Quasi-periodic earthquakes: What is the evidence? What are the alternatives?

1. Quasi-periodic earthquakes: What is the evidence? What are the alternatives? David D. Jackson Department of Earth and Space Sciences UCLA

2. Thesis • Empirical evidence for QP earthquakes comes from retrospectively selected data. Prospective tests nearly always fail. • Parkfield • Round Valley • Seismic Gap Model 2 (Nishenko, 1991) • Heuristic models for quasiperiodic earthquakes require characteristic earthquake model (events that start and stop clock). They look ok in retrospect but fail prospective tests. No agreement on how to define characteristic event in advance. • Models based on QP behavior have been patched up to the extent that they are no longer falsifiable;

3. Applied Scientific Method • Observation; Hypothesis; Test; Validation; Application • Relevant quotation: Wolfgang Pauli, in review of paper expressing untestable model: “This isn't right, this isn't even wrong.” • Right > Wrong > Untestable

4. What might be quasiperiodic? • Characteristic earthquakes? Assumes • Nearly independent of other quakes • “gap filling”; restart clock by near-total stress drop • Near uniform displacement on segment • Rupture constrained by persistent feature • Slip on segment (along with some neighbors)? • Requires all of above, or that neighbors be qp too. • Slip at trench site on fault? • Uplifted terraces? • Quakes on isolated asperity? • Quakes in a box?

5. Things to remember • The co-seismic slip at any point on a fault surface almost surely initiated somewhere else on the fault. • Earthquakes are not one-dimensional, nor do their rupture surfaces consistently abut. • Thus, periodic initiation at some points does not imply periodic displacements at a trench, and vice versa.

6. Evidence for Periodic Recurrence • Parkfield: Retrospectively Selected Data (RSD) • Savage and Cockerham: RSD • Japan Stein et al. RSD • Nishenko and Buland; Ellsworth et al., 1997 RSD • Nishenko 91: Seismic Gap model Pacific Rim • Nadeau and Johnson : Central California small ones, RSD • Cascadia tremor: may be testable?

7. BSSA, August 1987; v. 77; no. 4; p. 1347-1358, 1987 Quasi-periodic occurrence of earthquakes in the 1978-1986 Bishop-Mammoth Lakes sequence, eastern California J. C. SAVAGE and ROBERT S. COCKERHAM, USGS Abstract … the five principal events in the Bishop-Mammoth Lakes earthquake sequence occurred at intervals of about 1.5 yr with a standard deviation … of 0.25 yr. Some data selection was involved in identifying the principal events, although the choices seemed reasonable. The recent Chalfant Valley earthquake (ML = 6.4; 21 July 1986) followed the last prior principal event in the … sequence by 1.65 yr… the Chalfant Valley earthquake could have been forecast from the observed periodicity. However, the precision of the forecast (±0.8 yr for the 95 per cent confidence interval) is not sufficient to furnish convincing evidence that the Bishop-Mammoth Lakes sequence is quasi-periodic. Extrapolation of the trend established by the six previous events suggests that the next event in the Bishop-Mammoth Lakes sequence would be expected in December 1987 ± 0.7 yr (95 per cent confidence interval). The regularity of the Bishop-Mammoth Lakes sequence is comparable to that of the Parkfield, California, sequence (average … interval 20.8 yr with a standard deviation … of 6.2 yr). Both sequences consist of six events.

9. A new probabilistic seismic hazard assessment for greater Tokyo, BY ROSS S. STEIN, SHINJI TODA, TOM PARSONS, AND ELLIOT GRUNEWALD In press, Phil. Trans. R. Soc. A.

11. Nishenko’s Circum-Pacific Seismic Gap Model, 1991 Tables included characteristic magnitudes and probability estimates.

13. Ten-year Prospective Test of Seismic Gap and Null (Poissonian Smoothed Seismicity) models Rank zones by decreasing probability of characteristic earthquake; accumulate area, predicted earthquake number, and actual earthquake number.

14. Shifted and stacked magnitude distributions for Nishenko’s seismic gap zones, before and after zones were selected Selection criteria favored zones with higher than average seismicity during learning period; that high seismicity did not persist during test period; magnitude distribution approximates Gutenberg Richter Learning period Test period

15. The Gutenberg-Richter magnitude-frequency distribution Number of events greater than magnitude 5 is about 10 times the number greater than 6, etc.

