Bulletin o the Seismological Society o America, Vol. 85, No. 6, pp. 1873-1878, December 1995 Testing a Model o Earthquake Nucleation by Rachel E. Abercrombie,* Duncan C. Agnew, and Frank K. Wyatt Abstract Some laboratory models o slip ind that a critical amount (or velocity) o slow slip is required over a nucleation patch beore dynamic ailure begins. Typically, such patch sizes, when extrapolated to earthquakes, have been thought to be very small and the precursory slip undetectable. Ohnaka (1992, 1993) has proposed a model in which oreshocks delineate a growing zone o quasi-static slip that nucleates the dynamic rupture and suggests that it could be large enough (-1 km across) to be detectable and thus useul or short-term earthquake prediction. The 1992 Landers earthquake (M 7.3) had a distinctive oreshock sequence and initiated only 7 km rom the strain meters at the Piion Flat Observatory (PFO). We use this earthquake to investigate the validity and useulness o Ohnaka' s model. The accurate relocations o Dodge et al. (1995) show that the oreshock zone can be interpreted as expanding rom an area o 8 m (along strike) by 9 m (in depth), to 2 by 32 m in the 6.5 hr beore the mainshock. We have calculated the deormation signals expected both at PFO and 2 km rom the oreshock zone, assuming either constant slip or constant stress drop on a circular patch expanding at 5 cmsec over 6.5 hr. We ind the slips or stress drops would have to have been implausibly high (meters or kilobars) to have been detectable on the strain meters at PFO. Slightly better limits are possible only 2 km rom the source. Even though the distance rom Landers to PFO is small compared with the average spacing o strain meters in Caliornia, we are unable to prove or disprove Ohnaka' s model o earthquake nucleation. This suggests that even i the model is valid, it will not be useul or shortterm prediction. ntroduction Laboratory studies o rictional sliding in rocks (Dieterich 1979, Ohnaka and Kuwahara 199) show that subsonic slip is observed over an expanding area prior to dynamic ailure. the same type o slip occurs beore earthquakes at detectable levels, it would be very useul or short-term earthquake prediction. One motivation or observing crustal deormation is to search or such short-term precursors. Most observations o crustal strain have not detected any preseismic slip, however, and thus can only be used to limit the maximum preseismic moment release in the source region. The size o the limit depends on the time interval considered because the noise spectrum o these measurements increases with period (Agnew, 1992) and also on the distance rom the source. Johnston et al. (1987) ound the maximum preseismic moment over the inal ew minutes to be 2% or less o the seismic moment o the subsequent earthquake, or ive earthquakes * Present address: nstitute o Geological and Nuclear Sciences, Kelburn Research Centre, 32 Salamanca Road, P.O. Box 132, Wellington, New Zealand. (M 3 to 5.5), with strain meters between 28 and 55 km away. Wyatt (1988) ound preseismic moment to be limited to as little as 1% o the seismic moment or earthquakes in southern Caliornia. The tightest constraints come rom observations o the 1989 Loma Prieta (M 7.) and 1992 Landers (M 7.3) earthquakes, or which the limits over the inal ew minutes are less than.1% o the seismic moment or both events (Johnston et al., 199, 1994; Wyatt et al., 1994). These data suggest that preseismic slip is very small and not easily detected, perhaps not even with instruments directly over the source zone. Ohnaka (1992, 1993), however, has proposed a model or earthquake nucleation, implying that preseismic slip might occur over areas o order 1 km across and thus be readily detectable. This model interprets immediate oreshocks as occurring within the growing nucleation zone; since such oreshocks were observed or the 1992 Landers earthquake, we considered it worth testing using the available deormation data. Ohnaka et al. (1987) and Ohnaka and Kuwahara (199) developed a model to explain the slow but accelerating slip observed beore dynamic rupture in laboratory experiments o rictional sliding. This model was extrapolated to the 1873
