Earthquake probability in engineering—Part 2: Earthquake recurrence and limitations of Gutenberg-Richter b-values for the engineering of critical structures

Engineering Geology, 36 (1993) 1-52

1

Elsevier Science Publishers B.V., Amsterdam

Earthquake probability in engineering Part 2: Earthquake recurrence and limitations of Gutenberg-Richter b-values for the engineering of critical structures The Third Richard H. Jahns Distinguished Lecture in Engineering Geology E l l i s L. K r i n i t z s k y

Geotechnical Laboratory, Waterways Experiment Station, Corps of Engineers, Vicksburg, Miss., USA (Received June 30, 1993; revised version accepted June 30, 1993)

ABSTRACT Ellis L. Krinitzsky, 1993. Earthquake probability in engineering--Part 2: Earthquake recurrence and limitations of Gutenberg-Richter b-values for the engineering of critical structures Eng. Geol., 36: 000-000. Gutenberg-Richter b-values are dysfunctional for site-specific applications in the engineering of critical structures. Their dysfunction results from differences in the mechanism of faulting and nonuniformity in the occurrences of earthquakes over time and space. The mechanisms of faulting include stick slip, various categories of controlled slip, and a multitude of thermodynamic slip processes which range from rock melting to stress releases by hydrothermal and other fluids at or near lithostatic pressures. These processes cause accelerated fault movements and chaotic earthquake occurrences, while asperities and barriers along faults contribute to temporary clustering effects that develop characteristic earthquakes but do not give them continuity through time. B-line projections must incorporate these complexities, but they can do so only when they are inclusive for large, seismically active areas such as southern California, the Aleutian arc, etc. Within the relatively small earthquake source areas that determine damaging earthquake ground motions at individual engineering sites, b-values become dysfunctional at M>~5.0. Because b-values are the determinants of probabilistic seismic hazard analyses, there are severe restraints on the usefulness of probabilistic methods to assign earthquake ground motions for the engineering of critical structures. The latter include major dams, nuclear power plants, liquefied petroleum gas installations, repositories for dangerous wastes, military command centers, sensitive industrial and defense installations, fire stations, schools, and hospitals.

Introduction I w a n t to raise a few q u e s t i o n s a b o u t the Gutenberg-Richter earthquake magnitude and recurrence relation, o r the b - v a l u e a n d b-line. O f c o n c e r n is the use in engineering o f b-lines a n d b-line p r o j e c t i o n s for p r o b a b i l i s t i c seismic h a z a r d analyses.

The earthquake magnitude and recurrence relation By the 1930s, seismologists h a d o b s e r v e d t h a t small e a r t h q u a k e s were the m o s t n u m e r o u s a n d 0013-7952/93/$06.00

the larger they b e c a m e the fewer there were in w h a t seemed a steady, t i m e - d e p e n d e n t rate o f change. I f d e t e r m i n e d , this p r o g r e s s i o n p r o v i d e d an a t t r a c t i v e p r o s p e c t for p r o j e c t i n g the future sizes a n d occurrences o f e a r t h q u a k e s t h a t s h o u l d be expected. This e a r t h q u a k e m a g n i t u d e a n d recurrence r e l a t i o n b e c a m e the basis for seismic p r o b ability t h e o r y . T h e c o n c e p t h a d its first f o r m u l a t i o n in a p a p e r b y I s h i m o t o a n d I i d a (1939). T h e i r scaling o f e a r t h q u a k e sizes was b a s e d initially o n the p e a k m i l l i m e t e r s o f swing in a s e i s m o g r a p h stylus for e a r t h q u a k e s over a t w o - y e a r p e r i o d . T h e y o b t a i n e d a linear p r o g r e s s i o n in a l o g - l o g p l o t with the

© 1993 - - Elsevier Science Publishers B.V. All rights reserved.

2

ELLIS L. KRINI'IZSK~

equation:

log-linear in which: (1)

NAm=k

log N = a + b ( 8 - M )

where: N = number of earthquakes; A = maximum amplitude of ground motion in mm: K = constant (520); and m = constant (1.74). From this demonstration of linearity in the relation of numbers and sizes for earthquakes, they expanded the analysis to include the recorded Japanese earthquakes from 1924 to 1937 for motions in interpreted peak accelerations. Figure 13 shows their results. Their equation was:

where: N=number of earthquakes; M=earthquake magnitude; a =constant for the overall recurrence rate in the source area; and b = constant controlled by the numbers of earthquakes at the magnitude levels. The relation was based on earthquakes from magnitudes 3.0-8.5 and the data were global. Gutenberg and Richter (1944) noted that neither extremely small nor extremely large shocks were as frequent at the equation indicated and that events are not strictly independent. A great shock, representing a regional release of strain, may be followed by a period of abnormal quiet. Their 1949 publication incorporated additional worldwide data and they observed that the proportionality of very large earthquakes varies over different portions of the globe. Additionally, they showed that numbers of earthquakes per magnitude unit varied significantly between shallow, intermediate, and deep earthquakes. The Gutenberg-Richter equation has come to

(2)

am'n = k'

(3)

where: a = acceleration in gals; n=number of earthquakes; k' = constant (14.57); and m' = constant (0.96). Intensity V in the Japanese scale is equivalent to Modified Mercalli VII-VIII (see Appendix A, Fig. A-l), thus the curve does not represent strong or damaging earthquakes which were left uninterpreted. Gutenberg and Richter (1944, 1949) presented their earthquake size and recurrence relation as

200 (o IdJ v <

0 "iI.< LLI LL 0 n" ILl '~ Z

100 50 20 10 5 2 1 0.5 0.2 0.1

,

0.1

0.2

0 I

,

0.5 PEAK

INTENSITY (JAPANESE) I II III ,I , I , I 1

2

5

10

ACCELERATION

20

~ e I

50

IV I r

i

100 200

v I

I

500

(a), gal ( c m / s e c 2)

Fig. 13. Number of earthquakes versus intensity and peak horizontal acceleration (from Ishimoto and Iida, 1939).

EARTHQUAKEPROBABILITYIN ENGINEERINGPART2

3

be widely used in the following form: log N = a - b M

(4)

N may be for a magnitude increment (noncumulative) or it may be N equal to M plus all smaller magnitudes (cumulative). The practice today is to prefer cumulative values. Any magnitude scale with linearity may be used, including moment magnitude, which is suitable in the range for Mw of 2-8. The cutoff at 8 derives principally from the nonlinearities in earthquake scales that are discussed later. Also, epicentral intensity (Io) in the Modified Mercalli or other intensity scales can be used in place of M.

Assumptions in probabUistic seismic hazard analysis Probabilistic earthquake ground motions for an engineering site are calculated based on the Gutenberg-Richter magnitude and recurrence relation as follows: (1) Establish the earthquake sources affecting the site. These are: (a) specific faults, or segments of a major fault; and (b) seismic zones, which are areas with approximately uniform levels of seismicity for which fault sources are not identifiable. (2) Calculate time-dependent recurrences of different sizes of earthquakes for each source based on the activity rate and b-value for the inclusive source area. (3) Attenuate earthquake ground motions from the sources to the site. (4) For designated periods of time (1000, 5000, 10000 years) estimate corresponding peak ground motions that affect the site. The above analyses are performed with numerous assumptions needed principally to compensate for inadequacies in the data base. The assumptions are as follows: (1) B-values for a large area can be used to model individual faults and zones within the area. (2) Earthquakes occur uniformly at random through time. (3) Earthquakes occur uniformly at random through space. (4) An exception to (2) and (3) is made for characteristic earthquakes, meaning a predominance of earthquakes of a certain size. A further

assumption is necessary that the characteristic earthquake will recur with an established regularity. (5) The occurrence of earthquakes is independent between sources. Example: a fault is not influenced by another fault. (6) Projected b-lines are successful predictors of earthquake occurrences through time. Comment

This paper will show that the above assumptions, though essential for the workings of probability theory, have limited validity. To accept them without severe restraints can lead to results that are unsatisfactory for the engineering of critical structures.

Time and space for engineering Simple approximations of engineering time are shown in Table 8 in the form of lifetimes for various types of construction. Most constructions last 100 years or less. Some dams are exceptions with slightly longer lives to 150 years. These estimations are for limits in time, when wear, obsolescence, consequences from damage, disruption of service, and hazards to life come to be too appreciable to be continued. The financial payout will have been still shorter, 50 years or less, determined by financing, depreciation and tax rates. The construction will have a salvage value at the TABLE 8 Lifetimes for engineering Type of construction

Lifetime (Years)

Nuclear power plants Buildings, pipelines Bridges, tunnels, flood control structures, navigation locks Dams Solid waste disposal in landfills (U.S. Code of Federal Regulations, Title 40, Ch. 1, 7-1-92 Edition, Part 258:14) Repositories for hazardous nuclear wastes (U.S. Code of Federal Regulations, Title 40, Ch.l, 7-1-92 Edition, Part 191.13)

40-80 50 100 100-150 250

10,000

4

ELLIS k. KRINI I'ZSK'I

end of depreciation and before the end of usefulness. Generally, the total period of usefulness is small, seldom more than a century and the period of financial payout is closer to 50 years. Disposal sites for solid wastes in landfills and repositories for hazardous nuclear wastes are mandated to be safe for 250 and 10,000 years respectively, which are exceptional cases. Table 9 gives maximum distances from earthquake sources over which engineered works can be damaged. Construction on firm sites can begin to be affected by 0.15 g or M M VIII. (See Appendix A for meanings of earthquake measurement scales.) The distance from a causative fault is short, 50 km for a magnitude 8 earthquake. Worldwide, earthquakes of magnitude 8 occur in the interior of a continent less than once per century, but along a plate boundary as often as three times in a century. Amplification of motions on soft ground can increase these limits. The values in Table 9 for fault source to site for soil liquefaction are taken from work by Youd and Perkins (1978) and Youd (1991). They represent limits at which permanent ground displacement occurs, resulting in potential damage to structures. These are not the limits at which liquefaction has been observed. Seismic wave amplification in shallow basins of soft soils can have effects at great distances, as

happened in Mexico City in 1985. Those are very special circumstances both for sizes of earthquake required and for site conditions. Comment

Structures have short lifetimes. The distance over which an earthquake can cause damage is usually small. There are important exceptions, but such events serve to prove the rule. Consequently, earthquake hazard assessment must focus narrowly both in time and space to be useful in engineering.

B-line irregularities A b-line is not a single, unvarying line that can be replicated by different investigators. Table 10, compiled by Johnston and Nava (1984), shows no less than 15 b-lines, all for the New Madrid earthquake source. They were determined by nine investigators over a ten-year period, and are mostly from the same basic earthquake catalogue. The recurrence of an Ms 8.8 earthquake ranges from 224 to 2573 years, a full order of magnitude. Professor Nuttli gave three interpretations: 240, 773, and 1050 years. Several causes can produce those results:

TABLE 9 Maximum distances for earthquake damage to good construction, based on mean values for seismic excitations: Western United States Damage to construction (Minimum Earthquake)

Minimum site acceleration (g)

Earthquake M

Io

Stable foundation (M = 6.0)

0.15

Soil liquefaction, permanent ground displacement (M =.5.3)

O.10

Seismic wave amplification in soft soil (M = 7.0)

0.05

6.0 7.0 8.0 5.3 6.0 7.0 8.0 7.0 8.0

VIII X XI VII VIII X XI X XI

* ~ 150 km for intraplate,

Maximum distance, earthquake (source to site) (km) 20 32 50* 1 10 50 150 230 400

EARTHQUAKEPROBABILITYIN ENGINEERINGPART 2 TABLE 10 Interpretations of b-lines and recurrences for the New Madrid Seismic Source (from Johnston and Nava, 1984, 1985) Authors

Year

log (No)=

Average recurrence time (years)

a-bM

or log (N) = a - bm

Nuttli

1974

Stauder et al

1976

Nuttli and

1978

Herrmann

Nuttli

1979

Howell

1980

Johnston

1981

Perry

1981

Nuttli

1981

Stauder

1982

Johnston and Nava 1984

log (N) = 3.55-0.87m b log (N) = 3.76 - 0.92m b log (No)= 3.20 - 0.75m b log (Arc)= 3.90 - 0.92m b log (N~)= 3.95 - 0.92m b log (N0)= 3.31 - 0.77m b log (N~)= 3.63 - 0.87m b log (N¢) . 3.82 - 0.92m b log (No) = 3.27 - 0.89m b log (Arc)= 3.132-0.873m b log (Arc)= 3.123- 0.895mb log (N¢)= 3.33-0.87m b log (Arc)= 3.437 - 0.783m b log (No)= 3.43 - 0.88m b for large zone log (No) = 3.32 - 0.9 lm b for small zone

(1) Differences in the boundaries selected for the source.

(2) Whether the earthquake tabulations are cumulative or non-cumulative. (3) Different normalizations of the information. (4) Additions of data to the earthquake catalogue. (5) Reworking of the catalogue to eliminate duplicate listings, aftershocks and noises. All such influences became greatly leveraged because small changes are enormously magnified in the logarithmic projections. Furthermore, these

mb6.0 (Ms6.3)

mb7.0 (Ms8.3)

47

347

773

58

497

1117

30

169

224

42

347

810

37

309

721

21

120

240

69

510

1100

.

.

mb7.3 (M~8.8)

.

118

912

1687

127

953

1741

176

1387

2573

78

525

1050

not applicable to large events 70

--

550

140

--

1100

effects are not unique for New Madrid; they occur everywhere. The following sections review some significant variations that have been observed relative to b-lines.

Irregularities with depth Gutenberg and Richter (1944) observed that the number of earthquakes per magnitude unit decreased with depth for shallow, intermediate and

6

ELLIS L KRINITZSK'~

deep earthquakes. The latter were in subduction zones. The trend implied less frequent larger earthquakes with increasing depth. This trend is contrary to observations of major earthquakes. Eaton et al. (1970) found pronounced variations in numbers and magnitudes for micro-earthquakes on the San Andreas fault between Parkfield and Cholame within depths to 15 km. Their study was based on aftershocks of the July 27, 1966 Parkfield-Cholame earthquake of M = 5.5, recorded from July to September 1966. A refined database of 474 hypocenters was used. Figure 14 shows the relation of depth with number of earthquakes and magnitude thresholds. Peaks in the numbers occur at depths of 3-4 km and 8-9 km. They are separated by an abrupt decline in numbers at 5-7 km. The 8-9 km interval has a pronounced increase in magnitude level. Figure 15 shows the data in the form of b-lines for 2-km intervals through the section of brittle crust. Note that the b-value has a range of 0.61-1.03. Eaton et al. (1970) speculate that the variation may be an irregularity in the slip surface across the fault, changes in the rock types, or a depth control in the behavior of rocks. Figure 15 may be evidence of asperities on the fault that control the magnitude at which a large earthquake can occur. These data suggest that b-values for larger earthquakes taken from site to site across the entire brittle crust can be affected by rock and fault properties in ways

15

0

20

NUMBER

40

60

80

OF EARTHQUAKES

Fig. 14. Variation by depth for number of earthquakes and magnitude thresholds for aftershocks on the San Andreas fault in the Parkfield-Cholarne region, July to September, 1970 (from Eaton et al., 1970).

that are distinctly different but may not be determinable. Work by Rydelek and Sacks (1989) appears to have encountered the above sort of divergence through a process of testing the completeness of earthquake catalogues in relation to their b-values. They examined crustal earthquakes, 0-30 km deep, from three seismic arrays. Biases in the data were removed and the catalogues were tested for completeness. The b-values for the three catalogues were 1.06, 0.87 and 1.00. However, the lowest magnitude with completeness did not necessarily fall on the linear b-line. In one of the arrays, it was distinctly away from the b-line and on the roll-off from the b-line. This commonly occurs at small magnitudes and is attributed to incompleteness in the data. They concluded that their results pointed to an important deviation from linear b-value curves and as such are a violation of the concept of self-similarity in the earthquake process.

Effects of large earthquakes Pacheco et al. (1992) examined the behavior of moderate to large earthquakes, Mw>~5.0, in relation to self-similarity in the earthquake process, utilizing global and regional catalogue data. Figure 16 shows their results using the Harvard Centroid Moment Tensor Solutions (CMTS) catalogue which has reported global moment based magnitudes of Mw/> 5.0 from 1977 and is complete at Mw~>5.6. Figure 16 which gives a global b-line for shallow earthquakes, ~<70 km, shows a break at M , 7.4. From 5.6 to 7.4, the b-value appears to follow the power law. Because the worldwide data combines local sources that can be very dissimilar, the b-values obtained would not apply to local zones or specific faults. Figure 17 shows the change which occurs in the orderliness of the b-line when seen in regional data examined in a narrower context, in this case for transform faults with depths ~<20 km. This is the depth range for most of the earthquakes in California. The data are from the southern California Caltech seismic network, complete from the magnitude 3.0 level since 1932. A break in the b-line occurs at about M , 6.2 and another at 6.7. The b-line disintegrates at 7 and above.

