Seismic Intensities of Earthquakes of 

Conterminous United States 

Their Prediction and Interpretation JL
Seismic Intensities of Earthquakes of 

Conterminous United States 

Their Prediction and Interpretation

By J. F. EVERNDEN, W. M. KOHLER, and G. D. CLOW

GEOLOGICAL SURVEY PROFESSIONAL PAPER 1223

Description of a model for computing intensity patterns for earthquakes. 

Demonstration and explanation of systematic variations of attenuation 

and earthquake parameters throughout the conterminous United States

UNITED STATES GOVERNMENT PRINTING OFFICE, WASH INGTON: 1981
UNITED STATES DEPARTMENT OF THE INTERIOR 

JAMES G. WATT, Secretary

GEOLOGICAL SURVEY 

Doyle G. Frederick, Acting Director

Library of Congress catalog-card No. 81-600089

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

Washington, D.C. 20402
CONTENTS

Page

Abstract ___________________________ ___ 1

Introduction __ ____________________ 1

Rossi-Forel intensities versus Modified Mercalli intensities __ 2

Presently available models for predicting seismic intensities __ 3

California ___________________________ 3

Conterminous United States _______________ 4

Examples of observed versus predicted intensities____ ___ 7

Santa Barbara earthquake of June 29, 1925 _ ___ ___ 7

Monterey Bay earthquake of October 22, 1926 ______ 7

San Jose earthquake of July 1, 1911 _______________ 10

Fort Tejon earthquake of January 9, 1857 ________ _ 12

Long Beach earthquake of March 10, 1933 ________ 13

Bryson earthquake of November 21, 1952 __________ 15

Kern County earthquake of July 21, 1952 _________ 19

Page

Examples of observed predicted intensities Con.

Seattle earthquake of April 13, 1949 ____________ 23

Lompoc earthquake of November 4, 1927 __________ 27

Earthquakes of Eastern United States _ _______ _ 36

Fault length versus moment, magnitude, and energy release

versus k region._______________________ 36

Crustal calibration as function of region __ _ _________ 42 

Length of break versus moment versus k value throughout the

United States and suggested interpretation _______ 43 

Maps of predicted intensity patterns _______________ 47

Estimate of dollar loss for individual potential earthquakes __ 48 

Mathematical details of model for predicting intensities _ __ _ 51 

Details of Rossi-Forel and Modified Mercalli intensity scales __ 54 

References cited ____ ________ -_________- 55

ILLUSTRATIONS

[Plates are in pocket]

PLATE 1. Maps showing ground-condition units digitized on Vfc-minute by Vfe-minute grid and predicted Rossi-Forel intensities

for the 1857 Fort Tejon earthquake, southern California. 

2-5. Maps of conterminous United States showing:

2. Ground-condition units and attenuation factors digitized on 25-km by 25-km grid.

3. Predicted Rossi-Forel intensities on saturated alluvium and on digitized ground-condition units for the 1906 San 

Francisco, California, 1755 Cape Ann, Massachusetts, and potential Wasatch fault, Utah, earthquakes.

4. Predicted Rossi-Forel intensities on saturated alluvium and on digitized ground-condition units for the 1886 

Charleston, South Carolina, and 1872 Owens Valley, California, earthquakes.

5. Predicted Rossi-Forel intensities on saturated alluvium and on digitized ground-condition units for the 1811 New 

Madrid, Missouri, 1949 Seattle, Washington, and 1857 Fort Tejon, California, earthquakes.

Page

FIGURE 1. Map showing area of California for which geology has been digitized on a Vfc-minute by Vfe-minute grid __ 3 

2. Graph showing intensity.data of Oroville earthquake ______________________ 6

3-21. Maps showing:

3. Reported and predicted R/F intensity values for Santa Barbara, Calif., earthquake, 1925 __ __ 7

4. Predicted R/F intensity values on saturated alluvium and on ground-condition units digitized on 6-minute by

6-minute grid, Santa Barbara earthquake, 1925 ____________ __ 8

5. Predicted R/F intensity values on ground-condition units digitized on Mi-minute by Vis-minute grid, Santa Barbara

earthquake, 1925 _____________________________________________ _____ 9

6. Location of main shock, aftershocks, and isoseismals, Monterey Bay earthquake, 1926 10

7. Predicted R/F intensities for saturated alluvium and ground-condition units digitized on 6-minute by 6-minute grid,

Monterey Bay earthquake, 1926 __________________ - --- 11

8. Predicted M/M and R/F intensities for the 1933 Long Beach, Calif., earthquake ___________________ 15

9. Predicted M/M intensities for saturated alluvium and for 6-minute by 6-minute ground-condition units, Bryson,

Calif., earthquake __________________________ __ 19

10. Observed and predicted M/M intensities for Kern County earthquake, 1952, for all of California 21

III
IV CONTENTS

Page

FIGURE 11. Comparison of observed and predicted M/M intensities for region of k=lV2, Kern County, Calif., earthquake, 1952 22

12. Predicted M/M intensities for Kern County earthquake, 1952, for range of ground conditions and focal depths __ 23

13. Predicted R/F and M/M intensities for Kern County earthquake, 1952 __________________________ 24

14. Predicted M/M intensities for Seattle, Wash, earthquake, 1949, for saturated alluvium conditions and different

fault lengths _________________________________________________________ 26

15. Predicted M/M intensities for Seattle earthquake, 1949, ground conditions from 25-km by 25-km grid ______ 26

16. Predicted and observed R/F intensities for Lompoc, Calif, earthquake, 1927, for two hypothetical fault breaks

through epicenter located by Byerly__________________________________________ 27

17. Predicted and observed R/F intensities for Lompoc earthquake, 1927, for two hypothetical fault breaks through

epicenter located by Hanks ___ ___________ _ ______ _ _____ - _______ _________ - 28

18. Predicted and observed R/F intensities for Lompoc earthquake, 1927, for hypothetical fault with orientation and

length suggested by Hanks _____________________ _____________________________ 29

19. Predicted and observed R/F intensities for Lompoc earthquake, 1927, based on hypothetical fault placed so as to

yield isoseismals in agreement with observed intensities __________________________ 29

20. Predicted and observed R/F intensities for Lompoc earthquake, 1927, for various lengths of Hosgri fault and various

ground conditions ____________________________________________________ 30

21. Fault models used in calculations of site-intensity values for Lompoc earthquake, 1927 ____________ 31 

22-24. Graphs showing:

22. Lengths of fault break as a function of seismic moment and area within intensity VI contours for k= 1% and k= 1% 39

23. Length of fault break as a function of seismic moment for all k regions of conterminous United States___ ___ 44

24. Area within intensity VI contour as a function of seismic moment for all k regions of conterminous United States 45 

25. Map of California showing fault breaks used in models for estimating replacement value of damaged wood-frame

construction _________________________________________________________ 46

TABLES

TABLE 1. Correlation of geologic and ground-condition units in California ________________________ 3

2. Correlation of ground-condition units of California and assigned relative intensity values ___________ 3

3. Correlation of geologic and ground-condition units, conterminous United States _____________________ 5

4. Correlation of ground-condition units and assigned relative intensity values, conterminous United States ___ 5

5. Observed and predicted intensities, Santa Barbara earthquake ___________________________ 8

6. Observed and predicted R/F intensity values, Monterey Bay earthquake_________ 10

7. Observed and predicted R/F intensities, San Jose earthquake ___________ -___ _ 12

8. Observed and predicted R/F intensities, Fort Tejon earthquake _______________________________- 12

9. Observed and predicted M/M intensities, Long Beach earthquake _______ ________________ 14

10. Calculated parameters for the Long Beach earthquake _____________________________________ 16

11. Observed and predicted M/M intensities, Bryson earthquake _____________________ 17

12. Calculated parameters for the Bryson earthquake _________________ _________-_____ 17

13. Calculated parameters for the Bryson earthquake _________________________ ____________ 18

14. Observed and predicted M/M intensities, Seattle earthquake _________________ 25

15. Predicted and observed intensity values at specific sites, Lompoc earthquake of November 4, 1927___ _ _ _ 30

16. Average predicted intensities for saturated alluvium and Mi-minute by %-minute ground-condition units, Lompoc

	earthquake ________________________________________________________ 31

17. Calculated parameters for the Lompoc earthquake using midpoint of Byerly's (1930) "observed" intensity bands, k =

	1.75 __________________________________________________________________ 32

18. Calculated parameters for the Lompoc earthquake using modified "observed" intensities, k = 1.75 _____ 33

19. Calculated parameters for the Lompoc earthquake using midpoint of Byerly's (1930) "observed" intensity bands, k =

	1.675 _____________________________________________________________________________________________ 34

20. Calculated parameters for the Lompoc earthquake using modified "observed" intensities, k = 1.675 35

21. Observed and estimated parameters for selected earthquakes in the Eastern United States _____________ 37

22. 2L, "E0", and "M" values for selected earthquakes in the United States ___ _ _______ _______ 37

23. Observed and calculated parameters of earthquakes in regions of k = 1% and k = I1/., California and Idaho _ 38

24. Observed and calculated 2L values for selected earthquakes _________________________________ 40

25. Predicted replacement value of wood-frame construction (and all construction) damaged by potential earthquakes in

	California______________________________________________________ 50

26. Magnitude (M) relative to length of break (2L) and energy density (eD) ________________________ 52

27. Influence of variations in L and C on predicted intensity values (y = 4, Y = 0) _ 53

28. Influence of variations in y and k on predicted intensity values (C = 25, Y = 0) 53

29. Effect of length of time window on predicted intensity _______ ____ __ 54

30. Observed and predicted intensity values for the San Francisco earthquake of 1906 ________________ 54
SEISMIC INTENSITIES OF EARTHQUAKES OF CONTERMINOUS

UNITED STATES 

THEIR PREDICTION AND INTERPRETATION

By J. F. EVERNDEN, W. M. KOHLER, and G. D. CLOW

ABSTRACT

We elaborate and expand our descriptions of the procedures given 

in previous papers for calculating intensities of earthquakes of the 

conterminous United States. We discuss the contrast between 

Modified Mercalli (M/M) intensities and Rossi-Forel (R/F) intensities 

and stress the necessity for taking account of this contrast when interpreting intensity data. Two new techniques, one graphical and 

one statistical and both based on our usual mathematical model, are 

described and used to analyze several earthquakes. Further examples of the interpretability of observed intensity values in terms of 

location of fault, fault length and orientation, k value, and depth of 

focus are presented. In addition, we present a scheme for estimating 

expected replacement value of damage to wood-frame construction as 

the result of any hypothesized California earthquake. This scheme is 

shown to agree with published values of losses from the San Fernando earthquake. It is applied to numerous potential earthquakes 

in California and provides a means for estimating the approximate 

relative impact of these several earthquakes.

In a reevaluation of an earlier analysis, the statewide intensity 

values for the Kern County earthquake of 1952 are more accurately 

predicted, the predictions in this paper taking account both of variations in attenuation within California and of different definitions of 

R/F and M/M intensity units. Available intensity data of the Fort 

Tejon earthquake of 1857 are almost perfectly predicted by the 

model. Location of the Lompoc earthquake of 1927 was on the Hosgri 

fault, the intensity data allowing no other conclusion.

By use of published intensity data and seismic moments, we have 

established the relation between length of break and moment for all 

attenuation (k) regions of the conterminous United States, determining that there is nearly a thousandfold increase in moment for a 

given length of break (2L) for earthquakes in regions of k= 1 relative 

to earthquakes that occur in regaions where k=l%. We also show 

that energy in the frequency pass-band relative to intensity measurements (approximately 2-4 Hz) is a function only of length of 

break and not of k value. These two observations, illustrating drastic 

heterogeneity in stress storage in the vicinity of essentially all 

earthquakes, are shown to be consistent with a model of earthquakes 

that is based on the following assumptions: all fault zones are very 

similar and comparatively weak; high-frequency energy derives 

from breakage of asperities, while all fault breaks of a given 2L have 

similar asperity strengths and distribution; low-frequency energy 

derives from large volume relaxation; and the basic difference between fault zones as a function of k is that the weak fault zone is 

surrounded by a more and more rigid crust as k value decreases. The 

theory of weak inclusions as developed by Eshelby serves as the basis 

of this quantitative explanation.

Estimates of replacement value for wood-frame construction (and 

for total construction by scaling from the San Fernando earthquake) 

indicate that the potential California earthquakes that would cause

the greatest losses due to shaking are repeats of San Francisco 1906 

and Hay ward 1836. These earthquakes would cause losses nearly 

three and two times greater, respectively, than the expected loss 

from a repeat of Fort Tejon 1857. The total loss or replacement value 

for damage to buildings from a repeat of the Fort Tejon earthquake of 

1857 was calculated by means of our simple model to be $1.2 billion 

(1977 dollars and prices). Only about half of this loss or replacement 

value is related to wood-frame construction. Earthquakes causing 

losses one half as great as those for a repeat of Fort Tejon 1857 are a 

repeat of Long Beach 1933 and a 20-km break on the Whittier fault. 

The hypothetical 31-km break on the Malibu Coast fault and the 

32-km break on the Santa Monica fault are calculated to cause losses 

amounting to 60 percent and 190 percent, respectively, of losses 

caused by a repeat of Fort Tejon.

INTRODUCTION

Two recent papers (Evernden and others, 1973, and 

Evernden, 1975) presented a procedure for estimating 

Rossi-Forel intensity patterns for earthquakes 

throughout the conterminous United States. Evernden 

(1975) showed that the major factor controlling intensity patterns was the regional attenuation factor, k, 

which is a measure of crust/mantle attenuation properties; somewhat surprisingly, this factor correlates 

with maximum length of permissible fault break. 

Depth of focus is of secondary importance but does play 

a role in determining peak intensities in the epicentral 

region.

This report describes and illustrates a computer program for predicting intensities of any hypothetical 

earthquake at any hypothetical location in the conterminous United States. The program takes account of 

changes in k value in the calculation of intensities for 

earthquakes in regions of k equal to IVfe or less. Two 

new techniques, one graphical and one statistical and 

both based on our usual mathematical model, are described and used in analysis of several earthquakes. In 

addition, further examples of the interpretive power of 

the program in conjunction with observed isoseismal 

patterns are presented. Several examples of prediction 

are given, including detailed predictions for a repeat of 

the 1857 Fort Tejon and 1933 Long Beach earthquakes. 

Finally, a scheme for calculating expected dollar loss

1
SEISMIC INTENSITIES OF EARTHQUAKES OF CONTERMINOUS UNITED STATES

from any earthquake is described, along with its application to numerous potential earthquakes in California.

ROSSI-FOREL INTENSITIES VERSUS MODIFIED 

MERCALLI INTENSITIES

In 1931, the U.S. Coast and Geodetic Survey 

(USCGS) changed from Rossi-Forel (R/F) intensities to 

Modified Mercalli (M/M) intensities in their annual reports of intensity data of United States earthquakes 

(see section entitled "Details of Rossi-Forel and 

Modified Mercalli Intensity Scales"). From our point of 

view, this change was an unfortunate one for two 

reasons. First, it confused the literature. The two 

scales are distinctly different, but there is a tendency 

to ignore their significant differences and to treat all 

intensity maps as being on the same scale. Second, the 

R/F intensity units scale better with physical measurements and agree with nearly all other scales in 

their stepwise structure, but the M/M units do neither. 

Evernden, Hibbard, and Schneider (1973) pointed out 

that intensity predictions based on a model supposing a 

doubling of peak acceleration for a unit increase of 

intensity (ignoring high-frequency g values at short 

epicentral distances) correlated better with R/F intensities than with M/M intensities. In addition, Medvedev (1961) showed that intensity values defined by 

twofold steps in peak response of a pendulum instrument designed for accentuating periods near 4 Hz (the 

range of periods of relevance in normal intensity observations) achieved excellent agreement with R/F intensities (as well as with numerous other intensity 

scales) but clearly disagreed with M/M values. We believe that a return to the R/F scale would be very desirable. R/F intensity X should be converted to a shaking 

intensity and followed by intensity values of XI and 

XII representing ground failure. What we most certainly do not need is a new intensity scale, a step that 

would create additional confusion in the U.S. literature 

and in reading of the U.S. literature by others.

Continual introduction of more restrictive building 

codes for wood-frame structures in California will require redefinition of intensity zones. When homes 

could be thrown off their foundations, intensity R/F 

IX-X could be reported; if all wood-frame homes are 

bolted or strapped to their foundations, intensity IX 

may disappear. Recent years have seen the introduction of building styles that, though meeting codes, are 

poor earthquake risks. Further proliferation of such 

styles may create a sufficient number of seismically 

vulnerable areas for high intensities to continue to be 

reported in California.

Figure 10 (Long Beach earthquake) and figure 15 

(Kern County earthquake) and the table on page 26

(Seattle earthquake) illustrate the impact on intensity 

maps caused by the change from R/F to M/M intensities. Because the scales are equal at X (shaking intensity) and nearly one intensity unit different at R/F 

VIII (Neumann, 1931 and later volumes of "United 

States Earthquakes"), nearly 2.5 M/M intensities are 

included within 1.5 R/F units, and M/M IX is virtually 

eliminated as an observed quantity (R/F 9.5 is seldom 

reached). The absence of intensity IX values for Long 

Beach, Kern County, and Seattle earthquakes was 

noted in all reports for these earthquakes but with no 

recognition that the reason was the change in reporting units, not something to do with the earthquakes.

Given that, in a study such as this, one must convert 

M/M values to R/F or vice versa, the literature allows 

two or three schemes:

(1) Follow Medvedev (1961) and assume IV, V, and 

VI are identical for R/F and M/M. Since 2L (the length 

of fault break) values are generally set by sizes of V, 

VI, and VII boundaries, such a scheme would predict 

the same 2L values for M/M and R/F. However, trouble 

in predicting higher intensities might well appear because Medvedev places M/M VII, VIII, and IX as 

equivalent to R/F VII and VIII. Also, Medvedev's presentation of the comparison of these scales differs 

significantly from that resulting from reading of the 

scales and from that given by Neumann (1931). Medvedev (1968) uses an RF/MM relation quite similar to 

that suggested in (3) below.

(2) Interpret symbolism such as IV-V in Neumann 

(1931) as meaning IV %. Then, M/M, IV, V, VI, VII, 

VIII, IX, and X are equivalent to R/F IV %, V %, VI %, 

VII %, VIII %, IX %, and X, respectively. With this 

scheme, and setting 2L by V, VI, and VII boundaries, 

2L values are greater for the same radii of M/M V, VI, 

and VII than of R/F V, VI, and VII. The Kern County 

earthquake was analyzed in this manner. Treatment of 

the published isoseismal values of this earthquake as 

R/F leads to a predicted 2L of about 30 km, whereas 

proper use of the M/M values leads to a predicted 2L of 

about 60 km. See discussion below of Kern County 

earthquake.

(3) Assume that the scaling law between M/M and 

R/F values is a continuous function and use the following table of relative values in a scheme of linear interpolation:

R/F ......... 1 3 5 7.75 8.75 9.5 10

R/F-M/M .........0 0 0.50.750.75 0.5 0

This scheme will lead to nearly the same answers for 

2L as (2) and assumes a smooth rather than stepwise 

relation of R/F values and M/M values. We have implemented this scheme as an option in our program, 

and examples of its use are given below (Long Beach, 

Bryson, and Seattle earthquakes).
PRESENTLY AVAILABLE MODELS FOR PREDICTING SEISMIC INTENSITIES

PRESENTLY AVAILABLE MODELS FOR 

PREDICTING SEISMIC INTENSITIES

CALIFORNIA

The program described in Evernden (1975) for predicting intensities of California earthquakes has not 

been extended, other than to add the capability to predict M/M intensities. (See section entitled "Mathematical Details of Model for Predicting Intensities.") For 

an earthquake near the boundary between k regions of 

1% and ll/2, a special, as yet unprogrammed, type of 

calculation must be made. See the reanalysis given 

below of the Kern County earthquake (July 21, 1952) 

for an example of such a study. In the analysis of the 

Fort Tejon earthquake (January 9, 1857), this problem 

was avoided by using only the intensity data obtained 

in the region of k equal to 1%.

A major addition to calculational capability has resulted from digitization on a Ms-minute by Va-minute 

grid of the geologic map of California for all of western 

and nearly all of central California (fig. 1). The data

124

FIGURE 1. Area of California for which geology has been digitized 

on a Va-minute by Vk-minute grid.

used were the sheets of the Geologic Map of California 

(Olaf P. Jenkins edition) published at the scale of 

1:250,000. All geologic rock units indicated on those 

maps were grouped into 10 seismic response units (table 1). For purposes of predicting expected intensity 

values, these 10 groups were assigned relative R/F intensity values (table 2) on the basis of experience in the 

San Francisco Bay area, using procedures originally 

developed by Borcherdt (1970).

TABLE 1. Correlation of geologic and ground-condition data units in 

California

[Vii-minute by '/2-minute grid. Source: State 

Geologic Maps, scale 1:250,000]

Geologic map 

units

Ground-condition 

unit

Granitic and metamorphic rocks _________________________A

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

pCc, pCgr, pC, epC, TI) 

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, Mm, ME, <&e, $) 

"Plio-Pleistocene" sedimentary rocks ____________ ___ _ G

(Qc, OP, PC, Puc, Pu) 

Tertiary volcanic rocks __________________________-----__-__H

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

Quaternary volcanic rocks ___________________________!

(Qrv, Qpv) 

Quaternary sedimentary deposits _______-_____--_---_ _____J

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

TABLE 2. Correlation of ground-condition units of California and 

assigned relative intensity values

Mi-minute by Va-minute grid

Ground-condition unit Relative intensity

A

B

C

D

E

F

G

H

I

J

-3.0

-2.6

-2.2

-1.8

-1.7

-1.5

-1.0

-2.7

-2.7

0.

6-minute by 6-minute grid

A.

B. 

C. 

D.

Ground-condition unit

Granite

Coast Ranges 

Coastal marine sedimentary rocks 

Alluvium

Relative grid

-2.50

-1.75 

-0.80 

0.
SEISMIC INTENSITIES OF EARTHQUAKES OF CONTERMINOUS UNITED STATES

The most critical point to note relative to predictions 

given later is that all alluvial terrains (J of table 1) are 

treated in all predictions as being thick and saturated 

with water to zero depth. This assumption is certainly 

untrue in many cases, particularly today. For older 

earthquakes, the condition of full saturation was probably true in nearly all alluviated valleys and areas 

such as the Los Angeles basin, so comparison of observations and prediction for these events should be made 

on the basis of full saturation. Where the water table 

has been lowered by about 10 m, there is a drop of at 

least one intensity unit relative to that occurring when 

the water table is at the surface (Medvedev, 1962). 

Therefore, any use of the maps of this report for prediction of expected intensities and damage estimation 

should allow for this factor. One should ascertain actual depth to water table at all sites of concern, then 

lower the intensity values for alluvium shown on the 

figure by one unit if the water table is at a depth of 10 

m and IVz units if the water table is at a depth of 30 m 

or more. Also, corrections for type and thickness of alluvium should be made. Work is progressing on this 

important aspect of predicting intensities.

For studies concerned with predictions on a 

statewide or regional basis, the 6-minute by 6-minute 

grid described in Evernden (1975) was used (table 2).

CONTERMINOUS UNITED STATES

Since rates of decrease of intensity are so low in 

many areas of the United States (Evernden, 1975), the 

capability to predict intensities across changes in k 

values is a necessary aspect of a generally applicable 

program. This capability has been introduced into the 

program, there being now the capability to predict 

across multiple k boundaries. The logic used depends 

upon the fault break appearing as essentially a point 

source at adequate distance of the k boundary from the 

center of the break; this condition is fulfilled at four 

times the fault length or greater. Because potential 

fault lengths are 60-80 km in regions where k = 1V6, 

about 20 km in regions where k = l1^, and 5 km or less 

in regions of k = 1, this distance requirement is easily 

met in nearly all situations of interest in these regions. 

In regions where k = 1% or where the earthquake is 

too near the k boundary to be treated as a point source, 

an as yet unprogrammed technique is followed (see discussion of the Kern County earthquake of July 21, 

1952).

Plate 2 indicates the pattern of k values now incorporated in the program, the figure actually giving 4k 

values. Stepwise changes in k values are almost certainly erroneous, but no more sophisticated model 

seems warranted at this time.

A few additional comments on this plate are appropriate. Milne and Davenport (1969) studied attenuation rates of intensity and acceleration in eastern 

Canada and Northeast United States, using data of the 

1925 St. Lawrence, 1929 Grand Banks, 1935 Timiskaming, 1939 St. Lawrence, and 1944 CornwallMassena earthquakes. They found a k value of very 

nearly 1.0 as appropriate for this general region, a 

value in agreement with that used by us.

The map shows a region of 4k = 5 intruding along 

the St. Lawrence River into the great area of 4k = 4 

that includes most of the Eastern United States. This 

region of 4k = 5 is established on the basis of analysis 

of several earthquakes (Evernden, 1975). Peter 

Basham of the Dominion Observatory, Ottawa, 

Canada has indicated (oral commun., 1978) that 

analyses conducted by the group at Dominion Observatory confirm the existence of this zone. They have 

analyzed data of some small events along the St. Lawrence River and have established the boundary between the zone of 4k = 4 north of the St. Lawrence and 

the zone of 4k = 5 along the St. Lawrence. Thus, nearly 

all major seismic activity in the eastern part of the 

continent can be related to the region of 4k = 5. All 

activity along the St. Lawrence and the Cape Ann and 

Charleston earthquakes are certainly in such regions, 

and the possibility exists that the New Madrid earthquake was also in such a region (Evernden, 1975). The 

detailed placement of 4k boundaries on figure 2 has a 

degree of uncertainty about it. Along and east of the 

Mississippi embayment, the 4/5 boundary is placed 

along the inland limit of Tertiary subsidence. Westward, the location of the zone of 4k = 5 between zones 

of 4 and 6 is pure conjecture, and its extent northward 

into Canada is even less certain.

The Geological Map of the United States published 

in the National Atlas of the United States of America 

(p. 74 and 75) was used for the complementary geologic 

base. Digitization was on a 25-km by 25-km grid. Table 

3 indicates the seismic units that correspond to the 

geologic units of the geologic map, plate 2 shows the 

United States mapped in terms of these seismic units, 

and table 4 gives tentative relative intensity values for 

these units.

In the study of an earthquake, three maps are 

printed routinely. The first map presents the groundcondition data in terms of seismic response units. The 

second map indicates predicted R/F or M/M intensities 

on saturated alluvium. For earthquakes in California 

and using the ^-minute by Vfc-minute grid, either a 

contoured or digitized version of this map can be presented. The third map presents predicted R/F or M/M 

intensities in accordance with the ground-condition 

data of the first map. The third map is always printed
PRESENTLY AVAILABLE MODELS FOR PREDICTING SEISMIC INTENSITIES

in digitized form. A variety of map formats can be produced, several of which are illustrated in following 

figures.

It is important to remember that the depth sensitivity of the intensity values is controlled by a factor C 

(Evernden, 1975), which is an unknown function of 

depth and, therefore, does not have a value equal to 

depth. For earthquakes of normal depth in western 

California, the C value that yields intensity values in 

best agreement with observations is 25. In general, it 

appears that C is about equal to depth of focus plus 15 

to 20.

Through no basically new modes of calculating event 

parameters from intensity data have been designed, we 

have developed two new techniques for making such 

calculations. The first technique was stimulated by 

Hanks' use of AVi (area within intensity VI contour 

on published intensity maps) values (Hanks and others 

1975). When we tried to use such AVi values for estimating event parameters, we found that they commonly yielded invalid estimates of 2L and values of 2L 

in disagreement with estimates based on use of all intensity data. The errors were greatest for small values 

of AVI (less than 1014 cm2 ). Therefore, we designed a 

technique that tried to avoid the problem of small AVi 

values, used all intensity contours, and was useful with 

published intensity maps.

We do not use intensity areas from these maps. 

Rather, we use the maximum distance of each contour 

from the epicenter (for long faults, we use maximum 

distances both perpendicular and parallel to the fault). 

The logic behind this procedure is the recognition that 

ground condition can seriously perturb contour values, 

particularly for small-area contours. We assume that 

the maximum dimension of any intensity contour i (Rj) 

is the best estimate we can make from the contours of

TABLE 3. Correlation of geologic and ground-condition units, conterminous United States

[Source: National Atlas of the United States]

Units of geologic map Ground-condition unit

Sedimentary rocks

Quaternary ______

Upper Tertiary ___ 

Lower Tertiary _____

Cretaceous _______

Jurassic arid Triassic 

Upper Paleozoic ______

Middle Paleozoic ____

Lower Paleozoic ______

Younger Precambrian 

Older Precambrian___

Volcanic rocks

Quaternary and Tertiary volcanic rocks.

Intrusive rocks

All ages__._________________________

_K

the maximum distance that any given intensity was 

felt on saturated ground. In estimating 2L, we also use 

the reported local magnitude (ML) and the maximum 

recorded intensity (I(MX), corrected for ground condition if necessary). We interpret the "Limit of Detection" (L.O.D.) contour as intensity 3.0 if there is an 

intensity IV contour and as intensity 3.0-3.5 if there is 

no intensity IV contour. This usage of the L.O.D. contour derives from analysis of numerous intensity maps.