1874 Short Notes earth's crust using both computer simulations (Yamashita and Ohnaka, 1992) and investigation o the physical characteristics o the crust (Ohnaka, 1992) to estimate possible values or slip and area o the nucleation zone. As noted above, this model allows the size o the oreshock zone to be used to iner the size o the nucleation zone; the oreshocks are due to small dynamic instabilities that do not propagate ar. Ohnaka (1992) suggests that earthquakes without oreshocks are nucleating in regions that are less heterogeneous so that no dynamic instabilities are triggered. For example, earthquakes nucleating at the base o the seismogenic zone may ollow a nucleation process conined to the more ductile and more homogeneous lower crust. Ohnaka (1993) considers the oreshock sequence o the zu Oshima sland earthquake (7.2 M, 1978) and inds that the oreshock zone grows at a rate o 1 to 4 cmsec, reaching a diameter o 1 kmjust beore the mainshock occurred. He suggests that a nucleation zone size o 1 km may be typical or an M 7 earthquake. t is worth noting that the oreshocks o the zu Oshima earthquake all occurred oshore; it is not clear how accurate the locations were. Since lower accuracies usually disperse the locations, the oreshock zone could have been less than 1 km across. The Landers (1992) Earthquake Sequence The 28 June 1992 Landers earthquake (M w 7.3) was the largest event in Caliornia in 4 yr (Fig. 1) (Hauksson et al, 1992). t was preceded by a well-recorded oreshock sequence o 35 events (ML 1.5 to 3.6), 3 o which occurred 2 months beore the mainshock, and 24 o which occurred within the last 7 hr. Dodge et al. (1995) relocated the oreshock s using a waveorm correlation technique, to a relative accuracy o < 1 m horizontally and <2 m in depth. This makes this sequence ideal or constraining Ohnaka's model. As shown by Figure 1, the Landers earthquake is also only 7 km rom the long-base strain meters at Piion Flat Observatory, which, though running through the entire sequence, detected no preseismic strain (Wyatt et al., 1994). To determine whether the Ohnaka model is consistent with the Landers oreshock sequence, we show in Figure 2 both the along strike and depth position o the oreshocks as a unction o time. The three early oreshocks deine a smaller zone than the immediate oreshocks, which is consistent with some growth o the zone. The size o the zone o immediate oreshocks, however, shows small sign o expansion either along strike or in depth (i the one outlier is removed). This conclusion is also reached by Dodge et al. (1995). t is possible, however, to interpret these last oreshocks as being part o an expanding zone, as shown in Figure 2. This interpretation is used here in order to investigate whether any preseismic slip over a nucleation patch delineated by the oreshocks (as suggested by Ohnaka) could have been large enough or detection. For this purpose, the oreshocks are considered here as deining a zone.8-km V Z tm o, 34.6 34.4-34.2 34. 33.8 33.6 Landers...---'~W, Rupture Mainshock -'~~. Foreshocks,\ ~ k 116.8 116.6 116.4 116.2 W Long (deg) l PFO Figure 1. Map showing the location o the Landers oreshocks and epicenter relative to the Piion Flat Observatory (PFO). See Figure 2 or explanation o symbols. across by.6-km deep initially, increasing at about.5 mm sec or 41 days, to a size o.9 by.8 km. n the last 6.5 hr, the zone would expand at about 5 to 1 cmsec to about 2 by 3 km just beore the onset o the mainshock. there were such an expanding zone, could subsonic slip on it be detected by the strain meters at Pinyon Flat? This depends on how much slip occurred in the zone, something Ohnaka's model does not address. We consider two distinct models o slip. We assume in both cases that the radius over which some preseismic slip has occurred is r = vt, where t is time and v is the velocity o growth, which is about 5 cmsec or the last 6.5 hr. n one case, we assume that as the slip ront passes, a slip o size s takes place, not
