ML20004B685

Scaling Laws for Large Earthquakes - Consequences for Physical Models.

ML20004B685
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. SCALING LAWS FOR LARGE EARTHQUAKES CONSEQUENCES FOR PHYSICAL MODELS Christopher H. Scholz Department of Geological Sciences and Lamont-Doherty Geological Observatory of Columbia University, Palisades, New York 10964 ABSTRACT It is observed that the mean slip in large ear thquakes correlates linearly with fault length L and is not related to fault width, W. If we interpret this in terms of an elastic model, it im' plies that static stress drop increases with aspect ratio (L/W). We also observe a tendency, particularly for strike-slip ear thquakes , for aspect ratio, and hence static stress drop, to increase with seismic moment. Dynamic models of I

rupture of a rectangular f aul t in an elastic medium show that the final slip should be controlled by the fau1c width and scale with the dynamic

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stress drop. The only way these models can be reconciled with the obser-vations is if dynamic stress drop correlates with fault length so that it is' also nearly proportional to aspect ratio. This could 'nly happen if faalt length is determined by the dynamic stress drop. There are several serious objections to this, which lead us to suspect that these models may be poor representations of large earthquakes. Firstly, it conflicts with the observations for small earthquanes (modeled as circular sources) that stress drop is nearly constant and independent of source radius. Secondly, Bl $

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2 it conflicts with the observation that fault length is of ten determined by rupture zones of previous earthquakes or cectonic complications. We speculate that the boundary condition at the base of the fault, that slip is zero, is unrealistic because that edge is in a ductile region at the base of the seismogenic layer. In a model in which slip is not so con-strained at the base of the fault nor at the top (the free surface), such that no healing wave originates from these edges, final slip would be determined by fault length. The observations would then be interpreted as meaning that the static and dynamic stress drops of large earthquakes are nearly constant.

These two alternatives predice very different scaling of the dynamics of large earthquakes. The width-dependent model predicts that average particle velocities are larger for long ruptures but the rise time will be the same as in a shorter event of the same width. The length-dependent model predicts the opposite. -

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.. 3 INTRODUCTION A central problem in earthquake seismology has been to find scaling laws that relate the static parameters such as slip and stress drop to the dimensions of the rupture and to understand these relationships in terms of the dynactic parameters, the most fundamental of which are rupture velocity and dynamic stress drop.

In doing so, it is essential to distinguish between small earthquakes and large earthquakes. Tectonic earthquakes nucleate and are bounded within a region of the earth between the surface and a depth h,, the seismogenic layer. The seismogenic depth, h,, depends on the tectonic environment but in a given region the maximum width of an earthquake occurring on a fault of dip 6 is W,= h,/ sin 6. We will define a small ..

earthquake as one with a source radius r i W,/2 and a largs earthquake as one in which r > W, /2. Thus a small earthquake can be represented as a circular source in an elastic medium, whereas a larc; earthquake is more .

suitably treated as a rectangular rupture with one edge at the free sur f ace .

It has been repeatedly demonstrated (e .g . , Aki, 1972; Thatcher and Hanks,1973; Hanks, 1977) that the stress drops of small earthquakes are nearly constant and independent of source dimensions. This result, when interpreted with dynamic models of finite circular ruptures (Madariaga, 1976; Archuleta, 1976; Das, 1980 ), simply means thac the dynamic stress drop is constant.

If the same were t:ue for large earthquakes, the dynamic models of rectangular faulting in an elastic medium (Day,1979; Archuleta and Day,

w. , ,. - , . _. , , - - - -

. 4 1980; Das,1981) would predict that the mean slip is a linear function of fault width. In the next section we will show that this prediction is not borne out by the observations.

What is observed instead is that slip correlates linearly with fault length. The principal point of this paper is to discuss the consequences of that observation for the physics of large earthquakes .

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I 9

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o OB$ERVATIONS For small earthquakes, using the definition of seismic moment, M,,

and the relationship Ao = y-

.shere r is source radius, u is mean slip, and de is stress drop. If stress drop is constant, the relationship between M, and fault area, A, is M

o =( p 3/2) A . (1)

Large earthquakes, however, are more nearly rectangular ruptures of vidth W and length L and in this case, for an elastic model in which slip is restricted to be within W, Ao=CE W (2) where C is a geometrical constant.