These several values for each earthquake [R, values, 

I(MX), and (ML )] are plotted on a figure for the appropriate k value. See figure 2 as an example of such an 

analysis. We then make a somewhat subjective interpretation of the data (that is, ignoring highintensity radius if it disagrees badly with other data), 

selecting the 2L value that seems to give the best fit to 

all data. The 2L estimate obtained in this simple manner has always been within a factor of two of that obtained by detailed station-by-station analysis. When 

the Rj, I(MX), and ML values yield a consistent estimate of 2L, the agreement with detailed analysis is 

improved.

Because of the satisfactory agreement between the 

detailed calculations and those by the technique just 

described, all analysis of earthquakes of the Eastern 

United States will be by the latter technique.

The second new technique of analysis was developed 

to satisfy requests that we generate a statistical approach to analysis of intensity data. The approach we 

have followed is to use observed station values of intensity as the input data (corrected for ground condition) and to calculate fault centers, fault lengths, and 

fault orientations that minimize several fitting 

criteria, all calculations of intensity being as in our 

regular calculations.

The observational data are treated singly in some 

criteria and are grouped into bandwidths of observed 

intensity value in other criteria. When all data are 

considered in a criterion, either all points are treated 

separately or bandwidth values are weighted according 

to the inverse of the bandwidth. Thus, for the Lompoc

TABLE 4. Correlation of ground-condition units and assigned relative intensity values, conterminous United States

Ground-Condition unit Relative intensity

A 

B 

C 

D 

E 

F 

G 

H 

I 

J 

K 

L

0

-1.00

-1.50

-2.00

-2.25

-2.50

-2.75

-2.75

-2.75

-3.00

-3.00

-3.00
6 SEISMIC INTENSITIES OF EARTHQUAKES OF CONTERMINOUS UNITED STATES

earthquake, Byerly (1930) reported intensity values as 

IX, VIII, VI-VII, and IV-V, that is, bandwidths of 1, 1, 

2, and 2.

The several criteria we have investigated are:

(a) H - L, called (H - L) in tables;

(b) 2 H - L|j, called H - L in tables; 

I

(c) 1/nS (Obs - CalcX, called (O - C) in tables; 

i

(d) 1/nS Obs - Calc| b called O - C in tables; 

i

(e) l/n2 (Obs - Calc)f, called R.M.S. in tables; 

i

(f) On plot of (Obs - Calc)i versus ObSj, calculate 

absolute value of area between line Obs - 

Calc = O, regression line (Obs - Calc)i = 

a+b(Obs)i, and lines Obs = 3.5 and Obs = 

9.5. The actual parameter used is width of 

the rectangle of equivalent area and length 

on the Obs - axis. This parameter is called 

CP in the tables. This criterion seeks a 

minimum of residuals against a prescribed 

and reasonable pattern of residuals rather 

than merely seeking the conventional 

minimum of (e). Also, it allows estimates of 

probability of nonminimum values. Criteria 

(e) and (f) should yield nearly the same estimate of event parameters.

In the above formulae,

H = number of stations having calculated intensities greater than band of observed value, 

L = number of stations having calculated intensities less than band of observed value, 

I = band value,

i = observed intensity at station i, all Obs values having the central value of each band,

i = calculated intensity at station i. 

n = number of observing stations. 

These quantities are calculated for a network of potentially possible sets of source parameters. The calculations begin with a denned fault line (straight or 

curved), either as observed (Hosgri fault for Lompoc 

earthquake, Newport-Inglewood fault for Long Beach 

earthquake) or as assumed (extension of Hosgri fault 

south of Point Sal). The coordinates S (slip) and T 

(translation) are measured parallel and perpendicular 

to the great circle best fitting the fault trace. We select 

a reference center of break on the basis of an initial 

analysis of the intensity data. We then select a pattern 

of S, T, and 2L values as test solutions. If deemed appropriate, we vary the C value (depth parameter), k 

value, and orientation of the modeled fault (rotate an 

angle 3> counter-clockwise through assumed center of 

fault after slip and translation).

With observed data well distributed in all quadrants 

and at all distances around an epicenter and with accurate corrections for ground condition, the several 

criteria should yield minima with nearly the same 

event parameters. If data are too limited at short 

ranges, the CP criterion can fail when using fourquadrant data. When observations well distributed in 

distance are limited to about a 120° quadrant including 

axis of fault and its perpendicular, the CP criterion will 

yield an excellent minimum, especially when combined 

with independent geologic data, and will be very sensitive to the best k value. We reserve further discussion 

of this mode of analysis until we discuss the several 

quakes analyzed by this technique.

10000

1000

100

10

OROVILLE EARTHQUAKE

PARAMETERS FROM DATA:

I (MX), ML, Ri VALUES

k(1.50), C(25) 

PARAMETERS FOUND:

2L=1.5km 

AVI =1.3x10" cm2

10 15 u

1013

100 10 1

LENGTH OF FAULT BREAK, IN KILOMETERS

I (MX) 10 9 8 7

1012

FIGURE 2. Analysis of intensity data of Oroville, Calif., earthquake August 1,1975.
EXAMPLES OF OBSERVED VERSUS PREDICTED INTENSITIES

EXAMPLES OF OBSERVED VERSUS PREDICTED 

INTENSITIES

SANTA BARBARA EARTHQUAKE OF JUNE 29, 1925 

(ROSSI-FOREL INTENSITIES; BYERLY, 1925)

Known parameters:

(1) k = 1% (epicenter in western California)

(2) C = 25 (normal depth for California earthquakes)

(3) Location of faulting (denned by observed intensities) 

Unknown parameter:

(4) 2L

Location of the fault break and its length are constrained by the observed intensities. In a region where 

k = 1%, intensity values of IX or greater extend only a 

comparatively few kilometers laterally from the fault 

break, particularly when fault breaks are in the range 

of 30 km. Therefore, the pattern of published isoseismals (fig. 3) requires a break length of 30-40 km and a 

location of the break near or just onshore.

Fault lengths of both 30 km and 40 km were investigated; figure 3 illustrates predicted intensities for 2L = 

40 km. The observed and reported intensity values are 

in good agreement, and the reported values are assumed to be relevant to saturated alluvium because 

nearly all reporting localities were on alluvium. The

120°30'

SANTA BARBARA EARTHQUAKE 

JUNE 29, 1925

120°00' 119°30'

35°00'

34"30'

FIGURE 3. Reported and predicted R/F intensity values for Santa 

Barbara earthquake, June 29, 1925 (2L = 40, C = 25, k = 1%). 

Reported values are in Roman numerals.

detailed shape of the intensity VIII contour from 

Byerly (1925) is quite certainly the result of trying to 

include within one contour line all VIII observations, 

even though these are distributed on both sides of the 

Santa Ynez Mountains. The solid or predicted intensity 

lines on figure 3 are based on saturated alluvium and 

do not indicate geologic factors. If these are taken into 

account, the predicted shape of the intensity 8 contour, 

if the presence of the Santa Ynez Mountains is ignored, 

is as reported by Byerly (fig. 4). Figure 5 indicates the 

detailed pattern of predicted intensities when using a 

1/2-minute by 1/2-minute geologic grid.

Byerly (1925) acquired intensity data only along or 

near the present route of Highway 101, that is, along or 

near the road extending from Ventura through Santa 

Barbara to Santa Maria and San Luis Obispo. Thus, no 

observations were collected for the entire northeast 

quadrant. The absence of values in this area does not 

indicate low intensities but lack of data.

Note on figure 3 that the predicted area of intensity 

VI reaches only as far to the northwest as was observed. Shortening of the fault by a factor of 2 (to 2L = 

20) would yield predicted intensities that are too low 

for stations north of the mountains. A comparison of 

predicted versus observed intensities versus length of 

2L is given in table 5.

Even for 2L = 40, predicted values may be slightly 

too low. Attempts to estimate 2L by size of the reported 

IX area are complicated by the fact that there may not 

have been reports at the full range of actual IX-level 

shaking. The reported length of the IX area is 42 km, 

but a 2L of 40 km predicts a IX-length of 74 km and a 

2L of 30 km predicts a IX-length of 55 km. These values would suggest a 2L of 20 or less, which would 

markedly disagree with the data of table 5. The 

seemingly most reasonable conclusion is that the 

length of the IX region for saturated alluvium is not 

expressed by Byerly's (1925) contouring and that the 

individual station reports at greater distances provide 

the best basis for estimating the fault length (2L). 

Thus, we conclude that a 2L of 30 to 40 km is in near 

agreement with observations, and an estimate of 2L = 

40 is favored.

MONTEREY BAY EARTHQUAKE OF OCTOBER 22, 1926 

(ROSSI-FOREL INTENSITIES; MITCHELL, 1928)

Known parameters:

(1) k = 1% (western California)

(2) C = 25 (normal depth)

(3) Location of fault break (aftershocks-main 

epicenter)
SEISMIC INTENSITIES OF EARTHQUAKES OF CONTERMINOUS UNITED STATES

(4) 2L = 20-40 (maximum length of 40 by aftershocks)

The parameters of this earthquake can be set quite 

well without recourse to intensity data. However, an 

apparent discrepancy between 2L values based on aftershocks and on intensity values can be shown. The 

epicenter of the main shock is well controlled and is 

just offshore from Monterey. Aftershock locations, 

based on S-P times at Berkeley, were placed as far 

north as the coastline west of Santa Cruz (Mitchell,

TABLE 5. Observed and predicted intensities, Santa Barbara earthquake

Site

San Luis Obispo

Arroyo Grande

Nipomo

Santa Maria

Orcutt

Los Alamos

Los Olivos

Gaviota

Goleta __ _

Ventura

Santa Barbara

Observed Predicted intensity1

intensity 2L = 40 km

__ ___JV 4(6)

. __ _-.VI 5(6)

___ __VII 6(6)

_ _ VII 5-6(6)

__ ___ VII 6-7(7)

- . VII 7(7)

______ VIII 7(7-8)

________VI 7(7)

 -VIII 8(8)

___ ___ _VIII 7-8(8-9)

____ IX 8(9)

___ _ _VII 7-8(7-8)

________X 8(9)

2L = 30 km

4(5-6) 

5(5)

6(6) 

5-6(6) 

6(6-7) 

6-7(6-7) 

6-7(7) 

6(6) 

8(8) 

7(8) 

8(9) 

7(7) 

8(9)

'First number incorporates ground condition as on 6-minute by 6-minute grid. Second 

number is for saturated alluvium.

1928)/(fig. 6). If the aftershock zone is deemed a measure of 

length of faulting at time of the main earthquake, a 2L of 44 km results. For comparison, we calculated predicted intensity values for 2L values of 22 and 

44 km, both fault breaks extending northward from the 

epicenter of the main event (see table 6 and fig. 7). 

Table 6 presents observed and predicted R/F intensities 

for 2L values of 22 and 44 at various sites. The stations 

are arranged by increasing latitude, and the two 

modeled fault breaks are indicated in proper latitudinal relation to the stations.

Both models show excellent agreement between predicted and observed intensities for stations south of the 

breaks. For stations at the same latitude or more 

northerly latitudes, the intensities predicted by a 2L of 

44 are clearly too high. Average observed intensity for 

these 14 stations is 5.2, average predicted intensity for 

2L of 22 is 5.6, and average predicted intensity for 2L of 

44 is 6.3. Our conclusions are that a fault break of 22 

km is an appropriate length to use for modeling the 

high-frequency source of the main event and that this 

source was the southern portion of the aftershock zone. 

One might, of course, suggest use of a 2L of 44 km with 

the energy density reduced below the normal value 

(Evernden, 1975). Intensities to the north would still 

be predicted as too high.

121° 120°

SANTA BARBARA EARTHQUAKE

JUNE 29, 1925 

2L=30km, C=25, k=l%

119° 121

35°

34°

IdVlb

100 KILOMETERS

FIGURE 4. Predicted R/F intensity values, 6-minute by 6-minute grid, Santa Barbara earthquake, June 29, 1925 (2L = 40, C = 25, k 

1%).A, Saturated alluvium. B, 6-minute by 6-minute ground-condition units (table 2).
EXAMPLES OF OBSERVED VERSUS PREDICTED INTENSITIES

A point of possible significance is the prediction of 

too-high intensities for San Jose, Morgan Hill, and 

Palo Alto. In the presently used codification of geologic 

maps, all Quaternary deposits are treated as of equivalent physical properties and of appreciable depth with 

the water table at the surface. This is a gross simplification that will lead to prediction of excessively high 

intensities in regions of thin and (or) unsaturated and

120°50' 

35°00'

120°40'

SANTA BARBARA EARTHQUAKE 

JUNE 29, 1925

2L=40km 

120°30' 120°20' 120°10' 120°00'

34°50'

34°40'

34°30'

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6

10 KILOMETERS

I I

FIGURE 5. Predicted R/F intensity values for 1/2-minute by Ms-minute ground-condition units, Santa Barbara earthquake, June 29, 1925. 

Computer plot of south half of Santa Maria sheet of Geologic map of California. 2L = 40.
10 SEISMIC INTENSITIES OF EARTHQUAKES OF CONTERMINOUS UNITED STATES

(or) physically different materials. Thus, for the sandcovered areas of much of western San Francisco, the 

use of a formulation that assigns all Quaternary materials the same ground condition leads to predicted intensities for the 1906 San Francisco earthquake that 

are much too high (9+ predicted, 7+ observed). In this 

case, thin unsaturated sand on bedrock (Franciscan 

Formation) reacted as essentially bedrock. Without details of local geology, we chose in this paper to predict 

the worst case while advising everyone of that fact and 

suggesting more refined work in local areas so that 

improved estimates of expected intensity values in 

areas of Quaternary deposits can be made.

Palo Alto circa 1926 was nearly entirely on ground 

now characterized as Older Bay Mud. It is stronger 

than Young Bay Mud. In Evernden, Hibbard, and 

Schneider (1973), the Young Bay Mud (F) was assigned 

relative intensity of ( + MO, while Older Bay Mud (E) 

was assigned a value of ( 1&).

123°

MONTEREY BAY EARTHQUAKE 

OCTOBER 22, 1926

122° 121° 120° 119°

Morgan Hill and San Jose are located in the Santa 

Clara Valley on thick valley alluvium. If the ground 

were saturated, these areas would be expected to reach 

nearly the intensity values predicted for our standardized Quaternary (J of table 2). However, by the 

time of the 1926 earthquake, the water table in the San 

Jose area had been lowered by several tens of meters. It 

may be relevant to point out that predicted intensities 

for San Jose resulting from the San Francisco 1906 

earthquake were correct but those for 1926 were too 

high. The predictions for San Jose and Morgan Hill for 

the Monterey Bay earthquake are probably too high 

because the present model fails to incorporate depth to 

water table in its predictions.

Thus, any predictions for a coming earthquake based 

on our present modeling of Quaternary deposits should 

be lowered by at least one intensity unit for parts of the 

Santa Clara Valley in which the water table has been 

lowered 10 m or more. One of the most effective ways to 

protect a community from high intensities (VIII + ) 

might be to lower the water table several tens of meters. Shaking intensities of greater than R/F VII-VIII

FIGURE 6. Location of main shock, aftershocks, and isoseismals, 

Monterey Bay earthquake, October 22, 1926.

SAN JOSE EARTHQUAKE OF JULY 1, 1911 

(ROSSI-FOREL INTENSITIES; TEMPLETON, 1911)

Known parameters: 

(1) k = 1% (western California) 

(2) C = 25 (normal depth) 

(3) Location (Wood, 1911) 

(4) 2L = 5-11 (aftershocks)

TABLE 6. Observed and predicted R/F intensity values, Monterey 

Bay earthquake

Site Observed 

Intensity

Santa Maria _ III

King City _____-_.______-_-___V-VI

Hollister _ _ IV- V

Santa Cruz _ _ _ VII+

Morgan Hill _ V

Palo Alto _ _ _ _ V

San Leandro V

Berkeley V

San Francisco (downtown)

Predicted intensity

2L=22

3-4 

3 

3 

4 

5-6 

6 

6-7 

7 

6 

7 

7 

7-8 

5 

6 

6 

6 

5 

5 

4-5 

5 4-5 

4 

5 

5 

4+

2L=44

4 

3 

3

5 

6 

6 

6-8 

8 

7 

8 

8 

8 

7 

7 

6 

7 

5 

6 

5 

5 

4-5 

5 

5 

5 

5 

5
EXAMPLES OF OBSERVED VERSUS PREDICTED INTENSITIES 11

This earthquake is of interest because it is one of the 

very few earthquakes of approximately magnitude 6 

that has occurred in central California since 1906. The 

location of this earthquake is as suggested by Wood 

(1911). To quote from him (p. 39) "Examination of the 

map and its explanatory table shows clearly that the 

circles of origin-distance for a majority of the shocks 

(and also, in the main, those most reliably determined 

having Mt. Hamilton at center) intersect the projected 

course of the Hay ward fault at frequent intervals all

the way from a point due south of Mt. Hamilton to a 

point due north of Gilroy, a distance of about 12 km 

along the course of the fault." Though more recent 

geologic mapping has led to the interpretation that the 

region considered by Wood to contain an extension of 

the Hayward fault actually contains an extension of 

the Calaveras fault, his basic mode of estimating fault 

length is still valid because the Calaveras fault in this 

part of its course lies exactly where Wood considered 

the Hayward fault to be. We modeled this earthquake

123 C

MONTEREY BAY EARTHQUAKE

OCTOBER 22, 1926 

2L=22 km, C = 25, k= 1%

121° 120° 123° 122

100 KILOMETERS 

_J

FIGURE 7. Predicted R/F intensities for Monterey Bay earthquake of October 22, 1926 (2L = 22, C = 25, k = 1%). A,

Saturated alluvium. B, 6-minute by 6-minute ground condition.
12 SEISMIC INTENSITIES OF EARTHQUAKES OF CONTERMINOUS UNITED STATES

using two different values of 2L, a value of 11 to agree 

with the aftershock zone, and a value of 5l/2 as half of 

that zone; we chose to use the south half of the aftershock zone. Table 7 gives a comparison of observed and 

predicted intensity values for 2L values of 11 and 5V6. 

The major unexplainable discrepancy between reported and predicted values is the area of San Francisco, for which Templeton gives a value of VI-VII; the 

model predicts only V on saturated alluvium. The reported San Francisco intensity is inconsistent with the 

entire pattern of other observed values. In order for 

intensity VII to be predicted at San Francisco, this 

earthquake would have required a 2L of 75, a totally 

inadmissable value in view of the absence of surface 

breakage and of the inconsistency of such a length with 

all other intensity data. In addition, McAdie (1911) reported "There was * * * no damage of any consequence 

in San Francisco." "Few objects were overturned * * *". 

The VI-VII value assigned by Templeton must be in 

error.

Gilroy, Watsonville, and Santa Cruz are all predicted to have experienced higher intensities than reported, the predicted intensities (table 7) having been 

derived from the assumption that these communities 

are situated on saturated alluvium. The explanation 

for these too-high predictions may be that the appropriate ground condition for these sites is less sensitive 

than saturated alluvium.

Both San Jose and Morgan Hill experienced intensities as predicted for saturated alluvium, in contrast

TABLE 7. Observed and predicted RIF intensities, San Jose earthquake

Site

Modesto

Sacramento

Santa Rosa

Monterey

Berkeley

Hayward

Stockton

Watsonville

Santa Cruz

Belmont

Pleasanton

Livermore

Oakland

Redwood City

Palo Alto _ __

Calaveras Valley

San Martin

Gilroy

Boulder Creek

Pescadero

San Francisco

Morgan Hill

Los Gatos

Saratoga

Santa Clara

San Jose

Coyote

Observed

intensity

 _____ 4

________4

4

________4

____ _ _5

______-_5

________5

________5

6

________5

 _____ 5-6

____ ___5

____ ___6

________6

________6

6

6

___.____6

6

________6-7

 _____6-7

________7

________?

7

______-_7

7

_____-__8+

Predicted intensity

2L=5V2

5

4

3-4

3-5

 5

5

5

1 6-7(A1)

6-7(Al)

5

5

5

5

5

6

6

6

7-8(Al)

5-6

5

5(A1)

7

7

6-7

6-7

7

8

2L=11

6

4

4

3-5

5

5-6

5

7(A1)

7-8(Al)

6

5

5-6

5-6

6

6

6

7

8

6

6

5(A1)

8

7

7

7

7

8

'(Al) signifies that predicted intensity values entered in table are based on saturated 

alluvium. Discussion of the discrepancies between observation and prediction for these 

stations is included in the text.

to the prediction for the Monterey Bay earthquake, 

thus supporting the conjecture made earlier about the 

effect of lowering of the water table in the Santa Clara 

Valley between 1906 and 1926.

The observed data appear to agree better with a 2L of 

5 x/2 than with one of 11, and averaging of observed and 

predicted values would suggest a 2L nearer 5V2 than 

11.

FORT TEJON EARTHQUAKE OF JANUARY 9, 1857 (MODIFIED 

MERCALLI INTENSITIES; AGNEW AND SIEH, 1978)

Known parameters:

(1) k = 1% (region of concern south and west of 

San Andreas fault)

(2) C = 25 (normal depth)

(3) Location of faulting (San Andreas fault)

(4) 2L = 320 (surface breakage Cholame to

Cajon Pass)

This earthquake has been reanalyzed (Evernden and 

others, 1973) using the model of Evernden (1975) and 

using a k value of 1%. The most interesting aspect of 

this study is that, thanks to the labors of Agnew and 

Sieh (1978), there is now available a compilation of 

numerous intensity observations for this earthquake. 

Intensity values experienced at numerous sites in 

California can now be compared with predicted values. 

Table 8 indicates Rossi-Forel intensity values estimated by us using the data of Agnew and Sieh (they 

chose to use M/M intensities) and R/F intensity values 

predicted on saturated alluvium for a fault break exTABLE 8. Observed and predicted RIF intensities, Fort Tejon earthquake_____________________

Site Observed

intensity

Predicted 

intensity

San Diego _________________ V-VI 5

San Bernardino _______________-__VII-Vin 8

San Gabriel Valley__________________Vin 8

Los Angeles (downtown) _________VII + 7 (high)

San Fernando Valley ____ ___VIII- 8

34.6°N. 117.4°W. ____________ _ _ __VIII- 8

34.1°N. 119.0°W. __________________VIII- 7

Ventura ___________________________-Vffl+ 8

Santa Barbara _______________ VII 7

San Andreas fault _________ ____ = IX ^9

Fort Tejon __________________.___VIII-IX 9

34.0°N. 118.7°W. ______ VIII+ 9

35.4°N. 119.0°W. ____________________VIII+ 9

35.9°N. 119.3°W. ____-_ VI- VII 7

36.2°N. 119.3°W______ --VII+ 7

Visalia _______________________ VII-VIII 6

36.7°N. 121.3°W. _____________________-VII 6

Monterey _________________IV-V+ 4-6

Santa Cruz _____________ III-V+ 3-5

San Francisco ___________--- V+ 4

Stockton ___________________IV 5

Sacramento _____________ V+ 4 1 

__________________________________5-62

'All path k=l%. 

2Part ofpathk=lH>
EXAMPLES OF OBSERVED VERSUS PREDICTED INTENSITIES 13

tending along the San Andreas fault from lat 34°18.3' 

N., long 117°3.15' W. to lat 35°55.0' N., long 120°27.9' 

W.

Agreement between prediction and observation is 

excellent, there being virtually no sites at which observed and predicted R/F intensities differ by as much 

as one (1) intensity unit.

The data for the 1857 earthquake substantiate the 

prediction that the peak intensity to be expected in the 

Los Angeles area from a great earthquake on the San 

Andreas fault is R/F VII/VIII, San Fernando Valley 

and eastern Los Angeles experiencing possibly VII. 

These intensities presume a zero depth to water table. 

The marked lowering of the water table in much of this 

area in the intervening 120 years should result in peak 

intensities VI/VII in most alluviated areas of the San 

Fernando Valley and Los Angeles.

We have modeled this earthquake in detail using the 

Mi-minute by V2-minute grid. Plate 1 indicates geology 

of the area and also indicates predicted R/F intensities 

with ground-condition corrections of table 2 applied 

and assuming zero depth to water table in alluviated 

areas (J regions of plate 1). This plate is as published 

by Blume and others (1978); they used our predictions 

in constructing it.

As pointed out by Algermissen (1973) and substantiated by Blume and others (1978) and this study, a 

repeat of the great 1857 Fort Tejon earthquake will not 

be a disaster of the magnitude sometimes imagined. 

San Fernando Valley will suffer less from an 1857 repeat than it did from the San Fernando 1971 earthquake. The remoteness of the San Andreas fault from 

heavily urbanized areas in southern California and the 

high rates of attenuation in the region will result in a 

repeat of the 1857 earthquake having a surprisingly 

small impact on the area as a whole. This conclusion is 

supported by results given in a later section in which 

predictions oflosses for numerous potential California 

earthquakes are given.

A fact worth mentioning here is a basic disagreement of the general near-fault patterns of predicted 

intensity shown on plate 1 and previously presented for 

the San Francisco 1906 earthquake (Evernden and 

others, 1973) with the reported pattern shown by Lawson (1908, maps 21-23) for the San Francisco earthquake. Lawson shows narrow zones of all intensities as 

the fault is approached, irrespective of ground condition and any ideas of attenuation as linked with depth 

of focus. No model incorporating legitimate values of 

attenuation and depth of focus can predict such patterns as shown by Lawson. In addition, there is total 

absence of data within Lawson (1908) to support the 

near-fault intensity contouring on his maps. In fact, 

the data of his study specifically refute his contouring.

Apparently, Lawson worked under the assumption 

that all intensities must occur between VI and X-XI, 

even though intensities VI through IX are largely defined by shaking criteria whereas X and IX are defined 

by ground rupture. It is perfectly possible to have severfeet of displacement associated with shaking intensities on only VII VIII. It is our belief that Lawson's 

near-fault contouring is almost totally a derivative 

of misconception and is quite erroneous. No modeling 

of expected intensities for a repeat of 1906 or any other 

earthquake should incorporate near-fault patterns of 

intensity as shown by Lawson.

LONG BEACH EARTHQUAKE OF MARCH 10, 1933 (MODIFIED 

MERCALLI INTENSITIES; NEUMANN, 1935)

Known parameters:

(1) k = 1% (western California)

(2) C = 25 (normal depth)

(3) Location of faulting (aftershocks)

(4) 2L = 22-44 (S and P travel times, aftershocks) 

This is an interesting earthquake for a variety of 

reasons, a principal one being that it was the first 

major earthquake to be reported by the U.S.G.S. in 

Modified Mercalli units of intensity. Thus, it is the first 

significant earthquake without reports of intensity IX 

in the epicentral region. It is certain that, if this earthquake had been reported in units of Rossi-Forel intensity, a clearly defined region of intensity IX would have 

been defined, and this earthquake would have been 

accorded greater status in the hierarchy of historical 

California earthquakes.

Two possible models for this earthquake seem appropriate. The first is to make 2L equal to the aftershock zone, that is, about 40 km, as reported in Hileman, Alien, and Nordquist (1973). The second is to follow Benioff (1938) and use a 2L of about 27 km, an 

estimate based on comparison of S-P arrivals at southern California stations, the solution being restrained to 

lie along the Newport-Inglewood fault as indicated by 

the aftershocks. In our initial studies, we used 2L values of 22 and 44 km with the south end of both models 

being at the epicenter (k of 1.750). Table 9 gives observed and predicted Modified Mercalli intensities for 

both 2L values. Assuming that all sites in alluvial 

plains or on beaches behaved as for saturated alluvium, a 2L value of 22 is indicated as appropriate. If 

the 6-minute by 6-minute ground condition is used, the 

values in square brackets are predicted for San 

Clemente, El Toro, and San Diego; these values are in 

better agreement with observed values. As to the appropriateness of the assumption of saturated ground 

near Long Beach, Wood (1933) points to the correlation 

between "bad natural ground" and "deep water-soaked
14 SEISMIC INTENSITIES OF EARTHQUAKES OF CONTERMINOUS UNITED STATES

alluvium." The general over-prediction of intensities in 

the VII zone when using a 2L of 44 would seem to imply 

too great a 2L because most of these sites were on alluvium. However, if pumping had lowered the water 

table to a 10-m depth, a 2L of 44 would be a better 

value. We conclude, on the basis of information in 

hand, that a 2L of 22 is more likely than a 2L of 44. 

Estimating the losses to be expected from a repeat of 

this earthquake depends strongly on knowledge of the 

depth to the water table in 1931 and today.

Wood (1933) comments on the absence of intensity 

IX values as being an indication of the small size of this 

earthquake. However, figure 8 makes clear that the 

change in definition of intensity units as of 1931 was 

the real reason for the absence of reported intensity IX 

values for the Long Beach earthquake.