16. Myth: Earthquakes must be QP, because we observe too few short intervals • In most cases, intervals depend on RSD (choice of magnitude threshold, spatial window, etc.) • Short intervals should be rare anyway, even given Poisson or clustered events, because large events are rare. • Community seems to demand evidence of repeat rupture on same fault, even thought that is not required for evidence of “characteristic earthquakes.” (e.g., Nishenko & Buland, Nishenko 1991, Parkfield). • Even so, short intervals are observed: • YYK will show comprehensive study of nearby events (avoids RSD) • Evidence of early repeat rupture on same surface follows

17. California Geology, December 1979, Vol. 32, No. 12. EFFECTS OF IMPERIAL VALLEY EARTHQUAKE October 1979, Imperial County, California By CHARLES R. REAL, RICHARD D. McJUNKIN, EDDIE LEIVAS, California Division of Mines and Geology …1940-1979 COMPARISON There are striking similarities between the May 18, 1940, and October 15, 1979, Imperial Valley earthquakes. Although of lesser extent, the October 15, 1979, ground rupture followed the same trace as the 1940 event, and showed many of the same features and characteristics. Both ruptures appeared to have maximum lateral displacement near the International Border, and predominant vertical displacement near the Mesquite Depression east of Imperial. Activity shifted to the north with both events having damaging aftershocks near Brawley. Also, like the 1979 event there is evidence that the Brawley fault underwent sympathetic movement in 1940 (Sharp, 1976). The similarities also extend to the distribution and types of damage as described for the 1940 earthquake (Richter, 1959; Sylvester, 1979).

18. Imperial Fault, 1940 and 1979From Meltzner, Rockwell, and Verdugo, AGU Abstract, 2003 • 1940 m6.9, slip 5-6 m in central section, <1 m in northern section • 1979 m6.4 matched slip in northern section (20 – 30 km); no slip in central or south section • Central section slipped in ~1680, 1940,==> Tbar = 260 yr, v = 20 mm/yr • North section slipped 4 – 5 times since ~1680, ==> Tbar> (1979 – 1680)/4 = 74 yr, v < 14 mm / yr • dT/Tbar < (1979-1940) / 74 = 0.53

19. JGR, VOL. 104, PAGES 23,111–23,126, 1999 • Noncharacteristic behavior and complex recurrence of large subduction zone earthquakes • Susan Y. Schwartz, University of California, Santa CruzAbstract • ... plate boundary segments that failed in • the 1957 (Mw=8.6), 1986 (Mw=8.0), and 1996 (Mw=7.9) Aleutian Islands • (2) the 1963 (Mw=8.5) and 1995 (Mw=7.9) Kuril Islands earthquakes; • (3) the 1971 (Mw=8.0) and 1995 (Mw=7.7) Solomon Islands earthquakes; • (4) the 1968 (Mw=8.2) and 1994 (Mw=7.7) northern Honshu earthquakes. … The 1994 northern Honshu and 1995 Solomon Islands earthquakes primarily fill in areas of slip deficit left by their preceding events …. The 1995 Kuril Islands and the 1996 Aleutian Islands earthquakes both rerupture portions of an asperity distribution defined by preceding events but with variable amounts of slip. … Recurrent fault slip … does not support characteristic slip models either where failure on an entire fault segment occurs repeatedly in events with nearly identical rupture lengths, locations, and slip magnitudes or where failure of individual asperities occurs with identical slip functions through consecutive earthquake cycles.

20. Myth: Earthquake catalog is a “snapshot” not useful for constructing or testing a source model • Earthquake rate becomes more stable for longer times and larger areas. • Empirically, a century seems adequate for California • If the big earthquakes (1857, 1906) affect subsequent rates, they don’t invalidate use of the catalog to test statewide models.