If stress drop were constant, we would expect to find that M .etW2 (3) o C 2

In Figure 1 we show a plot of log LW n. log M , for the large interplate thrust and strike-slip earthquakes from the data set of Sykes

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. 6 I and Quittmeyer (1981) . These observations are listed in Table 1. The data for each type of earthquake define a line, but with a slope less than one, indicating that stress drop systematically increases with moment. The offset between the data for the. strike-slip and thrust events is also an important feature that we will discuss later.

These data indicate that u is not simply related to W and that M is not constant for large earthquakes. On the contrary, many workers (e.g.,

Bonilla and Buchanan,1970; Slemmons,1977) have argued that u correlates with L, and recently Sykes and Quittmeyer (1981) have argued that the correlation is linear. Plots of u n. L on linear scales are shown in Figures 2 and 3 for strike-slip and thrust earthquakes, respectively.

In slew of the usual uncertainties in the estimates of u and L, and any naturally occurring variations in dynamic stress drop (with which slip should be expected to scale), the correlation betneen u and L is fairly -

strong. Wa fit it with a straight line with an intercept at the origin u=at (4) and find that c : 2 x 10-' for the thrust events and 1.25 x 10-5 for the strikr slip events. At least for the strike-slip events, slip is clearly not cependent on width because the widths of all the events in Figure 2 are between 10-15 km, i.e. , they are essentially the same.

From this observation we would then expect that i

2 M, 2 val W (5) l

.,, . . , m.__ - - _ . . . _ _ _ _ _ . . . . _ _ . _ . . . _ _ _ _ _ . . . . _ . . _ _ _ _ , , . . _ , . . _ _ _ . _ _ _ _ _ _ . . _ , , _ . _ . _ . - _

7 which is confirmed in Figure 4. For reference, the line drawn through the data has a slope of one.

Since .

L2 g 3 g3 /2( )b and since the aspect ratio L/W varies only by a factor of about 20 in the data-set, we would have found a good correlation between M, and A ! , as did Aki (1972) and Kanamori and Anderson (1975) had we plotted log A vs.

2 log M,. The question is not whether M, correlates better with L W than with A /2 The issue of concern is that Kanamori and Anderson's inter-pretation of their correlation as meaning that stress drop is constant is

! only true if L/W is constant, because from (2) and (4), we have L -

Ao = Cug . ,

(6)

That L/W is a constant is an explicitly stated assumption of Aki (1967, 1972) and Kanamori and Anderson (1975); and although Abe (1975 ) and l Celler (1976) attempted to observationally justify this assumption, it is not generally true. In Figures 5 and 6 we plot ao n. L/W for the two types of earthquakes. The correlation between them is very clear for the strike-slip events, and less so for the thrust events, for which there is a much smaller variation of aspect ratio. That L/W does not have a large vari-ation for the thrust events seems to simply result from the fact that the seismogenic width of subduction zones, ,W , is about 100 km, so that only extremely large events can achieve high values of aspect ratio.

We can now understand why stress drop increases systematically with M,, as shown in Figure 1. The width of large strike-slip earthquakes is l

! .- . , . . . . , _ _ . . - _ . . , - . - . . ._,----_--_.,c--. . ~ - - . . - - --4 - - - - - - - - -- ~ ~ - - - - - - - - - - - - - - - - - - ----'

l 8 -

limited by the seismogenic depth to W , ; 15 km so that they grow princi-pally in the L direction.

This results in a systematic increase in L/W, and hence aa, with M,. The subduction zone thrust earthquakes have dif-forent widths but L increases faster enan W with increasing moment, pro-ducing th. same result, i.e., ao increases with L/W or M,. The offset between the data for thrust and strike-slip even:s in Figure 1 occurs simply because the widths of the thrust events are much greater than those of the strike-slip events. A strike-slip event must have a much greater aspect ratio, and hence stress drop, than a thrust event of the same moment.

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9 PHYSICAL CONSEQUENCES

, The principal feature of the observations that we wish to explain is l

the correlation between slip and fault length. It is a surprising obser-vation because intuition would first lead one to expect slip to depend on i

width, yet this is not observed. This intuition is re-inforced by the I

results of dynamic models of rectangular faults in an elastic medium (Day, l 1979; Archuleta and Day,1980; Das,1981 ). These models show that slip is controlled by the width of the f ault and that it scales with dynamic stress drop.

The situation is illustrated in Figure 7, which shows surface slip along the fault for two representative strike-slip ear thquakes. These i earthquakes have essentially the same width, and differ only in length. If j

the dynamic stress drop were the same for these two ear th qua'kes , then according to the theory, the Ft. Tejon earthquake would be the equivclent of six Mudurnu earthquakes placed end to end. Clearly that is not the Cast.

