EARTHQUAKE HAZARDS AT SLAC. This note summarizes some recently published information relevant

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1 EARTHQUAKE HAZARDS AT SLAC SLAC-TN-76-1 John L. Harris January 1976 Summary This note summarizes some recently published information relevant to the expectation of damaging earthquakes at the SLAC site. Conclusions are drawn that: a> the probability of a strong (m = 6.5 to 8.5) earthquake originating in the proximate section of the San Andreas fault is in the range of.05 to.1 per annum and may be increasing with time. b) Peak acceleration to be expected may be in the range of 0.5 g to 2.0 g. Typical records of acceleration, velocity and displacement are attached. _-----_--- A. Probability and Magnitude The magnitude of earthquakes is defined by the Richter scale. This describes an earthquake by the relationship A M = loglo A, where M is the Richter magnitude. A is the maximum amplitude recorded on a Wood-Anderson seismograph 100 km away from the fault. A0 is a normalizing amplitude of 1 micron. In practice data is extrapolated from seismographs at various locations to get a calculated amplitude at 100 km. The total energy released in an earthquake in relation to the magnitude has been estimated to conform to the formula

2 log E = M. Thus a Richter 7 earthquake will dissipate 32 times the energy of a Richter 6 earthquake. This relationship is of little practical value for sites close to the fault, however, since the energy is not released at a single point. A larger magnitude earthquake will release energy both by larger amplitude displacement on the fault and by a rupture over a longer length of the fault. Bonilla(1) has suggested an empirical relationship between magnitude and displacement of: log D = 0.57 M where D is displacement in feet, and a similar relationship for the length of fault rupture and displacement of: log D = 0.86 log L where L is the length of fault in miles. The logarithm of the probability of occurrence in a given region of an earthquake larger than a given magnitude varies approximately inversely with magnitude. That is, the probability of a magnitude 6 or larger quake is about 10 times the probability of a magnitude 7 or larger quake. This relationship holds only up to magnitude 8. Above that the probability falls sharply to zero at slightly more than M = 8.5. Some authors conclude that this represents an upper limit for the energy storage mechanism. A recent report (2) suggests that this falloff in the frequency of occurrence is in fact an artifact of the means of measurement. The authors calculate a quantity known as the seismic moment, M 0 which is the product of the fault area multiplied by the fault displacement multiplied by the rigidity modulus. When MO is plotted against cumulative frequency a linear relationship is evident through the largest -2-

3 known earthquakes. This suggests that there is in fact no upper bound to earthquake size expressed as MO. (To illustrate the difference, the 1964 Alaska earthquake had a Richter magnitude of 8.4 and a seismic mom- 29 ent of 7.5 x 10 dyne centimeters while the 1960 Chile earthquake had 30 a Richter magnitude of 8.5 and a seismic moment of 2.5 x 10 dyne centimeters.) SLAC is situated a few kilometers from the San Andreas fault, close to a section of the fault which has the reputation of being "locked" and in which energy is periodically released in large earth- quakes. Two large earthquakes are known to have occurred in this sec- tion in recent times: the 1838 quake (>6.5) and the 1906 quake (8,3), In 1957 a 5.3 quake occurred some 40 km north of SLAC. The probability of a future earthquake can be estimated in several ways. John Blume & Associates in early considerations of earthquake problems at the SLAC site(3) estimated the probability by considering the active fault length within 30 miles of the site, comparing it to the total active fault length in California and using this ratio to multiply the observed earthquake frequency in California. By this method they drew the conclusion that a magnitude 6.2 or greater quake with an epi- center less -than 30 miles away could be expected with a frequency of.05 per annum. Another approach is to start from the assumptions that a> The relative motion between the Pacific plate and the North American plate is steady and predicted to continue. (Motion is about 4.5 cm/year.) b) The proximate section of the San Andreas fault has the char- acteristic that strain is periodically released in large mag- nitude events between m = 6 and m = 8.5, rather than in more -3-