EARTHQUAKE

PROBABILITY

IN ENGINEERING

loo

.

PART 2

loo

bd.07

b=aBl e-a .

N

10

10

~~~ .

riti% lolOlzKM

ITOOIW

1

. -1

0

1

2

3

. -1

M

0

1

l-1 3

2

M

M

Fig. 15. Changes in b-line with focal depth on the San Andreas fault in the Parkfield-Cholame (from Eaton et al., 1970).

3 ,

2

-I

-

DEPTH 5 7OKm (SHALLOW)

-1

_21_l 5

6

.. F I

I

2

8O

region, July to September, 1970

[r:

1

c =

0

!!

-1 1

7

8

-25J

J

MAGNITUDE, M w MAGNITUDE, M w Fig. 16. Changes in b-lines for shallow earthquakes, depth < 70 km, worldwide. Note the break at M, 7.4 (from Pacheco et al., 1992).

Fig. 17. Changes in b-lines for transform faults, depth < 20 km, worldwide. A break between b, and b, occurs at M, 5.9-6.0 and a disintegration of the b-line takes place beginning at M, 6.5 (from Pacheco et al., 1992).

The above breaks may result in part from the manner of propagation of fault rupture. Earthquakes, with dimensions less than the thickness of brittle crust, can propagate in all directions within a plane. Larger earthquakes that rupture

the entire brittle crust from the free surface at the top to the ductile zone below can propagate farther only in the horizontal dimension (see Scholz, 1991). Consequently, small earthquakes and large earthquakes may be self-similar, but not with each

8

ELLISL KRINITZSK'~

other. However, large earthquakes are faced with an additional problem, the breakup of linearity shown in Fig. 17. Moreover, these composite data represent all of southern California and the question becomes, to what extent can it be applied to individual faults? The behavior of individual faults themselves must be known to adequately assess seismic hazards at an engineering site. A major earthquake generates so many abrupt and continuing changes that affect a typical b-line that the lineation must encompass a range of dynamic qualities. Patterns for such changes were assessed by Watanabe (1989) for several major Japanese earthquakes. He also made a review of aftershock patterns for all major historic earthquakes in central and southwestern Japan. Figure 18 shows b-lines in the Tottori area which experienced an M = 7 . 2 earthquake in 1943 and M=6.2 in 1983. Note that the respective b-lines each have the same slope but are displaced by two magnitude units. Both earthquake events abruptly deviate from the b-lines and show that b-lines in this area underestimate large earthquakes. Figure 19 shows the Fukui earthquake which had an event of M = 7.1 in 1948. Again the b-lines are two magnitude units apart. Additionally, the slopes of the b-lines have changed respective to each other. And again, the b-lines underestimate the large earthquake when it occurs.

EARTHQUAKES: TOTTORI, JAPAN, 1943, M=7.2 1983, M=6.2

10000 -

1000 .

10000 EARTHQUAKE: FUKUI, JAPAN, 1948, M= 7.1 1000 ~

o*~""-'-"~ 1976-1985

100 Z

~ ~ o q ~ . ,

•.,

10

-

o

%

2. . 3. . .4

;

1948-1949

%

5

-;,

6

8'

M

Fig. 19. B-lines for earthquakes at Fukui, Japan (after Watanabe, 1989). Watanabe made comparisons of earthquake densities through time following a major event. He identified progressions of fall-off in densities that he took to be diminutions of the aftershocks. Figure 20 shows a generalization from an interpretation Watanabe developed for the time factor in the dying off of aftershocks. The rates vary with the sizes of earthquakes: A magnitude 6 event would have diminishing numbers of aftershocks for about 30 years after which they would have ceased, magnitude 7 for up to 100 years, and

M 8.0

/ / AFTERSHOCKS

-1988

/

/

/ 100

/ •,.

/

% m o ~ ''~ 1943-1944

Z

10

/

7.0

/ NO AFTERSHOCKS

/ /

I

/ /

6.0 I

I

I

I

I

0

1

2

3

4

l

5

I

I

I

6

7

8

M Fig. 18. B-lines for earthquakes at Tottori, Japan (after Watanabe, 1989).

I

10

100

!

YEAR

1000

RANGE IN AFTERSHOCK ACTIVITY

Fig. 20. Years of continuing aftershocks following major earthquakes (after Watanabe, 1989).

9

EARTHQUAKE PROBABILITY IN ENGINEERING PART 2

magnitude 8 for as much as 200 years. Clearly, the problem of cleansing the catalogues of aftershocks becomes acute, especially for large events, yet there is no dependable procedure for identifying aftershocks. Without removing the aftershocks, the population density of the main sequence of events will not have a Poissonian distribution since two populations of events would remain merged. This combination may be significant for short-term predictability, but the success of interpreting the main-sequence events through time would suffer. Watanabe's interpretation implies that the New Madrid area may be still feeling aftershocks from 1811-1812. Another aspect of the variability of b-lines is their ability to alter greatly prior to and after an earthquake. Suyehiro et al. (1964) studied data from the Matsushiro Seismological Observatory for a perceptible earthquake of M = 3.3 and found that the b-line for foreshocks had a slope of 0.35 against 0.76 for aftershocks. The foreshock and aftershock behavior was examined further by Smith (1981) for nine earthquakes around the world with magnitudes of 3.8-6.8. He estimated there were precursory times for the b-line changes that ranged from 6 months to 7 years. Figure 21 shows b-value changes that preceded the M = 6.8 earthquake of 1968 at Inangahua, New Zealand. The b-value grew steadily from 0.6 to 2.1 in a period of 6 years, culminating in the occurrence of the earthquake. Figure 22 shows Smith's range of b-values pre-

2.0

N

INANGAHUA,

w.zef,,No

,-

.

~1.5 J < ~1.0

//

7 M=6.8

0.5 1960

1970

b-VALUE AS EARTHQUAKE PRECURSOR Fig. 21. Changes of b-values through time preceding the Inangahua, New Zealand earthquake of 1968 (from Smith, 1981).

1.5

• SAN FERNANDO, CA 1971

D .~ 1.0

1960

1970

b-VALUE AS EARTHQUAKE PRECURSOR Fig. 22. Changes of b-values through time preceding the San Fernando, California earthquake of 1971 (from Smith, 1981).

ceding the San Fernando, California, earthquake of 1971, M=6.4. The precursory period is about 7 years and begins at a drop in b-value that occurred during two smaller earthquakes. An oscillation effect of the b-values ranges over a full unit of b and occurs over periods of 5-7 years. A rise in b-value can signal a major earthquake. The b-value also can drop before the earthquake, thus decreasing its sensitivity as an indicator. The b-values must be focussed from the area of the fault in question, because the changes are obscured when they are part of larger areas. Thus, the technique has limitations for prediction, but is significant for showing that b-values have great volatility over several years when a fault is changing from inactive to active.

Unreliability of b-line projections in the central United States There are problems with the linearity of recurrence rates besides the variances in b-lines already noted. Any deviation from linearity brings into question the projection to obtain recurrence rates for the larger earthquakes. Figure 23 shows a b-line interpreted by Nuttli and Herrmann (1978) for the New Madrid source. The solid line represents the approximate extent of the seismic data from which the b-line can be constructed. The period of record is 1806 to 1975. The numbers of earthquakes by magnitudes are: mb = 3.35-3.85:100 earthquakes mb = 3.85-4.35:51 earthquakes rnb= 4.35-4.85:20 earthquakes rob= 4.85-5.35:6 earthquakes

10

ELLIS L, K R I N I T Z S K Y

NEW MADRID REGION 0.1

\

\ \

\ \ 1843 X\®®

0.01

\

1895

\ \ \ x

\

1811-1812

®

0.001

®®® \ \ \ \ \ \

o.ooo I

I

4

,

I

,

I

6

5

I

I

7

r~

jected the b-line as given in Fig. 23 to obtain recurrences. The Memphis and Charleston earthquakes of 1843 and 1895 recur once in a hundred years. The New Madrid earthquakes of 1811-1812 recur about once in a thousand years. But there is some question about 1811-1812 because the earthquakes spread over a full magnitude unit. The decision on where it falls on the b-line becomes arbitrary. Assigning recurrences in this way is circular reasoning and requires a determined suspension of disbelief. Remembering Watanabe (1989), it is more appropriate to move the 1811-1812 earthquakes into another b-line that reflects the temporary but greatly heightened seismicity. This approach was made by Mitchell et al. (1991) and is shown on Fig. 24. The solid b-line is for central United States for a period of 166 years. Added are the four largest earthquakes for New Madrid and southern Illinois. They identify the greatest earthquakes in the New Madrid region. Central United States for Fig. 24 covers the area

m b

,~Q

Fig. 23. New Madrid b-line (from Nuttli and Herrmann, 1978). Dashed line shows projection beyond the limits of data. Recurrences are unknown for the large earthquakes of 1811-1812, 1843 and 1895.

The data for estimating recurrence rates on a per-year basis ends at about rnb= 5.0. The large historic earthquakes are the four New Madrid major events of about mb=6.8--7.8 during 1811-1812; the Memphis, Tennessee, earthquake in 1843 of mb = 6.0; and the Charleston, Missouri, earthquake in 1895 of mb=6.2. N o t shown are aftershocks of the New Madrid earthquakes. Street and Nuttli (1984) estimate that six aftershocks occurred that were mbLg=6.2--7.0 and 197 of mbLg=5.2--6.2. I f Watanabe is right, smaller aftershocks are still going on. The Charleston and Memphis earthquakes are single events about 200 km apart. The New Madrid earthquakes are the equivalent of a single event in time. Nothing in the seismic data gives us recurrence rates for these earthquakes. Consequently, the b-line has been called on to assist the design evaluation (see Table 8). Practitioners have pro-

x

1000

,

i

J

,

~

i

- - NEW MADRID MAINSHOCKS ",, A,,/ AND AFTERSHOCKS x x JIV DEC. 16, 1811-MAR. 15, 1812 V " 0~UNEr-oR~ MOmHS)

% %%% .

100

~,o %%%1D%%%.%%

"e

Z

10 %%

MEMPHIS,TN 1843

t l

4

ADAPTED FROM0001) MITCHELL AND OTHER8

TE: b-LINE8

I

I

5

I

mb

I

I

6

Fig. 24. B-lines for central United States from 1820-1986 and for New Madrid from December 16, 1811 to March 15, 1812 (by Mitchell et al., 1991). The earthquakes from South Illinois, Memphis, and Charleston have unknown recurrences.

EARTHQUAKE PROBABILITY IN ENGINEERING PART 2

from the Gulf of Mexico to Canada and Kansas to Ohio, a broad expanse of 3,000,000 km 2 (see Mitchell et al., 1991). However, the earthquakes noted on the b-line lie within the Modified Mercalli intensity VII zone of Fig. 7 for the Ozark Uplift, New Madrid, and Terre Haute (also known as the Wabash source). The area is about 100,000 km 2. In it have occurred 14 earthquakes of m b = 4.9-5.4 (see Nuttli and Herrmann, 1978). In all of the rest of central United States, there are 10 more for a total of 24. By increasing the area 30-fold, the seismic data allow justification of a b-line to about mb = 5 . 5 , but this is done by making the b-line of questionable appropriateness for any specific site. Ignoring the dynamic changes in b-lines that we discussed previously, Figs. 23 and 24 show that New Madrid b-lines are statistically suitable for recurrence estimates up to rob= 5.0 and mb = 5.5 respectively. Projection of the b-lines beyond those limits makes an assumption that the mechanisms for generating earthquakes are the same for all sizes of earthquakes and that changes in magnitudes follow dependable time schedules. Paleoseismic evidence might be a means to validate b-line projections and confirm their reliability. Several such investigations have been undertaken in the New Madrid area and results to date are proving of great significance. Figure 25 is a location map for paleoseismic studies that have been made to date. Following are determinations from these studies:

(1) The Reelfoot fault The Reelfoot fault (seen in Fig. 25), is a proven active fault with a distinct surface trace. It is one of the very few in the region and it is by far the most pronounced. The Reelfoot fault borders the western edge of Reelfoot Lake. Both are in the Mississippi River floodplain in the northwestern tip of Tennessee. The Reelfoot fault is significant for the region because of implications on recurrence of a major New Madrid earthquake that were developed by the U.S. Geological Survey in trenching across this fault by David P. Russ (1982). The scarp of the Reelfoot fault is a gentle feature but has 6-8 ft of maximum vertical displacement. The feature was recognized in the 1940s and a row

11

of ten borings was placed across the scarp by the Corps of Engineers as part of an investigation of faulting in the lower Mississippi Valley (see Krinitzsky, 1950). These borings found a 40-ft vertical displacement along the fault in the Middle Eocene sediments at a depth of about 180 ft below the ground surface. There was progressively less displacement nearer to the surface as would be expected from a continuing activity. Russ undertook to locate his trench as close as possible to the line of these borings. Russ' trench exposed a normal fault in the alluvium with a zone of disturbance about a half meter wide. He interpreted three distinct movements on this fault all associated with soil liquefaction. He dated these movements as occurring over 2000 years based on radiometric C-14 ages obtained on gastropod and pelecypod shells recovered in the trench. All three movements, at 700 year intervals, Russ interpreted as New Madrid maximum earthquakes. There are some serious problems with the Russ interpretation. Radiocarbon dates on shells are not reliable, because the invertebrates eat older shells and carbonate nodules in the soil for calcium carbonate to build their new shells and this consumption does not change the age of the calcium carbonate. Thus, the dating by Russ can be defective and, if so, is a defect on the high side. The Reelfoot fault is not the New Madrid fault. It is an assumption that the liquefaction-related movements each correlates with a different New Madrid size earthquake particularly since liquefaction can be induced by much smaller earthquakes, even earthquakes as moderate as M = 5.3. One reasonable explanation is the three movements Russ observed in the trench were all associated with the 1811-1812 earthquakes rather than from earthquakes over a 2000-year period. However, all of the alternative views must remain speculative, as is Russ's interpretation. Simpson et al. (1992) reported the results of a trench they dug across the Reelfoot fault. They noted two scarp-derived coUuvial deposits. The stratigraphic relationships that they exposed in the trench permit four possible interpretations of late Holocene deformation as follows: (a). One episode in 1811-1812. The two colluvial

12

E L L I S L. K R I N I T Z S K ' f

~OSAHGY "E

FA UL T

'4D ;ORPS OF EN~NEERS ~RAINAGEDITCH ETEEXAMINED Y WESNOUSKY ND LEFFLER

L

7 50km

Fig. 25. Sites at which paleoseismic investigationswere made in the New Madrid source area. units and all liquefaction features resulted from the 1811-1812 earthquakes. The minimum age of deposits at the surface suggests a recurrence interval of more than 800-1000 years. (b). Two episodes. The two colluvial units may be two distinct scarp producing events, one during 1811-1812 and the other after 1190 to 1000 B.P. The return period would be less than 800 to 1000 years. (c). Two episodes. Both colluvial units formed in 1811-1812. An extrusive sand is older. Therefore the return period is much greater than the 800 to 1,000 years noted above. (d). Three episodes. The two colluvial deposits are related to separate, scarp-forming earthquakes, the surface deposit is an extrusive sand and is an earlier third event of less than 800 to 1000 years. The above interpretations were recast by Kelson and others (1992) to favor at least one and possibly three late Holocene earthquakes that affected the Reelfoot fault. The best support is for the New

Madrid event. A possible prior event occurred 450 to 680 years B.P. Another more equivocal event occurred l l00 years B.P. Sizes of earthquakes, other than 1811-1812, are not indicated. More recently, Rodbell and Schweig (1993) dated liquefaction effects found in upland terraces about 25 km south of Reelfoot Lake and determined them to be 1811-1812. They observed no other evidences for liquefaction in the loess and alluvial materials that are 21,600 years in age or older. The New Madrid earthquake appears to have been a unique event. The work done in the Reelfoot fault area to date has not established a prior occurrence of New Madrid earthquakes though the sediments are more than 20,000 years old.

(2) The Towasahgy archaeological site The Towasahgy archaeological site, shown in Fig. 25, is an area of Indian occupancy that has been excavated and dated. An earthquake-induced

13

EARTHQUAKE PROBABILITY IN ENGINEERING PART 2

liquefaction vent was observed to have broken through the lowermost midden at a time when the site was occupied. The top of the sand flow was capped with younger midden. There are also other sand-filled fissures that slightly post-date the midden phase of the settlement. Saucier (1991) reports radiocarbon dates that identify an earthquake in a period within 100 years prior to 1450 B.P. and another between 1450 and 1000 B.P. The latter earthquake coincides with one by Simpson and others at the Reelfoot fault. The two sites are about 50 km apart. There are uncertainties concerning the magnitudes of the earthquakes that caused the disturbances in the middens. None of the older liquefaction features are believed to have resulted from major New Madrid-size earthquakes because they are not recognizable extensively in the New Madrid area. Most significantly, the site has an apparent absence of earthquake effects of any sort for thousands of years preceding the oldest earthquake recognized which occurred between 1450 and 1000 B.P. The results at this site are instructive in confirming the observation seen in the Reelfoot area; there are long gaps between recurrences of major New Madrid earthquakes.

(3) The Priestly archaeological site The Priestly archaeological site (see Fig. 25), is a midden that shows occupancy of the site between the years 1490 and 990 B.P. Saucier (1989) reports that there is no evidence of ground disturbance other than the New Madrid events of 1811-1812 for at least 1300 years prior. The site does not reflect the earthquakes noted above at Towasahgy and at the Reelfoot fault.

(4) The Vaughn excavations In the Missouri bootheel area (shown in Fig. 25), Vaughn (1991) made a series of excavations of liquefaction features seen along Corps of Engineers drainage ditches with the objective of determining earthquake recurrences. Part of the area is peripheral to and part is outside the severe liquefaction area of 1811-1812. Vaughn obtained dates by radiocarbon testing of wood and carbon, pedological observations,