, If the dynamic, elastic models are correct representations of earth-I quakes, then the only way they can be reconciled with the observations is if dynamic stress drop correlates with aspect ratio. Since the width of strike-slip events is nearly constant, and the , width varies much less than length for the thrust events, 'this would be approximately true if dynamic stress drop correlates linearly with fault length. The only way this can happen without violating causality is if fault length is determined by dynamic stress drop. This is not an entirely unphysical proposition, because dynamic stress drop determines the stress intensity factor, which

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is important in fracture growth. .It is not obviously apparent, however, why L should increase linearly with Aed, the dynamic stress drop.

There are several major objections to this interpretation. The first is that we have to assume that for large earthquakes da determines the d

rupture length, which directly contradicts the observations for small earth quakes. Although st'ress drop appears to increase with source radius over a limited range in sane data sets (Aki,1980), it shows no obvious variation with source radius over a very broad ranga Gianks , 1977 ). We can offer no reasonable explanation for why large earthquakes should behave differently than small earthquakes in this important respect.

A second objection is that this assumption conflicts with the prin-cipal observaticas that led to the concept of seismic gaps: that the i

length of large earthquakes is of ten controlled by the rupture zones of previous earthquakes or by structural features transverse to the fault -

zone. Of course, one could sof ten the original assumption to: aa deter-d j mines the length unless the rupture encounters a rupture zone of a previous earthquake or a transverse feature. The rejoinder is that if the latter were as comon as is thought, it would have the effect of destroying the correlation between u and L that is observed.

It is worth giving a specific example. If we compare the 1966 Park-field earthquake (L = 30 km, u = 30 -cm, W = 15 km) and the 1906 San Fran-cisco earthqrake (L = 450 km, u = 450 cm, W = 10 km) we need to explain the difference in u by a difference in da f about a f actor of 15. Since d

the correlation between 5 and L is also good in these examples, we also need to argue that Lad determined L in these cases. On the other hand, it can be argued that the length of the 1966 earthquake was determined by the length of the gap between the rupture zone of the 1857 earthquake (or the

. 11 fault offset near Cholame) and the southern end of the creeping section of the San Andreas fault. S imila rly , the 1906 earthquake filled the gap between the northern end of the creeping section at San Juan Bautista and the end of the fault at Cape Mendocino. If our argument' that M deter-d mines L is true, then these latter observations are coincidences. Almos t identical arguments can be made for many of the other earthquakes in our data set.

The third point is less an objection than a surprising consequence of this interpretation. The Hoei earthquake of 1707 ruptured about 500 km of the Nankai trough in Japan (Ando,1975; Shimazaki and Nakata,1980) . The same plate boundary was ruptured twice subsequently, in two sets of delayed multiple events, the Ansei I and II events of 1854, and the Tonankai and Nankaido events of 1944 and 1946. In support of a time predictable model of earthquake recurrence, Shima:aki and Nakata argued that the greater -

recurrence time between the first two sequences (147 years) and the second I (91 years) is because the slip (and stress drop) were greater in 1707 chan in either 1854 or 1946, the greater uplif t at Muroto Point in 1707 (1.8 m)

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than in 1856 (1.2 m) or 1946 (1.15 m) being the evidence. The reason why l

this should happen is readily explaine'd by the correlation between u and L.

Thus the ratio of fault length of the Hoei and Ansei II ear thquakes ,

500 km/300 km = 1.7 can explain the ratio of uplift at Muro to Point, I

l 1.8/1.2 = 1.5 and recurrence time, 147/91 = 1.6.

However, if this is interpreted as being due to a difference in dynamic stress drop, then one has to argue that a significant change in dynamic stress drop (50%) can occur on the same fault zone between succes-sive earthquakes. One could argue that this could occur because the slip

! in one earthquake c,ight change the relative position of asperities on the l

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fault. Howeve r, since the slip in an earthquake is about 10-5 L, this would mean that the gross frictional properties of the fault are controlled by asperities of dimensions on the order of 10-5 or less of the rupture dimensions. Since there will be a very large number of such small fea-tures, the average change between successive earthquakes would more likely be expected to be negligible.

1 In the above discussion we have created enough doubt about the appli-l cability of the dynamic rectangular models to consider that they may be

! failing, in sane' fundamental way, to properly describe th: +ysics of large earthquakes .