4 frequent low magnitude events. c> That the strain will always be released before some maximum value is reached. These assumptions lead one to the conclusion that the energy re- lease will be quasi-periodic. The probability of a large magnitude earthquake would then not be a fixed number, but would conform to a sawtooth function, increasing with time from the last event. Since we are already 70 years from the last movement of this section of the San Andreas fault one might conclude that the contemporary probability of an earthquake in this section may be large, say 0.1 per annum. Re- sults of recent U. S. Coast and Geodetic surveys in the Bay Area tend to confirm that there has been a progressive increase in strain in a (4) direction parallel to the San Andreas fault in the years since B. Local Conditions - Postulated Earthquake To provide a basis for rational planning we may make a postulate which will include such factors as: the magnitude of the earthquake, the section of fault in which it originates, the consequent ground motion resulting and possible other hazards such as landslides, floods or collapse of ground due to liquefaction or spreading. A convenient postulate has been described by Borcherdt et al (5) which we may use. It describes a 6.5 magnitude event originating in a fault rupture with a right-lateral surface displacement some 40 km long centered on SLAC. There would be a residual displacement of about 1 M with the land west of the fault moving toward the north. The main zone of surface rupture will range in width from a few meters to several tens of meters. Small fractures and permanent ground dis- -4-

5 tortion may extend to much greater distances. C. Ground Motion To estimate the resulting ground motion at the SLAC site we refer to the data of Page, Moore and Dieterich (6). Figure 1 shows the rela- tionship of peak acceleration to distance from the fault slippage in earthquakes of magnitude Most of the SLAC site is 3-5 kilometers from the fault where little or no data is available, but we may reasonably assign a value of g for the peak acceleration. Records of motion from a site having a similar distance to the fault causing the 1971 San Fernando quake (magnitude 6.6) are shown in Fig. 2. They show peak accelerations of about 1.2 g, peak velocities of 110 ems/second and peak displacements of about 40 ems. The reference asserts that the dominant frequencies at a bedrock site are: for acceleration 2 to 10 Hz, for velocity 0.5 to 2 Hz and for displacement 0.06 to 0.5 Hz. The authors emphasize that the duration of the strong ground motion (>lo seconds) may be an important cause of damage or failure. With the possible exceptions of parts of the site where structures have been built on fill or where steep cuts have been made in the bedrock, hazards from landslides or settlement may be ignored. The 280 kv power line crosses an area of former landslides and must be considered vulnerable to serious damage from this cause. D. Largest Possible Earthquake The San Andreas fault has the capacity of producing an earthquake of larger magnitude (>8) which would produce serious damage over a wider area, but the consequences at sites very close to the fault may -5-

6 not be greatly different. Peak accelerations for earthquakes of this magnitude have not been measured closer than 75 km to the causative fault. An educated guess would suggest that peak acceleration at the fault might reach or exceed 2 g and that the duration of ground shaking might be as much as 30 seconds. The probability of a 7-8+ magnitude earthquake on this section of the San Andreas fault is quoted as from.ol to.ool per annum by Wesson et al (7). References (1) M. G. Bonilla, Surface Faulting and Related Effects, in Earthquake Engineering, Prentice Hall, 1970 (2) Michael A. Chinnery, Robert G. North, The Frequency of Very Large Earthquakes, Science, 19 December (3) Report i/l, Earthquake Design Criteria for SLAC, John Blume Associates, July 31, (4) Bruce A. Bolt, Causes of Earthquakes in Earthquake Engineering, Prentice Hall, (5) Borcherdt, Brabb et al., Predicted Geologic Effects of a Predicted Earthquake: in Studies for Seismic Zonation of the San Francisco Bay Region. U. S. Geological Survey, Department of the Interior, (6) Page, Moore and Dieterich, Estimation of Bedrock Motion at the Ground Surface, in Studies for Seismic Zonation, etc. (7) Wesson, Helley, Lajoie and Wentworth: Faults and Future Earth- quakes: ibid.

7 c DISTANCE, IN MILES I I I I I III I I I rrllry l * MAGNITUDE Rock 0 Alluvium 0- * I I Illll I 1 I Illll I I I DISTANCE, IN KILOMETRES Figure 1 -- Peak horizontal ground acceleration in relation to shortest distance to slipped fault for earthquakes of magnitude 6.0 to 6.9 as a function of site geology.

8 lw) - Ground velocity I I I Ground displacement c 50 0 I I TIME, IN SECONDS Figure 2 -- Records of N. 14' E. component of horizontal ground motion at Pacoima damsite for San Fernando, Calif., earthquake of February 9, 1971 (after Trifunac and Hudson, 1971). Velocity (center and displacement (bottom) records are obtained by integrating acceleration record (top) once and twice, respectively.