Short Notes 1875 %- e- v o O9 k_ ri- d3 E -2-4 -6-8 -1,edl events, along strmke o 17 ~ i m -1.. 1. 2. ~ 1-2 -4-6 -8 [],rn,rl, 4 6 All events, vs aepm []! 8 1 %` v L 1-1 \ -2 r-\ OO -a \ -4 \ -5-6 " [ [] Final events, along strike oo ~ [] [] i \oo ~ -1.. Distance N o 1. 2. Start (km) 1-1 -2-3 -4-5 -6-7 Final events, vs depth, $oo o []! 4 6 8 1 Depth (km) Figure 2. The growth o the Landers oreshock sequence with time. The oreshocks are plotted as squares. The asterisk gives the location o the two small subevents that began the rupture, and the star is at the onset o the main energy release (Abercrornbie and Mori, 1994). increasing thereater so that the total moment depends only on the total area A. The seismic moment (Mo) divided by the shear modulus ~, taken to be 3 1 l Nm) is the source strength or creating crustal deormation, and this is then just M -- = sv:t:. (1) iz Our second model is that o an expanding crack, in which we assume the stress drop (Aa) to be constant; we can then use the result o Eshelby (1957) or a circular crack: Mo 16Aat3r 3 ~ 7~ (2) Figure 3 shows the moment increasing with time or these two models or our possible values o stress drop and slip. We used a standard dislocation program to compute the deormation seen at Pinyon Flat rom a N-S-striking slip plane at the location o the oreshocks. Applying this to the equations above, we calculate the expected NW-SE strain at Piion Flat Observatory or s = 1 m and Aa = 1 bars, both values comparable to the seismic slip on this part o the rupture (Wald and Heaton, 1994). The recorded strain and GPS displacement data at Piion Flat Observatory are also shown, and it is clear that even these large amounts o preseismic slip would not have been detected. We cannot, thereore, rule out Ohnaka's model, but can provide no positive evidence in support o it. Concluding Remarks This investigation o Ohnaka's model o earthquake nucleation demonstrates that there is a lack o direct evidence in support o it and that current data cannot disprove it. More importantly, this study shows that even i Ohnaka's model o earthquake nucleation does apply to Caliornian earthquakes, the preseismic slip it predicts is not readily detect-
1876 Short Notes Expanding-Crack Model Slip-Front Model 116 E 15 zl t- Q) E o 114 113 o = 1 bar 1 bar 1 bo -6-5 -4-3 -2-1 hours beore moinshock 116 115 114. 113 s = loo cm 1 cm 1 c.,.1 cm d, -6-5 -4 hours beore J -3-2 -1 moinshock Figure 3. Time dependence o the preseismic moment predicted by the two slip models or dierent possible values o slip and stress drop. able at signiicant distance. At closer distances, matters are somewhat better. Figure 4 also shows the strain signals to be expected at a site 2 km rom the oreshocks. n this case, strain data o the quality o those presented here would easily be able to detect large preseismic slip and perhaps place valuable bounds on what could have occurred. This is not, however, the case with all types o deormation data. We also show in Figure 3 the expected displacement 2 km rom the oreshocks and show or comparison actual GPS data collected at Pinyon Flat. t is clear that even or such a avorable location, the sensitivity o the GPS system alls ar short o what might be needed to detect plausible amounts o preseismic slip. t is worth noting the growing number o observations o small seismic precursors to many large earthquakes, e.g., Landers (Abercrombie and Moil, 1994), Gul o Corinth (Abercrombie et al, 1995), and earthquakes in Mexico (Anderson and Chen, 1995) and northern Caliornia (Ellsworth and Beroza, 1994). These precursors, or small onsets, to larger earthquakes may represent small events that trigger the mainshock or possibly slow but just seismic slip that nucleates the mainshock. n either case, as they are typically <1% o the mainshock moment (M w 4.4, Aa - 1 bars, or Landers, Abercrombie and Moil, 1994), their existence implies that any preceding aseismic slip would be even smaller (considerably smaller than that shown in Fig. 4), decreasing the chances o its being detectable, even at short distances, and so useul or short-term earthquake prediction. Acknowledgments The authors are grateul to D. Dodge or providing a preprint o his recent work and also his relocations o the Landers oreshocks. We are especially grateul to D. Tralli (NASA-JPL) or providing us with his analysis o the PFO GPS data prior to publication. We also thank C. Sammis or helpul discussion and C. Langston or an extremely timely review. This work was supported by the U.S. Geological Survey, the National Science Foundation, and the Southern Caliornia Earthquake Center (Contribution Number 215). Reerences Abercrombie, R. E. and J. J. Mori (1994). Local observations o the onset o a large earthquake: 28 June 1992 Landers, Caliornia, Bull. Seism. Sac. Am. 84, 725-734. Abercrombie, R. E.,. G. Main, A. Douglas, and P. W. Burton (1995). The nucleation and rupture process o the 1981 Gul o Corinth earthquakes rom deconvolved broadband data, Geophys. J. nt. 12, 393-45. Agnew, D. C. (1992). The time-domain behavior o power-law noises, Geophys. Res. Letts. 