For a rupture propagating at a constant rupture velocity, v, the slip, for both circular and rectangular faults, is very close to [ Day,1979; Das, 1980, 1981]

2)}1/2 g g 2 (x2 y 2 2)1/2 ~

u(x,y,t) = u,(t -

2 v I*1Uh (7) v where x and y are measured relative to the point of rupture initiation.

Equation (7) is the self-similar solution of Kostrov (1964 ). The asymp-totic particle velocity, u, which scales the slip is, ( Kos trov, 1964; Dahlen, 1974 )

• ha u dg o

=K (8) u where K is a function of rupture velocity.

i When the rupture reaches its final perimeter and stops, a healing wave propagates back into the rupture, arriving at time th. For t > th slip

! decelerates and comes to a halt. The healing wave is not the stopping phase, which is a wave radiated in all directions from the tip of a l

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13 stopping crack (Savage,1965 ). A st;opping phase cannot physically stop the slip in these models because such a wave will lose energy with distance whereas the results of the models are independent of dimension. A healing wave must be interpreted as a vave that propagates into the interior of the rupture in an analogous way, and for analogous physical reasons, as the

• stopping of cars on a highway propagates up the stream of traffic.

Causality restricts it to' travel at a velocity slower than a stopping phase. Thus Madariaga (1976, p. 648') observed, "It appears as if a

' healing' wave propagates inward from the edge of the f ault some time af ter the P and S stopping phases."

Since slip is terminated by the healing wave, the rise time and final slip at any point on the fault is deternined by the distance to the nearest  :

boundary (Day,1979 ; Das ,1981 ). Therefore it is easy to see why mean slip on a rectangular fault should be controlled by the fault width.

A healing wave is the result of the boundary condition that u = 0 at the edges of the fault. If the models are poor representations of large earthquakes, the most likely problem is that these boundary conditions are  ;

unrealistic. The models are of rectangular faults embedded in an elastic l

whole space. The boundary condition u = 0 is imposed on all edges of the  !

fault and healing waves thus propagate from each edge. Since large earth- l quakes rupture the f ree surface, slip is unconstrained there and a healing I wave will not propagate from that edge. However even if an elastic half-space model were available, we would still expect slip to be width-dependent since it would be controlled by the healing wave from the base of the fault.

In large earthquakes the base of the f ault is at the bottom of the seismogenic layer. A plat.sible explanation for the seismogenic depth is

v r

14 that it is the result of a brittle-ductile transition. Thus a large earthquake cannot propagate to greater depth because the energy at the crack tip is dissipated in plastic deformation. A more realistic model then may bh one in which the base of the fault is in a plastic, rather than elastic, region and therefore the conditicn u = 0 is no longer valid at

,that edge.

We illustrate in Figure 8 the difference between an elastic model and an elastic plastic model. The most significant difference is that in the elastic-plastic model (Figure 8b) slip at the base of the fault may be allowed to be greater than zero as a result of plastic deformation in a zone surrounding the rupture tip. This is simply the equivalent, in shear, of the blunting of a crack tip that occurs in tensile crack propagation in ductile materia.2. The plastic deformation around the base of the fault emooths out the stress singularity associated with finite slip there, and will continue as long as slip continues. This* may have the effect of -

inhibiting a healing wave from originating at the base, and if healing waves propagate only from the ends of the fault, slip and rise time will depend on fault length, not width.

No model is available with these boundary conditions but we can approximate one. If we make the approximation that slip stops abruptly with the arrival of the healing wave, then the final slip on the f ault will be, from (7),

l 2 2 u(x,y) = (t 2 ~ (x ,7 )) U2 (I) h v2 I

l which we can calculate. This is a 'quasidynamic' model (Boatwright, 1980),

i.e., a kinematic model that simulates a dynamic model.

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o 15 It can readily be shown for the circular case that (9) yields final slip values that are everywhere within 5% of that of the dynamic numerical models of Madariaga (1976) and Das (1980), and Day (1979) has shown that

,( 9), when properly truacated, also yields a very good approximation to final slip in his rectangular models. We use it to simalate an elastic-plastic half-space model by simply assuming that no healing wave propa-gates from either the top or bottom of the fault.