TABLE 9. Observed and predicted Modified Mercalli intensities, 

Long Beach earthquake

[All values for saturated alluvium]

Site

Anaheim

Bellflower

Costa Mesa

Cypress

Garden Grove

Huntington Beach

Newport Beach

Santa Ana

Seal Beach

Signal Hill _____________

South Gate..- ________

Willowbrook

Torrance

Redondo Beach

Norwalk

Manhattan Beach

East Los Angeles

Lomita

Laguna Beach

Huntington Beach

Artesia

Fullerton ..

Alhambra

Beverly Hills __ _ __ _

Covina

Culver City

Fillmore

Gardena

Glendale

Montebello

Oxnard

Pasadena ..

Placentia

Pomona

Santa Monica

Simi

Ventura

Whittier __ __ _ _ _

San Clemente

Escondido _ Moreno

EIToro __.. _ ____ _

Cardiff-by-the-sea

Carlsbad

Santa Maria

San Diego

Observed

8

8

8

_________8

8

8

8

_________8

8

8

8

8

7

7

7

7

7

7

______-__7

7

_________7

7

6

6

6

6

6

6

6

6

6

6

6

6

6

6

_____ _ _6

g

.___ _____5

5

5

5

4

4

_________3

._- _ - -3

Predicted intensities

2L=22

7/8

7

8

7

8

8

8

8

8

8

7

7

7

7

7

7

7

7

7

7

7

7

6

6

6

6

5

7/6

6

7/6

5

6

7

6

6

5

5

7

7/6 [5] 1

5

5

7/6 [6] 1

5

5

3/4

5 [3] 1

2L=44

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

7

8

8

8

8

8

8

7/6

6

7

6

5/6

8/7

6

8

5/6

7

7

7

7

6

5

8

7

_

_

] 6-minute by 6-minute ground condition.

As an example of the further refinement in estimation of event parameters apparently possible by use of 

the statistical model described earlier, we analyze the 

data of the 45 reporting stations via the several criteria 

mentioned earlier. We consider the earthquake to have 

been on the Newport-Ingle wood fault, so the only parameters evaluated are length of break (2L), position 

on the fault line (S), and the appropriate k value, there 

being the possibility that actual k values in any given 

area of western California are slightly different from 

the 1% value routinely used for this region.

Table 10 presents the results of these calculations (A 

through D are for k = 1.750, and E, F, and G are for k = 

1.825). Table 10A, presenting values of (H-L) and 

|H-L , indicates (H-L) to have a zero value at about 2L 

= 22 for S = -8 and 2L - 25 km for S = -12. We 

include within the dashed line the most likely 2L/S 

values. Table 10B presents (Obs-Calc) values, the 

minimum value being at 2L = 22, S = -8. The s.d.(0bscaio is such that a great range of 2L/S values are permissible at 95 percent confidence (area within dashed 

lines). Table 10C gives |Obs-Calc| values, the 

minimum value being at 2L = 22, S = -12, with a 

large range of 2L/S values permissible at 95 percent 

confidence. Table 10D presents CP values, the 

minimum being at 2L = 22, S = 4 with 2L = 22 and 4 

^ S ^ -8 as well as 2L = 24, -4 ^ S ^ -12 acceptable 

at 95 percent confidence. The only area of overlap of all 

criteria at 95 percent confidence is 2L = 24, -8 ^ S ^

-12.

The solution 2L = 24, S = -10 has its south and 

north termini at latitudes 33°38.9' N. and 33°48.8' N., 

respectively. These are to be compared with the reported latitude 33°37' N. of the Long Beach earthquake 

with the aftershocks extending srom 33°35'-37' N. to 

33°51'-53' N.

With the best solution for k = 1.750, there was a 

slight tendency for mean (O-C) values in each intensity 

band to be function of O values and thus of distance, 

implying a slightly incorrect value of k. Therefore, we 

redid the analysis using a k value of 1.825; tables 10E 

and F show these results. The best solution via (H - L) 

and H-L (table 10E) is 2L = 34-38 and S = -8. Table 

10F, based on CP values, gives as a best solution 2L = 

34, S = -4. Given the calculated CP and s.d. C p values 

for these coordinates (CP=.079, s.d.CP=.012), all solutions based on k = 1.750 are rejected at 99 percent 

probability. At k = 1.825, solutions within the 95 percent confidence area have 2L = 32 36 and 4 ^ S ^

-12. Table 10G gives an abbreviated listing of R.M.S., 

CP, and (H - L)/|H - L values, indicating essential 

agreement as to the best event parameters. The following table compares predicted location of fault break for 

2L - 34, S = -4 and -6 (CP solution and average of H

- L and CP solutions) and observational data.
EXAMPLES OF OBSERVED VERSUS PREDICTED INTENSITIES 15

Solution 2L = 34, S = -4 

Solution 2L = 34, S = -6 

Main shock epicenter 

Aftershocks

Latitude south end Latitude north end

33°39.3' N 33°53.4' N

33°38.5' N 33°52.5' N

33°37' N 

33°35'-37' N 33°51'-53' N

The marked decrease in CP value, the better fit to 

the aftershock zone, and the elimination of the dependency of residuals upon distance suggest that the solution based on k=1.825 is superior to that based on 

k=1.750.

BRYSON EARTHQUAKE OF 21 NOVEMBER 1952 (MODIFIED 

MERCALLI INTENSITIES; MURPHY AND CLOUD, 1954)

Known parameters:

(1) k = 1% (western California)

(2) C = 25 (normal depth) 

Unknown parameters:

(3) Location of epicenter

(4) 2L

This earthquake is of interest for two reasons. First, 

it is the only historical earthquake of significant magnitude that has occurred between the Lompoc and 

Monterey Bay earthquakes, though it was located on a 

different fault than either of these. Second, the reported intensities are apparently anomalous at first 

glance because intensities of VI and VII were reported 

to significant distances but no intensity VIII was reported. Even though the reported values were Modified 

Mercalli rather than Rossi-Forel, the reported intensity pattern appears anomalous. However, there is a 

logical explanation. Table 11 presents observed and 

predicted M/M intensities for two different models (2L 

= 20 and 40 km) of this earthquake. The fault break is 

distributed equally on either side of the calculated epicenter. The NOAA epicenter (Murphy and Cloud, 

1954) is lat 35.8° N., long 121.2° W. Recently, the location of this event was recalculated (W. V. Savage, oral 

commun., 1979), the result being lat 35°47.9' N., long 

121°11.4' W., while Bolt and Miller (1975) gave the 

location as lat 35°44' N., long 121°12' W. and assigned 

it a "b" quality. These locations agree with the NOAA 

epicenter but have an uncertainty of 10-15 km in the 

northeast-southwest direction.

All predicted intensity values in table 11 are for 

ground condition according to the 6-minute by 

6-minute California grid. Some entries show the estimated alluvium value included in square brackets. Entries designated (Al) indicate either that the assumed 

ground condition is saturated alluvium on the 

6-minute by 6-minute grid, although this assumption 

may be inappropriate (predicted greater than observed; 

San Simeon, for example), or that the peak value pre121° 120° 119° 118°

LONG BEACH EARTHQUAKE

MARCH 10, 1933 

2L=22 km, C=25, k = l%

117°

35°

121° 120° 119° 118° 117°

33°

M/M Intensities-Saturated alluvium

B

R/F Intensities-Saturated alluvium

100 KILOMETERS

FIGURE 8. Predicted M/M (A) and R/F (B) intensities for the Long Beach, Calif., earthquake of March 10,1933 (2L = 22, C = 25, k = 1%).
16 SEISMIC INTENSITIES OF EARTHQUAKES OF CONTERMINOUS UNITED STATES

TABLE 10. Calculated parameters for the Long Beach earthquake

Reference Fault: Newport-Inglewood

Reference Coords: 33°48.0' N 118°10.7'W

k = 1 750 T = 0 C = 25

Bands Used: VIII, VII, VI, V, IV, III

Upper Values: (H - L) Lower Values: j H - L |

N2L

S \

8

4

0

-4

-8

-12

-16

12 J 16

-14 -7 

16 17

-16 -7 

16 17

-20 -8 

20 16

-22 -11 

22 15

-21 -14 

21 18

-22 -15 

22 19

-22 -15 

24 17

20

-1 

17

-1 

13

-1 

13

-2 

14

-6 

16

-11

15

-12 

16

24

2 

16

3 

15

3 

16

4 

14

2 

12

-2 

12

-7 

15

28

6 

16

7 

17

7 

15

9 

11

8 

10

6 

10

1 

13

32

9 

19

10 

16

10

15

13 

13

12 

12

11 

11

7 

13

2L = 22, S = -8: (H - L) = 0,|H - LJ= 12

B

Reference Fault: Newport-Inglewood

Reference Coords: 33°48.0' N 118° 10.7' W

k = 1 750 T = 0 C = 25

Bands Used: VIII, VII, VI, V IV, III

Upper Values: (0 - C) Lower Values: s.d. (0 - c>

\2L 

S\

8

4

0

-4

-8

-12

-16

12

.402 

.400 

.410 

.432

.468

.512 

.565

16

.209 

.206 

.216

.238

.272

.316 

.370

20

.067 

(.100)

.062 

(.092)

0.69

(.085)

.090 

(.080)

.124 

(.076) 

.167

.219

24

-.068

-.073 

(.092)

-.066

(.085)

-.047 

(.080)

-.015

(.077) 

.028

.079

28

-.176 

-.178 

-.173 

-.154

-.127

-.087 

-.033

32

-.275 

-.276 

-.272 

-.253

-.225

-.187 

-.139

2L = 23, S = -8: (O - C) = 0, s.d.(0 _ c , = .076

Reference Fault: Newport-Inglewood

Reference Coords: 33°48.0' N 118° 10.7' W

k = 1 750 T = 0 C = 25

Bands Used: VIII, VII, VI, V, IV, III

Upper Values: j O - C (Lower Values: s.d. J 0 _ c j

\2L 

S\

8

4

0

-4

-8

-12

-16

12

.644 

.602 

.570 

.550 

.549 

.566

.609

16

.578 

.542 

.509 

.478 

.463 

.462

.483

20

.549 

.513 

.483 

.456 

.432

.422 

(.048)

.433

24

.537 

.503 

.472 

.452 

.430

.415 

(.043)

All

28

.547 

.512 

.481 

.455 

.442 

.435

.428

32

.574 

.536 

.505 

.473 

.460 

.459

.461

2L = 22, S = -12: O - C = .412, s.d.0 _ c = -041

TABLE 10. Calculated parameters for the Long Beach earthquake Continued

D

Reference Fault: Newport-Inglewood

Reference Coords: 33°48.0' N 118° 10.7' W

k = 1.750 T = 0 C = 25

Bands Used: VIII, VII, VI, V, IV, III

Upper Values: CP Lower Values: s.d.CP

\ ZJ-!

s XT

8

4

0

-4

-8

-12

-16

12

.292 

.298 

.317

.340

.373 

.405 

.439

16

.180 

(.041)

.163

(.046)

.161

(.051)

.173

.197 

.228 

.267

20

.154 

(.013)

.130 

(.012)

.118 

(.013)

.114 

(.017) 

.121 

.145 

.180

24

.191

(.048)

.167

(.052)

.148 

(.049)

.130

.124 

.126 

.149

28

.264 

.252 

.237

.216

.191 

.170 

.167

32

.355 

.343 

.329

.308

.283 

.256 

.226

2L = 22, S = -4: CP = .110, s.d.CP = .013

E

Reference Fault: Newport-Inglewood

Reference Coords: 33°48.0' N 118° 10.7' W

k = 1.825 T = 0 C = 25

Bands Used: VIII, VII, VI, V, IV, III

Upper Values: (H - L) Lower Values: | H - L |

Reference Fault: Newport-Inglewood

Reference Center: 33°48.0'N 118°10.7'W

k = 1.825 T = 0 C = 25

Bands Used: VIII, VII, VI, V, IV, III

Upper Values: CP Lower Values: s.d.CP

\2.L 

S \

12

8

4

0

-4

Q 

O

-12

20

-16

18

-15 

17

-15 

17

-20 

20

-22 

22

-21 

21

-21 

21

24

-8 

16

-10 

16

-10 

16

-10 

16

-14 

16

-17 

19

-18 

18

28

-6

18

-4 

18

-5 

17

_ Y 

15 

_ Y 

15

-11 

17

-13 

17

32

-3 

17

-2 

16 

_ i 

15

0 

14

-3 

15

-2 

14

-9 

15

36

0 

16

-1 

15

0 

14

3 

15

4 

12

1 

11

-1 

13

40

3 

17

2 

14

4 

16

4 

14

6 

12

5 

11

1 

11

\2L 

S\

8

4

0

-4

-8

-12

20

.312 

.327

.345 

.370 

.399 

.430

24

.214 

.200

.217 

.240 

.268 

.299

28

163 

.124

.124 

.139 

.162 

.192

32

143

.093 

(.020)

.085 

(.031)

.085 

(.024)

.099 

(.039)

.125

(.042)

36

147 

.104

.091

(.024)

.083 

(.016)

.086 

(.010)

.099 

(.016)

40

175 

.156

.146 

.130

.118 

(.044)

.115

(.026)

2L = 34, S = -4: CP = .079, s.d.CP = .012
EXAMPLES OF OBSERVED VERSUS PREDICTED INTENSITIES 17

TABLE 10. Calculated parameters for the Long Beach earthquake Continued

2L 

20 

20 

20 

20 

24 

24 

24

2L 

32 

32 

32 

32 

36 

36 

36 

36

G

Reference Fault: NewportReference Coords: 33°48.0' N 

Bands Used: VIII, VII, VI,

A. k = 1.7500 

S CP

-4 .114±.017

-8 .121

-12 .145

-16 .180

-4 .130

-12

S 

0

-4

-8

-12 

0

-4

-8

-12

.124 

.126 

B. k = 1.8125

CP 

.085 

.085 

.095 

.125 

.091 

.083 

.086 

.099

Inglewood 

118°10.7' W 

V, IV, III

RMS

.537

.521

.527

.557

.533

.510

.504

RMS

.578

.549

.537

.541

.572

.544

.527

.528

(H-L)/|H-L|

-2/14

-6/16

2/12

-2/12

(H-D/H-L 

0/14

-3/15

4/12 

1/12

0/13

TABLE 11. Observed and predicted M/M intensities, Bryson earthquake 

[Values for 6-minute by 6-minute ground condition]

Site Observed 

intensity

Predicted intensity

2L=20 2L=40

Bradley ___________._____7 7 7

10 miles NW of Bradley _______7 7 7

Bryson ________________________7 7 7

Arroyo Grande______________________6 5 6

Atascadero ______________________6 5 6

Cambria _________________6 6(A1) 7(A1)

Carmel Valley ______________6 5 5[6(A1)]

Cayucos__________________6 5/6 6

Chualar__________________6 5 6

Guadalupe ______________________6 5 5

Harmony ________________________6 5 6

King City ________________________6 6 7

Lockwood ______________6 6 7

Morro Bay_______________6 6 6

Oceano ________________6 5 6

Parkfield ______________________6 5 6

Paso Robles _______________6 6 6

Pismo Beach_________________6 5 5

Salinas __________________________6 5 5

San Ardo _________________6 5/6 6

San Luis Obispo __________________6 5[6(A1)] 5[6(A1)]

San Simeon ______________________6 7(A1) 7(A1)

Santa Margarita _____________6 5 5[6(A1)]

Templeton_________________6 6 7

Avenal ________________________5 5 6

BenLomond_____________________5 4 4

Big Sur __________________5 5 5

Buellton_________________5 4 5

Buttonwillow ______________________5 4 5

Casmalia __________________________5 5 5

Cholame _____________________5 5 5

Coalinga ________________________5 5 5

Corcoran ________________________5 4 5

Dos Palos _________________5 4 5

Hollister _________________5 5 5

Kettleman City _____________5 4 5

Lompoc _________________5 4 4[5(A1)]

Foot Hills _______ _________5 4 5

Maricopa ______________________5 4 4(A1)

Monterey ______.___________5 5 5(A1)

Nipomo ____________._______________5 4/4 5

Orcutt __________________5 5 5

San Miguel ______________________5 6(A1) 7(A1)

Santa Cruz ___________________5 4/5 5

Santa Maria-_________________5 4/5 5

dieted by model is below the reported value (predicted 

less than observed; Maricopa, for example).

It appears from the table that 2L values of 20 and 40 

bracket the best estimate of 2L, the suggestion being 

that 40 is somewhat too long because a few sites for 

which intensity 7 was predicted actually reported 6. Averaging all the predicted values indicates a 2L of 40 km 

to be nearly correct.

In addition to the studies above, we investigated the 

Bryson intensity data by use of our statistical programs. Though there were a greater number of reporting stations, their nonuniform distribution created a 

problem in use of CP. The virtual absence of stations in 

a 180° quadrant centered northwestward from Bryson 

for a distance of 75 km (that is, to intensity of about 

5.5) resulted in very poor control on S when solving for 

CP values. Tables 12 A-C indicate marked disagreement between R.M.S. and CP estimates of the event's 

parameters, the CP criterion actually having its

TABLE 12. Calculated parameers for the Bryson earthquake

A

Reference Fault: Nacimiento

Reference Center: 35°47.9'N 121°11.4'W

k = 1.750 2L = 30 C = 25

Bands Used: VIII, VII, VI, V, IV, III

Upper Values: CP Lower Values: RMS

10

0

-5

-10

-15

-20

-15 -10 -5 10 15

.457

.411

.366

.324 

[.466]

.284 

[.461]

.246 

[.468]

.211 

[.487]

.408

[.441] 

.192

[.449] 

.157

[-471]

.364 .328

.279

.231

.189 

[.455]

.147 

[.437]

.112 

[.442]

.078 

[.464]

.298

.249

.201

.159

.186 

[.432]

.148 

[.439]

.114 

[.462]

.377

.227

.184

.141

.105

.071

.121

[.455]

.084 

[.459] [.489]

.055 .047 

[.478] [.504]

.266

.218

.176

.135

.102

.073 

[.530]

.055 

[.540]

Values in box are for parameter values having CPT minima. See 

table 13 and text.

B

Reference Fault: Nacimiento

Reference Center: 35°47.9'N 121°11.4'W

k = 1.750 2L = 35 C = 25

Bands Used: VIII, VII, VI, V IV, III

Upper Values: CP Lower Values: RMS

-5

-10

-15

-20

-15 -10 -5 10 15

.268 .218 .175 .144 .123 .113

[.433] [.422] [.420] [.434]

.225 .173 .132 .103 .087 .081

[.422] [.409] [.409] [.423]

.185 .184 .094 .067 .054 .057

[.425] [.414] [.412] [.423]

.147 .098 .059 .041 .042 .055

[.431] [.429] [.440] [.463]

.115 .066 .037 .037 .063 .080

[.461] [.460] [.469] [.488]

.116

.087

.069

.067

.089

Values in box are for parameter values having CPT minima. See 

table 13 and text.
18 SEISMIC INTENSITIES OF EARTHQUAKES OF CONTERMINOUS UNITED STATES

TABLE 12. Calculated paramaters for the Bryson earthquake 

Continued

Reference Fault: Nacimiento

Reference Center: 35°47.9'N 121°11.4'W

k = 1.750 2L = 40 C = 25

Bands Used: VIII, VII, VI, V, IV, III

Upper Values: CP Lower Values: RMS

\. T

S ^\

10

5

0

-5

-10

-15

-20

-15

.293

.247 

[.424] 

.204 

[.407] 

.162 

[.398] 

.126 

[.415] 

.096 

[.439] 

.074 

[.473]

-10

.248

.202 

[.418] 

.157 

[.401]

.119 

[.405]

.086 

[.410] 

.062 

[.436] 

.058 

[.473]

-5

.209

.165 

[.424] 

.123 

[.407]

.088 

[.425]

.064 

[.415] 

.061 

[.441] 

.094 

[.479]

0

.182 

.138

.103 

[.429] 

.074 

[.455] 

.066

.095 

[.457] 

.129

5

.165 

.125 

.095 

.075 

.086 

.124 

.157

10

.158 

.122 

.096 

.085 

.107 

.143 

.175

15

.160 

.129 

.106 

.099 

.118 

.153 

.182

Values in box are for parameter values having CPT minima. See 

table 13 and text.

minimum on tables B and C at S =£ -20, an unacceptable location because the seismological data place a 

constraint of a very few kilometers on the northwestsoutheast position of the epicenter.

The problem with the estimate of S is that data to the 

north effectively cover such a short range of intensity 

that, given the noise level in the data, a CP minimum 

is found (that is, artifically low mean (Obs - Calc) 

value as a function of O) by moving the calculated fault 

south of its correct location. A technique for suppressing 

this effect is to multiply calculated Obs - Calc 

values by the cosines of the angles between the northward direction of the fault and the radials from the 

center of the fault to the stations before calculating a 

CP-type number. The quantity derived from this operation, called CPS , is used to find the best S value as a 

function of 2L and k.

The same effect that yields a poor value for S may 

also yield a poor estimate of T. Therefore, we calculated 

CPT values after the CPS values, CPT differing from CP 

in that all (Obs Calc) values for stations west of the 

fault are multiplied by (-1) prior to calculation of a 

CP-type number. We did not use a sine function because such a procedure suppresses the influence of 

near-station intensity values on the 2L estimate and 

thus on T.

Table 13 gives CPT and R.M.S. values for 2L, S pairs 

having small CPS values for T=0. R.M.S. values, of 

course, are as they were in tables 12 A-C. Use of CPS 

and CPT does effectively suppress the effects of poor 

station distribution in the intensity data, giving small 

CP values for k values of 1.6825 and 1.7500 over small

ranges of event parameter values while also giving 

best estimates very near those suggested by the R.M.S. 

values. We interpret the great range of equally acceptable 2L, S, T sets for k = 1.8125 as an indication of 

smearing of the analysis by use of an incorrect parameter value.

We conclude that the event's location probably was 

near the Nacimiento fault as given by all published 

locations, but we cannot certainly rule out a location 15 

km to the southwest, in the zone of active faults crossing San Simeon Point southeast to northwest.

Therefore, the intensity data indicate that this 

earthquake was as large or larger than the Santa 

Barbara or Long Beach earthquakes, both of which had 

significant areas experiencing Modified Mercalli intensity VIII. The explanation, of course, lies in the facts of

TABLE 13. Calculated parameters for the Bryson earthquake

Reference Fault: Nacimiento

Reference Center: 35°47.9'N. 121°11.4'W.

Bands Used: VIII, VII, VI, V, IV, III

2L

12

16

16

20

20

24

24

28

28

28

2L

30

30

35

40

40

45

45

50

S

-15

-15

-15

-10

-10

-10

-10

-5

-5

-15

S

-10

-10

-10

-5

-5

-5

-5

0

Minimum CPT at 55,

A. k =

T

0

5

0

-5

0

-5

-10

-5

-10

-15

B. k =

T

0

-5

-5

-5

-10

-10

-15

-15

C. k =

-5, -5 of

1.6875

CPS

.037

.008

.001

.027

.030

.013

.015

.027

.028

.035

1.7500

CPS

.029

.026

.015

.022

.023

.015

.004

.034

1.8125

.014±.049.

CPT

.044

.088

.008±

.037±

.075

.054 ±

.103

.085

.100

.155

CPT

.051

.046

.029 ±

.042

.081

.079

.120

.120

There

range of 2L values that give CPT values of less than .

= .105. Table

2L

60

60

65

65

65

70

70

70

75

75

75

80

80

RMS

.558

.470

.056 .473

.017 .434

.444

.008 .420

.412

.432

.416

.411

RMS

.451

.443

.019 .413

.409

.401

.398

.395

.398

results a great

014 + .049(1.64)

is for low RMS values.

S

-5

-5

0

0

0

0

0

0

0

0

0

5

5

T

-5

-10

-5

-10

-15

-5

-10

-15

-10

-15

-20

-15

-20

CPs CPT

.019

.071

.042

.060

.119

.056

.058

.096

.061

.082

.129

.086

.129

RMS

.396

.391

.396

.388

.394

.400

.385

.385

.391

.385

.391

.393

.395

Wide range of equally acceptable parameters interpreted as meaning 

incorrect k value with consequent smearing of analysis.
EXAMPLES OF OBSERVED VERSUS PREDICTED INTENSITIES 19

geology. The epicentral region of the Bryson earthquake is in a remote, nearly unpopulated region with 

only very small stream valleys and occasional ranches. 

Although an area of 2,700 km2 was predicted to experience M/M VIII on saturated alluvium, the nearly total 

absence of such material in the epicentral region led to 

peak reported intensities of VII. The contrasting M/M 

intensities for the Bryson earthquake as predicted for 

saturated alluvium and as predicted when incorporating the 6-minute by 6-minute ground condition are 

shown in figure 9.

According to table I of Evernden (1975), a 2L of 40 

km in western California leads to a predicted magnitude value of 6.85 as compared to a reported value of 

6± for this earthquake (Coffman and van Hake, 1973).

KERN COUNTY EARTHQUAKE OF 1952, (MODIFIED 

MERCALLI INTENSITIES; MURPHY AND CLOUD, 1954)

Known parameters:

(1) Location (main shock and aftershocks)

(2) 2L = 30-60 (observed fracturing and aftershocks)

BRYSON EARTHQUAKE 

NOVEMBER 21, 1952 

2L = 40km, C=25, k = ! 3/4 

120° 123° 122

100 KILOMETERS 

_i

FIGURE 9. Predicted M/M intensities, Bryson, Calif., earthquake (2L = 40, C = 25, k = 1%). A, Saturated alluvium. B, 6-minute by

6-minute ground condition.
20 SEISMIC INTENSITIES OF EARTHQUAKES OF CONTERMINOUS UNITED STATES

Unknown parameters:

(3)k

(4)C

This earthquake was studied in the first paper of this 

series (Evernden and others, 1973) with unsatisfactory 

results. In particular, the model used failed to predict 

the northward extent of intensities V and VI along the 

east side of the Sierra Nevada. When that paper was 

written, the existence of gross regional differences in 

attenuation had not yet been appreciated. The location 

of this earthquake near the boundary between regions 

of k = 1% and k = 1V2 should lead to pronounced perturbation of observations from predictions based on a 

uniform k model.

In order to construct a predicted intensity map for 

this earthquake, the following steps were taken:

(1) Define the line through California that separates 

regions having k values of 1V2 and 1%. Through the 

Central Valley, the boundary (shown as a heavy solid 

line in figures 10 and 11) is assumed to be along the 

contact between granite and the Franciscan assemblage buried under the Tertiary sedimentary rocks 

in the middle of the valley. By trying several models, it 

was concluded that the White Wolf fault, focus of the 

Kern County earthquake, is in the region of k = 1V2 

and the k boundary is to the west of the fault (see fig. 

10). The boundary is assumed to then swing sharply 

eastward, essentially paralleling the Garlock fault. It 

is assumed that a k value of IVfc applies all the way to 

Needles, Calif., that nearly all the path to San Diego 

has a k value of 1%, and that the position of the k 

boundary is uncertain along some intermediate southeast azimuths.

(2) Calculate expected intensities for different fault 

lengths (30 and 60 km) and a k value of 1V2. Compare 

with observations in regions having k values of 1V2. 

Select appropriate 2L value.

(3) From the boundary between 1V2 and 1%, propagate intensities predicted for k of 1V2 into regions of k of 

1% according to predictions for attenuation in k of 1%. 

This was actually done by: (a) noting that predicted I 

values along the k boundary near the epicenter were 

on the average about P/2 intensity units lower for k of 

1% than for k of IVfc when assuming uniform models of 

1% and 1V2; (b) thus, increasing all I values predicted 

by uniform k 1% model by 1V2 units in regions of k = 

1%; (c) adjusting the misjoin of the predicted intensities in the two k regions by assuming that values in k 

regions of 1V2 were correct, intensity values in k regions of 1% were correct if ray directions made large 

angles with the k boundary, and I values in other k 

regions of 1% were obtained by interpolation. Figure 

10 indicates the result of these several steps and the 

resultant predicted M/M intensities on saturated alluvium for 2L = 60 and C = 25. The figure also indicates the high intensity values reported in each region 

of predicted intensities, it being assumed that these 

reports of high intensities are correlative with presence of saturated alluvium or equivalent ground condition. There is excellent agreement between prediction 

and observation in both k regions. The much further 

northward extent of intensity V values east of the 

Sierra Nevada than along the coast of California is 

clearly predicted by this model. The predicted extent of 

intensities VII and VIII in regions of k of IVz and 1% is 

confirmed by observations.

As pointed out above, the model used for figures 10 

and 11 assumes a length of fault break of 60 km. A 

fault break of 30 km predicts too small an areal extent 

for intensity values of V through VIII.

Figure 11 indicates the difference in intensity between published contours (Murphy and Cloud, 1954) 

and those predicted when adjusted for 6-minute by 

6-minute ground condition. The difference is small up 

the Central Valley. However, there are large differences throughout the Sierra Nevada. The published 

isoseismals of Murphy and Cloud (1954) ignore the 

granite and are based solely on scattered sedimentary 

sites in and east of the mountains. On the other hand, 

the predicted values based on the 6-minute by 

6-minute grid give great regions of low intensity 

throughout the mountains. Thus, figure 10 predicts intensity IV for sites on saturated alluvial ground north 

and west of Lake Tahoe as observed, while figure 11 

shows all of this as intensity II because the 6-minute by 

6-minute grid sees only volcanic rocks and granite.