and the occurrence of Indian artifacts. He recognized three earthquakes and dated them as follows: First: About 22,000 years B.P. Second: Between 13,430 and 9,000 years B.P. Third: Between 1,210 and 970 years B.P. Vaughn's third earthquake between 1210 and 970 B.P. appears to coincide with Saucier's for the Towasahgy site at 1450-1000 B.P. and that of Simpson and others for the Reelfoot fault at 1190-1000 B.P. The sites are about 50 km from each other. Vaughn's earthquakes could range from moderate to great, however, the likelihood is that none of the earthquakes were of New Madrid magnitudes because for those time intervals there is an absence of the extensive New Madrid effects that would be expected to have occurred.

(5) The Wesnousky and Leffler excavations Wesnousky and Leffler (1992) examined drainage ditches that were reexcavated by the Corps of Engineers. These provided tens of kilometers of clean side-wall surfaces 2-3 m in height that could be inspected. They selected five localities for detailed studies. These are shown by the letters A to E in Fig. 25. These sites extend over most of the New Madrid source area. Wesnousky and Leffler found strong evidences of soil liquefaction from the 1811-1812 earthquakes in abundance but they saw nothing comparable in the soil section for the preceding 5000-10,000 years. Their interpretation with regard to the validity of a b-line projection is shown schematically in Fig. 26. The b-line gives a recurrence rate for a New Madrid earthquake of about 1000 years. The paleoseisimicity from their geological studies shows no previous New Madrid earthquakes for 10,000 years or longer. The work by Vaughn and by Rodbell and Schweig can be interpreted to extend this to more than 20,000 years. The paleoseisimic evidence fails to confirm projections for b-lines. Returning to what we do know: a b-line for the New Madrid source area can be statistically satisfactory only up to mb = 5.0. Beyond that, there is not a shred of evidence to substantiate b-line values for the recurrence of earthquakes in the magnitudes for M >~6.0, which is the level at which damage may occur to good engineering. Indeed,

14

ELLIS k. K R I N I ' I Z S K Y

0d •1

=< t,/)

w

>-

-

1

E

1811-12 New Madrid Earthquakes (Ms > 8.3) mb • 7.0

r:=. to

,L

\

".

"-

%

%

V-

10_ ",•

CI.

•o

~

100_

¢

600_

,2oo_14- "m'°", <

Geology 10000_

100000

I I I I I I I 23 456 7 Body-wave Magnitude

Fig. 26. Disparity between b-line projection and geological studies for determining recurrenceof major earthquakes in the New Madrid area (from Wesnouskyand Letfler, 1992). there is strong evidence that projecting b-lines to this level and greater causes them to diverge powerfully from reality. The 1811-1812 earthquakes produced Reelfoot Lake, a body of water 14 by 21 km in dimension. Until the 1920s the lake was covered with stumps of dead trees from a forest that was killed in the subsidence. Maximum vertical displacement at Reelfoot lake was about 6-7 m. To the southwest a rise known as the Tiptonville dome occurred with about equal size and displacement. Were these vertical movement dimensions repeated every thousand years, as required by b-line recurrences, and were they continued for a long period of time, they would have consequences that would have affected the geologic structure tremendously. Such is not the case. The rate of fault movement must have been, as the paleoseismic evidence attests, very infrequent. The Terre Haute source zone in Fig. 7 lies along an extension of the New Madrid trend. This area, known as the Wabash Valley, contains features

that offer a striking resemblance to New Madrid. Obermeier et al. (1991, 1992) found extensive ancient sand blows and liquefaction dikes which they excavated and dated. The features they identified are very likely the product of a single earthquake that took place between 2500 and 7500 years ago. The soils show no evidence of recurrence of these earthquakes. Their inferred magnitude is on the order of mb=6.7. Nuttli and Herrmann (1978) show a b-line for a Wabash source area that gives a recurrence rate of about once every 1000 years for this size of earthquake. Again, the b-line is defective as it is at New Madrid. The strong implication of these observations is that for areas of relatively low seismicity, b-line projections appear to greatly overestimate the recurrences of large earthquakes.

(6) The Johnston and Nava (1984, 1985) calculation of seismic probability for the New Madrid region Each of the 15 equations in Table 10 is a calculation for seismic probability in the New Madrid area. The two equations by Johnston and Nava (1984, 1985) deserve special notice. Their "small" zone fully encompasses the New Madrid source. The zone is about 300 km N - S and 150 km E-W. The New Madrid source has a length of about 180 km extending NE from Marked Tree in northeastern Arkansas to about Charleston in southeastern Missouri. The "large" zone is about 600 km N - S and 400 km E - W . It includes the Wabash Valley. The large zone was interpreted by these authors to be the more valid on an assumption that its crustal volume was needed to encompass the regional stresses that would be mobilized by a maximum New Madrid earthquake. They then went through statistical analyses using Poisson, Gaussian, Weibull and lognormal probabilities. The Poisson distributions were the least satisfactory because they have no statistical memory and do not model the initially low probability of an earthquake following a major event. The other methods have such memories. Of those, lognormal was taken to be the best. Statistical manipulation is only as good as the evidence on which it is based. A 40-63% probability was interpreted for an mb ~>6.0 earthquake

EARTHQUAKE

PROBABILITY

IN ENGINEERING

15

PART 2

in the New Madrid source by the year 2000. For a great 1811-1812 earthquake, it was less than 1% probable by the year 2000. But the b-line was constructed with the assumption that Russ (1982) was correct in interpreting three maximum New Madrid earthquakes in 2250 years. That assumption is extremely unlikely according to the paleoseismic evidence.

Fractals and the linearity of b-lines in southern California For the b-line to behave as a linear progression from small to large earthquakes requires that all the earthquakes be produced by the same mechanism and have a corresponding regularity in the time frame. The larger earthquakes prepare the stress fields for the smaller; the smaller coalesce and develop as the stress fields change, which lead again to producing the larger. The GutenbergRichter relation would then be a power law that ranges over all the scale levels. This concept received novel support from fractal theory. With the acceptance of fractal theory, the Gutenberg-Richter relation was recognized as a demonstration of fractals. The seismic data was chaotic but also invariant under changes of scale, or so it was alleged. Scaling changes imposed a kind of order that categorized the disorder. Fractal theory permits replacing an invariance in nature, the actualities of fault ruptures, by invariance in a statistical sense, the earthquake magnitudes. Also, under the fractal theory, a statistical invariance that proves to be discontinuous at certain points can be segmented into fractal sets. The way was paved to have fractal theory confirm the b-line concept. But, keep in mind, of the many serious problems that we saw in the b-lines, the most intractable was the question of relying on its projections where there was either no data or insufficient data. Mandelbrot (1983) states that self similarity can apply only within limits which he termed the effective dimension. The need is to maintain validity between mathematical statements and natural objects. The model in nature is conceived as threedimensional: a thread, a veil, a ball. To describe the models, the fractal sets must be modified by

bounding conditions. The effective dimension can be a subjective matter, one of approximation, therefore, of degree of resolution. But there is an essential need for cutoffs, inner and outer, that cannot be ignored. However, though fractals must be constrained within a sound database, a tail end of inadequate data can be extended in a limited sense through Information Theory. Aki (1981) was the first to apply fractals to seismicity. He interpreted seisms in the fractal dimension D of a branching fault as conforming to the Gutenberg-Richter relation with D = 1.5b. Turcotte (1989) interpreted the fractal dimension of regional or world-wide seismicity as D = 2b. A fractal-equivalent b-line for southern California, adapted from Turcotte (1989), is shown in Fig. 27. The b-value is 0.89, D is 1.78. The data from 1932-1972 are from Main and Burton (1986). Recurrence for a maximum credible earthquake on the southern San Andreas fault is from Sieh (1978). Deviation from linearity of the b-line begins at about M=6.2. Turcotte observes that the number of earthquakes greater than M = 6.5 is so small, about 6, that the statistical number are inadequate. He cautions also that the mechanics of faulting involving the shape of the fault plane

10 2 r-i SEISMICMOMENT RELEASE RATE, 1932 TO 1972. FROM MAIN & BURTON (1986) 10

SOUTHERN CALIFORNIA DEVIATION FROM FRACTAL CORRELATION

z

0

KERN COUNTY EQK 7-21-52

10-

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i

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Fig. 27. B-line for Southern California (from Turcotte, 1989). Note that the b-line, which combines values from many sources, does not represent individual faults in Southern California.

16

differ from small to large sizes of earthquakes and that geometrical self-similarity is not continuous. Turcotte warns that the fractal relation must be used with considerable caution for predicting large earthquakes and additionally, the level of seismicity may vary with time making extrapolations subject to considerable errors. Whereas Turcotte was extremely cautions over projection of the b-line, Main and Burton (1986) went ahead and developed a projection for southern California with the data shown in Fig. 27. They used seismic moment release values which they terminated at a value taken from paleoseismicity on the San Andreas fault. Their procedure was in accordance with the practice of Information Theory. Information Theory was applied by Main and Burton (1986) to regional seismicity by using a catalogue of earthquakes to develop the seismic moment release rate for a region and relating it to crustal deformation measured as slip rate. Paleoseismic information and dimensions of the segments of major faults, or of seismic gaps along such faults are used to provide limits to projections of the b-line through time. More recently, Main (1992) used paleoseismic data to bend a b-line projection in order to correct for the observed tendencies of b-lines to shift as noted by Pacheco et al. (1992). Main and Burton developed a table for southern California that compared earthquake magnitudes with average repeat times by years: a magnitude 6 earthquake to be expected every one or two years, 6.5 in 5 years, 7 in 10 years, 7.5 in 50 years, 8.0 in 200 years.

Integration of geology and seismic history for estimating earthquake recurrences in Japan Figure 28 shows data developed by Wesnousky et al. (1984) for southwest Japan, an intraplate area with many active faults and a rich seismic history extending over 400 years for the largest earthquakes. They relied on Quaternary fault data to estimate maximum earthquake magnitudes which they then used to bracket the potential seismic hazard. Their guiding assumption was that the observed distribution of earthquake magnitudes in the Gutenberg-Richter relation has to be

ELLIS L. KRINITZSKY

the consequence of a logarithmic distribution from combinations of individual fault dimensions, rather than any such relation on a single fault. Thus, the source area must be a large, encompassing province. Figure 28 shows observed data as the open triangles and circles and the calculated maximum potential seismic moment for faults as black dots. Also shown are b-lines converted to seismic moment. All show discontinuities in their progressions but, overall, a linear trend fits the data set. The b-lines deviate from the other trends and show the sharpest deviations for the largest earthquakes. The better agreement between observed seismicity (open symbols) and the predicted maximum magnitudes (dots) compared to the b-lines was interpreted to endorse the maximum magnitude model. They related seismic moment, source-to-site distances over a grid and attenuated ground accelerations to construct seismic risk maps over the region for 20-, 50-, 100and 200-year return periods for JMA intensities ~>V. The procedure was used later by Wesnousky (1986) to develop probabilistic seismic hazard maps for California. Those show average expected return time for ~>0.1g peak horizontal acceleration, and peak horizontal acceleration >~0.1g to be expected during the next 50 years. Additionally, Wesnousky developed contour maps for peak horizontal ground acceleration and peak horizontal ground velocity at a one-second period on rock during a 50-year time interval with a 10% probability of exceedance. The probabilistic methodology can be applied for large areas by combining data sources and despite the shortcomings which are: (1) an insufficiency of earthquake data through time, and (2) an unreliability in the predictive power of b-lines where large earthquakes are of concern. The methods offer a coarse-grained analysis. They are generalizations by which single progressions of b-lines or substitutes for b-lines serve for many fault sources in a region. For a critical site, independent site-specific evaluations for engineering-based distances are needed. And for such a site, the data needed for a probabilistic seismic hazard analysis covering individual faults will be

17

EARTHQUAKE PROBABILITY IN ENGINEERING PART 2

1000 _

&

SEISMICITY, 100 YEARS

0

HISTORY, 400 YEARS

•

MAXIMUM POTENTIAL SEISMIC MOMENT FOR FAULTS

X

(n I-z uJ >

~ ~ 100 - -

~ ~,

~

•

MAGNITUDE-RELATED B-VALUES FOR FAULTS

co.v , oo2%

LU It.

O r,. UJ m Z

10--

SOUTHWEST JAPAN

1 24

25

26 log (M o)

27

28

(dyne-cm)

Fig. 28. Breaks in the 400-year record for intraplate earthquakes in southwest Japan (from Wesnousky et al,, 1984).

even less sufficient than for the general region. However, the probabilistic method will be attractive to the inexperienced professional, because it promises types of information that are highly desirable. Discussion

Probabilistic estimations of the sort described above by Main and Burton (1986) or Wesnousky (1986) are greatly useful to justify defensive measures for public safety where earthquakes are a threat. The maps and numbers that they provide are ideal to alert the public to dangers, to educate them to mitigate hazards, to justify costly defensive measures in building codes, and to determine priorities for earthquake preparedness and response. They are basic also for the broad categorization that must be done in building codes, where they become merged with the much better knowledge which structural engineers have gained from practical experience. But probabilistic estimates cannot be regarded as site specific for the engineering of critical structures. We have just seen the powerful contradiction

encountered in seismic probability. For public safety, it fulfills compelling needs; yet its dependence on the predictive properties of b-lines is patently flawed. We saw b-values of small earthquakes vary from 0.6 to 1.0 over segments in a 15-km vertical section of the brittle crust (Fig. 15). B-values changed from 0.35 and 0.5 to 2.2 near a causative fault preceding activation (Figs. 21 and 22), and a shift of two magnitude units occurred between b-lines plotted before and after severe earthquakes (Figs. 18 and 19). It was shown that a major earthquake produces aftershocks that require centuries before the source adjusts to normal (Fig. 20). As if these vagaries were not sufficient, we saw b-line estimates of large-magnitude earthquake recurrence intervals vary over a full order of magnitude simply when different investigators interpreted essentially the same data (Table 10). In the New Madrid source area, assuming uniformity in the handling of the data, we saw that a b-line can be statistically satisfactory only up to m b --- 5.0 (Figs. 23 and 24). For larger earthquakes, there is no evidence to substantiate the validity of b-lines for projecting earthquake occurrences. On

18

ELLIS L. K R I N I T Z S K ' r

the contrary, the evidence is overwhelming that projected b-lines give erroneous interpretations for earthquakes of the sizes that affect engineering. For the much more seismically active area of southern California, the data for constructing b-lines becomes statistically inadequate on a regional level at about M = 6.0 (Fig. 27), which is the threshold at which earthquakes can be damaging to engineering (Table 9). At this level, other effects that cause deviations in the linearity of b-lines begin to be seen. These derive from changes in the mechanics of faulting that we will examine. The portion of the b-line, or seismic moment estimation, that can be valid in southern California smoothes out data by combining them from individual faults from a large area. The procedure applies only to the large area, not individually to the many important faults in southern California. So far we have seen only a small sampling of the vagaries and limitations in b-lines, and we have barely touched on the causes. A more in-depth analysis follows.

as moment, potency and radiated energy. The resulting b-lines are nonlinear in all cases. For shallow earthquakes in the Harvard catalogue, thrust fault and strike-slip earthquakes had much lower b-values, 0.86 and 0.77, respectively, than normal faults, which had a b-value of 1.06. B-values for secondary events, foreshocks and aftershocks, were nearly always higher than b-values for the mainshocks, but the differences were analyzed to be from associations of the earthquakes and not their intrinsic physical differences. Globally, Froehlich and Davis found that b-values from the four catalogues ranged from 0.72 to 1.34, about a 30% spread from the mean of the difference. This spread is logically attributed to unresolved problems in the gathering and assessment of earthquake data. The range is global, which tends to smooth out or miss the greater vagaries that we observe for specific locales. But these problems persist whenever the larger catalogues are used to supply data for regional and local evaluations.

Effects of systematic errors in global earthquake catalogues

Effects of earthquake mechanisms on b-lines