The procedure we use is very similar to that used by Day (1979, pp. 23-26), and simply involves the calculation of t. We assumed h

v = 0.98, for which the corresponding value of K is 0.81 (Dahlen, 1974),

and that the velocity of the healing wave is ES. In Figure 9 we show slip at the surface as a function of distance from the center of the fault for a bilateral case with L/W = 4. The mean slip is found to scale as -

u=2y L (10)

~

so this model would lead to the interpretation that the linear correlation between u and L that is observed means that the dynamic stress drop for large interplate earthquakes is approximately constant. Equating (10) with (4) we obtain ac c 12 bars and 7.5 bars for thrust and strike-slip d

earthquakes , res pectively. Returning to Figure 4, the line drawn through the data is the prediction of this toodel for ao = 10 bars. Furthermore, d

in this model, where C .p is unconstrained at top and bottom, static stress drop will also be a function of fault length, since the scale length that determines the strain change will be the fault length. The observation made earlier that de is a function of aspect ratio is due to the incorrect use of equation (2) to calculate it. According to this model, ac is also approximately constant for these earthquakes.

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. 16 -

DISCUSSION The observation that slip increases with faul t length in large earthquakes poses severe consequences when viewed in the light of dynamic rupture models.

In conventional dynamic models (W models), slip is deter-mined by fault width, rather than length. These models can only be recon-ciled with the observations if it is assumed that the dynamic stress drop determines the fault length, and the several major objections to this possibility were detailed earlier. With different assumptions concerning the boundary conditions at the base of the fault, it may be possible to construct a dynamic model in which slip depends on fault length (L model).

This model avoids the objections raised to the W model but is based on a speculative, al though not entirely ad hoc, assumption concerning the -

boundary conditions.

Furthermore, severe constraints are placed on L models from the geo- .

detic data obtained for the 1906 San Francisco earthquake. The simplest '

form of L model is one in which slip is totally unconstrained at the base of the fault. If this were the case, strain release would extend out to distances comparable to fault length, rather than depth, but as Brune (1974) has pointed out, the strain release in 1906 was concentrated within a few tens of km from the fault. From angle changes in the Pt. Arena triangulation network [ angle t from Thatcher (1975, Fig. 4)] one can estimate a strain drop of 8 x 10 ~5 within li km of the fault, a figure i

j somewhat more consistent with a W model chan an L model. Thus if L models are relevant, they musc be models in which slip is only partially con-,

strained at the base of the fault. In the absence of numerical modeling of i

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17 this type, one can' t tell if this type of model will result in L scaling or hybrid scal! sg intermediate to the L and W extremes.

l

( These L and W models represent, in many respects, oppos#.te extremes concerning the mechanism of large earthquakes and so it is useful to discuss the contrasting way in which they scale. For eartaquakes in which

! L < 2W, the models are indistinguishable in their gross manifestations.

l In Figure 10 we schematically show a comparisca between an earthquake of dimensions about L = 2W and one of the' s ame width but about 15 times longer. Specifically, this might be a comparison of the 1966 Parkfield earthquake, say, and the 1906 San Francisco earthquake.

On the lef t of the figure we show a snapshot of slip on the inuit during the smaller earthquake. We only show the part that is actually slipping during the snapshot. We also show the time history of slip at -

some representative point. For simplicity, it is simply shown as a ramp with a rise time, t On the right is shown the predictions of the two R.

models for the longer earthquake.

In a bilateral case, as shown, the W model predicts that the slipping portion of the fault splits into two patches of length % W that propagate away from each other at a velocity 2v as they sweep over the f ault surface.

Since the rise time t , remains the same but the slip is fifteen R

times greater, the dynsmic stress drop, and hence particle velocity, must be fifteen times greater.

In the L model, the rupture sweeps out over the fault as an expanding patch, with slip continuing within its boundaries until after the final dimensions are reached. In that model, the dynamic stress drop and par-ticle velocities are the same as in the smaller event, but the rise time, t R : L/2S is much longer.

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In tems of predicting the strong ground motions for a 1906 size earthquake, say, from observed ground motions for a 1966 size earthquake, the difference between the W and L model is critical. The W model would predict that the average particle velo:ities would be much higher and the duration would be about the same. The L model would predict nearly the opposite.