Though a model with parametrs of 2L = 60, C = 25, 

k = 1V2 satisfactorily explains intensity values of VIII 

and less, it does seem to predict too-high intensities in 

the epicentral region. Thus, as shown in figure 12A, a 

C value of 25 causes a prediction of a large area of 

intensity X (shaking intensity) for saturated ground 

condition. Figure 12B indicates that a C value of 40 

results in total elimination of predicted X and halving 

of the area of IX values, while figure 12C shows near 

elimination of IX values when incorporating 6-minute 

by 6-minute ground condition. We conclude that this 

earthquake occurred at significantly greater depth 

than is typical of western California earthquakes.

The absence of intensity IX values in the observed 

intensities for this earthquake, even though 8 feet of 

displacement was measured in a Southern Pacific Railroad tunnel, was simply a quirk of observation combined with the odd definitions of intensities VIII and IX 

on the Modified Mercalli scale. If M/M values are converted to R/F values, nearly all M/M VIII values become intensity IX, numerous M/M values of VII become VII to VIII, the result being to give a clearly
36° -

34° -

124°

EXAMPLES OF OBSERVED VERSUS PREDICTED INTENSITIES

122° 120° 118° 116C

21

114=

FIGURE 10. Observed (spot values) and predicted (contours) M/M intensities for Kern County, Calif., earthquake of July

21,1952 (2L = 60, C = 25).
22 SEISMIC INTENSITIES OF EARTHQUAKES OF CONTERMINOUS UNITED STATES

124° 122° 120° 118° 116° 114°

42°

40°

38°

34°

EXPLANATION

Difference between 

observed and 

predicted intensities

-3

-1

+ 1

+ 2

Not contoured

KERN COUNTY EARTHQUAKE 

2L=60km, C=25, k=!V2

100 KILOMETERS

I -

FIGURE 11. Comparison of predicted and observed M/M intensities for Kern County earthquake of July 21, 1952 (2L = 60, C = 25, k = 

IVa). Contours of observed values from Murphy and Cloud (1954). Patterned areas indicate difference between observed and predicted 

intensity values.
EXAMPLES OF OBSERVED VERSUS PREDICTED INTENSITIES 23

defined area of intensity R/F IX for this earthquake. 

Figure 13 indicates the contrast in intensity maps that 

results when using Rossi-Forel and Modified Mercalli 

units. As noted earlier, there are sound reasons for 

abandoning the Modified Mercalli scale and reverting 

to the Rossi-Forel scale.

Our conclusion is that a model based on juxtaposition of zones of k equal to 1% and IVz can satisfactorily 

explain the observations of intensity of the Kern 

County earthquake of 1952. In fact, we have been unable to explain the observations in any other way. The 

data of this earthquake constitute a beautiful confirmation of the existence of regions of varying k value, 

that is, of varying attenuation.

Another point that can be emphasized at this time is 

that these data are explained only by a model assuming a regional k value, combined with local ground 

condition responding to the energy delivered by the 

basement rocks. A model such as that used by Blume 

and associates (Blume and others, 1978) cannot accurately predict published intensity values from IX 

through IV. Their model must fail because it incorporates local ground condition as the ground condition

controlling attenuation along the entire propagation 

path.

Finally, it should be noted that there is marked discrepancy between the magnitude value (7.1) associated 

with a 2L of 60 km for western California and the 

magnitude value (7.7) observed for this earthquake 

(Richter, 1955). This discrepancy between the observed 

magnitude and that predicted for such an earthquake 

in western California serves as confirmation of regional changes in attenuation and of the location of 

this earthquake in a region having a k value of IVz. 

This matter of interregional discrepancy between 

magnitude values and energy release was discussed in 

some detail in Evernden (1975, 1976) and is discussed 

further in a following section.

SEATTLE EARTHQUAKE OF 13 APRIL 1949 (MODIFIED 

MERCALLI INTENSITIES; MURPHY AND ULRICH, 1951)

Known parameters:

(1) k = 1% (Evernden, 1975) 

Unknown parameters:

(2) C value

(3) Location of epicenter

120°

2L=60km, C=25, k=l :/2 

119° 118°

KERN COUNTY EARTHQUAKE 

JULY 21, 1952

2L=60km, C=40, k=l!/2 

119° 118°

35° 

100 KILOMETERS 

I

FIGURE 12. Predicted M/M intensities for Kern County earthquake of July 21, 1952 (2L = 60, C = 25, k = 1%). A, C = 25 (saturated 

alluvium).B, C = 40 (saturated alluvium). C, C = 40 (6-minute by 6-minute ground condition).
24 SEISMIC INTENSITIES OF EARTHQUAKES OF CONTERMINOUS UNITED STATES

(4) 2L value

This earthquake is the largest historical earthquake 

in the Seattle area. It is important to try to decide 

whether this is the maximum potential earthquake in 

the area. If not, can we estimate how large the 

maximum earthquake may be?

As for the Long Beach and Kern county earthquakes, 

use of the Modified Mercalli scale precluded reports of 

intensity IX for the Seattle earthquake.

As so many communities reported intensities for this 

earthquake, table 14 is limited to communities having 

population of 2,000 or greater in the 1960 census (National Atlas). It can be shown that a k value of 1.45 and 

a 2L of 40 km or a k value of 1.55 and a 2L of 100 km 

give very similar predictions and are nearly indistinguishable on the basis of available data. A recent study 

by Milne (1977), using observed accelerations in the 

Georgia Strait-Juan de Fuca Strait area for earthquakes of the region, found the appropriate attenuation factor (k value of the paper) to be 1.4, that is, in 

essential agreement with our analysis of the data of 

the Seattle earthquake. All calculations for table 14 

were based on a k value of 1.50. All predicted intensity 

values not in parentheses are predicted for saturated 

alluvium. Intensity values in parentheses are predicted using the ground condition of the 25-km by 

25-km grid of the United States map. Figures 14 and 

15 present maps of predicted intensities (2L = 40 km 

and 2L = 100 km) for the northwestern United States 

for saturated alluvium and for the 25-km by 25-km

KERN COUNTY EARTHQUAKE

JULY 21, 1952 

2L=60km,C=25, k=lM>

120° 119'

100 KILOMETERS 

I

FIGURE 13. Predicted Rossi-Forel and Modified Mercalli intensities for Kern County earthquake of July 21,1952 (2L = 60, C = 25, k

6-minute by 6-minute ground condition). A, Modified Mercalli. B, Rossi-Forel.
EXAMPLES OF OBSERVED VERSUS PREDICTED INTENSITIES 25

TABLE 14. Observed and predicted M/M 

quake

[Population » 2,000]

Sites

Aberdeen

Auburn

Berkeley

Centralia

Chehalis

Hoquiam

Kelso _______________

Longview

Olympia

Puyallup

Richmond Beach

Seattle __ _ __ .

Shelton

Tacoma

Tumwater

Arlington

Bremerton

Des Moines

Enumclaw

Everett

Kirkland

Seahurst

Vancouver

Astoria, Oreg.

Hillsboro, Oreg.

North Portland, Oreg. .

Oregon City, Oreg.

Portland, Oreg.

Seaside, Oreg.

Anacortes

Bellingham

Bryn Mawr

Chelan __________

Mercer Island

Montesano

Omak

Port Townsend

Prosser

Snohomish

Spanaway

Baker, Oreg. .

Beaverton, Oreg.

Corvallis, Oreg.

Dallas, Oreg.

Forest Grove, Oreg.

Gresham, Oreg.

Lebanon, Oreg.

McMinnville, Oreg.

Monmouth, Oreg.

Newberg, Oreg.

Newport, Oreg.

Prineville, Oreg.

Redmond, Oreg.

Salem, Oreg.

Silverton, Oreg.

Tillamook, Oreg.

Toledo, Oreg.

Woodburn, Oreg.

Bellevue

Colfax _ ____ __

Colville _____________

Ellensburg

Marysville

Pomeroy

Port Angeles

Sedro-Woolley

Spokane

Walla Walla ___ __.

Wenatchee

Yakima

Albany, Oreg.

Gresham. Oree.

Observed 

intensity

8

._ ____ 8

_ __________ 8

8

___________8

.__________8

. __ ___ 8

_ _____ 8

___________8

. __ __ _8

.__ __ 8

8

8

___________8

. ___ __ 8

7

7

. ____ 7

. __ __ 7

. _____ _7

7

_ _____ 7

7

7

. ____ _7

. __ _ _7

._ _ ____ 7

7

. ____ 7

. ______ 7

___________6

6

6

6

. ___ __ 6

. ______ 6

. _ ____ 6

6

.__ ___ 6

6

6

6

6

. __ ___ 6

. ____ _ 6

6

. ______ 6

6

._ _____ 6

__^ ____ 6

. _____ _6

_ _____ 6

.__ ____ 6

6

. ______ 6

_ _____ 6

6

6

6

_ ______ 5

5

5

.__ _ _ 5

. ___ __ 5

5

. __ _ -5

. ______ 5

.__ ___ _5

5

___________5

___________5

5

5

intensities, Seattle earthPredicted intensity

7 

7 

7 

2 7/8 

8 

7 

7 

7 

7 

7 

7 

7 

7 

7/8 

7 

7 

7 

7/6 

7 

7 

6/7 

7 

7 

6/7 

7 

6 

6 

6 

6 

6 

6 

7 

7 

5 

7 

7 

5 

6 

6 

6 

7 

4 

6 

5 

6 

6 

6 

5 

6 

6 

6 

5 

5 

5 

6 

6 

6 

5 

6 

7 

5 

5 

6 

6 

5 

6 

6 

4 

5 

6 

6 

5 

6

2L=100

7 

8 

8 

8 

8 

7 

8 

8 

8 

8 

8 

8 

7 

8 

8 

7 

7/8 

7 

7/8 

7/8 

7 

7 

7/8 

7 

7 

7 

7 

7 

7 

 7 

6 

8(6) 

7(8/5) 

6 

8(8/5) 

7(6) 

5/6 

7(5) 

6 

7(7/4) 

8 

5 

7(6) 

6 

6 

7(6) 

7(6) 

6 

6/7(6) 

6 

7(6) 

6 

5/6 

6 

6/7(5) 

6/7(5) 

6/7(4/6)7.0 

6 

7(6) 

7(5/7) 

5 

5 

6(4) 

6/7(4/7) 

5 

6(5) 

6(5) 

5 

5 

6(4) 

6(4) 

6(5) 

7<K\

TABLE 14. Observed and predicted M/M intensities, Seattle earthquake- Con tinned

Predicted intensity

Observed 

Sites intensity 2L-40 2L-100

Hood River, Oreg. 5 6 7(4)

La Grande, Oreg. 5 55

Milwaukie, Oreg. __ __ ____ 5 6 7(4/6)

North Bend, Oreg. _ 5 5 5

The Dalles, Oreg. _____ ___ 5 6 6(4) 

Eugene, Oreg. 4 5 5(5/3)

Saint Maries, Idaho 4 4 4/5

-Ground condition applied parenthesis. 

First value correct square.

ground condition. See the plates for correlation of 

latitude and longitude and of units of U.S. grid. 

Note first that a 2L value of 40 km predicts intensity 

7 at numerous sites where 8 was observed, 6 at 7, and 5 

at 6, indicating that a 2L of 40 is certainly too short 

with a k of 1.50. For a 2L of 100 km, the suggestion is 

that too-high values are being predicted. Though the 

intensity values given in parentheses are invariably as 

low or lower than observed (implying that ground condition may be the explanation for the observed values 

being lower than the intensity values predicted for 

saturated alluvium), it still seems that too many predictions are high. We conclude that a 2L value of about 

75 km is appropriate for this earthquake when using a 

k value of 1.50. 

To obtain the intensity values of table 14 required 

use of a C value of 60, a larger value than used for any 

other U.S. earthquake. As C is linked to depth of focus, 

becoming larger as depth increases, the requirement 

for a value of 60 for C means that intensity data are 

sensitive to depth of focus in the range 10-70 km. Nuttli (1951) reported a depth of focus of 70 km for this 

earthquake. The data of his paper do not allow 

evaluaton of the accuracy of that depth estimate, and 

there are no short-range S-P data for establishment of 

time of origin and thus of depth. There seems to be no 

doubt, however, that the depth was in the range 40-70 

km, so an unusual C value for a U.S. earthquake is in 

agreement with an unusual depth for a U.S. earthquake. 

A few reported intensity values are not explainable, 

such as the one at Baker, Oreg., where a VI was reported even though a 2L of 100 predicts only a 5.1. In 

addition, the paucity of reports of intensity IV is surprising. Where IV was reported, it was predicted. However, there is a vast area where IV is predicted, extending well into Montana and the northern Sacramento 

Valley of California, and from which there are no reports in Murphy and Ulrich (1951). It may be that distance from the epicenter was so great (800-900 km) 

that people were not canvassed or that they failed to
26 SEISMIC INTENSITIES OF EARTHQUAKES OF CONTERMINOUS UNITED STATES

associate shaking at intensity IV level with the Seattle 

earthquake.

The 2L of about 75 found when using k of IVfc, when 

considered in light of the discussion in Evernden 

(1975), implies that this earthquake is essentially the 

largest that can occur in the Seattle area. The only 

possibility for more severe shaking is to have a comparable earthquake occur at a shallower depth. For illustration, we present below predicted intensities for 

an earthquake of 2L = 75 km at various depths (C 

values), the shallowest event having a C value equal to 

that found appropriate for earthquakes of western 

California. Intensities are as predicted for saturated 

alluvium, Y = distance parallel to fault from center of 

fault, X = distance from line of fault. The column 

headed "I(X = 0, Y = 0)" indicates predicted R/F and

SEATTLE EARTHQUAKE

APRIL 13, 1949 

(M/M-SATURATED ALLUVIUM)

110

100

90

80

110

100

90

80

A. 2L=100 km, C=60, k=lM>

NC -

10 20 

B. 2L=40km, C=60, k=lM>

0 100 200 300 400 KILOMETERS

30

FIGURE 14. Predicted M/M intensities for Seattle, Wash., earthquake of April 13,1949, saturated alluvium. A, 2L = 100, C = 60, k 

= !J/2. B, 2L = 40, C = 60, k = 1%. NC, not contoured.

M/M intensities at the center of the break. The columns headed "X(km)(I = 8.5)" and "X(km) (I = 7.5)" 

indicate the perpendicular distances in kilometers 

from the center of the break to intensities 8.5 and 7.5 

on both the R/F and M/M scales.

C

25

40

60

KX = Y = O)

R/F M/M

10.5 10.5

9.7 9.4

9.0 8.3

X(km)(l = 8.5) 

R/F M/M 

74 48 

62 27 

43

XtkmHl = 7.5) 

R/F M/M 

132 68 

128 60 

120 51

It is clear that occurrence of an event like the one of 

April 13, 1949 at a depth of 5 to 10 km would be a 

drastically different experience for the Puget Sound 

area than was the actual event. The item for serious 

research in the Seattle area is determination of

no -

SEATTLE EARTHQUAKE

APRIL 13, 1949 

(M/M-25-km by 25-km ground condition)

100 -

110 -

100 -

80

10 20 

B. 2L=40 km, C=60, k=l

0 100 200 300 400 KILOMETERS

i i___I

FIGURE 15. Predicted M/M intensities for Seattle earthquake of 

April 13,1949, 25-km by 25-km ground condition. A, 2L = 100, C = 

60, k = 1%. B, 2L = 40, C = 60, k = 1%. NC, not contoured.
EXAMPLES OF OBSERVED VERSUS PREDICTED INTENSITIES 27

whether earthquakes comparable to 1949 can occur at 

shallower depths.

LOMPOC EARTHQUAKE OF NOVEMBER 4, 1927 

(ROSSI-FOREL INTENSITIES; BYERLY, 1930)

Assumed parameters:

(1) k = 1% (western California)

(2) C = 25 (normal depth) 

Unknown parameters:

(3) Location

(4) 2L

The location of this earthquake published by Byerly 

(1930) is far offshore. The purpose of the initial investigation of this earthquake was to ascertain whether 

the observed isoseismals were consistent with such an 

epicenter. Figure 16A gives observed intensities along 

with intensities predicted for a fault passing through 

Byerly's epicenter with a fault break of 600 km 

oriented parallel to the coast (that is, along the structural trend in this part of California). Figure 16B 

shows the results for a fault passing through Byerly's 

epicenter with a fault break of 600 km oriented eastwest and reaching within 5 km of Point Arguello (no 

onshore faulting was observed). Figure 16A shows 

what is certainly an excessively long break, but it was

used to illustrate the impossibility of reaching the observed intensities for such a location and orientation of 

faulting no matter what the length of break. Figure 

16.B illustrates that one way to attain high predicted 

onshore intensities is to have the end of a long fault 

near Point Arguello. However, this specific model has 

no credibility when considered in terms of the tectonics 

of the region. The predicted and observed intensities 

for this model have many similarities, but other 

models achieve better agreement with isoseismals and 

tectonic style.

Hanks (1978) calculated the epicenter on the basis of 

S and P data from stations in southern California (fig. 

17). Three different fault models were put through this 

epicenter. The first (fig. 17A; 2L = 300 km parallel to 

shoreline) was to illustrate the inability of any fault 

through this epicenter and parallel to the San Andreas 

fault to explain the observed isoseismals. This model 

does not predict any onshore IX values. It gives VIII 

values in much of the region in which VIII was observed but, in so doing, it predicts VIII, VII, and VI 

values far north of where they were observed.

The second model based on Hanks' epicenter (fig. 

175) hypothesizes a 2L of 300 km oriented east-west 

with the fault break reaching within 5 km of shore. 

Though this fault does predict IX values as observed, it

122° 121° 120° 119°

LOMPOC EARTHQUAKE 

NOVEMBER 4, 1927

118° 122°

37°

35° -

34° -

2L=600km, C=25, k=l%

Byerly's epicenter

Strike of fault: Parallel to regional structure

2L=600km, C=25, k=l%

Byerly's epicenter

Strike of fault: East-west,

east end of break very near shore

FIGURE 16. Predicted (arable numerals) and observed (roman numerals)R/F intensities for Lompoc, Calif., earthquake of November 4,1927. 

A, Based on hypothetical fault through Byerly's epicenter (Byerly, 1930) and parallel to shoreline (2L = 600, C = 25, k = 1%). B, Based on 

hypothetical fault through Byerly's epicenter and oriented east-west (2L = 600, C = 25, k = 1%).
28 SEISMIC INTENSITIES OF EARTHQUAKES OF CONTERMINOUS UNITED STATES

badly fails to predict VIII, VII and VI values.

The third model based on Hanks' epicenter (fig. 18) 

has a 2L of 80 km and an orientation as shown and as 

suggested by Hanks. Even when all observed VI values 

are treated as having been at sites on saturated alluvium, the predicted VI area is less than half that 

observed. There are no onshore IX values predicted, 

and the predicted VIII area is less than half that observed.

The basic failing of these models is placement of the 

fault too far offshore. Any technically credible orientation at such locations fails to generate sufficiently high 

intensities onshore. Even the tectonically incredible 

east-west faults fail in detail to predict observations. 

The actual fault break must have been near shore and 

must have been nearly parallel to the shoreline (no 

onshore fracturing), while the size of isoseismals requires a break length of several tens of kilometers.

Figure 19 presents the first effort to place the fault 

break so as to satisfy the isoseismals (2L = 125 km). A 

major point of this model and of all others that attempt 

to explain observations is placement of the south end of 

the break near Point Arguello in order to explain the 

observed IX values in this area. The main difference 

between this model and the one described below is its 

more northwesterly strike. The result is greater separation of faulting and shoreline northward and the 

resultant need for a greater fault length to explain onshore intensities. Though Figure 19 does indicate satisfactory agreement of observed and predicted VI values, 

the predicted area of VIII may be too small. Predicted 

areas of IV and V show great disagreement with reported observations.

Next, we model the fault break as suggested by 

Gawthrop (1978) along the Hosgri fault. The 2L length 

of 80 km was arrived at by trying several lengths between 50 and 125 km. Figure 2QA shows intensities 

predicted for saturated alluvium, while Figure 20B 

shows intensities as predicted using the 6-minute by 

6-minute ground-condition units. Figure 2QA shows 

excellent agreement between observation and prediction for intensities VI and VIII.

Figure 20B indicates marked shrinkage of the area 

of predicted intensity VIII, probably because some 

areas of saturated alluvium were ignored by the 

6-minute by 6-minute grid. All intensity IX values 

have disappeared for similar reasons. When the 

Vfc-minute by Mi-minute grid is used, predicted intensity 

IX values extend from Point Arguello northward along 

the coast as far as they do on Figure 20A.

An apparent failing of the last two models is that 

they predict too large an area of intensity IX. Many of

LOMPOC EARTHQUAKE 

NOVEMBER 4,1927

122° 121° 120° 119° 118° 122° 121 120°

34° 

2L=300 km, C=25, k=l%

Hanks' epicenter

Strike of fault: Parallel to coast

2L=300 km, C=25, k=l%

Hanks' epicenter 

Strike-of fault: East-west

FIGURE 17. Predicted and observed R/F intensities for Lompoc earthquake of November 4,1927. A, Based on hypothetical fault through 

Hanks' epicenter and parallel to shoreline (2L = 300, C = 25, k = 1%). B, Based on hypothetical fault through Hanks' epicenter and 

oriented east-west (2L = 300f C = 25, k = 1%).
EXAMPLES OF OBSERVED VERSUS PREDICTED INTENSITIES 29

the IX values are predicted along the beach and in 

sand-dune areas where there probably were no people 

at the time of the earthquake and where our use of the 

J category for all alluvium is in error. The other areas 

of predicted IX at some distances from the shore are 

along streams and rivers. Flowing water is seldom seen 

in these rivers, and some may have no surface runoff 

for years at a time. Building sites have not been developed in these river courses, however, because when 

there is enough rain to produce surface runoff, flooding 

is common. The absence of dwellings suggests the 

likelihood that no basis for observations existed. Also, 

low water saturation and the physical characteristics 

of the alluvial materials (cobbles in sand) would imply 

intensities below those expected for saturated alluvium. Therefore, we do not believe that differences 

between observed and predicted IX values are a basis 

for rejecting either of the last two models.

This conclusion requires that at such stations as Betteravia (VIII vs. 8.9), Casmalia (VIII vs. 9.0), Lompoc 

(VIII vs. 8.8), and Oceano (VIII vs. 8.9), for all of which 

Byerly reported intensity VIII, and all of which are 

shown as alluvium on the 1/2-minute by Va-minute grid 

and thus are treated as on saturated alluvium in the

LOMPOC EARTHQUAKE 

NOVEMBER 4, 1927

12r 121° 120° 119° 118°

EXPLANATION

 IV Observed

 6 Predicted

 ^ Fault

FIGURE 18. Predicted and observed R/F intensities for Lompoc 

earthquake of November 4, 1927, based on hypothetical fault 

through Hanks' epicenter with length and orientation as suggested by Hanks (2L = 80, C = 25, k = 1%).

calculations, predicted values were too high because 

the ground at these sites was somewhat less sensitive 

than saturated alluvium. The major remaining task 

relative to our program for predicting intensities is to 

identify and properly characterize various types of alluvium.

Hanks, on the basis of seismological arguments 

about S-P intervals and the consequent restraints on 

potential epicenters, suggested the shortening of the 

fault shown in figure 20C. The resultant predictions 

are in serious disagreement with observations, the 

predicted area of VI being half that observed, and the 

predicted area of VIII being a third or less of that observed.

As we did for several other earthquakes, we investigated the Lompoc earthquake by using site-intensity 

values. Table 15 lists sites for which Byerly reported 

Rossi-Forel intensities of VI or greater. The faults 

modeled (shown in figure 21) can be described as follows:

(A) Hosgri fault 70-km break

122°

LOMPOC EARTHQUAKE 

NOVEMBER 4, 1927

121° 120° 119° 118°

EXPLANATION

 IV Observed

 6 Predicted

2L=125km, C=25, k=l%

Epicenter selected so intensity IX could be predicted 

Strike of fault: Parallel to coast

FIGURE 19. Predicted and observed R/F intensities for Lompoc 

earthquake of November 4, 1927, based on hypothetical fault 

placed so as to yield isoseismals in agreement with observations 

(2L = 125, C = 25, k = 1%). Intensities as predicted on saturated 

alluvium.
30 SEISMIC INTENSITIES OF EARTHQUAKES OF CONTERMINOUS UNITED STATES

(B) Hosgri fault 52-km break (9 km off each end 

of (A) )

(C) Hosgri fault 25-km break (center third of 

(A) )

(D) Location suggested by Hanks 80-km break 

The observed and predicted intensities for these several models are given in table 15. Two modes of 

analysis seem justified, the one chosen depending upon 

one's point of view: (A) The first is to select the model 

for which the average predicted intensity for stations 

within a given intensity bandwidth is equal to the central intensity value of that bandwidth. Under ideal 

conditions, the same model will achieve such agreement or near agreement for all bandwidths; (B) The 

second is to select as small an earthquake as possible 

such that no (or nearly no) observed intensities are 

greater than predicted intensities on saturated alluvium. A model in which more than a very few observed intensities are greater than those predicted on 

saturated alluvium is inadmissible because no perturbation of ground condition permissible within the 

model could explain such stations.

For analysis of mode A, consider table 16A. The 

headings of the last three columns indicate observed 

intensity and center intensity of each bandwidth. S/A 

and G/C indicate whether calculations of intensity 

were based on saturated alluvium (S/A) or ground condition (G/C) as on Ms-minute by Ms-minute groundcondition data. Using the latter values, table 16A 

indicates that fault D is systematically predicting avTABLE 15. Predicted and observed intensity values at specific 

Lompoc earthquake of November 4, 1927

Site

Surf . _____________

Arlight ______________

Arroyo Grande__ ______

Cambria

Casmalia ____________

Guadalupe ____________

Harriston

Huasna ______________

Los Alamos __________ 

Los Olivos____________

Ni porno

Pismo Beach__________

San Luis Obispo

Santa Maria__________

Bakersfield

Buellton ______________ 

Button willow ________ 

Carpinteria

Creston

Goleta______ _ ______

Harmony 

King City _____ __ _

Naples ______________

Reward ___ _____ _

Santa Margarita ______ 

Solvang 

Taft__________________

Ventura

Wasioja

Population Fault A Fault B

1977 S/A G/C S/A

Intensity IX

9.3 8.3 9.0

____ 9.2 9.2 8.8

Intensity VIII

9.1 9.1 8.6

7,500 8.7 7.7 8.6 

400 8.9 8.9 8.7 

1,000 7.5 7.5 7.1 

250 9.0 9.0 8.9 

1,000 8.2 6.0 7.7 

____ 8.3 6.8 7.8

3,100 9.0 9.0 8.9

8.7 7.7 8.6

____ 8.9 7.9 8.7

____ 8.8 7.3 7.8 

25,300 8.8 8.8 8.5 

800 8.1 6.6 7.9 

200 7.6 7.6 7.3 

7,100 8.6 8.6 8.1 

3,600 8.5 8.5 8.4 

4,000 8.9 7.4 8.7 

2,600 8.9 8.9 8.7 

34,500 8.6 7.6 8.3 

32,700 8.5 8.5 8.4

Intensities VI and

____ 7.3 5.8 6.9

10,300 7.8 6.3 7.4 

69,500 5.3 5.3 5.2 

250 7.8 7.8 7.5 

950 5.9 5.9 5.7 

7,000 6.0 6.0 5.8 

15 6.6 6.6 6.4 

____ 7.5 6.5 7.2

75 7.7 6.2 7.3 

5,000 6.7 6.7 6.4 

5 7.8 5.6 7.3 

3,400 5.8 5.8 5.5 

25 7.8 6.3 7.4 

7.0 5.5 6.7 

85,000 5.4 5.4 5.2 

7,200 7.3 7.3 7.0 

6.2 6.2 6.1

70,200 6.4 6.4 6.1 

350 7.4 7.4 7.2 

1,000 8.1 6.6 7.8 

1,500 7.6 7.6 7.3 

4,300 6.0 6.0 5.8 

900 7.6 7.6 7.2 

58,000 5.7 5.7 5.4 

7.0 5.2 6.9

G/C

8.0 

8.8

8.6 

7.6 

8.7 

7.1 

8.9 

5.5 

6.3 

8.9 

7.6 

7.7 

6.3 

8.5 

6.4 

7.3 

8.1 

8.4 

7.2 

8.7 

7.3 

8.4

VII

5.4 

5.9 

5.2 

7.5 

5.7 

5.8 

6.4 

6.2 

5.8 

6.4 

5.1 

5.5 

5.9 

5.2 

5.2 

7.0 

6.1 

6.1 

7.2 

6.3 

7.3 

5.8 

7.2 

5.4 

5.1

Fault C

S/A

8.2 

7.9

7.7 

8.1 

8.3 

6.4 

8.4 

6.9 

7.0 

8.5 

8.1 

8.0 

7.4 

7.7 

7.3 

6.7 

7.3 

8.0 

8.2 

8.3 

7.7 

8.0

6.3 

6.8 

4.7 

6.9 

5.2 

5.3 

5.8 

6.6 

6.6 

5.8 

6.6 

4.9 

6.7 

6.1 

4.7 

6.3 

5.6 

5.6 

6.6 

7.1 

6.7 

5.4 

6.6 

4.9 

6.4

G/C

7.2 

7.9

7.7 

7.1 

8.3 

6.4 

8.4 

4.7 

5.5 

8.5 

7.1 

7.0 

5.9 

7.7 

5.8 

6.7 

7.3 

8.0 

6.7 

8.3 

6.7 

8.0

4.8 

5.3 

4.7 

6.9 

5.2 

5.3 

5.8 

5.6 

5.1 

5.8 

4.4 

4.9 

5.2 

4.6 

4.7 

6.3 

5.6 

5.6 

6.6 

5.6 

6.7 

5.4 

6.6 

4.9 

4.6

sites,

Fault D

S/A

8.4 

8.5

8.5 

7.9 

8.0 

7.7 

8.1 

8.0 

7.8 

8.1 

7.9 

7.9 

7.3 

7.9 

7.4 

6.9 

8.2 

7.1 

8.1 

8.1 

8.0 

7.7

7.2 

7.5 

5.1 

7.1 

5.6 

5.8 

6.4 

7.1 

7.1 

6.3 

7.9 

5.9 

7.2 

6.6 

5.3 

7.1 

5.9 

6.1 

6.9 

7.6 

7.0 

5.7 

7.4 

5.4 

6.6

G/C

7.4 

8.5

8.5 

6.9 

8.0 

7.7 

8.1 

4.8 

6.3 

8.1 

6.9 

6.9 

5.8 

7.9 

5.9 

6.9 

8.2 

7.1 

6.6 

8.1 

7.0 

7.7

5.7 

6.0 

5.1 

7.1 

5.6 

5.8 

6.4 

6.1 

5.6 

6.3 

5.7 

5.9 

5.7 

5.1 

5.3 

7.1 

5.9 

6.1 

6.9 

6.1 

7.0 

5.7 

7.4 

5.4 

4.8

LOMPOC EARTHQUAKE 

NOVEMBER 4, 1927

122° 121° 120° 119° 118° 122° 121° 120° 119° 118°

36°

b

- 0

 IV Observed

B 

EXPLANATION

 6 Predicted

122° 121° 120° 119° 118°

Fault

FIGURE 20. Predicted and observed R/F intensities for Lompoc earthquake of November 4, 1927. A, Based on location of Hosgri fault with 

placement and length of break chosen so as to predict isoseismals in agreement with observations (2L = 80, C = 25, k = 1%). Intensities 

as predicted on saturated alluvium. B, Same as A, but intensities as predicted using ground condition of 6-minute by 6-minute grid. C, 

Based on location of Hosgri fault with northward extent of break controlled by S-P arguments of Hanks (1978).
EXAMPLES OF OBSERVED VERSUS PREDICTED INTENSITIES 31

121°00' 120°40'

35°10'

35°00'

34°50'

34°40'

34°30'

FIGURE 21. Fault models used in calculations of site-intensity 

values (table 15) for Lompoc earthquake of November 4, 1927.

erage intensities that are too low. Any shorter fault 

break along this same line would show greater disagreement. As in the previous analysis, the intensity 

data appear to reject any location for the Lompoc 

earthquake as far at sea as that suggested by Hanks.