Systematic errors refer to unresolved problems in the gathering and processing of earthquake data. Froehlich and Davis (1993) examined b-lines that they derived from four world-wide earthquake catalogues: Abe's historical catalogue, the Harvard Centroid Moment Tensor Catalogue, the catalogue of the International Seismological Centre, and the Blacknest catalogue. They found no systematic global variation of b with depth, however, keep in mind that global averaging is insensitive to the detailed variations noted in the Parkfield-Cholame portion of the San Andreas fault. Systematic errors derive from problems in earthquake detection, earthquake location, foreshock and aftershock identification, and magnitude determination. Magnitudes determined at different stations differ typically by as much as 0.5, earthquakes less than 5.5 are missed' regularly, and there are intrinsic nonlinearities in the magnitude scales. Consequently, shortcomings can be expected in the equations that describe the relation between magnitude scales and other qualities of earthquake size such

Earthquakes of concern to engineering are the shallow events. The brittle crust normally produces earthquakes with focal depths to about 20 km. Deeper earthquakes occur in the subduction zones. Though earthquakes are known to occur to depths of about 700 km, their attenuated motions at the ground surface become too weak to be hazardous for engineering. Shallow earthquakes are those with depths to about 70 km. Complex processes produce shallow earthquakes and may be categorized as follows. (1) Stick slip. (2) Controlled slip. (3) Thermodynamic slip.

Stick Slip Laboratory tests have shown that two surfaces of rock are apt to slide over each other in jerky rather than smooth motions. This is called stick slip. The term appears to have been used since the late 1930s. During shear tests of thin samples of materials

EARTHQUAKE PROBABILITY IN ENGINEERING PART 2

sandwiched between circular flat anvils rotated under pressures up to 50,000 bars, Bridgman (1935, 1936) observed that deformations accompanying slip often involved intermittent "seizing" and "welding" of one surface to the other. Ductile metals usually deformed quietly and smoothly, but nonmetals emitted "grinding and snapping" noises and deformed in a manner that could be greatly irregular. Bridgman believed that molecular phase changes occurred in the materials. Those changes caused ruptures which threw the system into confusion until a selective reorientation of the deformations began. Orowan (1960) described the "jerky" motions of "stick slip" as a creep-initiated instability that resulted from oscillations between static friction and sliding friction. Orowan believed this process was initiated in nature from creep, which at a certain stage concentrates shear strain into a narrow zone in which the shear crack thus appears and propagates. The cycle of earthquake foreshocks, main shocks, and aftershocks results from the gradual concentration and relaxation of accelerations accompanying the creep. Brace and Byerlee (1966) expanded Orowan's observations on stick slip by describing a mechanism for sudden energy release from sliding in rock that was already fractured and broken. They determined that the resulting stress drop would release only a small portion of the total stress supported by the rock. Small stick-slip shocks were described from experiments by Burridge and Knopoff (1967) to be largely random in their time sequence. Relatively larger stick-slip shocks appeared to have a periodic occurrence that developed after the systems had experienced the smaller. This periodicity suggested that there are thresholds of potential energy above which there are progressive levels of instability. Small shocks, it would mean, are necessary for the rearrangement of stresses and for the loading of potential energy into a larger focal structure. Through a parameter of viscosity, stress moves to the near environment and causes other small shocks until the distributed and potential energy is released in a major shock. Aftershocks are then the result of coupling of larger stress gradients at the ends of a propagating fault rupture

19

with other prestressed faults nearby or on an extension of the fault on which the main shock occurred. Brace and Byerlee (1970) showed that stick slip gave way to stable sliding when temperature was increased into the range of 200-500°C. Increased temperature with depth would thus explain the disappearance of earthquakes that is observed consistently at the shallow depths of about 20 km in California. Byerlee and Brace (1968) and Brace (1972) listed the most important factors which determined whether stable sliding or creep would occur as opposed to stick slip. These were mineralogy, porosity, effective confining pressure, temperature, and thickness of fault gouge. Creep was seen to be enhanced by high temperature, low effective pressure, high porosity, thick gouge, and the presence of even small quantities of easily deformable minerals, such as serpentine and calcite. To these Byerlee (1978) added that, at low stress, rock friction is strongly dependent on the degree of surface roughness on fault planes; at high normal stress, friction is nearly independent of rock type. In addition, a time-dependent factor affecting the mechanics of stick slip was observed by Dieterich (1972, 1978). Static friction increases with the logarithm of the time that adjacent blocks remain in stationary contact. Furthermore, he noted that as brecciated material and powdered rock debris accumulate on the slip surfaces, stick slip becomes the dominant mode of sliding. Dieterich (1981) confirmed that an accelerating preliminary slip precedes the development of stick slip and Johnson (1981) showed that when a slip rate accelerates, the rate can either decrease to a stable driving rate or it can accelerate further and break into a stick-slip pattern at stress levels below the peak value. Okubo and Dieterich (1986) observed velocity jumps during stick slip and that shear stresses rapidly decrease to lower residual sliding stress levels. Dietrich and Conrad (1984) showed that time-dependent increases in friction and stick-slip instability are aided by moisture in test specimens. Other contributions to causes of stick slip have been postulated. Rice and Ruina (1983) described a nonconstant slip motion that resulted from a

20

constant relative displacement in which instability occurs by a flutter mode when a viscoelastic property of this material is reduced to a critical value. Alternations between static and kinetic friction are possible contributors to the oscillations. Thompson and Robbins (1990) reasoned that stick-slip motion involves thermodynamic instability of the sliding state, rather than purely dynamic instability. Frictional force on static objects is larger than on sliding objects. Uniform motion becomes dynamically unstable because the velocity may increase even as the force is decreased. The sliding produces stick slip under conditions of boundary lubrication that may be an interplay between molecular structure and a disorder that accompanies sliding. The contrast may develop between states with and without chemical bonds or elastic deformations that affect the coupling between moving surfaces. Most recently, Brune et al. (1993) observed in models, composed of stressed foam rubber blocks, that stick slip appeared to be controlled by interface vibrations and separations during slip. The tests suggested that dynamic changes in normal stress rather than changes in the coefficient of friction, may be the cause and the control for stick slip. Interface waves that introduce separation during slip may explain the heat flow paradox on strike-slip faults, such as the San Andreas where frictional heat appears to be of a lower order than might be expected for the motions that are involved.

Comment Stick slip has many distinct and varied explanations, however, the explanations are in agreement that the would-be mechanisms are for relatively small earthquakes because the theories involve instabilities that produce sharply limited bursts of energy. Those can be equivalents for microearthquakes and small felt earthquakes, but to obtain large earthquakes requires a coalescing of these bursts into greater and more coherent movements and requires mechanisms that produce stable sliding. However, the testing noted above does not confirm or deny that changes occur in the mechanisms that produce large earthquakes.

ELLIS L. KRINIIZSKY

The major concern at this point is to ask if magnitude limits should be assumed for the stickslip mechanics. Also, does stick slip have a dependable relation to b-lines?

Relation of stick slip to earthquake magnitude and recurrence Mogi (1962) conducted a series of tests with the view that elastic shocks recorded in laboratory specimens of granite, andesite, and pumice would represent small earthquakes resulting from brittle fracture in the earth's crust. He subjected the crystalline rocks to a uniform bending test and the pumice, packed as granular material in a metal case, to a compression test. He regarded the specimens as representing the heterogeneity found in nature, with the greatest heterogeneity in the pumice. He measured elastic waves acoustically and carried out the experiments under a constant stress and under increasing stress at a constant rate of increase. Data were plotted for numbers of acoustic emissions versus amplitude of deformation in mm and numbers of acoustic emissions versus time intervals in msec. The tests showed that the frequency of elastic shocks under a constant stress decreased exponentially with time. Mogi deduced that there was a constant transition probability between numbers of shocks and their sizes and that these patterns conformed analogously with the Ishimoto-Iida and Gutenberg-Richter relationships. Mogi's linearity was pronounced for tests run at a constant stress. However, the stress at a constant rate of 5.63 kg/cm2/min produced the results given in Fig. 29. The b-line regularities became two distinctly different lines. Mogi attributed this variance to a lack of control in his tests over a needed constant for stress. Where stress was constant, Mogi's tests obtained 20 curves that consistently showed a b-line progression in the diminishment of numbers of shocks with increases of amplitudes in the loading and in the resulting acoustic emissions. Mogi's work tends to reflect and confirm a self-similarity between small earthquakes. Under controlled loading the patterns are those of b-lines. Burridge and Knopoff (1967) continued this

EARTHQUAKEPROBABILITYIN ENGINEERINGPART 2

21

PUMICE SAMPLE A

/--

17 TO 24 kg/cm=

10 ' ~ ( O

z

•

10 TO 20 kg/crn=

1

Xo \ 01

L

0

I

2

I

I

4

I

I

6

I

I

8

M SEC Fig. 29. Numbers of elastic shocks in milliseconds obtained from pumice loaded with increasing stress at a constant rate of 5.63 kg/cm2/mm (from Mogi, 1962).

a single stick-slip mechanism is applicable for earthquakes of all sizes. The Burridge-Knopoff model of blocks drawn by springs was thought by Bak and Chen (1990) to have introduced a characteristic length which represented a dominance of characteristic events not formed in nature. Bak and Chen altered the model to incorporate their concept of selforganized criticality in which the critical state is perpetually on the verge of being triggered by events of any size. Figure 30 shows a schematic representation of stick-slip deformations. The fault zone deforms by static and dynamic friction. When the spring force on a block exceeds the critical static friction force, the block slides until the forces have been reduced to below the critical dynamic friction, then the sliding stops. Potential energy is first converted to kinetic energy and then is dissipated when deceleration occurs. The forces are redistributed into nearby blocks. While the forces are conserved, the density of the blocks is not. Wide fluctuations are allowed in the local density. The process of transferring forces to neighboring blocks allows for a chain reaction which is the

examination of stick slip and energy in laboratory tests. They related the laboratory tests to the Gutenberg-Richter equation (4) by introducing an energy equivalence for the earthquake magnitude M. M = • + fl log E

(5)

where E is the total seismic energy, and is assumed to be proportional to the potential energy released in an earthquake, and ~ and fl are constants. Merging Eqs. 5 and 4; they obtained: N log No = - b f l log E

(6)

The Burridge-Knopoff model was an elastic string in which blocks in frictional contact with a fixed surface were drawn by springs. The investigators compared peak kinetic energy with loss of potential energy in the sliding blocks. The scatter in the results was interpreted to mean that peak kinetic energy at the source is a poor indicator of potential energy release in a shock. Equivalence to a b-line progression was confirmed. The confirmation was for a single mechanism but the assumption is that

l Fig. 30. Model of stick-slip deformation (from Bak and Cben, 1990).

22

ELLIS L KRINITZSKY

E

°it

,,=,

o.o

2 .o

,IOO.O '

6oo.o '

o .o

id .o

TIME

Fig. 31. Evolution of stick-slip activity in the model of Bak and Chen (1990).

earthquake. Figure 31 shows the evolution of stickslip motions in this model. Figure 32 shows slippages in units of time for numbers of corresponding events. The progression is a b-line from the G u t e n b e r g - R i c h t e r power law expressed in a

°¢~1

od it--~

%_

m

"

'~.

10°

10~

102

10a

TIME

Fig. 32. Energy-equivalentb-line or Gutenberg-Richter power law for the Bak and Chen (1990) stick-slip model.

log-log plot corresponding to an energy equivalence. In the model, any movement that passes the critical point destroys pre-existing controls, thus it deflects the effects of memory. The outcome of an earthquake becomes unpredictable, because each additional event depends on minor details that are in a process of changing. The model presumes also that the power law is operative in an identical manner for all sizes of earthquakes, from the smallest to the largest. A question to ask is just how much credence should we put into models? An investigator develops an idea that explains how nature behaves and proceeds to build a model based on that idea. The model may or m a y not confirm the idea. When the idea is not confirmed, the model was useful because it had the creative power to force a revision. I f the idea is verified, and agrees also with some observed happenings, it m a y give us confidence to extend the idea into unobserved ranges. However, the model must remain tentative in those ranges until we can confirm in some fashion that nature behaves in the way that the model tells us.

EARTHQUAKE

PROBABILITY IN ENGINEERING

23

PART 2

Let us ignore for the moment those enormous vagaries that are endemic in b-lines. Let us ignore also the non-replicability of b-lines by different investigators. Let us admit that b-lines have very convincing power-law progressions where data are abundant, meaning small earthquakes. The Bak and Chen model agrees with those. However, their model clearly contradicts observations from Watanabe (1989), Wesnousky and others (1984), Wesnousky and Leffler (1992), and the work of others in the New Madrid area who showed that large earthquakes have deviated strongly from b-lines. Bak and Chen are in conflict also with a wealth of similar observations on large earthquakes made in the last two decades, in all parts of the world, that we will discuss later. At this point, some very germane observations by Shimazaki (1986), on the relation to each other of small and large earthquakes, are appropriate. Figure 33 shows a comparison of fault length versus seismic moment that Shimazaki developed for Japanese intraplate earthquakes. A pronounced break in the scaling occurs approximately at the seismic moment of 7.5 x 1026 dyne-cm, with an offset by a factor of 1.5-2.2. This break is at about M = 6.5. Shimazaki observed that for earthquakes below this break, 3,/o is proportional t o L 3, where L is fault length, but Mo is proportional to L 2 for larger earthquakes. A linear dimension of earthquakes at the transition is comparable to the thickness of the seismogenic layer. Shimazaki reasoned that the fault width for small earthquakes is unbounded while larger earthquakes are

.._1 b--

_.~ <

JAPANESE INTRAPLATE EARTHQUAKES

lOO

•

lO

•

""

California earthquake sequence

Main shock (M)

Average Length depth from (km) aftershocks (kin)

Watsonville, 1963 Corralitos, 1964 Antioch, 1965 Parkfield, 1966

5.4

7

30

- 0.41

5.0

12

4

- 0.66

4.9

l2

6

- 0.78

5.5

8

35

- 0.49

~

LL.

.001

TABLE 11 Earthquakes in the coast ranges of Central California with an abrupt change in the size of focal region above magnitude 5 (from McEvilly and Casaday, 1967)

1000

"1I--(5 Z

bounded by the thickness (depth) of the seismogenic layer. On this basis, he classified earthquakes into two categories, small and large. We may infer that their b-lines would separate accordingly. Shimazaki's distinction between small and large earthquakes was anticipated almost 20 years earlier by McEvilly and Casaday (1967) in a study of Coast Range earthquakes in central California that had magnitudes 4.9-5.5. The overall pattern of their observations is shown in Table 11. The lengths of the fault ruptures were determined from the records of aftershocks. Their study began with the Antioch earthquake of M = 4.9 in which the aftershocks had a nearly constant arrival-time pattern and a very uniform sense of first motions at the stations, suggesting a localized source and a uniform mechanism. The areal extent of the focal region was approximately 3 x 6 km. The pattern was very similar at Corralitos. At Watsonville and Parkfield there was an abrupt change in the sizes of the focal regions above M = 5.0. There were also strong contrasts in the b-values for the earthquake sequences, changing from - 0.66 and - 0.78 for the small earthquakes to - 0.41 and - 0.49 for the large. Each type occurred along a seismically active fault zone and in an only moderately active area. The conclusion is that there were at least two characteristically different earthquake sequences that were associated with main shocks of magnitude 5.0-5.5, and that an abrupt change occurred

,

i

•

L

.01

.1

1.0

10.0

100.0

SEISMIC MOMENT, 10~ dyne-cm

Fig. 33. Break in seismic moment scaling for fault length in Japan (from Shimazaki, 1986).

24