Suppose we start with a square rupture of width W and consider how peak particle velocity, u, and the asymptotic particle velocity, u,,

increase for ruptures of greater length. For a square rupture with dynamic S

stress drop, dad , the maximum value of u and the asymptotic value u, will be

.S S -

u = 0#

d o P

and (11)

.S S

= ba g o

Using the W model, for a rupture of width W, and length L > W , , the stress drop will have to be greater by the ratio W

ha d , L_

3 N a0 o so that

. to SL u = dag y 'qo P O

r

. 19 (12)

W gg 8 L_

u, = d W ,

For the L model, stress drop is the same but the scale length that deter-mines the maximum peak velocity becomes L rather than W, so that

,Aad '

P and (13)

.L S 0#

u, = d Comparing (12) and (13), the two models differ in the ratios

• L y 9 . -.

o

W L P

and (14) u

• L o . E W L "o

So that with a W model, from (12), both peak and asymptotic velocitics for a 1906 type earthquake would be about 15 times greater than for the Park-field earthquake. For the L model, from (13), the peak velocities would at maximum be about /15 greater for a 1906 than a 1966 event, but the asymptotic value would be the same.

a m i

. 20 -

These remarks, of course, apply only to the simple case of a smoothly propagating rupture. Any heterogeneity will produce local high frequency

variations in the velocities. However, they serve to point out the impor-tance of determining if large er rth quakes are better described by an L model or W model or by some intermediate case, if such can exist.

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21 ACKNOEEDGEMENIS My attempts at trying to understand the consequences of slip corre-lating with fault length had a rather long gestation period, during which the author benefitted from discussions with T. Hanks, J. Boatwright, P.

Richards, S. Das, S. Day, and R. Madariaga. Most of the work was done while the author was a visitor at the Department of Earth Sciences , Uni-versity of Cambridge, and a Green Scholar at the Institute of Geophysics and Planetary Physics, University of California, San Diego. Both are thanked for their support and hospitality. The work was supported by National Science Foundation grant EAR 80-07426 and National Aeronautics and Space Adminise ation grant NGR 33-008-146. I thank P. Richards and L.

Sykes for critical reviews. Lamont-Doherty Geological Observatory con- ,,

tribution no. 0000.

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Aki, K. (1980). Re-evaluation of stress drop and seismic energy using a i

new model of earthquake f aulting, in Source Mechanism and Earthcuake Prediction, p. 23-50, Edit. Centre Nat. Recherche Sci., Paris.

Ambras eys , N. (1970). Seme characteristics of the Anatolian fault zone, Te ctonoph ysics , 143-165.

Archuleta, R J. (1976) . Experimental and numerical three dimensional ,

simulations of strike-slip ear th quakes , Ph . D . thesis, Univ. of Calif., San Diego.

Archuleta, R. J. , a nd S . M. Day (1980) . Dynamic rupture in a layered medium: the 1966 Parkfield earthquake, Bull. Seismol'. Soc. Amer.,

20, 671-689.

Ando, M. (1975) . Source mechanisms and recconic significance of his-l l torie t arthquakes along the Nankai trough, Japan, Tectonophysics, 27, i

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B oatvright , J. (1980). A spectral theory for circular seismic sources; l

simple estimates of source dimens ion, dynamic stress drop, and radiated seismic energy, Bull. Seismol . Sec. Amer., 70, 1-27.

Bonilla, M. G. , and J. M. Buchanan (1970). Interim report on worldwide historic surf ace f aul ting, U. S. Geol. Sury. Open-File Rept. , Was h-ington, D.C.

l L

23 Brune , J. N. (1974). Current status of understanding quasi permanent fields associated with earthquakes, EOS, Trans. ACU, M, 820-827.

Dahlen,. F. A. (1974) . On the ratio of P-wave to S-wave corner frequen-cies for shallow earthquake sources, Bull. Seismol. Soc. Amer. , 64, 1159-1180.

Das , S. (1980). A numerical method for determination of source-time functions for general three-dimensional rupture propagation, Geophys.

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Das , S. (1979) . Three-dimensional spontaneous rupture propagation and implications for the earthquake source mechanism, Geoph ys . J. R.

Astron. Soc., in press.

Day, S. (1979) . Three-dimensional finite difference simulation of fault dynamics, Final Rept., NAS2-10459, 71 pp., Systems, Science and Sof tware, La Jolla, Calif. -

Celler, R. J. (1976). Scaling relations for earthquake source para-meters and magnitudes, Bull. S eismol. Soc. Amer. , 6_6, 6 1501-1523.

Hanks, T. C. (1977) . Earthquake stress drops , ambient tectonic stress, and stresses that drive place motions, Pure Aop1. Geo ch ys . , 115, 441-458.