Fault A gives the best agreement of average predicted and central intensity value in each bandwidth; 

B and C yield values that are too low. From these data, 

too, a break of almost 70 km along the Hosgri fault is 

suggested.

For analysis of mode B, consider table 16B. The 

number following the intensity value in the headings 

is the number of reporting stations in each bandwidth. 

High predictions under S/A are deemed permissible, 

low predictions under S/A are not permissible. We

TABLE 16. Average predicted intensities for saturated alluvium and 

l/z-minute by l/z-minute ground-condition units, Lompoc earthquake, using two sets of intensity data

Fault 2L

(km)

IX (9.0) 

S/A G/C

VIII (8.0) 

S/A G/C

VI VIII (6.5) 

S/A G/C

A 

B_ 

C_ 

D _ _

70

52

25

80

9.25

8.90

8.05

8.45

8.75

8.40

7.55

7.95

8.58

8.31

7.70

7.86

7.95

7.68

7.07

6.23

6.83

5.49

6.55

6.27

6.03

5.99

Fault 2L IX (2i 

S/A G/C

VIII (20) 

S/A G/C

VI-VII (25) 

S/A G/C

A 

B 

C 

D

70

52

25

80

OH/OL 

OH/OL

2L 

OH/1L

OH/1L

OH/1L

2L

OH/1L

13H/OL 

9H/2L 

OH/7L 

OH/3L

7H/4L 

5H/8L 

OH/12L 

OH/10L

7H/2L 

1H/2L

2H/3L

3H/4L 

OH/7L

OH/4L

H = Prediction above bandwidth 

L = Prediction below bandwidth

might expect a nearly equal number of low and high 

predictions under G/C. With less certainty, fault D is 

again rejected because 1 of 2 and 3 of 20 stations were 

predicted low even when assuming S/A conditions. As 

in other modes of analysis, fault A satisfies the mode of 

interpretation best. There are no L values for VIII and 

IX and only 2 of 25 for VI-VII under S/A conditions, 

while there are similar H and L values under G/C conditions.

Finally, we analyze the intensity data of the Lompoc 

earthquake via the previously described statistical 

model and present calculations of CP, s.d.Cp, and 

R.M.S.

Table 17 presents calculations based on a k of 1.750, 

2L values of 50, 60, 70, 80, 90, and 100 km, and S and T 

values of -30, -20, -10, 0, 10, and 20 km. For "observed" intensity values in calculations for these tables, we used the midpoint of each band defined by 

Byerly (1930)(IX, VIII, VII-VI, and V-IV.) As a matter 

of fact, nearly every point in band V-IV is certainly 

within the area of intensity V. Therefore, we redid all 

the calculations using an "observed" value in the 

(V-IV) band of 5.0 rather than 4.5 and obtained the 

results in table 18. Because of the possibility that a k 

value of 1.750 might be slightly in error, and because 

we were uncertain of the impact of such an error on the 

predicted fault parameters, we redid most of the calculations using a k value of 1.6750. The results of this 

procedure are shown in tables 19 and 20.

On all of these tables, we have marked the zone of 

geologically "acceptable" solutions, the definition of acceptability being that the fault break does not intersect 

land nor does the fault line extend into the Santa 

Barbara Channel. We consider any offshore position of 

the fault to be "acceptable." The reference fault line 

used is as shown on figure 21 with the following 

changes: (a) northward, the fault is extended according to published maps; (b) southward, it is extended 

arbitrarily along its general strike into the Santa 

Barbara Channel. This is done simply to provide the 

basis for calculations. The reference coordinates (S = 0,
32 SEISMIC INTENSITIES OF EARTHQUAKES OF CONTERMINOUS UNITED STATES

T = 0) are at lat 34°55.0'N., long 120°44.3'W., that is, 

at the center of the Hosgri fault as shown on figure 21. 

Table 17 indicates that a broad range of solutions 

yielding low values of CP and s.d.CP are found when 

using k = 1.750. All 2L values are found to yield CP 

values of around 0.10 at some combination of 2L, T, 

and S, all minima on all tables being geologically unacceptable. The minimum CP at an acceptable site is 

2L = 70, S = 0, T = 0 with an s.d.CP = 0.019. In a 

partial search for a true minimum, a CP of 0.147 with 

s.d.CP = 0.011 was found for 2L = 70, S = 0, T = 4. 

Thus, even 2L = 70, S = 0, T = -10 is strongly rejected 

(d = (0.329-0.177)70.019-8.0), while a location 30 km 

offshore is clearly impossible. The only other acceptable coordinates having a low CP value are 2L = 60 

S = 0, T = 0.

Table 18 (V-IV band treated as V band and termed 

MODIFIED on tables), shows a great reduction in CP 

values, implying that the change made in treatment of 

the (V-IV) band was appropriate. No low CP values 

are found for 2L = 50, but a long band of low CP values 

are found for all other 2L values, nearly all of them 

being geologically inadmissible. Geologically admissible low CP values are found for 2L = 90, S = 10, T = 0, 

and 2L = 80, S = 10, T = 0. The actual approximate 

minimum for 2L = 80 is at S = 10, T = 2, with 

CP = 0.029 and s.d.CP = 0.038. Values of CP as high as 

0.10 are rejected.

Table 19 gives calculations for k = 1.675 and band 

(V-IV) treated as (V-IV). The most significant result is 

that essentially all CP values are higher than for similar calculations when using k = 1.750. No CP values as 

low as 0.20 are found, while values below 0.10 were 

found in table 18. As expected, minima at each 2L 

move westward and the length of fault with the 

minimum CP gets shorter. However, the coordinates 

having minimum CP values are still near T = O. Thus, 

the smallest CP values at 2L = 60 are all at T = O. The 

smallest CP (0.206) at 2L = 50 is as S = -10, T = 0 

while slightly lower values (0.186 and 0.163) are at 

geologically unacceptable locations (S=-,T=10;S =

 20, T = 10). Again, any location more than a few 

kilometers west of the minimum is rejected.

Table 20 shows calculations for k= 1.675 and band 

(V-IV) treated as band (V). An interesting phenomenon here is the disappearance of the long line of similar 

CP minima that characterized nearly all values of 2L 

when using k = 1.750. No low CP minima are found for 

2L = 80 and 70, while there is only a small region of CP 

minima for 2L = 60 (S = 0, T = 0; S = -10, T = 0; S =

-20, T = 0), only points S = 0, T = 0 and S = -10, T - 

0 being geologically acceptable. Low minima are found 

for 2L = 50 at geologically unacceptable coordinates. 

This phenomenon, a line of minima on S versus T

TABLE 17. Calculated parameters for the Lompoc earthquake using 

midpoint ofByerly's (1930) "observed" intensity bands

A

Reference fault: Hosgri Reference Center: 34°55.0'N 120°44.3'W

k = 1.750 2L = 50 C = 25

Bands Used: IX, VIII, VII-VI, V-IV

Upper Values: CP Lower Values: s.d.CP

V T

s N.

30

20

10

0

-10

-20

-30

-30 -2

.978

.920

.888

.884

.908 -

.957

1.026 .6r

0 -10

.660

.577

.524

.510

.537

.594

"2 ~~ .495~ 4

0

.517

.421

.354

.329

.356

T4I2-1

.336

10

.420

.312

.230

.185

.198 

(.099)

.253 

(.106)

.219

20

.402

.293 

(.029)

.204 

(.030)

.140 

(.038)

.115 

(.058)

.145 

(.085)

.231

30

.470

.366 

(.022)

.281 

(-021)

.216 

(.022)

.181 

(.028)

.185 

(.039)

B

Reference fault: Hosgri Reference Center: 34°55.0'N 120°44.3'W

k = 1.750 2L = 60 C = 25

Bands Used: IX, VIII, VII-VI, V-IV

Upper Values: CP Lower Values: s.d.CP

\ T

s N.

30

20

10

0

-10

-20

-30

-30 -!

.885

.823

.784

.772

.787

.827

.887

20 -10

.574

.484

.420

.390

.399

.446

.520

0

.444

.342

.262

(.037)

.214

1Q48L 

.211

(.067)

.256

.337

10

.368

(.021)

.264

.179

.116

(.014) 

.085

(.029)

.105

(.063)

.177

20

.376

(-012)

.280

.205

.150

(.036) 

.111

(.041)

.091

(.015)

.119

(.037)

30

.457

(.012)

.367

.294

.239

(.027) 

.203

(.030)

.184

(-021)

.194

(.014)

Reference fault: Hosgri Reference Center: 34°55.0'N 120°44.3'W

k = 1.750 2L = 70 C = 25 

i Bands Used: IX, VIII, VII-VI, V-IV 

Upper Values: CP Lower Values: s.<LCP

\ T S^C

30

20

10

0

-10

-20

-30

-30

.824 

.760

.720 

.704 

.713

.744 

.795

20 -10

.521 

.431 

(.033) 

.364 

(.035) 

.329 

(.042) 

.328 ! 

i-51) i

.359 

.419

0

.405 

.306 

(.017) 

.228 

(.016) 

.177

LQ.19).. 

.159 

(.031) 

.177 

(.051) 

.234

10

.354 

.268 

(.020) 

.203 

(.035) 

.159 

(.052) 

.118 

(.054) 

.087 

(.020) 

.105 

(.036)

20

.386 

.319

.280 

.262

.230 

(.096) 

.171 

(.101) 

.122 

(.035)

30

.474 

.407

.358 

.323 

.292

.252 

(.064) 

.219 

(.037)
EXAMPLES OF OBSERVED VERSUS PREDICTED INTENSITIES 33

TABLE 17. Calculated parameters for the Lompoc earthquake using 

midpoint of Byerly's (1930) "observed" intensity bands Continued

D 

Reference fault: Hosgri Reference Center: 34°55.0'N 120°44.3'W

k = 1.750 2L = 80 C = 25

Bands Used: IX, VIII, VII-VI, V-IV

Upper Values: CP .Lower Values: s.d.CP

V\ T

S ^\

30

20

10

0

-10

-20

-30

-30 -5

.777

.716

.675

.657

.661

.684

.725

0 -10

.487 

(.024)

.400 

(.022)

.337 

(.023)

.302

(.027)

.293

(.034)

.309

(.045)

.351

0

.389 

(.011)

.302 

(.011)

.236

(.015)

r .19T 

(.016)

.162 

(.011)

.154 

(.019)

.179

(.041)

10

.370 

(.027)

.313

(.046)

.287 

(.075)

.271

(.087)

.228 

(.090)

.161 

(.090)

.110 

(.031)

20 30

.428

.400

.407

.397

.358

.292

(.098)

.204 

(.105)

E 

Reference fault: Hosgri Reference Center: 34°55.0'N 120°44.3'W

k = 1.750 2L = 90 C = 25

Bands Used: IX, VIII, VII-VI, V-IV

Upper Values: CP Lower Values: s.d.CP

\v T 

S \^

30

20

10

0

-10

-20

-30

-30 -!

.744 

.686 

.648 

.629

.6"27 

.641 

.672

20 -10

.469

(.016) 

.391 

(.013) 

.335 

(.013) 

.301 

i.Q15_} _,

.285 

(.020) 

.286 

(.030) 

.309 

(.042)

0

.393

(.015) 

.324 

(.025) 

.276 

(.034) j "23~8~ 

(.038) 

.201 

(.032) 

.172 

(.017) 

.164 

(.015)

10

.411 

.393 

.402 

.383

.336

(.087) 

.265 

(.092) 

.178 

(.090)

20 30

.495 

.513 

.532 

.518 

.472 

.401 

.311

Reference fault: Hosgri Reference Center: 34°55.0'N 120°44.3'W

k = 1.750 2L = 100 C = 25

Bands Used: IX, VIII, VII-VI, V-IV

Upper Values: CP Lower Values: s.d.CP

\. T 

S \^

30

20

10

0

-10

-20

-30

-30

.720

.667

.631

.610

7603

.610

.630

-20

.581 

(.021)

.519 

(.021)

.476 

(.021)

.450 

(.0231

.438 

(.027)

.439 

(.033)

.456 

(.041)

-10

.465 

(.010)

.398 

(.010)

.352 

(.010)

.318 

JL0091J

.295 

(.010)

.283 

(.016)

.287 

(.027)

0

All 

(.041)

.370 

.L.041J_I

.341 

(.053)

.309

(.057)

.265 

(.053)

.218 

(.040)

.182 

(.021)

10 20 30

.479

.501

.512

.491

.440

.368

.281 

(.096)

TABLE 18. Calculated parameters for the Lompoc earthquake using 

modified "observed" intensities

A 

Reference fault: Hosgri Reference Center: 34°55.0'N 120°44.3'W

k = 1.750 2L = 50 C = 25

Bands Used: IX, VIII, VII-VI, V-IV (MODIFIED)

Upper Values: CP Lower Values: s.d.CP

\. T

s^\

30

20

10 

0

-10

-20

-30

-30 -5

1.154

1.108 

1.084

1.085

1.111

1.162

0 -10

.756

.696 

.661

.653

.676

.732 

_J

0

.562

.498 

.458

.445

.464

.521

10

.398

.332

(.116) 

.290

(.112) 

.274 

(.112)

.288 

(117)

.343

(.125)

20

.317 

(.096)

.233

(.122) 

.192

(.118) 

.173 

(.118)

.183 

(.122)

.231 

(.130)

30

.360

(.073)

.258 

(.081) 

.190

(.105) 

.166 

(.120)

.167 

(.125)

.201 

(.133)

B

Reference fault: Hosgri Reference Center: 34°55.0'N 120°44.3'W

k = 1.750 2L = 60 C = 25

Bands Used: IX, VIII, VII-VI, V-IV (MODIFIED)

Upper Values: CP Lower Values: s.d.CP

\. T 

S\\

30

20

10

0

-10

-20

-30

-30 -'<

1.003

.958

.937

.940

.968

1.019

1.090

20 -10

.589

.530

.497

.493

.521

.579

.663

0

.391

.322

.284

.275

.301

.361

.451

10

.244

.148

.107 

(.108)

.097 

(.085)

.128 

(.068)

.175 

(.119)

.269

(.130)

20

.209

(.048)

.101 

(.039)

.016 

(.024)

.044 

(.027)

.076 

(.013)

.087 

(.038)

.147 

(.135)

30

.284 

(.035)

.186 

(.025)

.107 

(.014)

.052 

(.019)

.021 

(.051)

.023

(.114)

.102 

(.139)

Reference fault: Hosgri Reference Center: 34°55.0'N 120°44.3'W

k = 1.750 2L = 70 C = 25

Bands Used: IX, VIII, VII-VI, V-IV (MODIFIED)

Upper Values: CP Lower Values: s.d.CP

\v T

s^x

30

20

10

0

-10

-20

-30

-30

.886

.843

.824

.830

.859

.909

.978

20 -10

.469

.398

.368

.369

.402

.461

.543

0

.280

.187 

(.083)

.144 

(.100)

.142 

(.101) _,

T74 

(.106)

.237

(.113)

.326

10

.168 

(.036)

.068 

(.013)

.041 

(.105)

.070 

(.049)

.088 

(.023)

.095

(.022)

.138 

(.124)

20

.178 

(.012)

.121

(.071)

.151 

(.110)

.161 

(.110)

.138 

(.111)

.098 

(.073)

.059

(.012)

30

.267

.199

.168

.176

.163

.117

.040
34 SEISMIC INTENSITIES OF EARTHQUAKES OF CONTERMINOUS UNITED STATES

TABLE 18. Calculated parameters for the Lompoc earthquake using 

modified "observed" intensities-Continued

D

Reference fault: Hosgri Reference Center: 34°55.0'N 120°44.3'W

k = 1.750 2L = 80 C = 25

Bands Used: IX, VIII, VII-VI, V-IV (MODIFIED)

Upper Values: CP Lower Values: s.d.CP

\ T 

S N^

30

20

10

0

-10

-20

-30

-30 -'<

.791

.744

.725

.733

.763

.812

.877

20 -10

.379 

(.069)

.298

(.074)

.256 

(.090)

.261

.297

.356

.435

0

.211 

(.043)

.113 

(.035)

.043 

L.0361

.026 

(.099)

.063 

(.103)

.127 

(.110)

.213

(.117)

10

.153 

(.020)

.137 

(.107)

.173 

(.102)

.173 

(.103)

.138 

(.094)

.100

(.057)

.075 

(.013)

20 30

.212 

(.060)

.251

.290 

(.107)

.294 

(.108)

.263 

(.112)

.201 

(.119)

.110 

(.114)

E

Reference fault: Hosgri Reference Center: 34°55.0'N 120°44.3'W

k = 1.750 2L = 90 C = 25

Bands Used: IX, VIII, VII-VI, V-IV MODIFIED

Upper Values: CP Lower Values: s.d.CP

N\ T

S X^

30

20

10

0

-10

-20

-30

-30 -'<

.111

.668

.646

.650

.679

.726

.788

20 -10

.316

(.052)

.235

(.052)

.186 

(.059)

.174

L.075)^

.205 

(.098)

.263

(.102)

.339 

(.108)

0

.179 

(-014)

.108 

(.023)

.086 

£.097)

07<T 

(.098)

.035 

(.101)

.029 

(.091)

.112

(.114)

10

.199

(.077)

.257 

(.104)

.290 

(.100)

.283 

(.104)

.242 

(.104)

.173 

(.111)

.098 

(.075)

20

.306

.377

.415

.413

.375

.307 

(.116)

.216

(.124)

30

.352

.392

.435

.441

.411

.349

.263

Reference fault: Hosgri Reference Center: 34°55.0'N 120°44.3'W

k = 1.750 2L = 100 C = 25

Bands Used: IX, VIII, VII-VI, V-IV MODIFIED

Upper Values: CP Lower Values: s.d.CP

\v T

S N^

30

20

10

0

-10

-20

-30

-30

.654 

.608

.584 

.582

.601 

.642 

.700

-20

.455

.396

(.058) 

.362 

(.061) 

.354 

(.068J

.371 

(.079) 

.413 

(.094) 

.478

-10 0 10 20 30

.275 .186 .307 

(.034) (.026) (.109) 

.203 .167 .371 

(.030) (.082) 

.158 r~.l86~ " .399 

(.030) (.097) 

.136 .173 .388 

i.038) j (.096) 

.138 .130 .342 

(.058) (.099) 

.091 .067 .273 

(.091) (.104) (.107) 

.244 .014 .187 

(.105) (.068) (.115)

TABLE 19. Calculated parameters for the Lompoc earthquake using 

midpoint ofByerly's (1930) "observed" intensity bands

A

Reference fault: Hosgri Reference Center: 34°55.0'N 120°44.3'W

k = 1.675 2L = 50 C = 25

Bands Used: IX, VIII, VII-VI, V-IV

Upper Values: CP Lower Values: s.d.CP

\ T 

S \I

30

20

10

0

-10

-20

-30

-30

.745

.693

.664

.661

.684

-20

.607

.543

.504

.495

.516

-10

.480

.404 

(.025)

.351

(.028)

.331

(.035)

.347 

(.045)

0

.387

.304 

(.011)

.241 

(.011)

.206

1-0141 j

r .208 

(.026)

10

.354

.281 

(.028)

.226 

(.040)

.186 

(.046)

.163

(.029)

20 30

.389

.329

.290

.262

.226

B

Reference fault: Hosgri Reference Center: 34°55.0'N 120°44.3'W

k = 1.675 2L = 60 C = 25

Bands Used: IX, VIII, VII-VI, V-IV

Upper Values: CP Lower Values: s.d.CP

\ T 

S \^

30

20

10

0

-10

-20

-30

-30

.695

.643

.613

.605

.620

-20

.567 

(.022)

.504 

(.023)

.464 

(.026)

.450

.461

(.037)

-10

.457 

(.012)

.385 

(.011)

.334 

(.012)

.309 

(.016)

.312

(.023)

0

.395

(.017)

.327 

(.024)

.274 

(.031) _

.237 

(.030)

.217 

(.019)

10

.409

.371

.353 

(.091)

.324

.267 

(.095)

20 30

.477

.462

.458

.434

.384

Reference fault: Hosgri Reference Center: 34°55.0'N 120°44.3'W

k = 1.675 2L = 70 C = 25

Bands Used: IX, VIII, VII-VI, V-IV

Upper Values: CP Lower Values: s.d.CP

\ T SX\

30

20

10

0

-10

-20

-30

-30

.670

.620

.590

.579

.586

-20

.551

(.015)

.492 

(.015)

.454 

(.016)

.437 

(.020)

439

(.025)

-10

.459 

(.011)

.395 

(.012)

.350 

(.013)

.322 

1,01 11 j

.312 

(.011)

0

.431 

(.034)

.384 

(.046)

.347

£.057) j

.309

(.058)

.269

(.047)

10

.498

.502

.492

.457

.396

20 30

.595

.611

.605

.574

.518
EXAMPLES OF OBSERVED VERSUS PREDICTED INTENSITIES 35

TABLE 19. Calculated parameters for the Lompoc earthquake using 

midpoint of Byerly's 1930 "observed" intensity bands- Continued

D

Reference fault: Hosgri Reference Center: 34°55.0'N 120°44.3'W

k = 1.675 2L = 80 C = 25

Bands Used: IX, VIII, VII-VI, V-IV

Upper Values: CP Lower Values: s.d.CP

XT 

s X^

30

20

10

0

-10

-20

-30

-30

.658

.611

.582 

(.020)

.568 

(.023) ".568 '

-20

.550

(.010)

.497 

(.010)

.462 

(.010)

.441 

[.012)

435 

(.016)

-10

.478 

(.018)

.426 

(.023)

.386 

(.024)

.356 

(.021) - .334~~ 

(.015)

0

.491 

(.051)

.468 

L067)_,

r .445 

(.079)

.403 

(.081)

.347 

(.071)

10

.616

.630

.616

.575

.511

20 30

.729

.747

.737

.700

.637

TABLE 20. Calculated parameters for the Lompoc earthquake using 

modified "observed" intensities

Reference fault: Hosgri Reference Center: 34°55.0'N 120°44.3'W

k = 1.675 2L = 50 C = 25 

Bands Used: IX, VIII, VII-VI, V-IV (MODIFIED) 

Upper Values: CP Lower Values: s.d.CP

\ T

sXs^

30

20

10

0

-10

-20

-30

-30

.752

.719

.717

.743

.792

-20

.564

.519

.512

.536

.588

-10

.380

.319

.302

.324

.378

0

.224

.143 

(.059)

.102 

(.100)

.120

r_ __J

.175 

(.118)

10

.148

.073 

(.032)

.063 

(.110)

.051 

(.090)

.031 

(.011)

20 30

.174

.141

.159

.150 

(.120)

.104 

(.120)

B

Reference fault: Hosgri Reference Center: 34°55.0'N 120°44.3'W

k = 1.675 2L = 60 C = 25

Bands Used: IX, VIII, VII-VI, V-IV (MODIFIED)

Upper Values: CP Lower Values: s.d.CP

X T

sX^^

30

20

10

0

-10

-20

-30

-30

.638

.598

.586

.604

.649

-20

.457

.403

.380

.394

.442

-10

.290 

(.042)

.218 

(.045)

.178 

(.057)

.180 

(.079)

.226 

(.1061J

0

.179 

(.010)

.110 

(.021) ,

.070 

ri-066)_H

r .041 

(.107)

.024 

(.054)

10

.199

(.075)

.227 

(.106)

.238 

(.107)

.218

.162

20 30

.288

.326

.341

.326

.276

TABLE 20. Calculated parameters for the Lompoc earthquake using 

modified "observed" intensities-Continued

C

Reference fault: Hosgri Reference Center: 34°55.0'N 120°44.3'W

k = 1.675 2L = 70 C = 25

Bands Used: IX, VIII, VII-VI, V-IV (MODIFIED)

Upper Values: CP Lower Values: s.d.rp

V T

S ^\

30

20

10

0

-10

-20

-30

-30

.568

.526

.509

.519

.553

-20

.396

(.044)

.341 

(.046)

.314 

(.053)

.317 

(,063J_

.349

-10

.251 

(.020)

.185 

(.016)

.144 

(.018)

.129 

(.0311_,

.146 

(.056)

0

.204 

(.043)

.194 

(.098)

.197 

(.100)

.166 

(.105)

.106 

(.111)

10

.335

.372

.378

.351

.391

20 30

.439

.478

.488

.466

.410

D

Reference fault: Hosgri Reference Center: 34°55.0'N 120°44.3'W

k = 1.675 2L = 80 C = 25

Bands Used: IX, VIII, VII-VI, V-IV (MODIFIED)

Upper Values: CP Lower Values: s.d.CP

X T

S \^

30

20

10

0

-10

-20

-30

.520

.478

.460

.463

.487

-20

.360 

(.031)

.309 

(.031)

.282 

(.035)

.277 

L-043)

.294

-10

.246 

(.018)

.196

(.018)

.161 

(.021)

.137 

_i.014) _,

.128 

(.015)

0

.285 

(.097)

.316

(.097)

.312 

(.098)

.276 

(.102)

.215 

(.108)

10

.467

.502

.501

.468

.405

20 30

.576

.615

.619

.589

.529

plots or equivalent minima for several 2L values, results from the limited azimuth of observation of intensity values for this quake. Little more than 120° is 

subtended by all stations from the center of the fault. 

Thus, given somewhat noisy observations, several 

statistically equivalent solutions are possible, particularly when any model parameters are incorrectly set. 

This is the identical phenomenon observed when trying to locate earthquake epicenters with data from too 

limited range and azimuth and a slightly incorrect 

traveltime curve.