in that magnitude interval. Equally abrupt changes took place in b-values. Anderson and Bodin (1987) made a greatly relevant study that compared earthquake recurrence models and historical seismicity in the Mexicali-Imperial Valley. This region has experienced 34 earthquakes of mb >i 5.0 since 1852, seven of which were mb>~6.5. The severest was the February 23, 1935 Imperial Valley earthquake of mb = 7.1. They determined that there was a change in the magnitude distribution of earthquakes when the linear dimension of the fault rupture zone made a transition from smaller than the width of the seismogenic zone to larger. Their observations confirm those of McEvilly and Casaday, and Shimazaki. They found that the larger earthquakes could be explained by either a model that depends entirely on the distribution of stress drop along the fault rupture or a control of the rupture length by distance between barriers, thus producing barrier-type families of characteristic earthquakes. In either case, they found that earthquakes large enough to rupture the seismogenic zone were not dependably predictable by the Gutenberg-Richter b-line procedure. They placed the transition at M>~5.8. Stick slip can be produced during the occurrences of earthquakes at all magnitudes. The stickslip characteristic of discrete bursts of energy would be dominant when there are small earthquakes, especially those that rupture less than the width of the seismogenic zone. Larger earthquakes, the ones that propagate across the width and along lengths of the seismogenic zone, should be expected to include a greater component of energy release by stable sliding. The transition between small and large earthquakes begins at M-~5.0 in areas that are seismically active. This transition zone is also a zone of change for the Gutenberg-Richter b-line.

Comment (1) The stick-slip earthquake mechanism produces Gutenberg-Richter b-lines, at least when relatively small and discrete bursts of energy are dominant. (2) A transition that relates to the thickness of the brittle crust occurs for stick-slip b-lines begin at M-~ 5.0.

ELLIS k. K RINITZSKY

(3) For engineering, the lower range of stick-slip b-lines has limited application because the range is below the usual threshold of damage to properly built structures.

Con trolled slip Controlled slip results from constraints in nature that affect the location, size, timing, and character of fault movements. It causes earthquakes to cluster in time and space, and it makes certain earthquake magnitudes predominate over others. Thus controlled slip is an interference in the randomness of earthquake occurrence and a cause for making b-lines dysfunctional. Controlled slip is best seen in: (1) coupled fault zones, (2) faults with dominating asperities and barriers, (3) faults with characteristic slip rates and earthquake sizes, and (4) patterns of interacting fault segments.

Coupled fault zones Coupled fault zones are in operation everywhere but they can be recognized best where there are major fault zones with long and continuous historic records. (1) Turkey. Ambraseys (1971) noted that occurrences of earthquakes in Turkey during 2000 years of record were subject to marked fluctuations. Figure 34 shows the locations of the Anatolian fault zone and the Border zone and Fig. 35 shows numbers of damaging earthquakes through time for these zones. Note that during the years when one zone is quiet the other zone is active. Then the roles are reversed. It appears that movement of the continental plates can cause motion along one of the fault zones, while the other remains inactive, until the first fault has absorbed all the movement that it is capable of absorbing so that it locks and the motion deflects to the zone that has been inactive with the result that the roles are reversed. Correspondingly, the earthquake activity alternates from zone to zone. These alternations between the Anatolian and Border zones are measured in periods of five or more centuries. Ambraseys observes that the Border zone and the

25

EARTHQUAKE PROBABILITY IN ENGINEERING PART 2

40 °

30 ° r

aN_

-40 °

)

g

# i; 14

MEDITERRANEAN

SEA

EARTHQUAKE ZONESIN -300

?

, 1,oo

~

1~o =~o ~ o KM

~.,

/~ I

~

TURKEY

~"

Fig. 34. Locationof the Anatolianfault zone and the Border zone in Turkey,.(fromAmbraseys,1971). TURKEY

100

50

I

Z 100 I-f

I'~

I

f

f I

I

I

I

l

I

l

i

I

I

I

I

I

I

I

I

I

I

ANATOLIAN FAULT ZONE

5o

I

100

,500

~

I

I

1000

I

1500

YEARS, CE

Fig. 35. Time distribution of damaging earthquakes in the Anatolian fault zone and Border zone in Turkey. Note that activity in one zone is matched by an inverse of that activity in the other (from Ambraseys, 1971).

Dead Sea system to the south have been relatively quiet during the present century. Interpretation of earthquake activity from present-day instrumental data would be meaning-

ful in the short term but would be misleading in the long term. These variations in seismic activity would produce temporally varied b-lines. The earthquakes may be seen also as bunching or clustering in time during those active periods. (2) Iran. Ambraseys and Melville (1982) reported similar relationships between large regional earthquake zones in Iran. These are illustrated in Figs. 36 and 37. The zones are the Zagros, Northern, Kopet Dagh and Eastern. The shaded areas in Fig. 36 show the extent of effects from destructive earthquakes since 700 C.E. These areas are not intended to be seismic zones. They do not dismiss potentials from destructive earthquakes in other areas. Solid lines are major faults of Quaternary age, dashed lines show faults of late Tertiary age. In the Eastern and Northern zones, activity is in periods of two to three centuries alternating with quiescence of three to five centuries. Periods of activity in these zones are out of phase with each other by about two centuries. The Zagros zone is an interplate zone which appears to experience a steady rate of deformation without developing time-related clusters of seismicity. Zagros

26

E L L I S L. K R I N I T Z S K ~

i:.~i,,'4.!;~.

'

4'8

~

s'2 d(<~ ~,..~ ,_ g6

:::::i ~!'.""::::::":~.. :::~::.~.:..

-'"--N~.i..~:..!:..!~,~. "" :.. ~"~,,

'

6'0 ~

6"4 AFFECTED B Y:~ EA.T.QUA

. ':'"..,,.

"÷! ' : . ' : ' - . ; r ;

ES

.$ E A

Fig. 36. Earthquake zones in Iran. The stippled areas were most affected by damaging earthquakes through historic time (from Ambraseys and Melville, 1982). earthquakes are the least severe of those in all the zones and have a m a x i m u m of M = 7.3, compared to M = 7.5-7.9 in the other zones. It is significant that m a x i m u m earthquakes are different for the different zones, at least for the active periods that are identified. Ambraseys and Melville observed from Fig. 37 that the frequency of earthquake occurrences may not be a r a n d o m process. Large earthquakes m a y occur in broad clusters instead of being uniformly spread through time and that the generic process, which is the cause, also appears to be non-random. They examined the G u t e n b e r g - R i c h t e r relation for the zones and found that a b-line for 1900-1979 calculated for all zones combined, agreed fairly well with a b-line for all zones combined through all o f historic time. However, the relation was seen to be fortuitous. The 1900-1979 b-line overestimates the earthquakes for any one of the individual

zones. Moreover, each zone encompasses a huge area, a quarter to half a million square kilometers. The b-lines for either the region or a zone will not reflect what happens in a specific area of a few thousands of square kilometers which would be the area of concern for an engineering site. Also, it is clear that the high rate of current seismic activity would not be predictive of earthquake occurrences for long periods of time such as those that are specified for storage of hazardous nuclear wastes (Table 8). In the United States, where there is only a short seismic history, the indiscriminate use of a b-line, without insight on the above influences, can introduce major errors.

Fault asperities and barriers The effective shear stress acting on a fault varies spacially over the area of the fault plane subject

EARTHQUAKEPROBABILITYIN ENGINEERINGPART2

27

IRAN KOPET DAGH ZONE L = 7 0 0 KM, d = 1 5 0 KM

100

NUMBER OF /

0 .--J ZAGROS ZONE L = 1600 KM, d = 250 KM

100 II

5OO

l-Z UJ ~0

0

400

0

c

O'J

.

cn uJ

o ,,-

> I-< .j

X

-

NORTHERN ZONE

-200

L = 1 3 0 0 KM, d = 2 3 0 KM

-~

3OO

200

-100

5

0 =E

r---"'--'---

H ~; 0

/~51/S

~

lOO

L.._r----~ EASTERN ZONE L----IO00 KM, d = 2 3 0

3 ~

1000

1500 YEARS,

KM

20OO

CE

Fig. 37. Historic earthquake activity in the principal earthquake zones in Iran. L and d represent length and width of faults (from Ambraseys and Melville, 1982).

to rupture and asperities are that part of the plane where the failure stress is relatively high. When failure stress of the weaker areas is reached, the weak areas will slip, thus causing complications in the applied stress with a concentration at an unbroken asperity. When the applied stress reaches the asperity failure stress, that asperity will break. In many cases the resistance of the strongest asperity determines the size of the largest earthquake. Large, strong parts of a fault serve as barriers and have the effect of forming boundaries to movements in a fault segment. Eventually the barrier itself must slip and when it breaks abruptly with an earthquake it then behaves as a special case of an asperity. Asperities are credited with the ability to cause faults to break with characteristic earthquakes,

meaning earthquakes of a size that corresponds to the failure stress level of the asperity. A characteristic earthquake contradicts the validity of a b-line. The asperity is assumed to persist from earthquake to earthquake. The best example is at Parkfield California, along the San Andreas fault, and is illustrated in Fig. 38 adapted from Bakun (1988).

Characteristic sizes and slip rates of earthquakes Figure 38 shows a series of six earthquakes at Parkfield, between 1857 and 1966, that are dominated by magnitude 6 events that recurred every 21 to 22 years with the exception of 1934 which is out of place by 10 years. The earthquakes have approximately the same epicenter and the same extents of rupture. This is a nearly perfect picture

28

ELLIS L. KRINITZSKY 2000 _

/

CHARACTERISTIC EQK

/

22 YEARS M=6

1966~= /-/

1950

6*

/ / 1934j/)

0::: W

19 2 2 , ~

M=6.

M= 6

/

19o ,$

1900

/ M = 6 (?)

/

1881 ~/M=6 /--

(?) * M = 5 FORESHOCK

/ =/ 1850

185~

1st

M = 7+ I

I

2nd

3rd

f

4 th

I 5 th

I 6 th

i NEXT

Fig. 38. Characteristic earthquakes on the San Andreas fault at Parkfield, California, (adapted from Bakun, 1988).

of characteristic earthquakes. Ideally, the next earthquake should be a magnitude 6 in 1988. Five years later, as this is written, earthquake junkies are still waiting and wondering because there has been no earthquake. This delay no doubt motivated a more critical examination of the recurrence progression by Toppozada (1992). He determined that the total seismicity, which included M ~ 5 shocks, was higher for 1870-1930 than for 1930-1990, and that a progressive decrease in seismicity with time can be postulated to have been occurring since the destructive 1857 earthquake of magnitude 7+. Along the same line, Savage (1993) examined the statistical probability density for predicting an event with the regularity needed for an earthquake in 1988 and found that alternative possibilities had not been considered. The 1934 earthquake may not have been out-of-place, as was assumed for the 1988 prediction, since an alternative is that Parkfield seismicity is contaminated by relaxation from the great 1857 earthquake and that the 1857 to 1966 seismicity is not predictive of the next earthquake. Additionally, on May 2, 1983, an earthquake of M=6.5 occurred at Coalinga, centered about 40 km from Parkfield, and was followed by thou-

sands of aftershocks, six of which were larger than magnitude 5 (see Person, 1984). Mavko et al. (1985) reported that during the six months preceding, five of the six creepmeters on the San Andreas fault nearest to Coalinga measured creep rates that were faster than normal. Also a station at Parkfield showed an abrupt increase in creep rate starting 16 h before the main Coalinga shock. Creepmeters along 200 km of the San Andreas fault were affected by the Coalinga events including some of the larger aftershocks. Seismic activity on neighboring faults, as a prelude to large seismic events in the San Francisco Bay area, was noted by Sykes and Jaum6 (1990). They found that moderate-size earthquakes on faults near major faults show a buildup in activity that precedes major earthquakes over periods of 15-30 years. The affected areas range from 2.2 x 109 m 2 for a mainshock of M=6.5 to 22.0 x 109 m 2 for M = 8.3. The implications are that alterations in the stress balance on a fault are affected by alterations on adjacent faults over appreciable areas. The rhythm of earthquake occurrences must be interpreted in terms of these clustering effects. By altering the stress balance in the area, the Coalinga events may have changed the rhythm of earthquake occurrences at Parkfield.

29

EARTHQUAKE PROBABILITY IN ENGINEERING PART 2

There are many short-term examples of characteristic earthquakes. They relate principally to fault asperities (Aki, 1984) and to fault barriers (Aki, 1979). The question becomes, is there something innate in faulting on a major scale that establishes a dominant size or dominant sizes for earthquakes? An interpretation that favored such a process was given by Davison and Scholz (1985) for earthquake zones of the Aleutian arc. They reasoned that the area was broken into discrete zones by transverse faults. The zones would have a large degree of permanence. The maximum earthquake potential would be related to the sizes of the zones (which vary greatly), to slip rates (cf., Youngs and Coppersmith, 1985) and to stress release. Schwartz and Coppersmith (1984) related these assumed processes to paleoseismic evidence from the Wabash and San Andreas faults. They used trenches to locate previous fault movements, date them, and estimate earthquake magnitudes. Magnitudes that occurred most often were taken to be characteristic. Youngs and Coppersmith (1985) developed the above methodology further by utilizing a slip rate constraint, which they related to seismicity. The slip rate for a fault served to interpret an upper bound magnitude which was taken to be the characteristic earthquake. Paleoseismic data may not be available for a single fault and both slip information and seismic record may be insufficient. If insufficient, the activity rates must be calculated for the region. The fault-specific recurrence, which is what one wants for engineering, is not obtained by their methodology, which includes several unjustified assumptions that: (1) a slip rate can be estimated dependably; (2) a slip rate is an indicator of earthquake magnitude; and (3) a slip rate remains constant through time. We have made the point from Ambraseys' work that slip rate should not be expected to be uniform through time. Lomnitz-Adler (1985) and Trifo and Radulian (1989) endorsed the concept of characteristic earthquakes and explained them as deriving from asperities which they believed could be analyzed by using percolation theory. The concept of percolation theory is that weakest asperities fail earliest leaving "free fields" from which the stresses migrate pro-

gressively to larger asperities. Failures occur in clusters that cause stress transfers ultimately to a major asperity that breaks with the characteristic earthquake. These scenarios are purely theoretical and they have a conceptual defect: they assume that powerful asperities will perform repetitively through time without changes. Nowhere is this concept substantiated. Problems with the concept of characteristic earthquakes were stated by Kagan (1993) as follows: (1) Identification of characteristic earthquakes comes from geological, geophysical, and interpreted mechanics of faulting that are qualitive and sometimes subject to contradictory interpretations. (2) The seismic record in most seismic zones is too short to estimate the distribution of earthquake sizes from the available data. (3) The characteristic hypothesis is not specified to the point where it can be subject to formal testing, it is known only in broad, qualitative terms. (4) It is almost impossible to verify or refute the characteristic hypothesis using available evidence.

Interacting fault segments Great faults, like the San Andreas, produce great earthquakes but only a part of the fault moves during any one of those earthquakes. Different parts of the fault, or segments, move during successive earthquakes until all of the fault has moved. Then, it is believed by some, the sequence repeats itself approximately as a sort of cycle. Meanwhile, segments that can be seen to have not moved become seismic gaps and their spaces are candidates for the locations of the next movements. The lengths of these segments become measures for the expected maximum earthquakes. Implied is a controlled regularity from which knowledge can be induced regarding expected earthquakes, their locations, sizes and to some extent their times of occurrence. This is wonderful knowledge to have if you are designing an important structure. But recent studies have been showing that the whole matter is disturbingly more complicated. Concerning interpretations of the place, size and time of earthquakes in seismic gaps, keep in mind that data from earthquake histories are too few to

30

provide statistical endorsals of cyclical patterns. Furthermore, there are acute problems in the assignment of seismic gaps. Elapsed time is not appropriate unless the known parameters also include the local variations in repeat times for both major and great earthquakes, with no missing events and, no subpatterns or clustering effects in the recurrence intervals. Also, the statistical distribution function, whether Gaussian, Weibull, etc., should be known. Paleoseismic studies may attempt to provide these data but they seldom produce a complete record. Where accomplished with exceptional success and apparently providing the needed information, they tend to include complexities that show simplifying assumptions to be misleading. In a discussion of models of earthquake recurrence and the slip history at Nankaido, Japan, where there is a 1200 year history, Scholz (1989) observed that radiocarbon dating cannot establish synchrony of rupture and that slip in each event is not determined better than about 20%. Scholz states that chaotic behavior occurs over some range of parameters but the important point is that it is aperiodic and unpredictable. Also, Scholz believes that we are able to estimate the time of the next rupture, and assuming such estimation might be approximately successful, one still cannot expect to know how far that rupture would propagate. This variation is intrinsic and precludes long range prediction. A study that appears to corroborate partially the above outlook, but also endorses characteristic earthquakes for some places and for extended periods of time, was reported by Sieh et al. (1989) for paleoseismic events along the San Andreas fault at Wallace Creek and Pallett Creek. Their observations are summarized in Fig. 39. Wallace Creek shows four paleoseismic earthquakes between 395 and 1495 C.E. that are characteristic events in both their sizes and times of recurrence. However, the characteristic patterns changed with the historic earthquake of 1857 and it is not possible to say with confidence what the pattern is at present. On the other hand, paleoseismicity at Pallett Creek greatly underestimates the 1812 and 1857 earthquakes for size and would impart some doubtful or misleading patterns for recurrence.