Kanamori, H., and D . L. Anders on (1975). Theoretical basis of some l

empirical laws of seismology, ' Bull. Seismol. Soc. Am. , M, 1073-1096.

Kostrov, B. V. (1964). Selfsimilar problems of propagation of shear l cracks, J. Aeol . Math . Mech. , 2_8,, 1077-1087.

Madariaga , R. (1976) . Dynamics of sn expanding circular f ault, Bull.

Seismol. Soc. Amer., 66, 639-666.

Savage, J. C. (1965) . The stopping phase on eismograms , Bull. Seismol.

Soc. Amer . , 5_5,, 47 -5 8.

i l

. 24 Shimazaki, K.,

and T. Nakata (1980) . Time predictable recurrence model for large earthquakes, _Ceophys. Res. Lecc., 7, 279-282.

Sieh, K. (1978). Slip along the San Andreas fault associs:;ed with the great 1857 earthquake,_ Bull. Seis. Soc. Amer., 68,, 8 1421-1448.

Slemmons , D. B.

(1977). State of the art for assessing earthquake hazards in the United States, Faults and earthquake magnitudes, U.S.

Army Eng. Waterway Exp. Sta. , Vicksburg, Miss . , pp. 229, 1977.

Sykes, L. R., and R. C. Quittmeyer (1981). Repeat times of great earthquakes along simple plate boundaries, , Third Maurice Ewing Symposium on Earthoudke Prediction, 4, edited by D. W. Simpson and P.

G. Richards , ACU, Washington, D.C.

Thateu r, W. (1975). Strain accumulation and release mechanism of the 1906 San Francisco earthquake, J. Geophys. Res. , 80,, 4862-4872.

Thatcher, W., and T. Hanks (1973). Source parameters of southern Cali-fornia earthquakes , J. Geophys. Res. , 78, 8547-8576.

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TABLE 1 PARAMETERS OF LARCE INTERPLATE EARTil00AKES (AVERACEO Fit 0H SYKES AND QUITTHEYER (1981))

Ho L W ii Ao No. Date Location 1027 dyne-em km km L/W em bars Strike-Slip Earthquales

1. 10 Jul 1958 SE Alaska 4.3 350 12 29 325 26

2. 9 Jan 1857 S. California 7 380 12 32 465 36 I

3. 18 Apr 1906 San Francisco 4 450 10 45 450 44

4. 19 May 1940 Imperial Va., Ca. 0.23 60 10 6 125 13 5.

27 Jun 1966 Parkfield, Calif. 0.03 37 10 4 30 4

6. 9 Apr 1968 Ilorrego Htn, Ca.

• 0.08 37 12 3 25 3

7. 15 Oct 1979 Imperial Va., Ca. 0.03 30 10 3 30 4

8. 4 Feb 1976 Cuatemala 2.6 270 15 18 150 9

9. 16 Oct 1974 Cibbs F. 2. 0.45 75 12 6 170 14

10. 26 Dec 1939 Ercincan, Turkey 4.5 350 15 23 285 18

11. 20 Dec 1942 Erhaa Hiksar, Turkey 0.35 70 15 5 112 8

12. 1 Feb 1944 Cerede-Holu, Turkey 2.4 190 15 13 275 18

13. 18 Mar 1953 CEnen-Yenice, Turkey 0.73 58 15 4 280 21

14. 22 Jul 1967 Hudurnu, Turkey 0.36 80 15 5 100 7 Thrust Earthquakes 15, 6 Nov 1958 Etorofu, Kuriles 44 150 70 2.1 840 37 16, 13 Oct 1963 Eruppu, Kuriles 67 275 110 2.5 445 12 ,

17. 16 May 1968 Tokachi-oki, Japan 28 150 105 1.4 355 10

18. 11 Aug 1969 Shikotan, Kuriles 22 230 105 2.2 180 5

19. 17 Jun 1973 llemuro-oki, 3apan 6.7 90 105 0.86 140 5

20. 4 flov 1952 Kamchatka 350 450 175 2.6 890 14

21. 28 Har,1964 Prince Wm Sound, Alaska 820 750 180 4.2 1215 18 0

22. 4 Feb 1965 Rat Island, Aleutians 125 650 80 8.1 480 10 23.10 Jan 1973 Coll.na, Mexico 3 85 65 1.3 110 5

24. 29 Ilov 1978 Daxaco, ikxico 3 80 70 1.1 110 5

25. 22 !!ay 1960 S. Chile 2000 1000 210 4.8 1900 21

26. 17 Oct 1966 c. Peru 20 80 14 0 0.6 360 12 6

26 -

FIdURE CAPTIONS Figure 1.