For the parameters used in table 12B (k = 1.6875, 2L 

= 60), the lowest determined CP and R.M.S. values are 

as follows:

s

10

10

10

T

20

-10

0

RMS

.690

.626

.632

CP

.402

.218

.110
36 SEISMIC INTENSITIES OF EARTHQUAKES OF CONTERMINOUS UNITED STATES

10

0

0

-10

-10

-10

0

10

-10 

0

.692

.637

.695

.658

.667

.178

.070

.238

.180

.041

Thus, minimum CP and RMS values are associated 

with nearly the same parameter values. We should 

point out that RMS values as low as those given above 

are found for 2L values of 70 and 80 km. However, 

these RMS values are associated with higher CP values (tables 12C and D). Since we consider the CP to be 

a more critical estimator of proper event parameters, 

we regard the solution based on a 2L of 60 km as 

superior to those based on 70 and 80 km.

The conclusion seems clear that, if we accept the 

general applicability of the model, the intensity data 

for the Lompoc earthquake require a location on or 

very near the Hosgri fault. Any location even a few 

kilometers farther west is rejected at high confidence. 

The tendency of the analysis based on k=1.675 to 

achieve a sharper minimum is interpreted to mean a 

more correct estimate of the k value. Thus, we conclude 

that the most probable parameters for this earthquake 

are a 2L of about 60 km centered at or a bit south of the 

lat 34°55.0' N., long 120°44.3' W. Solutions as long as 

75 km or so cannot be rejected. However, if such 

lengths are correct, k = 1.750 is more appropriate. 

Whatever the k value or 2L, the model requires that 

the fault break was very near the Hosgri fault. It seems 

to us that there is little doubt that the intensity and 

geologic data together require a location on the Hosgri 

fault.

An issue engendering much heated debate in recent 

years has been the seismic risk associated with the 

Diablo Canyon reactor (approximate coordinates lat 

35°13.5' N., long 120°22' W.). The site is within a few 

miles of the trace of the Hosgri fault opposite a part of 

the fault that probably broke in 1927 (fig. 23). If that be 

true, the site experienced in 1927 the maximum intensity that it will have to endure, because there is no 

evidence of a major fault nearer the site. We predict 

that the site would experience an intensity of 9.2 (R/F) 

if it were on thick saturated alluvium. However, the 

site is actually on Miocene shale of the Monterey Formation, a formation for which the predicted intensity 

would be 1.5 units less than that for saturated alluvium. Therefore, we predict that the site would experience a maximum intensity of 7.5-8.0 (R/F) or 7(M/M) 

for a repeat of the Lompoc earthquake. An even longer 

break would cause only a small increase in predicted 

intensity at the reactor site. According to the seismicgap theory, the next earthquake on the Hosgri fault 

would not include the 1927 break but would break

northward from the end of the 1927 break. Such an 

earthquake with 2L comparable to that of 1927 would 

give essentially the same predicted intensity at the site 

as predicted for the 1927 earthquake.

EARTHQUAKES OF EASTERN UNITED STATES

(EUS, K=l AND iy4 )

Several earthquakes in eastern North America have 

been studied via their published intensity contours and 

the graphic technique described on pages 4 and 5. Of 

particular interest is the Timiskaming earthquake of 

November 1, 1935, which is important because it is the 

largest earthquake (felt in much of eastern Canada 

and the U.S.) for which there are S-P data from several 

near stations. These data allow us to determine the 

earthquake's origin time unambiguously and thus to 

obtain a close estimation of depth of focus. Average 

estimated O.T. from use of S-P data of 5 stations is 06 h 

03 m 37.4 s G.m.t. Analysis of the teleseismic (A ^ 22°) 

data of the ISC with this restrained O.T. gives a depth 

of 10 km. The recalculated epicenter coordinates are 

lat 46.98° N., long 78.99° W., D = 10 km. Therefore, 

there is no doubt that the wide spacing of isoseismals is 

an attenuation phenomenon.

The estimated 2L and AVi values for this and a few 

other Eastern United States earthquakes are given in 

table 21. It is of interest to point out that, when radii of 

intensity zones for the Cornwall/Massena quake were 

measured along the St. Lawrence River, the solution 

required a k value of IV* if essential agreement between all data was to be obtained. This is just another 

example of the reality of the k=! 1/4 zone shown along 

the St. Lawrence River on plate 2.

The M0 values published by Herrmann, Cheng, and 

Nuttli (1978) for the Eastern United States earthquakes are included in table 21. The seemingly unusual pairing of calculated 2L and M0 values are discussed in a following section entitled "Length of Break 

Versus Moment Versus k Value Throughout the 

United States and Suggested Interpretation."

FAULT LENGTH VERSUS MOMENT,

MAGNITUDE, AND ENERGY RELEASE VERSUS K

REGION

It was pointed out previously (Evernden, 1975) that 

there is no direct correlation between size of intensity 

contours and energy release for earthquakes distributed throughout the U.S. The impact of differing rates 

of attenuation is so severe that totally erroneous conclusions have been drawn when this factor has been 

unappreciated or ignored. We will illustrate this fact in 

two ways.
FAULT LENGTH VERSUS MOMENT, MAGNITUDE, AND ENERGY RELEASE VERSUS K REGION 

TABLE 21 Observed and estimated parameters for selected earthquakes in the Eastern United States

37

Earthquake

Grand Banks2

East Missouri2

Cornwall/Massens

Illinois2

New Hampshire4

Timiskaming2

Missouri2

Date 

YR.MO.DY

1929.11.18

1965.10.21

1944.09.05

1968.11.09

1940.12.20

1935.11.01

1963.03.03

Latitude

44.5°N

37.9°N

45.0°N

38.0°N

43.8°N

46.8°N

36.7°N

Longitude

55° W

91.1°W

74.8°W

88.5°W

71.3°W

79.2°W

90.1°W

M

5.2

5.3

____

4.5

KMX)

VI

VIII

VII

VII

VII

VI

2L 

km

1.3 (1)

.03-. 04 (1) i.o (iy4 )3

.08 (1)

.016 (1)

.16 (iy4 )

.11 (1)

.022 (1)

Au 1014 cm2

20

56

6.4

4.8

0.78

1.2

6.8

1.1

'M,, 

1024 dyne-cm

63

0.1

2.5

1.0

1.0

1.0

3.2

0.1

'Herrmann, Cheng, and Nuttli (1978).

2Earthquakes used in figures 23 and 24.

3k=l not permitted by data. Result in agreement with Evernden (1975) and plate 2.

4k=l'A solution in agreement with local magnitude but earthquake in k 1 region of plate 2. Uncertain interpretation.

First, it is frequently assumed that energy release in 

earthquakes in the Eastern United States (EUS) is 

comparable to that in California, a conclusion based on 

the occurrence of three great historical earthquakes in 

EUS (Cape Ann, Mass., Charleston, S. Car., and New 

Madrid, Mo.,) and three in California (Fort Tejon, San 

Francisco, and Owens Valley, the last sometimes described as larger than the 1906 San Francisco quake). 

Table 22 lists calculated 2L and implied approximate 

E0 values (total energy released) for numerous earthquakes studied in one or more papers of this series 

(energy vs. 2L as in Everden, 1975, p. 1290). The 

earthquake often considered the largest and greatest 

U.S. earthquake December 16, 1811, New 

Madrid was in fact the smallest earthquake studied 

if energy released in intensity-relative frequencies is 

the primary measure of size. The earthquake classed 

by Wood (1933) as simply a large local earthquake 

March 10, 1933, Long Beach released approximately 

100 times as much elastic energy at such frequencies 

as did the New Madrid earthquake. As the Cape Ann 

earthquake was no larger than the Charleston earthquake, the total energy released in these "great" EUS 

earthquakes was of the order of 5 x 1021 ergs, while the 

three great California earthquakes released about 3 x 

1024 ergs, the Owens Valley earthquake (March 26, 

1872) providing less than 1/100 of this energy. Therefore, the intraplate region of EUS has released no more 

than about one thousandth the energy released in the 

three cited California earthquakes. According to the 

historical record, there have been other great California earthquakes since the Cape Ann event, so the contrast in energy release between EUS and California is 

even greater than here calculated. If these numbers 

are converted to ergs/km2/year, the results are:

for US east of long 100° W.3.9 x 1012 ergs/km2/yr,

for California ______6.2 x 1016 ergs/km2/yr, 

a contrast in energy-release rates of 1/15,000. There 

simply is no comparison between release rates of elastic energy (at frequencies relative to intensity data) by 

earthquakes in intraplate areas of U.S. and in California.

The second point we wish to emphasize is the clear

TABLE 22. 2L, "En, and "M" values for selected earthquakes in the 

United States

Earthquake

San Francisco 1906

Fort Tejon 1857 __ ____ _

Long Beach 1933 _ _._ _

Seattle 1949 ____________

Owens Valley 1872 _ __

Kern County 1952

Charleston 1887 __ _

New Madrid 1811-12 _ _

k

1%

1%

1%

- 1%

1%

__ 1%

- 1%

__ iy_

i

2L

400

320

22

75

60

60

20

20

5

log"^," 1

24.2

24.0

21.4

22.6

22.4

22.4

21.4

21.4

20.2

"M"2

8.25

7 98

6.48

7.98

7.85

7.85

7.92

7.92

7.83

; "E,," = 18.7 + 2.11(log 2L), (p. 51-54 and Evernden, 1975). 

1" by formulas of page 41.

correlation between observed seismic moments and the 

regional k factor, a relation indicating either correlation of stress drop and attenuation factor or the influence of regional characteristics subsumed under our k 

factor on observed seismic moments. To begin, we illustrate the correlation of calculated and observed 2L values and observed and calculated seismic moments in 

regions of k 1¥z and k 1%.

Hanks, Hileman, and Thatcher (1975) illustrated the 

general correlation between observed seismic moment 

and area included within the intensity VI contour (AVi) 

by either MM or RF intensities and in either k 1% or k 

1% regions. They found that use of such a mix of data 

types still yielded AVi vs. M0 data points that showed a 

general correlation over a large range of M0 values.

Because AVI values are strongly influenced by k 

value and intensity scale, we have reanalyzed the data 

used by Hanks, Hileman, and Thatcher (1975) while 

adding a few additional events, the intent being to 

normalize all intensity data to the same scale and to 

separate data from different k regions. In addition, we 

have compared observed and calculated 2L values and 

plotted observed M0 against calculated/observed 2L 

values rather than against AVi values.

All observed and calculated quantities are given in 

table 23. The "observed" 2L values are those actually 

observed or calculated on the basis of high-frequency 

spectral data or short-period seismograms. All calculated 2L values are obtained by use of observed intensity data and formulas of this and the previous report 

(Evernden, 1975).
38 SEISMIC INTENSITIES OF EARTHQUAKES OF CONTERMINOUS UNITED STATES

A few comments on the data of table 23 and the calculated values used in the subsequent discussion are 

required. In addition to use of AVI values for estimating 

2L and M0 , some events were analyzed by using the full 

set of intensity contours and our graphic technique. If 

the graphic technique was used, we always chose to 

accept the 2L values obtained from it, but we applied it 

only when the 2L and M0 estimates differed markedly 

from those obtained from the AVI data. Such discrepancies were found for only a few events for which AVi 

values were in the 1013 cm2 range, that is, small AVI 

areas. An aspect of the total intensity data included in 

table 23 is the maximum shaking intensity. Note that 

agreement between observed maximum shaking in- . 

tensity and calculated I(MX) is much better for graphic 

estimates of 2L than for several AV i values, again supporting use of the 2L and M0 values calculated from 

total intensity data. The values of 2L in table 23 that 

are used in figure 22 and the subsequent discussion are 

followed by an asterisk.

Table 23 illustrates that the mode of analysis followed here and originally presented in Evernden 

(1975) leads to estimates of 2L that are in essential 

agreement with observed breakage or with 2L values 

estimated by use of short-period seismograms or 

strong-motion records. This agreement is independent 

of whether the earthquake is in a region of k ll/2 or k 

1%, the 2L calculations for earthquakes in k ll/2 assuming an energy density equivalent to an earthquake of 

equal 2L in k 1%.

As an additional test of whether the 2L values determined for k IMs earthquakes are meaningful, we 

analyzed the published intensity data on all events of 

the region for which there is documentary evidence of 

length of surficial cracking or displacement (data provided by M.G. Bonilla of the U.S. Geological Survey). 

The graphic technique described earlier was used to 

make the analysis.

Table 24 shows reported and calculated 2L values for 

the earthquakes studied.

The only additional comments required are:

(a) The 2L value calculated for the Manix earthquake seems to be in serious disagreement 

with observed values of I (MX) and ML but in 

excellent agreement with the M0 values of 

1.4 x 1026 reported by Hanks and Thatcher 

(1972). (See figure 24 and note that, in k 1%, 

2L of 10 implies an M0 of 1.25 x 1026 dynecm.) Perhaps the low value for I (MX) is to be 

explained by a low water table, and the low 

ML value by the fact that it was measured at 

Pasadena (that is, although the earthquake 

occurred in a region where k=lV6, the path 

to the Pasadena station was mostly through 

a region in which k=l%).

(b) The intensity VI (5.5) dimension for the

TABLE 23. Observed

Earthquake

Hemet

Lytle Creek

Coyote Mountain

Parkfield

Desert Hot Springs

Long Beach

Santa Rosa Mt.

San Fernando

Borrego Mt.

Imperial Valley

San Francisco

Santa Barbara

Lompoc

Fort Tejon

Wheeler Ridge

Truckee

Bakersfield

Fairview Peak

Kern County

Oroville

Pocatello Valley

No. In.

01 MM

02 MM

03 MM

04 MM

05 MM

06 MM

07 MM

08 MM

09 MM

10 MM

11 RF

12 RF

13 RF

14 RF

15 MM

16 MM

17 MM

18 MM

19 MM

20 MM

21 MM

Reg.

7

6

7

7

7

7

7

7

7

7

7

7

7

7

6

6

6

6

6

6

6

Date 

YR.MO.DY

1963.09.23

1970.12.09

1969.04.28

1966.06.28

1948.04.12

1933.03.11

1934.03.19

1971.02.09

1964.04.08

1940.05.18

1906.04.18

1925.06.29

1927.11.04

1857.01.09

1954.01.12

1966.09.12

1952.08.22

1954.12.16

1952.07.21

1975.08.01

1975.03.28

Oroville earthquake was not used because it 

is so small (see discussion above). The 

ground condition in the Oroville area probably accounts for the small area mapped as 

intensity VI.

(c) The intensity data for the Hebgen Lake earthquake indicate that the attenuation region 

surrounding the epicenter is not uniform. 

They imply (via our model) an attenuation 

factor of k = lV2 in the area to the south (toward a region in which we know k to be ll/2 

on the basis of several earthquakes) but between k ll/z and k P/4 to the north and east. If 

a k value of 1.35 is used to the north and 

east, we obtain a 2L value similar to that for 

the data from the area to the south and k V/2.

(d) The Fort Sage Mountains and Galway Lake 

intensity data are grossly inconsistent with 

reported lengths of fracture. All Fort Sage 

Mountains data agree on a 2L of 1.0 km 

(versus reported 8.8 km), while all the Galway Lake data imply a 2L of well under 1 

km (versus reported 6.8 km of surficial 

breakage). Because the 2L values we calculate are for the equivalent k 1% earthquake 

to provide the energy required to develop the 

observed k l x/2 intensity pattern, these very 

short calculated 2L values suggest one of 

three conditions: stress drops were abnormally low, high-frequency energy was released from a short piece of the break (as at 

Parkfield), or observed surficial fracturing 

was influenced by factors other than rupture 

length at depth. Whatever the condition, the 

short calculated 2L values imply, if anything anomalous, that less energy is re-
FAULT LENGTH VERSUS MOMENT, MAGNITUDE, AND ENERGY RELEASE VERSUS K REGION 39

and calculated parameters of earthquakes in regions ofk=l% and k=l l/z, California and Idaho

OhsnrvnH Valups A

Mag.

5.3

5.4

5.9

5.5

6.5

6.3

6.2

6.4

6.5

7.1

8.2

6.3

7.3

8

6.6

6.4

5.8

7.0

7.7

5.9

6.0

Mom.

0.02

0.10

0.50

1.3

1.0

2.0

4

4.7

6

20

850

20

6.5

900

0.33

0.5

0.55

90

170

0.2

0.65

AVI

0.24

0.22

0.61

0.54

2.6

1.2

2.3

2.3

3.4

3.3

16

4.4

1.75

1.61

0.32

14

17

0.48

1.4

2L KMX) 

SHKG

VI

VII

VII

3 VII

VII

VIII

VI

16 IX

VII

IX

400 IX

IX

IX

320 IX

VII+

VII

VIII

40 VIII

60 IX

1.5 VII

3 VIII

Mom.

N,7

.026

.04

.023

6.0

11

.017

.053

Ay,

RF,7

0.48

0.44

1.2

1.0

4.7

2.1

3.9

3.9

5.6

5.4

0.65

0.60

0.11

4.8

5.8

0.18

0.52

2L

1.2

1.1

3.6

3.1

27

9

23

23

38

37

130

1.8

1.6

0.33

31

40

0.36

1.4

LVI Calculations

Mom. 

RF,7

.018

.015

0.19

0.12

6

0.8

4

4

10

9

150

0.04

0.03

.000

6.7

11

.002

.023

Mom. 

MM,6

0.5

0.41

.007

100

170

.018

0.28

ML 

7

4.7

4.7

5.4

5.3

6.6

5.9

6.5

6.5

6.8

6.8

4.9

4.9

3.6

6.7

6.9

4.0

4.8

KMX)

6.2

6.2

6.9

7.4

8.2

7.5

8.1

8.7

8.5

8.5

7.5

7.4

6.1

10

8.8

6.4

7.3

2L 

RF,7

1.1

10

22

19

60

400

40

70

320

2.1

60

1.5

3.0

Intensity calculations

Mom. Mom. ML 

MM,6 7

1

3.4

3

20

1500

11

31

900

23

0.09 5.6

6.0

6.5

6.4

7.1

8.3

6.9

7.2

8.1

0.54 5.1

241 7.1

0.35 4.8

1.13 5.3

KMX)

7.1

7.6

8.1

8.6

8.8

9+

9

9

9+

7.6

9.1

7.4

7.8

Notes: "In." = Intensity type of published data. "MM" = Modified Mercalli. "RF" = Rossi Forel. "Reg." = k region. "6" 

= H4. "7" = 1%. "Mom." = Seismic Moment in 1025 dyne-cm. "N" = Moment of Region 6 (IVfc) earthquake 

normalized to Region 7 (1%). "Ayi" = Area in 1024 cm2 included in intensity VI contour. "Observed AM" values 

are in intensity and regional units of columns 3 and 4. "ML" = Local Magnitude. "Observed" magnitude values 

in all regions are calculated with Richter formula for southern California (Reg. 7). "Calculated I(MX)" is 

maximum predicted shaking intensity and is in units (MM or RF) of observations. "In. Calculations" are based 

on full pattern of intensity observations. "2L" values followed by an asterisk are those used in figure 22. For 

event No. 17, Mom.(RF,7) entry under Av, Calculations is 0.0004.

1000

1013

AREA WITHIN INTENSITY VI CONTOUR, IN SQUARE CENTIMETERS 

1014 1015 1016

= 100

10

1Q26 1027 1028

11

-18- 

M 0 =2.56 log A w (M/M, 1V4M1.76

EXPLANATION

5 Earthquakes in k 1%, M 0 (observed) 

-17- Earthquakes in k IVz, M0 (observed) 

17 Earthquakes in k IVz, M 0 (observed) 

normalized to k 1% (see text)

1013 1014 1023 1Q24 10Z5 1Q26

SEISMIC MOMENT, IN DYNE CENTIMETERS

1027 1028

FIGURE 22. Length of fault break (2L) as a function of seismic moment (M0; right) and area within R/F and M/M intensity VI contours

(AVI ; left) for k = 1% and k = 1%.
40 SEISMIC INTENSITIES OF EARTHQUAKES OF CONTERMINOUS UNITED STATES

leased by the k IVz quakes than by k 1% 

earthquakes of equivalent 2L.

Thus all available data seem to indicate that 2L values fork 1V2 earthquakes as calculated by means of our 

model are quite accurate estimates of actual break 

lengths and, thus, that energy released in the intensity 

pass-band of k l x/2 earthquakes is essentially identical 

to that of k 1% earthquakes of the same 2L.

For our discussion of seismic moment (M0 ), we first 

consider events occurring in regions where k=l%. The 

left side of figure 24 indicates the theoretical relations 

between AVI and 2L for both M/M and R/F and k 1% and 

k 1%. The equivalent areas for the same 2L are determinable and are shown to increase by about a factor of 

ten from AV1 (M/M, 1.75) to AVi (R/F, 1.50). In order to 

relate AVi or 2L to M0 , an empirical relation must be 

established as done by Hanks, Hileman, and Thatcher 

(1975). On separating data of different k regions and 

intensity scales, we find a different scaling law of AVI 

and M0 than found by them. The relation found appropriate to k 1% data (normalizing Avt (M/M, 1.75) values 

to AVI (R/F, 1.75) values by figure 22) is:

log M0 =2.56 log AVi(R/F, 1.75) - 11.76 

This curve, drawn on the right side of figure 22, is 

expressed as a relation between 2L and M0 via the AVi 

(R/F, 1.75) vs 2L curve of the left side of figure 22. The 

non-underlined numbers plotted along the curve are 

calculated or observed 2L vs observed M0 values for k 

1% earthquakes. In most cases, there is excellent 

agreement with the empirical curve over the entire 

range of M0 values. This agreement implies that, for 

most k 1% earthquakes, both short- and long-period 

energy derive from the same fault length according to a 

single spectral scaling law.

Two events show marked disagreement with the 

curve. Event No. 4, Parkfield, is of particular interest 

because it has been described extensively in the literature. Numerous investigations of long-period data of 

this earthquake find an M0 value of 1025 and observed

surface breakage of 30 km or more. However, the 

strong-motion data indicate that the high-frequency 

energy came from a 3-4 km length of the fault (Lindh 

and Boore, 1981). In addition, the intensity VII contour 

is only 22 km long, a value that is totally anomalous 

for a normal California earthquake with a 2L of 20 km 

or more. As shown in table 22, the intensity data imply 

a 2L of 3 km. The Parkfield quake clearly was abnormal for California because the high-frequency energy 

was derived dominantly from a short piece of the fault 

at normal California stress levels, while the longperiod energy was derived from failure of a much 

longer, slowly breaking fault segment. On the basis of 

other analyses, discordance of the Parkfield datum 

point with the empirical curve of figure 22 should have 

been expected. Inadequate analysis has been done on 

event No. 3 (Coyote Mountain) to ascertain whether a 

similar explanation applies to that datum point.

As regards event No. 5 (Desert Hot Springs), the 

agreement with the curve shown on figure 22 would 

not have resulted from use of the AVi value reported by 

Hanks, Hileman, and Thatcher (1975). The reported 

intensity data for that quake show some remarkable 

inconsistencies in distribution of M/M VI values. These 

were reported as far away as Los Angeles but were 

interspersed with many much lower values. The 2L 

value of 27 km deriving from the AVi area used by 

Hanks and his coworkers predicts epicentral intensities that are too high and a felt area much too large.

The "Limit of Detection" (L.O.D.) boundary drawn in 

"U.S. Earthquakes" is usually near intensity 3.0. A 2L 

value of 10 km for the Desert Hot Springs earthquake 

places the 3.0 boundary inside the outer lobes of the 

L.O.D. In addition, a 2L of 10 km or less is required to 

predict intensities of only VII at Desert Hot Springs 

and only IV at Death Valley and Needles. Without ignoring the anomalous M/M VI values reported for this 

earthquake, but for purposes of making a 2L estimate 

most consistent with intensity observations, we use a

TABLE 24. Observed and calculated 2L values for selected earthquakes

Earthquake YR

Cedar Mountain, Nev. _ 32

Excelsior Mountain, Nev. 41

Hansel Valley, Utah 34

Manix, Calif. 47

Fort Sage Mountains, Calif.___ __ ___50 

Kern County, Calif. _ 52

Rainbow Mountain, Nev. 54

Rainbow Mountain, Nev. 54

Fairview Peak, Nev. 54

Hebgen Lake, Mont. 59

Gal way Lake, Calif. 75

Pocatello Valley, Idaho 75

Oroville, Calif. _ __ 75

MO

12

01

03

04

12

07

07

08

12

08

05

03

08

DY

20

30

12

10

14 

21

06

23

16

17

31

28

01

LAT(N)

38.8

38.0

41.5

35.0

40.1 

35.0

39.4

39.6

39.3

44.8

34.5

42.1

39.4

LONG(W)

118.0

118.5

112.5

116.6

120.1 

119.0

118.5

118.4

118.2

111.1

116.5

112.6

121.5

M(OB)

7.2

6.3

6.6

6.4

5.6

7.7

6.6

6.8

7.1

7.1

5.2

6.0

5.7

2L(OB)

61

1.4

8

4

8.8

18

31

48

24

7

3 3

34(1.5)

2L(PRED)

66

3.5

10

10

1 

60

18

36

40 2 28

1

3

1.5

'33 kilometers of fracture in bedrock. However, epicenter was about 30 kilometers away under Quaternary deposits. See text.

2By use of data to south of epicenter. See text.

3 2L values as determined from short-period seismograms. See text.
FAULT LENGTH VERSUS MOMENT, MAGNITUDE, AND ENERGY RELEASE VERSUS K REGION 41

2L value of 10 km, which yields a calculated M0 (1%) of 

1.0 x 1025 dyne cm, ML of 6.0, and I(MX) of 7.6.

Note again that a formula relating AV[ and M0 serves 

very well to predict most observations (fig. 22 and table 

23). The point of greatest relevance here is one mentioned only in passing above. If observed M0 values for 

earthquakes in k l x/2 regions are "normalized" to k 1% 

by the ratio of moments predicted via AVi (R/F, 1%) and 

AVI (M/M, IVk) values calculated for the 2L value found 

by observation or analysis of intensities, one obtains 

normalized M0 values that agree with predicted M0 

values for earthquakes of this 2L (underlined numbers 

in fig. 22) in k 1% regions. This correlation strongly 

suggests that observed M0 values of k ll/2 earthquakes 

are not directly comparable with observed M0 values of 

k 1% earthquakes insofar as implying relative levels of 

long-period energy release but are probably correlated 

with details of the relevant relaxation and radiation 

phenomena. The explanation of the high M0 values for 

k 1% earthquakes certainly is not a simple regional 

difference in Q attenuation. The absence of such regional differences in Q is demonstrated by the fact that 

for nuclear explosions, and thus for point sources, the 

Ms versus yield curve is independent of k region 

(Evernden and Filson, 1971).

Now note the reported and calculated ML values in 

table 23, wherein all calculated values are for equivalent 2L earthquakes in k 1% regions. In Evernden 

(1975), the relation:

ML = (log 2L + 3.2667V0.711

was empirically developed on the basis of data from k 

1% earthquakes. The validity of this relation with regard to the earthquake studied is shown by the fact 

that the average observed ML value for k 1% earthquakes of table 23 is equal to the average ML calculated 

via the above formula when 2L is either observed or 

obtained from analysis of intensity data.

The next point to note is the marked disagreement 

between reported ML values for k 1% earthquakes and 

the ML for an earthquake of equivalent 2L in k 1%. The 

average reported ML of studied k \Vz earthquakes is 

6.5, while the average calculated ML for the equivalent 

2L earthquakes in k 1% is 5.5, a difference of 1.0. This 

difference is an average measure of the inconsistencies 

routinely occurring in ML estimates of k 1% earthquakes. If magnitude estimates were used only as originally intended by Richter (1955), that is, as a scheme 

for ordering earthquakes of a region according to a 

generalized size parameter, the only error in the present calculations would be an incorrect attenuation 

formula for k P/2 earthquakes. However, since ML estimates are considered by many as measures of energy 

release, moment, and other parameters, a major inconsistency in present practice is to apply a formula developed in k 1% regions to earthquakes in all regions. We 

should be using a set of formulas of the following type:

Region

k 1% 

k 1% 

k 1% 

k 1

Formula

ML =log A + 1.75 log (D/100) 

= log A + 1.50 log (D/100) -a, 

= log A + 1.25 log (D/100) -a,, 

= log A + 1.00 log (D/100) -a3

The formula for k 1% is inconsistent with Richter 

(1958, p. 342), because it predicts a value for ML at 600 

km that is 0.5 lower than would be predicted from the 

data in Richter's table. It is interesting to note that the 

University of California at Berkeley often reports 

ML values about 0.5 ML greater than does California 

Institute of Technology, Pasadena, for southern 

California earthquakes (T. V. McEvilly, oral commun., 

1979). A possible explanation for the differing ML values is that the data used to establish Richter's curve 

may have been contaminated by multiprovince paths.

Using the formulae of Evernden (1975) and normalizing the set of equations so that earthquakes of the 

same high-frequency energy, and thus fault length, are 

given the same ML , it follows that al -0.5, a2 ;=1.0, and 

a3 =1.5. Universal use of the k 1% formula for estimating ML leads to errors for stations at about 200 km of 

0.6, 1.2, and 1.8 in k 1%, k iy4 , and k 1 regions, respectively. There are other possible schemes of scaling, 

and there are reasons why the scaling used in 

Evernden (1975) may not be directly convertible to 

maximum amplitudes versus distance. The disagreement between 1.0 and 0.6 suggests that additional factors may be influencing maximum amplitude.