ELLIS

9(]

s0

r

i

i

,

SAN ANDREAS

~ 2 o o KU APART

=o

i

i

i

FAULT

..~

If/rill

,,'8_o

=.,0 -

,3.6

KRINITZSK'J

i

z~3~

,,.~v.,, 1495_+30

,,s5±55

L

+,s

~,';.," .~~¢, ~

_

-

i

j

Date (AD) Fig. 39. Comparison of" earthquake dates from paleoseJsmicJty on segmentsof the San A.ndreas fault at Wallace Creek and Pa]]¢tt Creek (from Sich et al., 1989). The authors noted that their data suggests that the second or third earthquake at Pallett Creek

relates to earthquakes at Wallace Creek and that the first earthquake in each cluster does not. Within the clusters of earthquakes at Pallett Creek, the intervals between earthquakes are mostly less than 100 years, but the time between clusters is on the order of 200 and 330 years. Thatcher (1989) analyzed the historic recurrences of great earthquakes in rupture segments along the boundaries of the Pacific plate. Figure 40 shows succinctly that with the sole exception of southern Chile, an exception that proves the rule, there is a complete absence of comparable source areas from earthquake to earthquake. We may allow that fault segments and seismic gaps are real. Thatcher believes that rupturing of the same segment is typical rather than exceptional and that sequences of major earthquakes fill seismic gaps with remarkable order. However, we cannot know if a maximum earthquake is about to occur or a lesser earthquake. The length of a cycle appears to follow a pattern that is easier to interpret. Thatcher notes a 70-year cycle throughout the circum-Pacific by which major earthquakes in a segment can be expected to recur. When the earthquakes appear, they occur in clusters separated by periods of relative quiescence, much like Pallett Creek. What the historic and paleoseismic

EARTHQUAKEPROBABILITYIN ENGINEERINGPART2

S. CHILE 1835/37 and 1960

CONCEPCION 1835 and 1928160

/©

VALPARAISO 1906 and 1971/85

31

00

9

(

~ 1940

NEMURO-OKI,JAPAN 1894 and 1973

KANTO, JAPAN 160511703 and 1923153 1953

1605 " ' ~

;

/ - 198~,/ •

1918 1

1 7 0 ~

!96o

PERU 1746 and 1940/74

KURILE 1918 and 1963

NANKAI, JAPAN 1707,1854 and 1944/46 TOKAI,-'~" 7"

,.

;(t

iii!

i

YAKATAGA 1899 and 1979

ALEUTIANS

COLOMBIA 1906 and 1942179

1979

MICHOACAN 1911 and 1981/85 1985

1981

79 ~ , 1956 ~ / ~ / / 0 t

200 1

1,

400 I

l

600 I

I

800 km I

I

Fig. 40. Historic earthquake sequences in boundary segments of the Pacific plate (from Thatcher, 1989).

records of earthquakes in fault segments tell us is that such information will be unsatisfactory for establishing precise, short-term seismic potentials. For the short time spans appropriate for engineering, it is not possible to know from such information, with only reasonable accuracy, whether to expect a maximum earthquake or a lesser event or no substantial earthquake. As a practical matter, the record may serve only as a broad and categoric parameter for earthquake potential. It is thought by some that interpreting slip rates along faults can answer some of the questions concerning sizes and potentialities for earthquakes and allow us to constrain the probalities of recurrence of characteristic earthquakes or other controlled events. Slip rate is measured by methods that are either geologic or geodetic. The geologic method reveals movements over the long term, and it provides detail for recent individual earthquakes, but it is usually insensitive to complexities in earthquake occurrence through time. The average or regular slip rate shown in Fig. 41 from Wallace (1987) is

commonly what is obtained from field evidence. It misses precisely those critical buildups in earthquake activity that are essential for evaluation in engineering design. Typically, earthquakes occur in clusters that are separated by intervals of quiescence. Wallace notes that these clusters also shift or migrate across subprovinces, along belts, and inward, outward, and along individual mountainfront fault zones. These earthquake clusters are dispersed in time and space. The geologic method also has other shortcomings: (1) Geologic evidence may mix slip from nonseismic creep with co-seismic movement. Aseismic creep accounts for nearly all fault slip along 256 km of the central section of the San Andreas fault and occurs with a slip rate that is the same as along the seismically active portions of the fault (Thatcher, 1990). (2) Geology is ideal for measuring horizontal displacements along strike-slip faults, but less so for corresponding vertical displacements because the latter are not cumulative.

ELLIS L. KRINITZSKY

32 30 ( - -

i

20,000 i

oc:e,l'/"~r,,i,.-, ] r ~n,~i.i,~ I QUIESCENCE

IREaULARI

i

CLUSTERS OF EARTHQUAKES \

20

"'<,..,

40,000

i

60,000 - r ~.T

[ / ~ ~ ,- !

/ ~ ~ 11"~ ~."

~'~r~j ... ~ "~k~ .,~" ~AVERAGE

'

,--

20

Y

_~t'-

10

0

20,000

40,000

60,000

VEARS

Fig. 41. The geologic determination o f slip rate on faults commonly provides average values instead of the varied slip rates that are more typical. Earthquakes tend to cluster in time and space (from Wallace, 1987).

(3) Slip occurring on normal or thrust faults is often dispersed into complicated patterns on multiple fault planes. (4) Slip values become uncertain where there is no surface breakage during earthquakes. The Coalinga, California, earthquake of May 2, 1983 was interpreted by Stein and King (1984) as a rupture at depth that was taken up in a monoclinal fold. They noted that thrust earthquakes typically display less slip at the surface than at depth. (5) The geologic method has difficulty in dealing with the full areal extent of deformation zones. Movements over such a zone centered on the San Andreas fault has a breadth that varies from 50 to 200 km (Thatcher, 1990). The geodetic method is highly sensitive to current crustal movements but does not show how they relate to the longer term. Despite the obstacles in both methods, measurements or estimations of fault slip are calculated into seismic moment, which is to say they are a basis for calculating earthquake magnitude. Youngs and Coppersmith (1985) carried the procedure a step further by adapting the seismic moment calculations to accommodate what they interpret as characteristic earthquakes. They allowed fault slip rates to constrain earthquake

recurrences whereby characteristic earthquakes became the basis for specifying probabilistic earthquake ground motions for engineering sites. Characteristic earthquakes on faults were determined by geological field exploration, including trenching with dating of ancient fault movements, and slip rate was used to develop the periodicity of these earthquakes through time. Figure 42 from Schwartz and Coppersmith (1984) shows schematically how those authors reconcile characteristic earthquakes obtained from geologic data with a b-line obtained from limited seismic data. They state that b-line values obtained from seismicity over a region may not be appropriate for individual faults or fault segments and that b-line projections tend to underestimate the frequency of occurrence of large, characteristic earthquakes. They imply that characteristic earthquakes must occur at the expense of moderate earthquakes. They feel that the characteristic earthquake is determined by the constitution and strength of fault zone materials and by the style of stress application. Thus, the characteristic earthquake acts continuously through seismic cycles and defines the behavior of the fault in a fundamenlOG

1

I

I

[

[

[

CONSTRAINTS I

l OF

CHARACTERISTIC

10

EARTHQUAKE ON B-LINE

E Z

E

1.0~-

0.1

\

\\

Z

0.01

2

3

4

5

FAULT

6

7

8

9

Magnitude, M

Fig. 42. Schematic reconciliation of a characteristic earthquake from geologic field evidence with a b-line from seismic data (adapted from Schwartz and Coppersmith, 1984).

33

EARTHQUAKE PROBABILITY IN ENGINEERING PART 2

tal manner. Figure 42, taken from their analysis, shows the b-line to be dysfunctional at magnitudes 5 to 6 and that the characteristic earthquake has no relation to the b-line. We have seen from Thatcher (1989) that a fundamental characteristic behavior pattern for faults is not substantiated by worldwide experience with large historic earthquakes. Working with records for southern California as a whole, Anderson (1979) used slip values to estimate the rate at which seismic moment is released on major faults. He found that the estimates of seismicity based on slip rates from geology were consistent with historical records for seismicity in southern California as a whole. He assumed that this agreement would also apply to smaller areas but the assumption could not be tested because of the short historical record for earthquakes. This assumption, Of reasoning from large areas to small, is another form of the principle of scale invarience which is an essential condition for making use of the b-line. From a geological pointof-view, this assumption has been under a cloud almost constantly as a result of detailed geological studies of earthquake generating faults on a regional basis. Wallace (1981, 1984 and 1987), working with geological field evidence over most of western United States but chiefly in the Great Basin province, determined that both nonuniformity in tectonism through time and great differences in slip rate characterized seismogenic faulting. Faults, tens of kms long and with a meter or more of earthquake displacement, were not uniformly distributed in either time or space. Fault activations were concentrated in belts and restricted areas and there were migrations through time for these concentrated areas of events. However, there was a contrast between continuity of activity on the large dominant faults and the smaller faults with more widespread occurrences. The large faults reactivated with much greater continuity than the lesser faults, however, even for the larger faults, quiescence could be in thousands and tens of thousands of years. For the most dominant fault of all, the San Andreas, reactivation for major earthquakes at any one place is in centuries. Bucknam and Algermissen (1982) documented

the above type of contrast by comparing the geologically determined return rate of earthquakes on the Wasatch fault with those of the many lesser faults in the Great basin, and both of those with a b-line obtained from seismicity for the region. Their relation is shown in Fig. 43 using averages for both Wasatch fault segments and Great Basin faults. Note that the b-line underestimates large earthquakes on the Wasatch fault, but overestimates earthquakes that are spread among the scattered faults in the Great Basin. The range between average values for Wasatch and other faults is about 90 times. The values are for large areas. The evidence, developed for clustering of earthquakes and migrations of earthquake activity, suggests that at any specific site the values can be expected to be enormously more dispersed. Clearly, using fault-related slip rates and estimated earthquake magnitudes is not a viable way for either validating or extending the b-lines developed from seismicity. Comment

Controlled slip resulting from coupling between faults, asperities on faults, and segmentation of activity on faults, is restrictive of earthquakes that

1,000

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FAULT 200-400 y r s (GEOLOGY)

WAEATCH

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t

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Fig. 43. Recurrence relations for the Wasatch fault and for faults of the Great Basinprovince and comparison of the b-line with geologicalstudies(fromBucknamand Algermissen,1982).

34

can be generated and contributes to earthquake clustering and the presence of characteristic earthquakes. Concerning the occurrence patterns of these earthquakes: (1) Characteristic earthquakes are real, but only on a short-term basis. (2) The effects of controls and the occurrences of corresponding characteristic earthquakes can be expected to change unpredictably. (3) Unpredictability likewise applies to earthquake behavior in fault segments. (4) As a consequence, paleoearthquakes gleaned from the geologic past, must be used with caution for identifying earthquake hazards for today. The effect of controlled slip on b-lines is that it is a powerful contributor to deviations from linearity. Attempts to correct b-lines for characteristic earthquakes admit that there is a dysfunction of the b-lines.

Thermodynamic slip Introduction When a fault moves, the energy expended to overcome friction is converted to heat and, under some circumstances, the wall rock may melt. The molten material becomes glass when the heat is quenched quickly as it would be at a shallow depth. Allen (1979) estimated this depth to be less than about 5 km. Eventually, the glass devitrifies, sometimes rapidly. At greater depths, slower cooling of a melt may allow it to recrystallize directly from the molten condition either partially or completely. The rocks produced are called pseudotachylites (Pseudotachylyte is another spelling). Alternatively, there may be no melting of the rock but the water in a fault zone can become heated. Also, a fault rupture can allow a temporary entrance into the fault zone of superheated fluids from the ductile layer beneath the brittle crust. These processes cause abruptly increased pore fluid pressures that weaken and lubricate an activated fault. Thus, they may cause a sudden and powerful acceleration of fault slip. The resulting behavior produces earthquakes that are unpredictable. These processes are shown schematically in Fig. 44.

ELLIS L, KRINI'IZSKY

THERMODYNAMIC- SLIP MODEL ~, O ~

INCREASED PORE FLUID PRESSURE WITH LUBRICATION AND ACCELERATEDFAULTSLIP METEORIC WATER

HYDROTHERMAL FLUIDS

(HEATED)

(RELEASEDFROM DUCTILE ZONE)

PSEUDOTACHYLITES (MELTING OF ROCK)

P,, ,v MYLONITES (DUCTILE ZONE: PLASTIC DEFORMATION)

Fig. 44. Heat related effects during large earthquakes: the thermodynamic-slip model.

Strain heating of rock Pseudotachylite that formed when molten rock was produced on a fault during one or several major earthquakes is shown in Fig. 45. The melt was injected into dilatational fractures adjacent to the fault plane. This injection-vein complex disrupts Lewisian gneiss of Archaean age in the Outer Hebrides thrust zone on the Isle of Lewis, Scotland. The pseudotachylite was formed deep in the subsurface and was exhumed by erosion. A detailed view of two generations of pseudotachylite from the Lewisian gneiss are seen in the backscattered electron (BSE) micrograph shown in Fig. 46. An interpreted devitrified glass occurs on the left of the image and reconstructed microlitic feldspar on the right. The contact between layers is sharp.

Fig. 45. Pseudotachylite in a fault and injection-vein complex disrupting I_~wisian gneiss, Outer Hebrides, Scotland (photo courtesy of Richard H. Sibson).

EARTHQUAKE PROBABILITY IN ENGINEERING PART 2

Fig. 46. Backscattered electron (BSE) micrograph of two generations of pseudotachylite: devitrified glass on left and recrystallized microlitic feldspar on right. Bar in lower right comer ,~ 100 p,m. From Lewisian gneiss, Outer Hebrides, Scotland (courtesy of Robert H. Maddock).

Referring again to Fig. 45, pseudotachylite characteristically forms an abrupt contact with its host rock. Pseudotachylites have been observed since the beginning of the last century (see Francis, 1972), but early observers thought the material was produced by extreme crushing during fault movement and that even the injection into dilatational fractures was in the form of a dry powder. In fact, a fine comminution by shock-like fault movement can produce an aphanitic texture that resembles pseudotachylite. Wenk (1978) described pseudotachylite veins that he analyzed by transmission electron microscopy and interpreted to be intense brittle deformation. Similar observations were made by Knipe and White (1979) who observed sandstones in Wales and identified microfracturing

35

as a first phase, followed by intracrystalline plasticity followed by heterogeneous deformation and recrystaUization along cleavage zones. Kerrich et al. (1980) describe microstructural and chemical transformations that accompany a superplastic flow along fault planes that produce a behavior suitable for producing mylonites. Weiss and Wenk (1983) experimentally produced finely comminuted material of this sort during failure of a gabbro under rapidly applied stresses. Engelder (1979) pointed out that there is evidence for a variation of friction along fault zones based on asperities and Scholz (1980) implies that such variances in shear effects may range from crushing to melting along the same fault at the same time. Masch et al. (1985), studying landslide slip planes in Austria and Nepal, found unmistakable evidence of partial to almost complete melting of granitic to granodioritic host rocks. The melting appeared to be the result of frictional heating on the gliding planes of the landslides. They termed the heat-generated material hyalomylonite, which we may take as a synonym for pseudotachylite. The process of frictional fusion in fault zones became firmly established by the work of Philpotts (1964), Ermanovics et al. (1972), McKenzie and Brune (1972), Sinha-Roy and Kumar (1985), Sibson (1975, 1982), Wallace (1976), Allen (1979), Maddock (1983, 1986) and others. Their work showed that pseudotachylites are formed throughout the brittle zone and that water content in the crystal lattices of hydrous minerals promotes melting. Spray (1987, 1988) used radial friction in the laboratory to produce pseudotachylites. He observed that melting and crushing, or gouge formation, occurred simultaneously in different regions of the interface. He also noted that, as soon as the melt formed, the frictional resistance dropped and less heat would have been generated. Continued movement would have involved mechanical disruption of the pseudotachylite followed by more heat generation, melting, and gouge formation through a repeat of the process. Philpotts (1964), Ermanovics et at (1971), and Maddock (1986) presented chemical analyses of pseudotachylite and its host rock which show the pairs of materials to be remarkably similar. The

36