19, 333-336. Anderson, J. G. and Chen, Q. (1995). Beginnings o earthquakes in the Mexican subduction zone on strung motion accelerograms, Bull. Seism. Sac. Am., in press. Dieterich, J. H. (1979). Modeling rock riction: 1. Experimental results and constitutive equations, J. Geophys. Res. 84, 2161-2168. Dodge, D. A., Beroza, G. C., and W. L. Ellsworth (1995). The oreshock sequence o the 1992 Landers, Caliornia earthquake and its implications or earthquake nucleation, J. Geophys. Res. 1, 9865-988. Ellsworth, W. L. and G. C. Beroza (1994). The seismic nucleation phase: implications or earthquake rupture dynamics, EOS 75, 426. Eshelby, J. D. (1957). The determination o the elastic ield o an ellipsoidal
Short Notes 1877 Strain 61~ ObservedExpected at PFO(NW-SE LSM) L~ ~~.~._~.w.~.. ~r'~ - C ~ - 1-- ~ m i ~ i- i.5-6 -5-4 -3-2 -1 1.7 na na o oreshocks c (NW-SE str J n -6-5 -4-3 -2-1 Displacement l~o ObservedExpected at PFO (N-S GPS) mm ~ -.7 1-6 -5-4 -3-2 -1 mm,-~ E. 1. ~. -1. ~" -2. o -3. Expected 2 km S o oreshocks (N-S displacement) -6-5 -4-3 -2-1.k-.2 mm -.67 mm Seismicity i l [ -6-5 -4-3 -2-1 Time beore Moinshock (hr) Figure 4. The top panel shows the observed strain at Piion Flat Observatory and that predicted by the slip ront model (dashed, slip = 1 m) and crack model (solid, 1 bars). The second panel shows the strains or the same models predicted 2 km rom the source. The third and ourth panels are the same as the top two but or displacement as measured by GPS. The GPS data are two minute samples o the JPLM- PNT baseline, processed with GPSYOASS with daily multipath signals removed. n all our panels, the cumulative strain and displacement predicted by the models at the start o the mainshock are given on the right. The bottom panel shows the occurrence o the oreshocks in time.
1878 Short Notes inclusion and related problems, Proc. Roy. Soc. London, Series A 241, 376-396. Hauksson, E. L., L. M. Jones, K. Hutton, and D. Eberhart-Phillips (1993). The 1992 Landers earthquake sequence: seismological observations, J. Geophys. Res. 98, 19835-19858. Johnston, M. J. S., A. T. Linde, and D. C. Agnew (1994). Continuous borehole strain in the San Andreas ault zone beore, during and ater the 28 June 1992, Mw 7.3 Landers, Caliornia, earthquake, Bull. Seism. Soc. Am. 84, 799-85. Johnston, M. J. S., A. T. Linde, and M. T. Gladwin (199). Near-ield high resolution strain measurements prior to the October 18, 1989, Loma Prieta M s 7.1 earthquake, Geophys. Res. Lens. 17, 1777-178. Johnston, M. J. S., A. T. Linde, M. T. Gladwin, and R. D. Borchedt (1987). Fault ailure with moderate earthquakes, Tectonophysics 144, 189-26. Ohnaka, M. (1992). Earthquake source nucleation: a physical model or short-term precursors, Tectonophysics 211, 149-178. Ohnaka, M. (1993). Critical size o the nucleation zone o earthquake rupture inerred rom immediate oreshock activity, J. Phys. Earth 41, 45-56. Ohnaka, M. and Y. Kuwahara (199). Characteristic eatures o local breakdown near a crack-tip in the transition zone rom nucleation to unstable rupture during stick-slip shear ailure, Tectonophysics 175, 197-22. Ohnaka, M., Y. Kuwahara, and K. Yamamoto (1987). Constitutive relations between dynamic physical parameters near a tip o the propagating slip zone during stick-slip shear ailure, Tectonophysics 144, 19-125. Wald, D. J. and T. H. Heaton (1994). Spatial and temporal distribution o slip or the 1992 Landers, Caliornia, earthquake, Bull. Seism. Soc. An 84, 668-691. Wyatt, F. K., D. C. Agnew, and M. Gladwin (1994). Continuous measurements o crustal deormation or the 1992 Landers earthquake sequence, Bull. Seisrr~ Soc. Am. 84, 768-779. Wyatt, F. K. (1988). Measurements o coseismic deormation in southern Caliornia: 1972-1982, J. Geophys. Res. 93, 7923-7942. Yamashita, T. and M. Ohnaka (1992). Precursory surace deormation expected rom a strike-slip ault model into which rheological properties o the lithosphere are incorporated, Tectonophysics 211, 179-199. Depattlnent o Earth Sciences University o Southern Caliornia Los Angeles, Caliornia 989-74 (PEA) GPP 225 University o Caliornia, San Diego La Jolla, Caliornia 9293-225 (DCA, FKW) Manuscript received 19 May 1995.