original definitions. The two procedures can be briefly 

described as follows:

1. Greatly expand the current definitions to incorporate damage estimates to the full spectrum of (1) 

important building types and (2) characteristics that

Rossi-Forel Intensities 

23456783 10

i I I I I I 

Rl1 Rock Types

-2

I I _

I___I I I I

G %

sl

4 

3 o

23 4 5678910 

Modified Mercallt Intensities

Figure 195. Maximum velocity (all bands) versus intensity and velocity units (right-hand scale) used in figure 19E

.001*2~(Un1t-l) TO .001*2~CUnit) (g)

122 121 120

Figure 190. Predicted values of RMS acceleration (band 2, 

0.5-3 Hz) for all rock types on ground condition L from a 

repeat of the Fort Tejon earthquake of 1857. Map units are 

defined in the figure and indicated in figure 19/4.

Vel - 2MUnlt-l) TO 2MUnit) (cm/sec)

122 121 120 1 19 118

Figure 19£. Predicted values of maximum velocity (full 

bandwidth) on ground condition L for a repeat of the Fort 

Tejon earthquake of 1857. Map units are defined in the 

figure and indicated in figure 195.

Final Remarks 25
33

122 121 120 119 1IB 117

A. Pre-1940 wood-frame buildings on ground condition J.

122 36i 121 120 119 lie

35

33

117

36

35

122 121 128 119 118

33

117

C. Post-1940 wood-frame buildings on ground condition 

L (one Rossi-Forel intensity unit less than saturated alluvium).

respond to energy in the frequency band relevant to 

the original definitions. This procedure was followed 

explicitly in the People's Republic of China (Evernden, 1983).

2. Redefine intensity units in terms of expected RMS 

acceleration (or some other ground motion parameter) in the intensity-relevant bandpass, basing the 

correlations of ground motion and intensity on the 

original definitions of the intensity units. Then use 

tables or figures to express the correlation of 

expected levels or types of damage to various structural styles.

Although these two procedures appear different 

formalistically, they are simply different ways of looking 

at the same solution. Thus, the model given in Part II of 

this paper can be considered effectively a mix of the two 

procedures given above. All of the suggested procedures

34 -

33122 121 128 119 lie 117

B. Post-1940 wood-frame buildings on ground condition 

J.

Figure 20. Predicted percentages of loss as a result of a 

repeat of the Fort Tejon earthquake of 1857. Loss versus 

intensity relationship is as given by Freeman (1933) and as 

used by the Association of Bay Area Governments and by 

others (see Evernden and Thomson, 1985).

clearly and explicitly address the fundamental problem 

of the inadequacy of current definitions of intensity 

units for all current structural types.

It would seem obvious that the most logical procedure would be that described above as procedure 1. 

One must understand clearly, though, that such definitions would include as elements of intensity IX:

 Total destruction of cities built as Tungshan, China, 

was before the earthquake that flattened it in 1976.

 Average damage levels to unreinforced concrete 

structures approaching effectively total loss, 

although many would not actually collapse.

 Total loss of "modern" buildings that flaunted the 

reality of earthquake shaking or circumvented the 

spirit if not the letter of current building codes.

 Only slight damage (none of structural significance) 

to properly designed wood-frame or reinforced concrete buildings or other properly engineered structures.

Actually, such expanded definitions of intensity units 

might be useful, as they would effectively state that 

structural design can indeed defeat the levels of shaking 

associated with even the largest earthquakes. The problem with this procedure would be the cumbersome 

character of die requisite definitions. To construct 

intensity maps of future earthquakes in California, definitions such as those envisaged here will be absolutely 

necessary if the intensity maps of those earthquakes are 

to be interpretable relative to maps of older earthquakes.