data show that frictional fusion is more likely to be total and not selective for minerals that melt at lower temperatures. Field associations show that low intergranular pore fluid pressures are essential in order to have melting of the rock. Fluids in a fault zone decrease shear resistance by decreasing the effective normal stress on a sliding surface. McKenzie and Brune (1972) noted that large earthquakes may release all of their accumulated strain by lubricating the fault plane with molten rock. We may infer that where large numbers of surfaces are present on which slippage can occur, the less would be the heat generated on each of them. Thus a broad fault zone with breccia or an abundance of slip surfaces, and especially if it contained water, would not produce rock melting. Strain energy released by an earthquake has several forms, principally radiated seismic energy, fracture energy, and frictional heat released on the moving surfaces. Of these, fracture energy represents the breaking of rock and its shattering into breccia and gouge. Laboratory tests by Yoshioka (1986) showed that fracture energy is very small, occupying only 0.01-0.1% of the total energy released by the testing machine. Heat due to friction and the elastic wave energy are the main forms of energy release. Friction on a fault affects the radiated seismic energy in important, complex, and unpredictable ways. Das and Kostrov (1988) point out that friction is a direct cause of nonuniform fracture propagation along a fault, therefore producing nonuniform slippage and introducing complexity in the time history of seismic excitation. Friction also reduces the slippage area which could cause a shortening of the earthquake duration. Therefore, the rate of slip propagation is reduced, which increases the duration, up to the time when melting, or other rapidly increased fluid pressure in the fault completes the strain release. These interactions impart an enormous complexity in the excitations and, because of rapidly changing frictional resistance, brings into question the reliability of using seismic moment to evaluate strain or total earthquake energy. Faults should be expected to have a considerable range in their ability to generate frictional heat. Studies of heat flow associated with the San

I;,I.LIS L. K R I N I I Z S K Y

Andreas fault have not produced evidence of measurable frictional heating (see Lachenbruch and Sass, 1988, 1992; Zoback and Lachenbruch, 1992; Sass et al., 1992; Zoback and Healy, 1992). The implications are that the San Andreas fault zone is weak and, though imbedded in rock that is strong, the fault moves in response to small effective shear stresses. The heat determinations are said to be consistent with a frictionless fault (see Sass et al,, 1992). Nonetheless, the above observations do not exclude the mobilization of extreme heat along the planes of slippage during the short times in which earthquakes take place. Lachenbruch (1986) provides theoretical calculations which indicate that peak temperatures developed on the day of an earthquake, and within a meter of the fault plane, will be reduced to a third in one week and to an eighth in three months, at which time the heat gain at 5 m from the fault will be negligible. On the San Andreas, where the temperature studies cited above were performed utilizing data from a test well drilled to a depth of 31/2 km, there has been no major earthquake since 1812. McKenzie and Brune (1972) observed that the lack of a heat anomaly can be used as an argument for fault lubrication resulting from fault melting. Thus heat effects that result in accelerated stable sliding during major earthquakes remain as viable options, even when rock melting does not occur because abundant water is present in the fault zone. Rock melting along moving fault planes may be a great deal more common than is generally believed. Francis (1972) and Scholz (1990) suggest that pseudotachylites are widespread but are not recognized because they can be difficult to identify. Marshall (1961) showed that devitrification and the reconstruction of minerals which requires a million years in the dry state can be rapid, even within experimental-range, when water is present and temperatures are no more than 300°C. Between these extremes, hydrothermal reconstruction takes place extensively. Comment

Rock melting, resulting in pseudotachylites, develops along fault surfaces during large earth-

37

EARTHQUAKE PROBABILITY IN ENGINEERING PART 2

quakes chiefly in crystalline rocks that are relatively dry and are not filled extensively with breccia or other gouge material. Rock melting has the following effects on earthquakes: (1) It causes powerful acceleration of sliding along an activated fault, resulting in abrupt strain release. (2) Calculation of seismic moment becomes a problem because of extreme and difficult-tointerpret changes in frictional resistance. (3) The Gutenberg-Richter b-line becomes deviatory because there is an abrupt alteration in the mechanism of faulting and a change in the level of seismic excitation. Meteoric waters Groundwater anomalies during earthquakes are extensive and pronounced. They involve two fluid systems: one is dominated by contributions from meteoric waters, including those in aquifers; the other by hydrothermal fluids from metamorphic processes in the ductile zone at depth. The two systems can respond together to large earthquakes, however, we will consider them separately in order to observe their individual effects. Stream flows are changed by powerful earthquakes: The Hebgen Lake, Montana, earthquake of August 17, 1959, caused the Madison River to increase its flow by 8 0 0 , or 0.54 cfs per square mile of drainage area (see Stermitz, 1964). The Borah Peak, Idaho, earthquake of October 28, 1983, caused stream discharges in the area to increase from 150 cfs to 400 cfs on the Big Lost River at Howell's Ranch and 50 cfs to 120 cfs upstream at the confluence of North and East forks. The increases in flow are roughly proportional to the areas of drainage (see Woods et al., 1985). The Loma Prieta, California, earthquake of October 17, 1989, caused increases in stream flow from 10 L/s to about 80 L/s before discharges became still higher from rains. In the mountainous source areas, wells went dry that had 21 m and 40 m of water above bottom. Subsequent measurements of water in wells throughout the area showed declines in water level on the order of 1.5m/month (see Rojstaczer and Wolf, 1992). During the Honeydew, California, earthquake of August 17, 1991, the Mattole River increased its flow from

0.8 to 2.3 m 3 per s in the six days following the earthquake. The flow waned gradually to preearthquake levels in about 60 days (see McPherson and Dengler, 1992). The effect of the earthquake shaking is to increase permeability by opening up fractures and enhancing ground water flow paths. The groundwater supply becomes depleted, the flow paths heal themselves, and the groundwater regime returns to normal. We may infer that meteoric waters in fault zones also are involved in the process of fault slippage. In vertical, strike-slip faults such as the San Andreas, the meteoric water may be sealed in cells along the fault by this healing process. During an earthquake, a small change in the volume occupied by fluid could have strong effects on pore pressure and resulting frictional resistance. Lachenbruch (1980) states that when confined water is heated, as it could be by friction during fault movement, the pressure increases rapidly, on the order of 10 bars/°C. This in turn could cause a sharp reduction of effective normal stress and relieve friction on the fault surface. However, there are other factors depending on duration, particle velocity, initial friction, the volume of fluid, and its continuity. The possibilities cover an enormous range. None of them are predictable with any reliability and all of them would affect the calculation of seismic moment in unknown ways. Hydrothermal fluids For the purpose of this discussion, hydrothermal fluids are those heated and pressurized fluids, enriched with mineralizations, that are expelled from the ductile zone into the brittle crust. Their passage is facilitated along faults that serve as conduits. Figure 47, adapted from Axen (1992), shows schematically how these fluids move. The flows are episodic and are generally related to seismic events that are initiated in the lower part of the brittle crust. Between earthquakes, the faults become hydraulically sealed. Evaporites and clayey sedimentary deposits in contact across a fault develop bondings and what Axen calls sedimentary seals. Also, precipation from supersaturated fluids seals the faults and fills dilatational spaces with secondary minerals, commonly silica. Blanpied

38

ELLIS

L. K R I N I T Z S K Y

imentary seal Mineralization ::iii"infaults

=======================.... =======

crobrecc a

seal

•

t

::!i~,.~

. -,-

tq,,,, 111N

.

HIGH PtrtESsuFIEFLUID

~,,, OZ

Fig. 47. Schematicdiagram of episodicmovementof hydrothermal fluids into fault zones (adapted from Axen, 1992). et al. (1992) showed from flow-through experiments with supersaturated fluids at high temperatures in crystalline rocks that these seals may form rapidly in the laboratory, in hours to days. These restraints cause hydrothermal fluids to become highly pressurized. Their periodic release, facilitated and accompanied by earthquakes, was described by Sibson et al. (1975) as "seismic pumping" and by Sibson (1990a) and Sibson et al. (1988) as "fault-valve" behavior. Figure 48 shows sheet-like veins of quartz deposited in a steep reverse fault of the Melones fault zone in the western foothills of the Sierra Madre, California. Each layer of quartz represents a slip of the fault in a major earthquake accompanied by the surge of a sheet of water through the activated fault. These events were repeated many times in order to build up incrementally the layers seen in the veins. Figure 49 shows sheets of calcite deposited incrementally in a minor fault of the Gower Peninsula in South Wales. Note that continued movement along the fault caused brecciation of older vein deposits. That fluid flow can be released by fault movement was seen by Sibson (1982) to be evident in transitory surface flows during and following earthquakes and in hydrothermal vein systems associated with ancient faults. Wallace and Morris (1986) observed that faults throughout the depth of the brittle zone are not large, single planes but are multiple shears that are developed by many incremental displacements that populate complex zones. The shears are branching, anastomosing even greatly curved, and are associated with fault gouge, foliated rock, and zones of

Fig. 48. Incrementally deposited veins of quartz in a steep reverse fault of the Melones fault zone, western foothills of the Sierra Nevada, California (photo courtesy of Richard H. Sibson).

fractured rock. The widths of fault zones are proportionate to the overall lengths of these composite displacements: zones with kilometers of displacement tend to be 100 m or more wide; while those a few hundred meters in length may be only 1 m or less wide. Byerlee (1993) notes that the slip on a short single shear can be transferred to another by a compressional effect, a dilatant jog, or even an accentuated bend. Seals that form in these zones cause the development of individual fluid compartments. As a result, pore pressures can be greatly varied. An earthquake rupture will not redistribute these pressures evenly in the few seconds of the dynamic event and there will be a transient temperature rise that will add to the pore pressure instability (Byerlee, 1993). McCaig (1988) noted that though fluid flow is

EARTHQUAKEPROBABILITYIN ENGINEERINGPART 2

Fig. 49. Incrementally deposited veins of calcite with brecciated older veins along a minor fault, Gower Peninsula, South Wales (photo courtesy of Richard H. Sibson).

episodic and contingent on the occurrence of earthquakes, fluid-flow patterns increase in volume with development of the fault zone to the point where there is significant meeting and intermingling of meteoric and hydrothermal fluids. These conditions are recognized in the isotope contents of the resulting precipitates (see Kerrich, 1986). Fault-valve release requires that the vertical fluid pressure gradient for the hydrothermal source exceeds the hydrostatic gradient and the fault ruptures in response to the prevailing stress field. Additionally, confined hydrothermal fluids may develop pore pressures that approach the lithostatic pressures. Evidences of hydrofracturing can be found. In these cases, the hydrothermal fluids may be a critical element that combines with the regional stress to initiate fault ruptures (see Sibson 1990a).

39

Supralithostatic fluid pressures were suggested by Sibson (1990b) to be related especially to unfavorably oriented faults, particularly steep reverse faults and strike-slip faults that are severely misoriented in relation to regional stresses. In these cases, high fluid pressure may be essential for fault activation, and New Madrid could be an example. The New Madrid fault zone is a combination of strike-slip and reverse faulting and displays evidence of episodic hydrothermal action at high fluid pressures. Figure 50 shows shear planes in which the planes were filled with incremental layers of calcite. The core is Cambrian black shale of the Bonneterre formation, recovered from the Dow Chemical No. 1 Garrigan well in the Reelfoot rift of northeast Arkansas at a depth of 11,420 ft. Diehl et al. (1992) performed mineralogical studies on cores that showed the presence of fluid-flow conduits through both stylolites and shear planes. The stylolites demonstrate effects of rock solution during pressurized fluid flow. They also contain precipitates of monazite and pyrite that were derived from hydrothermal fluids. The stylolites also have slickensided clay which indicates slip in the planes of the stylolites. For the stylolites to have opened and permitted fluid flow, pore pressure must have exceeded the lithostatic pressure. Figure 50 shows precipitation into dilatational crevices along with the episodic multilayered deposition into shear planes. The fillings are indica-

Fig. 50. Fault fractures with incremental layers of calcite in black shale of the Bonneterre formation, Dow Chemical No. 1 Garrigan well, Reelfoot rift, northeast Arkansas. Depth 11,420 ft (photo courtesy Sharon F. Diehl).

40

tive of excess fluid pressures. McKeown and Diehl (In press) see overpressurization by fluids also in the clay fabrics of the shale. Layers of randomly oriented clay platelets are interlayered with well oriented platelets that are characteristic respectively of overpressurized and normal layers. Petrographic examination of the mineralization and microstructures in the vein fillings indicates several generations of epigenetic mineralizations were involved with fluid flows. McKeown and Diehl describe additional evidences of present-day and ancient excess fluid pressure in the New Madrid seismic zone citing Brahana and Mesko (1988). They found that the zone of intense seismicity coincides with high artesian groundwater pressures and with anomalously warm water above the geothermal gradient. A1-Shukri and Mitchell (1988) showed that the crustal rocks in the New Madrid seismic zone have relatively low seismic velocities with a maximum reduction of compressional wave velocity of 7% in the upper 5 km and at least 4% between 5 and 14 km. These reductions indicate fluid-filled pore spaces in which pore pressure is a substantial part of external pressure. These fluids may play a part in the susceptibility of the zone to earthquakes in accord with the ideas of Sibson, Byerlee, and others. Sibson (1990b) believes that besides the faults of the New Madrid seismic zone, other examples of unfavorably oriented faults include Miramichi in northern New Brunswick with a rake of 70 °, Coalinga in California on a thrust dipping ~ 30 ° SW and steepening to 55 °, and the San Andreas, which though it is strike-slip is severely at an angle to the regional stress field. Such faults, unfavorably oriented to the regional stresses, are susceptible to effects of lithostatic fluid pressures for generating earthquakes. Sleep and Blanpied (1992) extended the above observations by showing that developments of lithostatic fluid pressures can result also from compaction of fault gouge during ductile creep. Increases in pore pressure may then facilitate sliding at low effective stress.

Problems of large earthquakes in b-line projections It is commonplace for large earthquakes to deviate from b-lines, and examples of such devia-

I-,LLIS I.. K R 1 N I q Z S K Y

tions were given in Fig. 18 for the Tottori earthquakes of 1943 and 1983 in Japan, Fig. 19 for the Fukui earthquakes of 1948-1949 in Japan, and Figs. 23 and 26 for the New Madrid earthquakes of 18 ! 1-1812 in central United States. All of these were accompanied by greatly heightened periods of seismicity. The periods were temporary and their events were strikingly unconformable with established b-lines. In these examples, b-line projections clearly did not serve to predict large earthquakes. Other regions of the world are evaluated as follows. The Mexican subduction zone

Singh et al. (1981) observed that shallow earthquakes of the Mexican subduction zone have distinctly different patterns of occurrence depending on the areas. The Tehuantepec and Michoacan gap areas have not experienced large earthquakes and either such earthquakes do not occur or their repeat times are anomalously large for an active belt of seismicity. In other parts of the subduction zone, strain is released mostly in large earthquakes, M~> 7.4, without experiencing smaller ones in the numbers indicated by b-lines. This preferential occurrence of a dominant size of earthquake is a reality and it denotes a characteristic earthquake. Singh et al. (1981) concluded that the b-lines were not meaningful. Subsequently, a more extensive study of earthquake recurrence along the subduction zone was made by Singh et al. (1983). The regions studied are shown in Fig. 51. They are Jalisco, Michoacan, Guerrero and Oaxaca. Interpretations of seismicity in relation to b-lines are given on Fig. 52. Instrumental data from 1963-1981 were normalized to 75.5 years in order to match the data from historic earthquakes of that period. The meaning of such normalization can be argued. The b-values range from 0.62 to 1.08. Poweful divergences from the b-lines occur consistently in all the regions for magnitudes of Ms ~>5.5-6.0. This is further evidence that b-lines are dysfunctional for estimating earthquakes in the magnitude range damaging to engineering. Kagan (1993) noted that Singh et al. (1983) compared observed earthquake numbers with

EARTHQUAKEPROBABILITYIN ENGINEERING PART 2

41

20 ° N

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Fig. 51. Location map of study areas in the Mexican subduction zone (from Singh et al., 1983).

expected numbers in cases where relatively high deviatory values could have been the result of random fluctuations because the numbers of events involved were small. On the other hand, the deviations follow a consistent pattern, which have been observed widely in seismically active areas; invariably the b-lines underestimate the larger earthquakes. The Aleutian arc subduction zone