The important point is that the high ML values presently assigned to earthquakes on faults with small 2L 

in k ll/2 areas indicate that an invalid formula was 

used for calculating ML , not that stress drop was higher 

for these quakes than for k 1% earthquakes of equivalent 2L. We suggest that the following formulae be 

used until more detailed work has been done:

Region Formula for M/

1% log A + 1.75 log (D/100)

H/2 log A + 1.50 log (D/100) - 0.75

1% log A + 1.25 log (D/100) - 1.50

1 log A = 1.00 log (D/100) - 2.25,

where A is amplitude in micrometers, D is epicentral 

distance in kilometers, and amplitudes are as measured on standard Wood-Anderson seismometers. A 

suggested pattern of k values for the United States is to 

be found on plate 2. Corrections for multiregional 

paths must be made.
42 SEISMIC INTENSITIES OF EARTHQUAKES OF CONTERMINOUS UNITED STATES

CRUSTAL CALIBRATION AS FUNCTION OF 

REGION

To elaborate further on the theme of the last paragraphs, one of the major continuing errors in estimating seismological parameters is the use of invalid 

calibration formulas. The routine mb values presently 

published by USGS use a B(A) term in the distance 

range 0°-20° that was demonstrated to be invalid years 

ago (Evernden, 1969). The ML B(A) term (in ML = log A 

+ B(A)) used universally is the one empirically determined by Richter (1955) as being appropriate to southern California. It is certainly invalid (that is, does not 

yield consistent estimates of ML) in regions of different 

attenuation.

A recent example of the use of such methods to calculate mb and ML is seen in the data for the earthquake of 

March 28, 1975, in Pocatello Valley on the Idaho-Utah 

border. The published parameters for this quake 

(Arabasz and others, 1981) are

AVI (M/M, 1.50) = 1.4 x 1014 cm2

ML =6.0 

I(MX) = VIII M/M

2L = 3.0 km (analysis of

short-period seismograms) 

M0 = 6.5 x 1024 dyne-cm.

The mb values are as calculated and published by the 

USGS. One anomaly in these data is that values of 6.6 

to 7.0 are listed in the 8°-9° range; that is, an incorrect 

calibration curve for mb is still being used in this distance range. In Evernden (1969), the incorrect shape of 

the B(A) curve routinely used in the Western United 

States was extensively discussed and the resultant 

errors in estimation of mb were illustrated. The mb 

values reported for stations in the distance range 

0°-20° for this earthquake should be ignored.

Secondly, the mean mb value reported for stations in 

the range 20°-54° is 5.8, while the mean mb value reported for stations in the range 65°-83° is 6.1. It was 

pointed out in Evernden and Clark (1969) that the 

Gutenberg B(A) curve for P waves is inconsistent with 

modern observational data, as this curve yields mb 

values that are 0.4 higher in the range 65°-83° than 

values in the 20°-54° range. If calibration is made 

against the nearer stations, the reported mb for this 

earthquake becomes 5.8, and all reported values 

within this range fall at or between 5.5 and 6.1

Finally, how does this magnitude compare with that 

expected for the same event occurring in western 

California and recorded at low-amplitude stations 

(Evernden and Clark, 1969; Evernden, 1977)? The

source calibration is assessed to be in the neighborhood 

of 0.25 mb unit (Evernden, 1969). Nearly all stations in 

the 20°-54° range are in shieldlike areas, that is, EUStype crustal structure, a condition that leads to an expected difference of 0.5 mb unit relative to lowamplitude stations (Evernden and Clark, 1969). Therefore, when compared with the magnitudes used in 

other reports by this author, the mb value for this event 

would have been mb 5.0 if it had occurred in western 

California and been recorded at low-amplitude stations.

Next, consider the reported ML value of 6.0. The B(A) 

curve used by the USGS and by Arabasz, Richins, and 

Langer (1978) in converting Wood-Anderson data to 

estimates of ML is the curve established by Richter 

(1955) for southern California. In other words, a calibration curve appropriate for a region of k 1% is being 

used in a region of k IVfc, a procedure that is almost 

certain to lead to gross errors if ML values in k IVfc are 

to be both independent of distance and correlative in 

some way with ML values of events in k 1% regions.

Ignoring all USGS ML values because of the great 

distance of the stations used, consider only the two ML 

values reported by Arabasz, Richins, and Langer 

(1981), that is, 5.9 at 210 km and 5.8 at 310 km. We 

assume that these values indicate an average value of 

5.8-5.9 in the range 200-300 km. If the value for k is 

assumed to be 1% while it is actually ll/2, magnitudes 

in the 200-300 km range may be overestimated by 

0.6-0.9 ML unit. Therefore, a calibrated ML value for 

this event would have been about 5.0-5.3.

The reported AVi (M/M, 1.50) value of 1.4 x 1010 cm2 

leads to a predicted 2L value of 1.35 km and a predicted 

M0 (1.50) of 2.8 x 1024 dyne cm, while our graphic 

technique predicts a 2L of 3 km and an M0 of 1.1 x 1025 

dyne cm. Both values of M0 are to be compared with the 

reported value of 6.5 x 1024 dyne cm, which would 

predict a 2L of 2.0 for an earthquake in a region of k 

1V2. All of these values are probably indistinguishable 

from the 2L of 3 km calculated on the basis of shortperiod seismograms. A 2L of 3.0 implies an earthquake 

of ML 5.3 for a region fo k 1%. Thus, the intensity data, 

ML data, and mb data imply that this event was much 

smaller than usually considered (about ML 5% if in k 

! 3/4), and all the data agree with the 2L estimate based 

on high-frequency data. In addition, the 2L value of 3.0 

km for a k IVfe earthquake is predicted to be associated 

with an IMAX (M/M) of 7.8. This value is consistent with 

the observed value of VIII in a very small area. All 

these observations appear to establish that this earthquake was of small dimension (2L of 1.5 to 3.0 km) and 

that its energy output in the pass-band typical of intensity values and ML values (approximately 0.5-3 Hz) 

was equivalent to that of an earthquake of equivalent 

2L in western California.
LENGTH OF BREAK VERSUS MOMENT VERSUS K VALUE 43

LENGTH OF BREAK VERSUS MOMENT

VERSUS K VALUE

THROUGHOUT THE UNITED STATES AND 

SUGGESTED INTERPRETATION

A point that probably requires reemphasis is just 

how meaningful, in a physical sense, are the 2L values 

we calculate from the intensity data. The procedure for 

calculating these 2L values must be reiterated. Given 

the appropriate k value for a region, the intensity data 

are then used to calculate the energy required at the 

focus to create the observed quantitative pattern of intensities. Then, we determine the 2L value required in 

a region where k=l%, that is the region of calibration 

for 2L versus energy, to supply the calculated energy 

requirements. To evaluate whether these calculated 2L 

values in each region are meaningful, we compare 

them with other data that establish actual lengths of 

break for earthquakes for which we have such estimates. Where k=l%, we should and do get nearly correct values because this is the region of calibration. 

The data in tables 23 and 24 prove that the procedure 

described above serves successfully to estimate the 2L 

values of earthquakes in regions where k=ll/2. All k 

IVfe events with known or presumably known 2L values 

are included in these tables, which show that the 

agreement between observed and calculated 2L values 

extends over at least the 2L range from 1 to 60 km.

As for 2L estimates in regions further east, we stress 

again (as was done in Evernden, 1975) the agreement 

the calculated 2L (20 km) of the 1886 Charleston 

earthquake and the size of the high-intensity isoseismal for that quake. In addition, we point out that locations of presently occurring small earthquakes in the 

Charleston area cluster along a 20-km zone exactly 

placed to fit within the high-intensity contour of the 

1886 earthquake (Arthur C. Tarr, written commun., 

1979). Finally, master-event locations by James Dewey 

(oral commun., 1979) of all historical and instrumentally locatable earthquakes in the Charleston area are 

along this same 20-km zone. Several earthquakes 

originally placed offshore can be proven to have occurred in this 20-km zone. Thus, all seismic activity in 

the Charleston area for the past several decades has 

consisted of aftershocks of the 1886 earthquake. In 

other words, there is only one seismic locus in the region, and it seems certain to have been the locus of the 

1886 earthquake.

There are no other earthquakes in the Eastern 

United States for which unequivocal demonstrations of 

length of break exist. On the basis of geologic and 

seismologic evidence, Frank McKeown (written commun., 1979) has concluded that there are no fault segments longer than 10 to 20 km in the New Madrid 

area. To quote from his letter addressing this point:

I believe that source dimensions of so-called New Madrid earthquakes are small, e.g., not more than 10-20 km in length. The basis 

for this opinion is that faults in the postulated New Madrid fault 

zone of Heyl and Brock, as mapped in the Illinois-Kentucky fluorspar 

district, are of such dimensions (see Heyl and McKeown, 1978). Also, 

about that time, I started thinking about an apparent relationship of 

mafic instrusives to earthquake source zones in eastern U.S. This 

resulted in a speculative paper (McKeown, 1978) which would be 

different if I were to write it today, but short fault lengths were 

postulated based upon some circuitous reasoning. I still don't think 

the ideas in the paper are all wrong, but more emphasis should have 

been made of the evidence of intraplate rifts and associated rocks. As 

you know, evidence of a rift and associated structures and intrusives 

has been accumulating. Hildenbrand, Kane and Stauder (1977) show 

pretty clearly a rift-like structure that appears to be terminated by 

northwest-trending structure of some kind near New Madrid. Prior 

to the aeromagnetic and gravity data, the presence of alkalic mafic 

intrusives in the subsurface of the embayment and surface around 

the embayment was indicative of rifting. Evidence for short faults in 

the New Madrid area can be inferred from the seismicity pattern, 

focal mechanisms, and reflection profile data. The subsurface structure near New Madrid must be very complex with no apparent 

through-going long faults, as indicated by diverse epicenter trends 

and differing focal mechanisms. South of Caruthersville, Mo., the 

seismicity trend appears to be in the center of the riftlike structure. 

One can infer that it is related to a fault or fault zone about 100 km 

long. If, however, a typical east-African type of intraplate rift is 

present in the subsurface, I cannot believe that the seismicity is 

along a single long fault. Rifts do not have such faults according to 

the maps and literature that I have examined. A rift contains 

numerous parallel-to-subparallel normal faults that apparently result from the tensional stress across a broad arch that preceded formation of the rift. Perhaps if the seismicity were confined to one side 

of the rift, a long fault zone could be postulated, but even the bounding faults of rifts are commonly en echelon.

Our estimate of a 2Vfe- to 5-km 2L value for this 

earthquake (k=l, Evernden, 1975) may or may not be 

consistent with these field observations. Because we do 

not know the correct k value (anything between 1 and 

1.25 being permissible on the basis of the available 

data), we cannot deny the possibility that the fault is as 

much as 10 km long.

There is positive evidence that our technique for estimating 2L values yields accurate results in several k 

regions (k 1% to k V*), there is no reason why the technique should fail in regions of k=l, and available data 

in the New Madrid area indicate that, indeed, it does 

not fail but yields accurate 2L estimates.

The conclusion that one must draw from these results is that the fault zones in all regions of the United 

States are very similar. Asperities must be of essentially equal strength and equal mean distribution on 

fault surfaces in all regions. Whatever the effective 

stress conditions are in one region, they are duplicated 

in all others. The inhomogeneity in stress on fault surfaces in k 1% regions (San Andreas fault), expressed by 

asperities with stress drops of several hundred bars 

while average stress drop is a few tens of bars, is now 

common knowledge. What is new here is that this pattern is probably similar in all regions of the United
44 SEISMIC INTENSITIES OF EARTHQUAKES OF CONTERMINOUS UNITED STATES

States. The mean stress can rise somewhat without 

affecting high-frequency energy but cannot rise an 

order of magnitude.

Given the validity of our estimates of 2L and its associated implications, the next point to note is the 

strong dependence of the 2L vs M0 relation on k value. 

All of the data of tables 22 and 23 are plotted on figure 

23. It is obvious that the relation between moment (M0 ) 

and 2L is not fixed across the United States. Moment 

actually increased by a factor of about a thousand for 

the same 2L from k 1% to k 1. Because 2L is estimated 

from high frequencies (-1-4 Hz), while M0 is measured on the basis of long periods (20 seconds to infinity), figure 23 can be considered as a plot of shortperiod energy versus long-period energy, and the plot 

implies a thousandfold increase in long-period energy 

relative to short-period energy from k 1% to k 1.

As a point of interest, the correlative Avt versus M0 

data for the earthquake of figure 23 (plotted in fig. 24) 

show a similarity between the M0 versus AVi relations 

for regions k 1% and k 1V2 , while the relations of 2L

1000 c

versus M0 for these two regions are markedly different. 

This insensitivity of AVi versus M0 to change from k 1% 

to k IVz is why Hanks, Hileman, and Thatcher (1975) 

were able to get a common curve for AVi versus M0 

when they mixed the data of earthquakes from regions 

of 1% and k 1%.

The question, then, is how to explain the 2L versus 

M0 relation of figure 25. To be specific, how is it possible 

for an M0 value of 1026 dyne-cm to be associated with a 

2L value of 1 km, the paired values on the k= 1 curve of 

figure 23? No permissible association of (JL, L, D, and H 

in a uniform half-space could possibly explain these 

values. There must be another operative inhomogeneity. We suggest that earthquakes of the 

Eastern United States are along fault zones that constitute soft inclusions in an otherwise highly rigid and 

strong crust.

Following Eshelby (1957), we consider the following 

situations:

(a) uniform elastic medium of shear modulus (JLO

(b) soft inclusion (sphere) of shear modulus /JL I imEXPLANATION

o k earthquakes

0.01 1022 1023 1024 1025 

SEISMIC MOMENT, IN DYNE CENTIMETERS

1026 1027 1028

FIGURE 23. Length of fault break (2L) as a function of seismic moment (M0) for all k regions of conterminous United States.
LENGTH OF BREAK VERSUS MOMENT VERSUS K VALUE 45

bedded in an otherwise uniform elastic

medium of shear modulus jU0 .

Presuming shear stress to be applied at distances 

that are large compared with dimensions of the soft 

inclusion, we investigate shear stress, TI? at the center 

of the space and at the center of the sphere in terms of 

the remotely applied shear stress, TA .

In case (a), rt = TA

In case (b), r, = r^J^^ - /3(jU0 - /tti)] 

where j80 = 0.1333 (4 - 5v0 )/(l - v0\ and v0 = Poisson's 

ratio outside the inclusion.

For PO = 0.25, j8 = 22/45 = l/2 

Then, we find the following relations:

0.50

0.67

0.10

0.18

0.05

0.10

Thus, the stress within the soft inclusion is less than 

the distantly applied stress. Or, in order to achieve a 

given level of shear stress on a fault within the inclusion, it will be necessary to apply a greater distant 

shear stress. If yui is one-tenth of jU0 , the externally 

applied stress must be 5.5 times the stress required on 

the fault surface. If IJL I is one-twentieth of jii0 , the externally applied stress must be ten times that required on 

the fault surface. Thus, if mean shear stress required 

for failure is 100 bars, regional stresses outside the 

inclusion must be 550 to 1,000 bars, that is, a lowstress-drop quake in a highly stressed regional environment.

Now, consider the comparative changes in strain energy associated with fault-zone failure at shear stress 

TI. Since strain energy change is a measure of moment, 

this analysis will be relevant to figure 23.

Consider the following situations, assuming total 

stress drop on the fault:

(a) As before, that is, uniform space;

A Ea = 8rV/7/Ho 

where r= radius of circular fault patch.

10"

 TO15 tr\ * *-'

2? 1014

EXPLANATION

o k 1 earthquakes

 k l l/2 earthquakes

n k 1% earthquakes

2L=5km1022 1023 1024 1025 

SEISMIC MOMENT, IN DYNE CENTIMETERS

1026 1027 102

FIGURE 24. Area within intensity VI contour (AV] ) as a function of seismic moment (M0 )for fault lengths (2L) of 5, 50, and 400 km in all k

regions of conterminous United States.
46 SEISMIC INTENSITIES OF EARTHQUAKES OF CONTERMINOUS UNITED STATES

200 KILOMETERS

' ~ '" *"" ''"'

(21B)

FIGURE 25. Fault breaks used in models for estimating replacement value of damaged wood-frame construction.
MAPS OF PREDICTED INTENSITY PATTERNS 47

(b) there exists a soft region with radius R and shear 

modulus fjii,

A Eb = 8r3T,2/7/*i ,r « R:

(c) same conditions as (b) except that total stress 

drop is presumed to take place within the entire volume of the soft inclusion;

A E = for 8 =

We then obtain the following values:

/KI//UO 1 0.5 0.10 0.05 0 

Eb/Ea -- 1 2 10 20 oc 

Ec/Ea R/r= 2.5 29 43 157 300 oc 

Ec /Ea R/r= 5 229 343 1250 2405 oo 

Ec/Ea R/r=10 1832 2749 1007919242 oo 

It is apparent that nearly any desired ratio of 2L and 

M0 is possible in concept. The asperities on the fault 

surface provide nearly all the high-frequency energy, 

while inhomogeneous relaxation of much lower average stress level can provide the long-period energy. 

The questions that arise are:

1 Why should one hypothesize total volume relaxation?, and

2 What are reasonable values of R (given a satisfactory answer to 1)?

The basis for a total-volume-relaxation hypothesis is 

founded on:

(a) The conclusion, based on intensity and 2L data, 

that all fault zones are similar and thus 

strongly conditioned and weakened.

(b) The suggestion in observations that dilatancy 

may occur in the Eastern United States, such 

dilatancy implying extensive fracturing and 

weakening of the volume surrounding the 

fault.

(c) The fact of high values of measured ambient 

stress in many Eastern United States rocks 

along with the fact of pervasive fracturing of 

rocks in the epicentral region of the New Madrid earthquake (Frank McKeown, oral commun., 1977).

This highly fractured mass may then relax partially 

or entirely with release of the fault surface (and may 

keep on relaxing for decades, as at Charleston?).

We suggest that the difference between the environments of earthquakes of the Western United States 

and Eastern United States is mostly the differences 

away from the fault zone, everything being "soft" in 

regions where k=l%, while only the inclusions are 

"soft" where k=l. We must hypothesize that the relevant /z,t is not that associated with propagation of shear

waves through the inclusion but a IJL I related to stress 

storage, that is, a pseudo-/x related to nonlinear deformation of a highly fractured mass.

An increase in M0 of probably no more than a factor 

of 100 is required to overcome the limitations of 

standard models for estimation of M0 . Thus, given a 

/JL-i/fjiQ ratio of 0.1, only very limited volumes of total 

relaxation are required, or only partial relaxation in a 

larger volume is needed. The required dimensions do 

not seem to be denied by any available data.

A point that we address only qualitatively is that of 

the corner-frequency effects noted by investigators of 

Eastern United States earthquakes and the implication of these effects regarding 2L values within conventional models. We suggest that rapid fault breakage followed by a slower rate of relaxation in an appreciable volume of soft inclusion leads to a spectral shape 

uninterpretable by homogeneous models.

Some interesting relations are suggested. A major 

implication is that one should seek sites of potentially 

damaging Eastern United States earthquakes by seeking zones of low ambient stress. High stress implies 

high rigidity and little or no chance of fault failure. 

Low ambient stress and extensive fracturing, possibly 

associated with evidence of fluid movement from depth, 

should typify seismic zones in the Eastern United 

States.

Another interesting possibility is that high deformation associated with relaxation in a finite volume 

(radius of 1 to several kilometers) would provide the 

environment in which detectable small strains could be 

seen many kilometers from the epicenter. If an inclusion deformed premonitorily before an earthquake 

with small 2L, there should be concomitantly detectable deformation in the strong region surrounding the 

weak inclusion. Thus, there may be a mechanism for 

effecting measureable strains at distances inconceivable under a model based upon a homogeneous elastic 

model.

MAPS OF PREDICTED INTENSITY PATTERNS

As illustrations of the use of our programs for predicting expected intensity patterns for earthquakes 

anywhere in the conterminous U.S., we include several 

plates, all of which are in the pocket on the rear cover. 

Plate 2 consists of two maps:

Digitized geology of the United States (see table 3 for 

correlation of geologic and ground-condition units and 

table 4 for designated relative intensities for groundcondition units of plate 2) and the pattern of 4k values 

presently in our program.
48 SEISMIC INTENSITIES OF EARTHQUAKES OF CONTERMINOUS UNITED STATES

Plate 3 consists of two maps:

Composite Predicted Intensities on Saturated Alluvium:

(1) San Francisco 2L - 400 km, k = 1%, C = 25

(2) Wasatch fault 2L = 60 km, k = 1V6, C = 25

(3) Cape Ann 2L = 10 km, k = P/4, C = 40 

Composite Predicted Intensities Corrected for Ground 

Condition:

(1) San Francisco 2L = 400 km, k = 1%, C = 25

(2) Wasatch fault 2L = 60 km, k - 1%, C = 25

(3) Cape Ann 2L = 10 km, k = I 1/*, C - 40 

Plate 4 consists of two maps:

Composite Predicted Intensities on Saturated Alluvium:

(1) Charleston 2L = 15 km, k = P/4, C = 40

(2) Owens Valley 2L - 60 km, k = 1V2 , C = 25 

Composite Predicted Intensities Corrected for Ground 

Condition:

(1) Charleston 2L = 15 km, k = iy4 , C = 40

(2) Owens Valley 2L = 60 km, k = 1%, C = 25 

Plate 5 consists of 2 maps:

Composite Predicted Intensities on Saturated Alluvium:

(1) New Madrid 2L = 20 km, k = iy4 , C = 40 

or (2L = 5 km, k = 1, C = 40)

(2) Seattle 2L = 40 km, k = 1%, C = 65

(3) Fort Tejon 2L = 320 km, k = 1%, C = 25 

Composite Predicted Intensities Corrected for Ground 

Condition

(1) New Madrid 2L = 20 km, k = iy4 , C = 40 

or (2L = 5 km, k = 1, C = 40)

(2) Seattle 2L = 40 km, k = 1%, C = 65

(3) Fort Tejon 2L = 320 km, k = 1%, C = 25

We estimate that the earthquake models used to 

produce these maps represent almost the maximum 

credible earthquakes in each area.

It should be remembered that the grid size on the 

U.S. map is 25 km by 25 km. Therefore, nearly all river 

beds, that is, sites of saturated poor ground, will not 

constitute the dominant ground condition in hardly 

any grid element and will thus not be sensed on the 

maps corrected for ground condition. Those maps are 

useful, therefore, only for indicating intensities to be 

expected on bedrock.

The New Madrid earthquake was modeled as if it 

were in a region of k = 1 1A rather than one of k = 1. It 

was pointed out in Evernden (1975) that this earthquake can be modeled either way because only in the 

epicentral region (50 km) at most does k = P/4.

The south westward projection of intensity V on plate 

3 for the Cape Ann earthquake results from calculational problems concerned with the grid size and proximity of the irregular boundary between k = 1 and k = 

IVi to the hypothetical epicenter. The implied pattern 

is probably erroneous.

For all k regions except k = 1%, the program takes 

account of k boundaries and changes attenuation rates 

in accordance with plate 2. Adequate documentation to 

justify all details of plate 2 does not now exist.

The regional contrasts in length of break (energy 

release) and size of felt areas are apparent on all of the 

maps.

ESTIMATE OF DOLLAR LOSS FOR INDIVIDUAL 

POTENTIAL EARTHQUAKES

As a guide to relative risks associated with different 

faults and potential earthquakes on these faults, we 

have developed a simple program to estimate expected 

replacement value for wood-frame construction. We 

know of most of the inherent dangers in such estimates, but we believe that it is important to have the 

capability to make rapid estimates of relative potential 

damage from different potential earthquakes, even if 

the estimates are too large or too small by a factor of 

two.

The procedure followed closely parallels that used in 

Blume and others (1978). Because we have made some 

changes from their procedures and because their report 

is not in the hand of many potential readers of this 

report, we will briefly outline the technique. It has 

been implemented for cities in California, and it could 

be implemented for any region.

Data sets required:

(a) List of all California cities and unincorporated 

areas with populations of greater than 950 

in 1977, including county, population, 

latitude and longitude, and ground condition;

(b) List of all Vz' by Vz latitude and longitude 

points in California;

(c) Estimated dollar value of wood-frame construction in a city of 75,000 in California

(1977) $1.06 billion (population/75,000) 

(Blume and others, 1978);

(d) Table of percentage of damage (P) expected to 

wood-frame construction versus Rossi-Forel 

intensity (RFI), based on values given in 

Freeman (1932), Association of Bay Area 

Governments (1978), and Blume and others

(1978);

(i) if RFI < 5.9 P=0 

(ii) 5.90 *s RFI < 6.00 P=(RFI-5.90) 

(iii) 6.00 =£ RFI < 6.80 P=(RFI-6.00)x0.25+0.1 

(iv) 6.80 =s RFI < 7.40 P=(RFI-6.801x50+0.3

(v) 7.40 « RFI < 7.85 P=(RFI-7.40)xl.11+0.6

(vi) 7.85 as RFI < 8.25 P=(RFI-7.85)x2.25 + l.l

(vii) 8.25 =s RFI < 8.70 P=(RFI-8.25)x3.33+2.0

(viii) 8.70 as RFI < 9.05 P=(RFI-8.70)x7.14+3.5

(ix) 9.05 ^ RFI < 9.50 P=(RFI-9.05)x6.67+6.0

(x) 9.50 =£ RFI < 10.00 P=(RFI-9.50)x6.00+9.0 

(xi) 10.00 as RFI P=12;
ESTIMATE OF DOLLAR LOSS FOR INDIVIDUAL POTENTIAL EARTHQUAKES 49

(e) Parameters of each hypothesized earthquake 

- 2L and coordinates of points on fault, k 

value, and C value. We virtually ignore 

character of fault motion (see below). 

For the time being, we assume that ground conditions at all sites are one intensity unit less than appropriate for saturated alluvium. Most communities are in 

alluviated valleys, and in most of these valleys, the 

water table is at least 10 m deep today. The program 

can use any or all of three specified ground-condition 

values. We now calculate and list loss estimates for J 

(saturated alluvium), J-l, and A (granite) for all sites. 

For this paper, we tabulate relative losses based on J-l. 

The procedure of calculation is as follows (given 

earthquake parameters):

(a) For each community:

i calculate expected RFI (J, J-l, and A) by

normal formulas;

ii calculate expected percentage of damage, 

P, to wood-frame construction (table 

under (d) above);

iii calculate expected replacement value for 

wood-frame construction for J, J-l, and 

A (population/75,000) x 1.06 x P; answer in billions of dollars.

(b) For each county:

Sum expected replacement values for all communities in county.

(c) For state:

Sum expected replacement value for all counties.

(d) For each l/2° by l/z° grid point and for center and 

ends of fault, calculate expected RFI (J, J-l, 

A) and expected percentage of damage. 

The results of such calculations (through step c above) 

for several potential earthquakes are given in table 25. 

Figure 25 and table 25 show all fault breaks modeled 

" for estimates of replacement value of damaged woodframe construction. The numbers on figure 25 refer to 

equivalently numbered earthquakes in table 25.

Because the San Fernando earthquake is the only 

one for which we have relevant damage data, a few 

comments on the models used for that earthquake are 

in order. Most California earthquakes modeled would 

occur on vertical strike-slip faults. For these, we placed 

our line source along the surface trace and used a C 

value of 25, such a C value having been appropriate for 

such earthquakes by study of the 1906 San Francisco 

quake (Evernden and others, 1971). Within our simple 

model, radiation pattern as well as depth of focus are 

subsumed under a "best fit" C value.

For the San Fernando earthquake, we used a 2L of 

19 km (appropriate for M 6.4), placed the epilocus of 

the hypothetical line source 6 km in the downdip direction from the surface trace of the fault (halfway between the surface trace and the epicenter), and applied 

C values of 25 and 20. A C value of 25 predicted intensities that were too low very near the fault (maximum 

predicted value on saturated alluvium of 8.6), while a 

C value of 20 gave satisfactory near-field intensities 

(9.2) but did not affect far-field values. Calculation of 

damage to wood-frame construction in southern 

California changed from $190 million with C = 25 to 

$260 million with C = 20, and most of this increase was, 

of course, in San Fernando and nearby parts of Los 

Angeles. Following Blume and others (1978), and 

using the data from the San Fernando earthquake as a 

basis, we doubled this figure to obtain an estimate of 

total replacement value and obtained values of $380 

million and $520 million. These values are to be compared with the reported value of $498 million (Steinbrugge and Schader, 1973). Thus, both peak intensities 

and dollar damage suggest that a C value of 20 is more 

appropriate than one of 25 for this thrust-generated 

earthquake. Therefore, for the several thrust faults 

modeled, we placed the epilocus of the line source 6 km 

in the downdip direction from the surface trace of the 

fault and give the dollar-loss estimates relative to C 

values of 20 and 25. All strike-slip earthquakes are 

modeled with the epilocus along the surface trace and a 

C value of 25.