26 Model for Ground Motion Parameters Associated with Large Earthquakes
A final topic for discussion is the need for-specific statements within intensity scales of the bandwidth 

of significance. It is clear from figures given earlier that 

the data for bands 2 and 3 (0.5-10 Hz) appear to scale 

similarly relative to current definitions of intensity and 

to obey nearly the relationship between ground motion 

and intensity assumed in the predictive model. This 

bandwidth may require further refinement, but it is 

quite certain that current intensity definitions link very 

closely on a physical basis with strong ground motion 

parameters from 1 Hz to several Hertz. However, it is 

just as clear that this correlation does not extend to 

lower and higher frequencies. Thus, ultimately, it would 

seem desirable to explicitly define frequency-dependent 

intensity scales. We would suggest that one of the bases 

of such definitions would be a twofold change in the 

strong motion parameter for a one-unit change in the 

frequency-dependent intensity. In this way, all "intensity 

IX" designations would have the same level of expected 

ground motion, a probably useful relationship. Since we 

are not at all sure that the community is yet prepared 

for such a leap in concept, we forego the pleasure of 

demonstrating a set of such maps.

REFERENCES CITED

Evernden, J.F., 1975, Seismic intensities, "size" of earthquakes, and related phenomena: Seismological Society of 

America Bulletin, v. 65, p. 1287-1315.

 1983, Intensity patterns in eastern Asia: Chinese 

Geophysics, v. 2, p. 405-438.

Evernden, J.F., and Thomson, J.M., 1985, Predicting seismic 

intensities, in Ziony, J.I., ed., Evaluating earthquake hazards in the Los Angeles region An earth-science perspective: U.S. Geological Survey Professional Paper 

1360, p. 151-202.

Evernden, J.F., Kohler, W.M., and Clow, G.D., 1981, Seismic 

intensities of conterminous United States Their prediction and interpretation: U.S. Geological Survey Professional Paper 1223, 56 p.

Evernden, J.F., Archambeau, C.B., and Cranswick, E., 1986, 

An evaluation of seismic decoupling and underground 

nuclear test monitoring using high frequency seismic 

data: Reviews of Geophysics, v. 34, p. 143-215.

Freeman, J.R., 1932, Earthquake damage and earthquake 

insurance: New York, McGraw-Hill, 904 p.

Helley, E.J., Lajoie, K.R., Spangle, W.E., and Blair, M.L., 

1979, Ratland deposits of the San Francisco Bay region, 

California Their geology and engineering properties, 

and their importance to comprehensive planning: U.S. 

Geological Survey Professional Paper 943, 88 p.

Joyner, W.B., and Fumal, T.E., 1985, Predictive mapping of 

earthquake ground motion, in Ziony, J.I., ed., Evaluating 

earthquake hazards in the Los Angeles region An 

earth-science perspective: U.S. Geological Survey Professional Paper 1360, p. 203-220.

Lindh, A.G., and Boore, D.M., 1981, Control of rupture by 

fault geometry during the 1966 Parkfield earthquake: 

Seismological Society of America Bulletin, v. 71, p. 

95-116.

Tinsley, J.C., and Fumal, T.E., 1985, Mapping Quaternary 

sedimentary deposits for areal variations in shaking 

response, in Ziony, J.I., ed., Evaluating earthquake hazards in the Los Angeles region An earth-science perspective: U.S. Geological Survey Professional Paper 

1360, p. 127-150.

Wilson, R.C., and Keefer, D.K., 1985, Predicting areal limits 

of earthquake-induced landsliding, in Ziony, J.I., ed., 

Evaluating earthquake hazards in the Los Angeles 

region An earth-science perspective: U.S. Geological 

Survey Professional Paper 1360, p. 317-346.

Youd, T.L., and Perkins, D.M., 1978, Mapping liquefactioninduced ground failure potential: Proceedings of the 

American Society of Civil Engineers, Journal of the 

Geotechnical Engineering Division, v. 104, no. GT4, p. 

433-446.

Ziony, J.I., ed., Evaluating earthquake hazards in the Los 

Angeles region An earth-science perspective: U.S. 

Geological Survey Professional Paper 1360, 505 p., 235 

figs.

References Cited 27