Davison and Scholz 0985) made observations in the aleutian arc that are remarkably similar to those of Singh et al. (1983). The zones by Davison and Scholz are shown on Fig. 53. There are four zones in which major earthquakes extended across most of the respective areas. These occurred in 1938, 1946, 1964 and 1965. Additionally there are four zones that are interpreted to be seismic gaps. These are Kommandorski, Unalaska, Shumagin and Yakataga. The boundaries represent seismic rupture segments and were assumed to be sites for recurrent great earthquakes. Sykes (1971) noted that large earthquakes in the Aleutian chain exhibit regularities in space, time and size. The ends of aftershock zones for great earthquakes tend to coincide with major transverse features that intersect with the Aleutian arc. B-lines shown in Figs. 54 and 55 represent all of these zones. The numbers of earthquakes in the zones are cumulative. Crosses show an 18-year data set and circles

85 years. The interpreted maximum value was calculated for an earthquake rupture that crosses each zone. All of the data sets were normalized to the recurrence time of the largest earthquake in each zone. The time needed for recurrence was calculated from an assumed moment accumulation rate. In Figs. 54 and 55, there are disparities between the instrumented records and the historic felt earthquakes. These are continuous only in the 1964 zone. The instrumental b-line breaks at 1023--1025 dyne-cm or mb= 5.0-6.0, which is typical in the shallow, brittle layer and the Mexican subduction zone. Davison and Scholz note from these figures that the b-line underestimates the "characteristic" earthquake by one order of magnitude for the 85-year data set and 2.5 orders of magnitude for the 18-year data set. Seismic moment did not provide continuity on the graphs, although conceptually the moment scale is designed to impart a linear relation to earthquakes through all magnitudes. Davison and Scholz combined all the data for the Aleutian arc into the composite diagram shown in Fig. 56 and in which the 85-year data predicts the 1964 Alaska earthquake. They interpret Fig. 56 to mean: (1) The b-value is useful when the area includes all sizes of major fault zones. (2) The b-value provides no insight on the moment value of earthquakes, and instead indicates the

42

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Fig. 52. Deviationsfrom b-lines in the Mexican s u b d u c t i o n combined distribution of the lengths of the earthquake generating faults in the region. Each fault may have its characteristic size of maximum earthquake. (3) Any b-value data that models only a single large fault is invalid.

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tabulations is the marked deviation from linearity of both. Bath thought that the data were probably complete for M > 5.5-6.0, or precisely in the area above that of b-line divergence, and valid for a period of 58 years. He interpreted the "bulges" in the curves to be due to physical conditions relating to the earthquake sources by which "characteristic" earthquakes occurred. Additionally, he felt that there is a gap in magnitude between a main shock and its largest aftershock. This causes the interruption seen in what should have been a monotonically linear projection in Fig. 58. Bath's interpretation is that when faults produce

EARTHQUAKEPROBABILITYIN ENGINEERINGPART 2

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from the b-lines observed in the Mexican subduction zone, the Aleutian subduction zone, the New Madrid source area, and elsewhere, would be seen to be characteristic earthquakes. The implications from Bath's work are: (1) The b-line is not valid for large earthquakes. (2) Characteristic earthquakes for a fault can be identified and used to correct the b-line. We saw that Thatcher (1989) examined a dozen zones in the circum-Pacific that had been ruptured by major earthquakes and in which other large earthquakes had occurred (Fig. 40). There was a nearly total absence of repeated earthquakes that might be called characteristic. Thatcher concluded that variability is the dominant feature of great earthquakes when they are reactivated and rupture the same fault segment. Furthermore, Kagan (1993) showed that it is almost impossible statistically to verify or refute the characteristic earthquake hypothesis, meaning that we cannot determine that it is a process with predictable effects. It is however observed as a

60'

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large earthquakes they produce them in sizes that reflect the inherent properties of the faults. The faults have characteristic earthquakes like that which peaks at M = 7.0 in Fig. 57. Those deviations

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44

ELLIS L. KRINITZSK'~ UNALASKA SEISMIC GAP KOMMANCORSKI SEISMIC GAP

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0 I

5

local but temporary process like that of the Parkfield example in Fig. 38. It is a specific dysfunction in the b-line during moderate to large earthquakes. Significantly, all of the authors who

1

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M Fig. 57. Non-cumulative frequency of earthquakes in Turkey with a "characteristic" earthquake of M = 7 . 0 (from B~th, 1981),

45

E A R T H Q U A K E P R O B A B I L I T Y IN E N G I N E E R I N G P A R T 2

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1970

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we have cited for their advocacy of characteristic earthquakes show the b-line dysfunction at M~> 5.0-6.0.

Summary and conclusions Gutenberg-Richter b-lines may be taken as valid when computed for large seismically active areas: southern California or the 3000 km length of the Aleutian arc. Davison and Scholz (1985) believed that b-lines developed in this way are successful because they represent the incorporation of great numbers of varied lengths of causative faults. We can add that these are faults that rupture by many different mechanisms and all of the mechanisms must be broadly encompassed. Also, when sizeable faults are ruptured, associated faults are affected within the regional stress field. Seismic hazard maps for large areas, with probabilistic values derived from b-lines, serve vital needs. They are essential for public awareness, emergency response planning, and as a basis for broadly applicable building codes designed to enhance seismic safety. The codes incorporate the experiences from earthquakes of geologists and engineers, especially structural engineers, and do not depend solely on the accuracy of the prob-

ability calculation. Recent earthquakes, such as Loma Prieta, have shown that current codes were very good, however, seismic hazard maps alone are not sufficient for designing critical structures, because their data is greatly uneven and may include unjustified interpretations. What constitutes a critical structure is itself a subjective judgement. The question to ask is what are the consequences of failure? If the consequences are intolerable, then the structure is critical. I would include in this category major dams, nuclear power plants, liquefied petroleum gas installations, repositories for high level nuclear waste, military command centers, sensitive industrial and defense installations, fire stations, schools and hospitals. With a few exceptions, engineering has short lifetimes, half a century to a century. Because the distances over which earthquakes can cause damage to engineering are small, on the order of 50 km for good foundations, earthquake hazard assessment must focus narrowly. For the engineering of critical structures, b-values are highly defective artifacts. They change dynamically before and following an earthquake and for long periods afterward. They change in response to fault type and to asperities on the fault. They are hostage to imprecisions in teleseismic data and to nonlinearities in magnitude scales including that of seismic moment. Also b-values by different investigators are rarely the same. Published b-values for New Madrid have a spread that is an order of magnitude, yet none of the values in this spread approximates the geologic evidence which deviates from the mean of the probability values by > 20 times. B-lines are affected by the varied mechanisms by which faults rupture. The mechanisms can be categorized as (1) stick slip, (2) controlled slip and (3) thermodynamic slip. Only stick slip appears to relate well to b-lines. Stick slip produces the generally valid b-lines that are observed up to M = 5.0-6.0. At that level, the geometry of earthquake rupture changes from an unrestricted propagation in all directions within a plane to a directed propagation in one or two directions. This change causes a significant break in the b-lines. The break is at the threshold for earthquake damage to good engineering and at

46

the level above which other disruptions in b-lines become pronounced. Controlled slip is a cause of deviations from b-lines. Control processes lead to clustering of earthquakes in time and in space and they are disruptive of linearity. Controlled slip also brings into question the reliability of paleoseismic information for interpreting present-day fault behavior. Thermodynamic slip deviates powerfully from b-lines. Thermodynamic slip refers to strain heat generated along faults during movements by steady slip. This occurs mostly during large earthquakes, which are the earthquakes of greatest concern to engineering. Strain heat may melt the host rock along a fault, or it may heat fluids in the fault and raise pore fluid pressures. Either will cause abrupt acceleration of the fault slippage. Also, hydrothermal fluids may enter the fault from the ductile zone below the brittle crust. Fluids can become sealed in compartments along the fault and in the periods between earthquakes may build up lithostatic pressures. This can contribute to initiating fault rupture. The above mechanisms produce inhomogeneities in the earthquake process that make b-lines defective for site-specific predictions of moderate to large earthquakes, or M_->5.0, These deficiencies make b-lines unsatisfactory as a basis for seismic hazard evaluations for the engineering of critical structures. Following are generalizations concerning earthquakes and their recurrence in relation to engineering: (1) Earthquakes do not occur uniformly at random through time. (2) Earthquakes do not occur uniformly at random through space. (3) The occurrence of earthquakes on a fault is affected by related movements on adjacent faults. (4) The expected number of earthquakes of magnitude M or greater occurring within an area can be described approximately by the magnituderecurrence relation, or b-line, when the area is both large and seismically active: southern California, southwest Japan, the Aleutian arc. (5) A b-line valid for a large, seismically active area is not valid for smaller parts of that area.

ELLIS L, K R I N I T Z S K ' ~

(6) B-lines do not apply to individual faults. (7) In the seismically inactive intraplate (central and eastern United States), b-lines apply only to earthquakes of M~<5.0 when calculated for large areas. (8) B-lines are dysfunctional at M~>5.0 and are unsuitable for use in site-specific seismic hazard evaluations for critical structures, because probabilistic seismic hazard analysis assumes regularities in nature that do not exist.

Acknowledgements Many people were helpful to me with constructive editing of my manuscripts. I especially want to thank George A. Kiersch, Jeffery R. Keaton, David M. Perkins, Gregory L. Hempen, Leland T. Long, John G. Anderson, Brian J. Mitchell, William F. Marcuson III, Paul F. Hadala, Ronald E. Wahl, Mary Ellen Hynes and Arley G. Franklin. In addition, Nicholas N. Ambraseys, Richard H. Sibson, Robert H. Maddock, Sharon F. Diehl and James D. Byerlee generously gave me materials from their work to use in my lecture and in this paper. I am grateful to all of them. The views that I express may or may not represent those of the Corps of Engineers.

Appendix A. Earthquakescales Magnitude Earthquake magnitude is a measure of the size of an earthquake related to the total strain energy released. Following are brief descriptions of the magnitude scales that are widely used. Table A I provides a general comparison of these scales.

Body wave magnitude (mb) The mb magnitude is measured as the common logarithm displacement amplitude in microns of the P-wave with period near one second. The value was developed to measure the magnitude of deep focus earthquakes, which do not ordinarily set up detectable surface waves with long periods. Magnitudes can be assigned from any suitable instrument whose constants are known. The body

47

EARTHQUAKE PROBABILITY IN ENGINEERING PART 2

waves can be measured from either the first few cycles of the compression w a v e s (mb) or the onesecond period shear waves (mblg).

Seismic moment scale (Mw) The scale defines magnitude based on the seismic moment: Mw=2/3 log M o - 10.7

Local magnitude (ME) This is the original magnitude definition by Richter. The magnitude of an earthquake measured as the common logarithm of the displacement amplitude, in microns, defined by a standard Wood-Anderson seismograph located on firm ground 100 km from the epicenter and having a magnification of 2800, a natural period of 0.8 s and a damping coefficient of 80%. The definition itself applies only to earthquakes having focal depths smaller than about 30 km. Empirical charts and tables are available to correct to an epicentral distance of 100 km for other types of seismographs and for various conditions of the ground. The correction charts are suitable up to epicentral distances of about 600 km. The correction charts are site dependent and have to be developed for each recording site. Surface wave magnitude (Ms) This magnitude is measured as the common logarithm of the resultant of the maximum mutually perpendicular horizontal displacement amplitudes, in microns, of the 20-s period surface waves. The scale was developed to measure the magnitude of shallow focus earthquakes at relatively long distances. Magnitudes can be assigned from any suitable instrument whose constants are known. Richter magnitude ( M) Richter magnitude is a general usage that is usually ME up to 5.9, Ms for 5.9 to about 8.0 and M Wup to 8.3 in the plate boundary. Seismic moment ( Mo) Seismic moment is an indirect measure of earthquake energy. Mo = GAD

(A1)

where: G=rigidity modulus, A = a r e a of fault movement and D=average static displacement. The values are in dyne centimeters.

(A2)

Intensity Earthquake intensity is a subjective numerical guide that describes the effects of an earthquake on people, on structures and on the earth's surface at a particular place. The scale in common use in the U.S. today is the Modified Mercalli (MM) Intensity Scale of 1931 with intensities indicated by Roman numerals from I to XII. In general, for a given earthquake, intensity will decrease with distance from the source. Following is an abridgement of the scale. I. Not felt except by a very few under especially favorable conditions. II. Felt only by a few persons at rest, especially on upper floors of buildings. Delicately suspended objects my swing. III. Felt quite noticeably indoors, especially on upper floors of buildings, but many people do not recognize it as an earthquake. Standing automobiles may rock slightly. Vibration like passing of truck. Duration can be estimated. 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 automobiles rocked noticeably. V. Felt by nearly everyone; many awakened. Some dishes and other fragile items broken; a few instances of cracked plaster; unstable objects overturned. Disturbance of trees, poles and other tall objects sometimes noticed. Pendulum clocks may stop. VI. Felt by all; many frightened and run outdoors. Some heavy furniture moved; a few instances of fallen plaster or damaged chimneys. Damage slight. 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 automobiles.

48

E L L I S L. K R I N I T Z S K Y

JAPANESE METEORO-

PEOPLES

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LOGICAL

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VIII

VIII

VIII

VIII

IX

IX

IX

XI

XI

Xl

Xll

Xll

X

VII

Xll

Fig. AI. Comparison of intensity scales. TABLE A 1 Equivalences between magnitude scales and intensity (magnitudes were modified from Nuttli and Shieh, 1987) M

mb

ML

Ms

Mw

Mo Epicentral (dyne-cm) intensity MM

3.0 3.6 4.6 5.6 6.6 7.3 8.2

4.1 4.5 5.2 5.8 6.6 7.3 8.2

1021 1022 1023

(1) Plate boundary

4.3 4.8 5.3 5.8 6.6 7.3 8.2

4.0 4.5 5.0 5.5 6.0 6.5 7.0

4.3 4.8 5.3 5.8 6.3 6.8 7.3

1024 1025 1026 1027

IV V VI VII VIII IX-X XI-XII

umns, m o n u m e n t s , walls. Heavy furniture overturned. Sand and m u d ejected in small amounts. Changes in well water. Persons driving a u t o m o biles disturbed. IX. D a m a g e considerable in specially designed structures; well-designed frame structures thrown out-of-plumb; d a m a g e great in substantial buildings, with partial collapse. Buildings shifted off foundations. G r o u n d cracked conspicuously. U n d e r g r o u n d pipes broken. X. Some well-built w o o d e n structures destroyed; most m a s o n r y and frame structures destroyed. G r o u n d badly cracked. Railroad rails bent. M a n y landslides on river banks and steep slopes. Shifted sand and mud. Water splashed over banks o f rivers and lakes. XI. Few structures remain standing. Unreinforced m a s o n r y structures are nearly totally destroyed. Bridges destroyed. Broad fissures in ground. U n d e r g r o u n d pipe lines completely out o f service. Earth slumps and land slips in soft ground. Railroad rails bent greatly. XII. D a m a g e total. Waves apparently seen on g r o u n d surfaces. Lines o f sight appear visually distorted. Objects t h r o w n u p w a r d into the air. Figure A1 shows a c o m p a r i s o n o f widely used intensity scales with the Modified Mercalli. The Rossi Forel scale which dates to 1883 is a forerunner o f the M M . O f the scales in use today, only the Japanese differs markedly. The Japanese scale can be related to the M M by the following equation: IMM= 0.5 + 1.5Ij~lA

(A3)

(2) Plate interior

4.3 4.8 5.1 5.4 6.4 7.4 8.4

4.0 4.5 5.0 5.5 6.0 6.5 7.0

-

2.9 3.4 4.4 5.4 6.4 7.4 8.4

3.8 4.1 4.8 5.4 6.1 6.8 7.4

1021

1022 1023

1024 102s 1026 1027

IV V VI VII VIII IX-X XI-XII

*M L generally not used in plate interior.

VIII. D a m a g e slight in specially designed structures; considerable in ordinary substantial buildings with partial collapse. Great d a m a g e in poorly build structures. Panel walls t h r o w n out o f frame structures. Fall o f chimneys, factory stacks, col-

Table A1 shows equivalences between the various magnitude scales and the M M intensity scale for epicentral values. References

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