The first earthquake for which estimates are given 

in table 25 is for a repeat of the 1906 San Francisco 

earthquake on the San Andreas fault. Evernden and 

others (1971) showed the necessity of extending the 

1906 break to Cape Mendocino in order to explain the 

observed isoseismals in northern California. The second earthquake of the table is for a fault break from 

Richmond to San Jose on the Hayward fault. The 

ground condition for all communities on the east side of 

San Francisco Bay is treated as J-l but several of them 

include areas in which the water table is very near the 

surface. Dollar losses rise by a factor of three (R/F 8.5 

to R/F 9.5 in most cases) if the J ground condition is 

used. However, the ground condition in parts of the 

East Bay may be J=1.5 or more, and intensities in 

areas east of Highway 101 on the San Francisco peninsula will probably be appropriate to the J ground condition (9.8-10). Losses there would be higher than 

assumed in the calculations. Thus, we consider it probably true that losses to wood-frame construction will 

be greater for a repeat of 1906 than for an M7 earthquake on the Hayward fault. The shorter hypothesized 

breaks shown for the Hayward fault represent the central part of the big break and a 30-km break opposite 

San Jose. Losses from the former are predicted to be 

twice as high as those from the San Fernando earthquake, while damage from the latter is predicted to
50 SEISMIC INTENSITIES OF EARTHQUAKES OF CONTERMINOUS UNITED STATES

equal about half that caused by the San Fernando 

earthquake.

We disagree with estimates by Wesson and others 

(1975) that a potential M7+ earthquake might occur 

on the "Zayante fault," because the character of the 

mapped surface trace of that "fault" (fortuitous coalescing of short, apparently separate failure zones) seems 

to deny the possibility of a simultaneous break along 

all the features that they assumed to be part of it.

The 4-km Santa Barbara break is intended to simulate the recent earthquake (1972); the east end of the 

break was placed at the epicenter of the main shocks 

and the length was constrained to predict no greater 

than an M 5.4 quake. All losses are predicted to be in 

Santa Barbara County, and almost all the damage 

would be in Santa Barbara. The aftershock zone is 

more than 4 km long (Lee and others, 1978), and 

whether a 2L of more than 4 for the main earthquake is 

appropriate is unknown.

The 320-km break on the central San Andreas fault 

is for a repeat of Fort Tejon 1857. The predicted losses 

are well below those for the two large earthquakes in 

the San Francisco Bay area, yet this earthquake is 

commonly considered to pose the greatest threat of

damage to southern California. As seen in table 25, our 

estimate of the replacement value of damaged structures is $1.2 billion (2 x 0.61), a value in essential 

agreement with the $1.3 billion estimated by Blume 

and others (1978). The high attenuation rates in southern California and the distance between the fault and 

the most heavily urbanized areas will lead to far lower 

losses than normally assumed (J-l intensities predicted for the city of Los Angeles range from R/F 7.5 to 

6.3 or M/M 6.8 to 5.7).

Table 25 clearly illustrates the existence of potential 

threats to southern California nearly as great or 

greater than that posed by the San Andreas fault. A 

break (13B of table 25) of 22 km (M 6.5) immediately 

north of the part of the Newport-Inglewood fault that 

broke in 1933 will cause losses comparable to those of 

an 1857 repeat (M 8.1), while a long break of 42 km (M 

6.9) (13D of table 25) along the same fault is predicted 

to cause shaking damage 1% times greater than a repeat of 1857. A 20-km break on the Whittier fault (M 

6.4) will cause greater losses than did San Fernando 

and about half the losses to be expected from an 1857 

repeat. Even a 31-km (M 6.7) break on the Malibu 

Coast fault will cause losses amounting to half as much

TABLE 25. Predicted replacement value of wood-frame construction (and all construction) damaged by potential earthquakes in California

Predicted replacement value (J-l)

No.

1

?A

?B

2C

3

4

5

6

7

8

9A

9B

10

11

12 

13A

13B

13C 

13D

14

15

16A

16B

17

ISA

18B

19

20

21A

21B

Fault

San Andreas (1906) 4

Hayward (1836?) _ ___ ]

Hayward

Calaveras (1911)

Palo Colorado 

San Gregorio

"Hosgri"

Hosgri (1927) ___ _ _ _

Nacimiento (1952) __

Santa Barbara (1925?)

Santa Barbara (1925?) _ __

Santa Barbara (1978?)

San Andreas (1957) __ _£

Laguna Beach-New Clemente

Newport-Inglewood

Newport-Inglewood (1933) __

Whittier

Raymond Hill

Elsinore (south)

Elsinore (north)

San Fernando (1972)

San Jacinto

San Jacinto

Malibu Coast

Santa Monica

Rose Canyon

2L

too

00

50

20

11

30

15

80

70

20

40

29

4

!20

40 

45

22

22 

42

20

10(0=20)

(0=25) 

70

30

19(0=20)

(0=25) 

30

38

31(0=20)

(0=25) 

32(C=20)

(0=25) 

51

32

M

8.3

7.4

7.0

6.4

6.1

6.7

6.3

7.3

7.2

6.4

6.9

6.7

5.4

8.1

6.9 

6.9

6.5

6.5 

fi Q

6.4

6.0

7.2

6.7

6.4

6.7

6.8

6.7

6.7

7.0

6.7

Lat1

N

36°51.00'

38°00.61'

37°48.89'

37°27.53'

37°09.10'

37°05.68'

37°02.43'

34°29.90'

34°36.00'

35°44.20'

34°28.20'

34°27.70'

34°22.20'

3418.30' 33°34.05' 

33°54.50'

33°54.50' 33°45.40' 

34°02.69'

33°58.99'

3412.18'

33°25.80'

33°40.54'

34°22.78'

34°03.04'

34°08.96'

34°06.10'

34°06.10'

32°53.11'

32°48.85'

Long1 

W

121°33.10'

122°22.92'

12213.73'

121°52.28'

121°34.90'

12218.31'

121°53.64'

120°54.50'

120°38.80'

121°07.70'

120°04.80'

120°00.10'

119°43.00'

117°31.50' 117°56.10' 

11817.40'

11817.40' 118°08.10' 

118°25.77'

118°00.00'

118°01.95'

117°00.00'

117°22.93'

118°30.31'

11716.76'

118°56.44'

118°33.17'

11718.05'

11714.44'

Lat2

N

4015.90'

3711.76'

37°24.46'

3711.76'

3714.20'

36°50.47'

36'56.55'

3512.20'

3511.90'

35°52.10'

34°25.70"

34°25.90'

34°23.34'

35°45.10'

3318.65' 

33°36.30'

33°45.50' 33°36.30' 

33°45.50'

33°55.14'

3410.35'

33°00.00'

33°29.19'

3418.62'

33°51.89'

33°51.89'

34°05.10'

3410.01'

32°30.41'

32°34.67'

Long2 

W

124°27.20'

121°44.62'

121°54.58'

121°44.62'

121°39.90'

12210.47'

121°47.03'

121°05.90'

120°54.50'

12116.90'

119°39.10'

119°41.40'

119°45.44'

12017.80' 117°36.92' 

117°58.80'

118'08.10' 117°58.80' 

118°08.10'

117°47.80'

118°07.80'

116°27.00'

117°09.27'

11816.55'

117°02.44'

117°02.44'

118°33.17'

118°09.27'

116°58.79'

117°02.40'

Wood-frame 

construction

$1.72B

1.14

.54

.11

.02

.04

.03

.01

.02

<.001

.023

.015

.003

.61

.16 

.90

.53

.33

1.05

.35

.26

.17 

.04

.03

.26

.19 

.06

.09

.38

.28 

1.14

.71 

.28 (J-l)

.07 (J-2) 

.23 (J-l)

.06 (J-2)

Total

$3.44B

2.28

1.08

.22

.04

.08

06

.02

.04

.046

.030

.006

1.22

.32

1.80

1.06

.66 

2.10

.70

.52

.34 

.08

.06

.52

.38 

.12

.18

.76

.56

2.28

1.42 

.56 (J-l)

.14 (J-2) 

.46 (J-l)

.12 (J-2)

'Coordinates at one end of break. 

2Coordinates at other end of break.
MATHEMATICAL DETAILS OF MODEL FOR PREDICTING INTENSITIES 51

or more than the damage associated with an 1857 repeat. The greatest apparent threat in southern 

California, however, is the Santa Monica fault, for 

which we predict a total replacement value of $1.5-2.3 

billion (2 x (0.7-1.14) ) as the result of an M 6.7 (2L = 

32 km) earthquake. However, this calculation illustrates the danger of calculating dollar loss without 

considering recurrence time. Evidence in hand, from 

marine terraces along the southern California coast 

and from geodetic measurements in the general region, 

indicates that significant displacements on the Santa 

Monica fault have been extremely rare in recent millenia and that the major active thrusts today are much 

farther north. Therefore, return times for an earthquake such as we have modeled may well be many 

hundreds to thousands of years. Combining a very long 

expected return time with an estimate of potential 

damage as high as we have calculated leads to a predicted annual loss that is very low.

Though the San Jacinto fault is the most active fault 

in southern California today, its location and the apparently limited size of earthquakes that occur on it 

render it a minimal regional threat, although it certainly is of great significance to San Bernardino and 

environs (ISA and 18B). Because the earthquakes 

hypothesized for the San Jacinto fault are assumed to 

be related to breakage along the northern 30 or 39 km 

of the fault, even doubling of that length by extension 

southward would not greatly increase the predicted 

losses.

The two modeled breaks on the Elsinore fault are 

probably larger than expectable. The 70-km break on 

the Elsinore fault was hypothesized to be the greatest 

earthquake that can have impact on San Diego. Predicted replacement value of wood-frame construction 

from such an M 7.2 earthquake is only $40 million. We 

did not know the appropriate dimensions to attach to a 

potential earthquake on the Rose Canyon fault. If a 

break of a few tens of kilometers can develop on this 

fault, damage in San Diego would greatly exceed $40 

million. Because San Diego is built largely on bedrock 

or marine terraces, and because reported intensities 

are frequently two units less than on saturated alluvium, we included replacement values of the earthquakes on the Rose Canyon fault (21A and 2 IB) for 

both J-l and J-2.

Table 25 clearly indicates that the California earthquakes with comparatively short return times that will 

cause the greatest damage are maximum expectable 

earthquakes on the Hayward fault and the northern 

section of the San Andreas fault. A repeat of the San 

Francisco 1906 is predicted to cause damage for which 

the replacement value would be nearly three times 

that of a repeat of Fort Tejon 1857. Even a 50-km break

on the central Hayward fault is predicted to cause 

losses comparable to those of a Fort Tejon repeat.

Although other fault breaks could have been 

modeled, the examples that we have cited illustrate 

that numerous possibilities exist for extensive damage 

from earthquakes in southern California. Our calculations indicate, however, that losses to wood-frame construction amounting to more than 5 times the damage 

caused by the San Fernando earthquake are not likely. 

An important point to keep in mind is that all damage 

estimates given above are based on damage due to 

shaking. Potential losses from dam failure and consequent inundation, rupturing of dikes, extensive fires, 

and other hazards are not included, nor are indirect 

costs resulting from disruption of a variety of services 

and industries.

MATHEMATICAL DETAILS OF MODEL FOR 

PREDICTING INTENSITIES

A long curved fault (k= 1%) is assumed to be a series 

of uniform point sources as closely spaced as desired. 

The formula used is

a = A

101 1/7 1/7 (1)

(effectively, equation (7) of Evernden, Hibbard, and 

Schneider (1973) with 7 = 4 and the coefficient of M = 

0.864 rather than 0.80) and

I = 3(0.5 + log a) (Richter, 1958) (2)

where

a = "acceleration"

I = intensity (Rossi-Forel) = I(R/F)

M = local magnitude = ML = Ms

n = number of equally spaced subevents used in the 

model to achieve nearly uniform release of energy 

along the fault break

e = lO11 -^ 1 - = energy (ergs) released by earthquake 

of magnitude M (Richter, 1958, p. 366).

RI = distance, in kilometers, from point i of n points 

on fault to point of observation

C = pseudo-depth term chosen so as to give proper 

near-range die-off of intensities. Intensity values 

beyond 50 to 100 km are nearly insensitive to variation in expected values of C for earthquakes in 

the United States.

k = term controlling rate of die-off of a (a °c A~k ) and 

thus effectively of I

7 = log [energy arriving at point]/a or a = [energy 

arriving at point] 1 /?

A = 0.779 = arbitrary leading coefficient selected so
52 SEISMIC INTENSITIES OF EARTHQUAKES OF CONTERMINOUS UNITED STATES

as to give correct intensity values at a uniform 

ground condition for a particular earthquake. 

Once set for the normalizing earthquake, it cannot 

be changed. The value given above is set to give 

identical short-range I values as given by equation 

(7) of Evernden, Hibbard, and Schneider (1973) 

with y - 4.

The points of the "fault" are distributed over a length 

(2L) appropriate to the M value (or an M value is used 

appropriate to the length of break 2L). See below.

When shorter faults in other regions are considered, 

equation (1) is slightly altered in order to simplify 

analysis and manipulation and to escape the multipoint aspect of energy release. Replace (Rj + C) by (Rj2 

+ C2 ) 1/2 and convert equation (1) into an integral expression of uniform energy concentration along the 

break (using "energy concentration along the break" as 

a semantic device while recognizing that the source of 

energy is not the fault but the strained volume of rock).

a = 0.779

10 1

2L

dl

_ L (R2 + C2 )4k/2 .

(3)

where definitions are as in the sketch below.

|S = point of observation

!Y

X, Y are coordinates of point of observation relative to 

the center of break with the Y axis oriented along the 

line of break.

R2 = X2 + (Y - n2

a = 0.779

where

JQ11.8+1.5M

2L \(X2

 i \ f

\(X2 + C2 /415 - 11/2 / )

V '

COS4k~2 0

0s

(4)

p = (X2 + C2 ) 1/2 , 0N = tan- 1 = tan

Now, we discuss the role of the various parameters in 

controlling predictions.

(a) L and M. As equation (4) stands, L and M are 

entered as separate quantities. A one-unit change in M 

with no change in L results in a 1.1-unit change in I for 

y = 4 or 0.8 for y 6, while a tenfold change in L with 

no change in M causes a 0.75-unit change in l(y = 4) or

0.50 (y = 6) plus an effect from the integral, the influence of this term being dependent upon position.

As a matter of fact, it appears from empirical 

California data that there is a general correlation between L and M. In all that follows, M is eliminated 

from the equation by assuming an L, M relation of a 

form designed to agree approximately with California 

L, M data

so that

and

leading to

2L = 10a X 

2L = 10 km for M = 6, 

2L = 400 km for M = 8.25

01 _ 1 Q0.711M - 3.2667

M - (3.2667 + log 2D/0.711.

If 1. » + 1.5 M

CD -

(ergs per kilometer of break), '

we obtain the results shown in table 26.

TABLE 26 Magnitude (M) Relative to length of break (2L) and 

energy density (eD)

-M

4 

4V2 

5

5 l/2

2L

0.4 

0.9 

2 

4.5

Iog«[>

18.2 

18.6 

19.0 

19.4

-M

6

6 .%

7 

7%

2L

10 

23 

50 

116

logei,

19.8 

20.2 

20.6 

21.0

2M

8 

8% 

8% 

9

2L

265 

400 

600 

1350

logei,

21.4

21.6 

21.8 

22.2

'Laws relating L and M are given in text.

-M, Local magnitude of California earthquakes.

(b) The C parameter The C parameter plays the 

role of depth in calculations. Although C must have a 

definite relation to depth of focus, the exact value does 

not agree with depths expected from travel-time 

analysis. Influence of uncertainty in C on estimation of 

k values can be largely eliminated by considering I 

values observed at distances of 50 km or more from the 

epicenter. Observations indicate that C values less 

than 25 do not seem to be appropriate for large U.S. 

earthquakes, and values greater than 60 or so seem 

irrelevant. Failure to achieve agreement between C 

value and probable depth of focus may well arise from 

the fact that the dominant energy influencing intensity 

is in trapped modes, whereas amplitudes of such modes 

show a complicated relation to depth of focus.

Calculated intensity values from equations (4) and 

(2) (I values reduced by 1.05 for reasons to be described 

below) are given in table 27. It appears that uncertainty as to whether C should be 25 or 50 will cause 

confusion in the estimation of k by less than 1A when 

using I data from 50 km. If the earthquakes used are 

large enough to give valid estimates of intensities to 

distances of more than 400 km, estimates of k can be 

based on intensity data from 100 km and more, thus 

eliminating any confusion in k estimates arising from 

uncertainties in C. If appropriate values of C are sug-
MATHEMATICAL DETAILS OF MODEL FOR PREDICTING INTENSITIES 53

TABLE 27 Influence of variations in L and C on predicted intensity 

values (y = 4,Y = O)

k

1%1%1%

1%1%1%1%1%1%1%1%1%

L

50

50

50

50

50

50

10

10

10

10

10

10

c

25

40

50

25

40

50

25

40

50

25

40

50

0

9.5

8.6

8.1

10.6

9.8

9.4

8.8

7.7

7.2

9.8

7.9

8.5

50

7.9

7.6

7.4

9.3

9.0

8.8

7.0

6.7

6.4

8.3

8.0

7.8

A (km)

100

6.6

6.5

6.4

8.1

8.1

8.0

5.6

5.5

5.4

7.1

7.0

6.9

400

3.6

3.6

3.6

5.5

5.5

5.5

2.5

2.5

2.5

4.4

4.4

4.4

800

2.0

2.0

2.0

4.2

4.2

4.2

0.9

0.9

0.9

3.1

3.1

3.1

gested by other data, confusion is eliminated. Also, 

peak intensities and estimates of L from field observations place very severe limits on permissible k values. 

Therefore, uncertainties in C have no serious impact 

on estimates of k from moderate or larger earthquakes. 

Table 27 shows that the behavior of intensity values 

at short ranges will lead to clear predictions of appropriate C values, subsequent to setting of k and L values.

(c) k and y. Equation (4) would suggest that k and y 

values might be strongly correlated. For a fixed k 

value, however, the y value influences primarily the eD 

factor (a factor not a function of k) and has minimal 

effect on (X2 + C2 )' 1^ 1 '/2 for y variation from 4 to 6 (the 

probable range requiring consideration); in addition 

the change in value of the integral is small for such 

changes in y. Table 28 illustrates these points. The I 

values for k = IVz, y = 6 are normalized to give the 

same I value at L = 200, A = 0 as for k = 1%, y = 4. The 

(y = 6, k = IVfc) I values are between those of (y - 4, K 

= IVz) and (y = 4, k = IMj), and they yield a rate of 

decay with distance more similar to (y 4, k = l x/4) 

than (y = 4, k = IVz). The actual predicted I values do 

not fall as rapidly with decreasing L for y = 6 as for y = 

4. Study of U.S. intensity data as reported in Evernden 

(1975) has shown the appropriateness of using a y 

value of 4.

(d) Leading coefficient. This coefficient is completely arbitrary and can be set once for a given ground 

condition. The coefficient used will be considered as 

that appropriate for predicting I values on saturated 

alluvium, that is, the ground condition with the zero 

correction factor in Evernden, Hibbard, and Schneider 

(1973), and has been chosen to give the correct I values 

for the San Francisco earthquake of 1906.

(e) Problem of energy to be summed for very long 

fault breaks. For long fault breaks such as the one 

produced by the San Francisco earthquake of 1906, a 

question can arise as to whether the integration in 

equation (4) should include energy from the entire 

length of the break or energy arising in a time window 

around the time of arrival from the nearest part of the

TABLE 28 Influence of variations in y and k on predicted intensity 

values (C = 25, Y = 0)

L

200

10

1

y

4

6

4

4

6

4

4

6

4

k

1%

P/2 1%1%

IMs 1 1A

1%

1%iy4

A (km)

0

11.1

11.1

12.2

9.8

10.3

10.9

8.3

9.3

9.3

100

8.8

9.0

10.4

7.2

7.9

8.6

5.6

6.8

7.1

400

6.4

6.8

8.4

4.4

5.5

6.4

2.9

4.4

5.0

800

5.1

5.6

7.3

3.1

4.3

5.3

1.5

3.2

3.7

81ioo

800

3.7

3.3

3.0

4.1

3.6

3.4

4.1

3.6

3.4

fault. Since the intent is to have one formula that is 

applicable over the scale from long breaks to short 

ones, this factor should be considered. The mode of 

analysis is to set the time window, then calculate from 

it which part of the fault would produce arrivals at the 

point of observation within the time window (assuming 

velocity of break of 3.5 km/s and velocity of wave propagation of 3.5 km/s). The next problem is how to select 

the appropriate time window. One second is certainly 

too short, and 100 s seems certainly too long. The windows considered are ±5 and ±10 s around the time of 

arrival of the peak increment (from the nearest point of 

the break). Throughout the study, it is assumed that 

the phasing of arrivals is not critical because the general prevalence of earth inhomogeneities is adequate to 

confuse phasings. Because all intensity values reported 

for the San Francisco 1906 earthquake were shown by 

Evernden, Hibbard, and Schneider (1973) to be explainable on the basis of short-period data, this assumption does seem appropriate.

Table 29A gives predicted I values for IT (total energy independent of window length), I5 and I10 (energy 

in time window ±5 and ±10 s around peak arrival) for 

the San Francisco 1906 event. It is seen that I5(7) and 

I10 (7) (I5 (7)NORM and I10(7)NORM also) are indistinguishable. I5 (7) and I5 (8) are I values for k-y of 4 x 1.75 and 4 

x 2.0, respectively. The superscript NORM signifies I 

values normalized to give IT(8) at an epicentral distance of zero. I5 (7) has essentially the same rate of 

decay with A as does IT(8). The formula for IT(8) is the 

exact one used for the San Francisco 1906 event by 

Evernden, Hibbard, and Schneider (1973). The A versus I data for the same earthquake (Y = 0) are as in 

table 30.

Thus, the I (observed), IT (8), and I5/1 o(7)NORM are 

nearly indistinguishable. Therefore, the rule of using 

windows 5 to 10 s on either side of peak arrival will be 

followed. This means that the k factor for the West 

Coast will be 1% instead of 2 as used in Evernden, 

Hibbard, and Schneider (1973). Data for other smaller 

California earthquakes where the time-window correction is not required support this change in k value. 

Since the fundamental setting of equation parameters
54 SEISMIC INTENSITIES OF EARTHQUAKES OF CONTERMINOUS UNITED STATES

TABLE 29. Effect of length of time window on predicted intensity

[Fault Breaks From Center: VH, = Vs = 3.5 km/sec]

(A) L = 200, C = 25, Y = 0 (San Francisco, 1906)

X

0

45

100

200

400

800

X

0

100

800

Case II, X =

I-,(6l = IT (6).

I.-,(7)

11.0

9.5

7.9

6.4

4.8

3.2

(BlL

Case I, Y = 0

I-,(6)

10.3

7.7

3.7

0; Y. Variable;

I,,,(7)

11.1

9.6

8.2

6.6

5.1

3.4

= 30, C =

I,(6)

10.4

7.9

3.9

IT(8)

10.0

8.4

6.8

5.2

3.6

1.8

25:1(6) =

Y

25

50

100

400

I,(7 )M>RM

10.0

8.5

6.9

5.4

3.8

2.2

I(y = 4, k =

CE

X

25

50

100

400

I1(,<7)M ""'

10.0

8.5

7.1

5.5

4.0

2.3

IVal

ise III

I-,<6>

9.7

8.6

7.3

4.5

I-,(8)

9.9

8.2

6.5

4.7

2.9

1.1

I,(6)

9.7

8.6

7.3

4.6

Key: VFB = velocity of fault break, Vs = velocity of shear waves. 

I5 (7) = I based on energy arriving ±5 sec re peak arrival (y = 4, k = 

1%). Ii 0 (7) = I based on energy arriving ±10 sees re peak arrival (y = 

4, k = 1%). I5 (8) = I based on energy arriving ±5 sees re peak arrival 

(y = 4, k = 2). I,(8) = I based on total calculated energy (y 4, k = 2). 

I_(7)Noiw = !.(7) normalized to give I at A = 0 equal to IT(8). I 1(,(7)NORM 

= IUi(7)5 normalized to give I at A = 0 equal to IT (8).

TABLE 30. Observed and predicted intensity values for San Francisco earthquake of 1906

A (km)

Kobs)

IT(8) I-(7)NORM

0

10 

10 

10

75

8 

7.6

7.7

110

7 

6.7 

6.9

160

6

5.8 

6.0

230

5 

5.0 

5.2

350

4 

4.0 

4.2

500

3 

3.2 

3.4

is accomplished by use of the 1906 San Francisco 

earthquake, the leading coefficient of equation (4) is 

changed so that predicted I values are reduced by 1.05 

(average difference between (I5 ,110 ) and (I5NORM , IIONORM ), 

so the final operative equation is

a =

(X2

cos4k-2 6>d6> (5)

where y will be set at 4 and k will take values dictated 

by patterns of isoseismals. It can be shown that, for 

fault lengths of 60 km or less, IT can be considered as 

equivalent to I5/10 .

Note that the leading coefficients in equations 3, 4, 

and 5 have been changed from those in Evernden 

(1975). The values in the earlier paper are incorrect.

DETAILS OF ROSSI-FOREL AND MODIFIED 

MERCALLI INTENSITY SCALES

ROSSI-FOREL

I. Microseismic shock. Recorded by a single seismograph or by seismographs of the same model, 

but not by several seismographs of different kinds; 

the shock felt by an experienced observer.

II. Extremely feeble shock. Recorded by several

seismographs of different kinds; felt by a small 

number of persons at rest.

III. Very feeble shock. Felt by several persons at 

rest; strong enough for the direction or duration to 

be appreciable.

IV. Feeble shock. Felt by persons in motion; disturbance of movable objects, doors, windows; 

cracking of ceilings.

V. Shock of moderate intensity. Felt generally by 

everyone; disturbance of furniture, beds, etc., ringing of some bells.

VI. Fairly strong shock. General awakening of 

those asleep; general ringing of bells; oscillation of 

chandeliers; stopping of clocks; visible agitation of 

trees and shrubs; some startled persons leaving 

their dwellings.

VII Strong shock. Overthrow of movable objects; 

fall of plaster; ringing of church bells; general 

panic, without damage to buildings.

VIII. Very strong shock. Fall of chimneys; cracks 

in the walls of buildings.

IX. Extremely strong shock. Partial or total destruction of some buildings.

X. Shock of extreme intensity. Great disaster; 

ruins; disturbance of the strata, fissures in the 

ground; rock falls from mountains.

MODIFIED MERCALLI (ABRIDGED)

I. Not felt except by a very few under especially favorable circumstances. (I Rossi-Forel scale)

II. Felt only by a few persons at rest, especially on 

upper floors of buildings. Delicately suspended objects may swing. (I to II Rossi-Forel scale.)

III. Felt quite noticeably indoors, especially on 

upper floors of buildings, but many people do not 

recognize it as an earthquake. Standing motor cars 

may rock slightly. Vibration like passing of truck. 

Duration estimated. (Ill Rossi-Forel scale.)

IV. During the day felt indoors by many, outdoors 

by few. At night some awakened. Dishes, windows, 

doors disturbed; walls make cracking sound. Sensation like heavy truck striking building. Standing motor cars rocked noticeably. (IV to V RossiForel scale.)

V. Felt by nearly everyone; many awakened. Some 

dishes, windows, etc., broken; a few instances of 

cracked plaster; unstable objects overturned. Disturbance of trees, poles, and other tall objects 

sometimes noticed. Pendulum clocks may stop. (V 

to VI Rossi-Forel scale.)

VI. Felt by all; many frightened and run outdoors. 

Some heavy furniture moved; a few instances of 

fallen plaster or damaged chimneys. Damage 

slight. (VI to VII Rossi-Forel scale.)
REFERENCES CITED 55

VII. Everybody runs outdoors. Damage negligible in 

buildings of good design and construction; slight to 

moderate in well-built ordinary structures; considerable in poorly built or badly designed structures; some chimneys broken. Noticed by persons 

driving motor cars. (VIII- Rossi-Forel scale.)

VIII. Damage slight in specially designed structures; considerable in ordinary substantial buildings with partial collapse; great in poorly built 

structures. Panel walls thrown out of frame structures. Fall of chimneys, factory stacks, columns, 

monuments, walls. Heavy furniture overturned. 

Disturbs persons driving motor cars. (VIII+ to 

IX- Rossi-Forel scale.)

IX. Damage considerable in specially designed 

structures; well-designed frame structures thrown 

out of plumb; great in substantial buildings, with 

partial collapse. Buildings shifted off foundations. 

Ground cracked conspicuously. Underground pipes 

broken. (IX+ Rossi-Forel scale.)

X. Some well-built wooden structures destroyed; 

most masonry and frame structures destroyed 

with foundations; ground badly cracked. Rails 

bent. Landslides considerable from river banks 

and steep slopes. Shifted sand and mud. Water 

splashed (slopped) over banks. (X Rossi-Forel 

scale.)

XI. Few, if any (masonry) structures remain standing. Bridges destroyed. Broad fissures in ground. 

Underground pipe lines completely out of service. 

Earth slumps and land slips in soft ground. Rails 

bent greatly.

XII. Damage total. Waves seen on ground surfaces. 

Lines of sight and level distorted. Objects thrown 

upward into the air.

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GPO 792-179/1001