Plot of log LW vs. log M for the large intraplate earthquakes from the data set of Sykes and Quittmeyer (1981). The lines of slope 1 are constant stress drop lines , assuming C = 0.6 for the thrust events, and 0.3 for the strike-slip events.

Figure 2.

A plot of mean slip, u, vs. faul t length for the strike-slip events.

The line drawn through the data has a slope of 1.25 x 10-5, Numbers are references to Table 1.

Figure 3.

The same as Figure 2, for the thrust events. The slope of the line is 2 x 10-5, Figure 4.

A plot of log L W vs. log M . The line drawn through the data -

has a slope of 1, for reference.

• Figure S. S tress drop plotted v s .' as pect ratio for the strike-slip  !

5, earthquakes .

Figure 6.

S tres s drop vs. as pe ct ratio for the thrust ear thquakes .

Event 22 is an oblique slip event for which stress drop was calculated based only on the dip slip component and is hence underestimated.

Evet.t 15 is an anomalously deep event in the Kuriles (Sykes and Qui ttmeye r, 1981) .

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In A, it is represented by rupture in an elastic half-space. The boundary condition at the base of the rupture is u = 0. In B, the rupture penetrates a ductile region. At the base u > 0, which is accommodated by plastic deformation in a zone surrounding the rupture tip.

Figure 8. Surface slip as a function of distance along the f ault plane for two representative strike-slip earthquakes of similar width but different depth. Data for the Mudurnu earthquake is from Ambraseys (1969) and for the Ft. Tejon earthquake from Sieh (1978).

Figure 9. Dimensionless slip, u' vs. length, L', at the free surface from the center to the end of the fault. The model is a quasidynamic -

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UNITED STATES OF' AMERICA

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NUCLEAR REGULATORY COMMISSION BEFORE THE ATOMIC SAFETY AND LICENSING APPEAL BOARD 4

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)

In the Matter of: )

)

PACIFIC GAS & ELECTRIC ) Docket Nos. 50-275 0.L.

COMPANY ) 50-323 0.L.

(Diablo Canyon Nuclear )

Power Plant, Units 1 & 2 )

)

)

CERTIFICATE OF SERVICE I hereby certify that on this ~24th day /orMay,1981 - 1"%

I have served copies of the foregoing MOTION TO REOPEN THE RECORD by mailing them through the U.S. Mail, first-class, postage pre - ,

paid, to those persons listed below, except those designated by an asterisk on whom service was made by messenger on May 25, 1981.

l

• Richard S. Salzman,

• Dr. John H. Buck Chairman Atomic Safety & Licensing Atomic Safety & Licensing Appeal Board Appeal Board U.S. Nuclear Regulatory O.S. Nuclear Regulatory Commission Commission 4350 East West Highway 4350 East West Highway Bethesda, Maryland 20014 Bethesda, Maryland 20014 l John F. Wolf i

• Dr. W. Reed Johnson Chairman Atomic Safety & Licensing Atomic Safety & Licensing Appeal Board Board l -U.S. Nuclear Regulatory 3409 Shepherd Street l Commission ,

Chevy Chase, Maryland 20015 l 4350 East West Highway Bethesda, Mary.and 20014

-,e,,-, ewer ->--------~m =c -- - = - -----y--n -- .-e+--e ----------%-m ,+rv- e 'v+- --e e v*N " " ' ' ~ -

Docket & Service Section Gordon Silver Office of the Secretary- 1760 Alisal Street U.S. Nuclear Regulatory San Luis Obispo, CA 93401 Commission Washington, D.C. 20555 Joel Reynolds John Phillips, Esq.

William J. Olmstead, Esq. Center For Law In-Edward G. Ketchen, Esq. The Public Interest

• Lucinda Low Swartz 10203 Santa Monica Boulevard Charles A. Barth Fifth Floor Office of the Executive Legal Los Angeles, CA 90067 Director - BETH 042 U.S. Nuclear Regulatory Bruce Norton, Esq.

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, Malcolm H. Furbush, Erg.

Vice President and General Counsel Philip A. Crane. Esq.

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, Pacific Gas & Electric Company I 31st Floor 77 Beale Street, Room 3127 San Francisco, CA 94106 1

7 . ' b 5 . T' d.A Ju_ I mg David S. Fleischaker, Esq.

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