21. Stationarity of California Earthquakes

22. Predicting second half of “Coastal California” catalog from first half

23. Quasi-prospective test of 1988 and 1990 WG estimates

24. Alternatives • Constant rate characteristic earthquakes • Coulomb stress, Rate-state models on sections: needs test! • Clustering models • Some versions tested in SW, NW Pacific • Can provide focal mechanism predictions • Quakes may need to be “migrated” to faults

25. Conclusions • No decent quasi-periodic model has survived a comprehensive prospective test. A strategy for testing is sorely needed. • Most of the data supporting quasi-periodic behaviour depends on Retrospectively Selected Data • There is no consensus on what should be QP; QP paleo ~=QP earthquakes • There is evidence of early recurrence! • QP models can be tested (weakly) using “clock rollback”. • Best alternative is power law clustering model

26. Estimating Earthquake Probabilities • Historical approach: f(m)future=f(m)past • Moment balance approach • Tectonic moment in equals earthquake moment out

28. Seismic moment balancemLWvt = Si(mAidi) d = v * t d2 d3 d1 W d4 L

29. Bulletin of the Seismological Society of America, Vol. 78, No. 2, pp. 636-650, April 1988 SPATIAL DISTRIBUTION OF TURN-OF-THE-CENTURY SEISMICITY ALONG THE ALASKA-ALEUTIAN ARC BY THOMAS M. BOYD* AND ARTHUR L. LERNER-LAM 1964 1938 1946 1957 1965 1986

30. Seismic Gap Model 1, McCann, Nishenko, Sykes, and Kraus, 1979

31. Old #3

32. New #3

34. ____________________________________________________________________________________________________________ _ ___________________________________________________________________________________________________________ Table 5.2. Recurrent Earthquake Sequences and Their Estimated Parameters for the Brownian Passage Time Model _ ___________________________________________________________________________________________________________ _ ___________________________________________________________________________________________________________ Location M Last N µ α µ0.5 Reference _ ___________________________________________________________________________________________________________ Copper River Delta, USA 9.2 1964 9 683 0.23 753 Plafker and Rubin, 1994. Willipa Bay, USA 9.0 1700 7 526 0.53 530 Atwater and Hemphill-Haley, 1997. Wairarapa fault, N.Z. 8.2 1855 5 1551 0.18 1355 Van Dissen and Berryman, 1996. Nankaido, Japan 8.1 1946 9 158 0.40 166 Ishibashi and Satake 1998. Tonankai, Japan 8.1 1944 7 210 0.75 192 Ishibashi and Satake 1998. Pallett Creek, USA 7.8 1857 10 146 0.97 115 Sieh et al., 1989. Wrightwood, USA 7.8 1857 6 150 0.71 138 Biasi and Weldon, 1998. Pitman Canyon, USA 7.8 1812 6 180 0.96 144 Seitz, Weldon and Biasi, 1997. Miyagi-Oki, Japan 7.5 1978 11 36 0.27 40 Utsu, 1984. Brigham City, USA 7 -130 6 1476 0.31 1645 McCalpin and Nishenko, 1996. Tanna fault, Japan 7.0 1930 7 972 0.65 866 Tanna Fault Trenching Research Group, 1983. Irpinia fault, Italy 6.9 1980 5 2058 0.58 2042 Pantosti et al., 1993. Parkfield, USA 6.4 1966 6 25.0 0.44 26.5 Bakun and Lindh, 1995. Stone Canyon (San Andreas fault) - Set 2 5.0 1995 4 14.6 0.40 18.6 Ellsworth, 1995. - Set 3 4.7 1986 3 20.3 0.37 24.4 " - Set 1 4.2 1995 5 14.7 0.29 16.2 " - Set 10 4.1 1995 7 10.2 0.25 11.3 " - Set 5 4.0 1990 6 10.6 0.32 12.4 " - Set 8 4.0 1990 5 12.3 0.35 14.7 " - Set 9 4.0 1990 5 13.0 0.42 14.7 " Parkfield (San Andreas fault) - PK1 1.4 1994 9 1.12 0.16 1.25 Ellsworth, 1995. - S46 0.9 1993 5 1.3 0.22 1.5 Nadeau and Johnson, 1998. - S44 0.9 1995 6 1.7 0.24 1.9 " - S40 0.8 1995 5 1.6 0.23 1.8 " - S39 0.7 1993 7 0.99 0.55 0.99 " - S35 0.7 1994 5 1.8 0.26 2.0 " - S34 0.6 1993 5 1.6 0.47 1.7 " - S33 0.5 1992 5 1.4 0.87 1.2 " - S27 0.5 1992 9 0.54 0.62 0.52 " - S25 0.4 1996 6 1.6 0.43 1.7 " - S22 0.4 1992 5 0.83 0.43 0.87 " - S21 0.3 1995 8 1.1 0.50 1.2 " - S20 0.3 1995 6 1.5 0.59 1.5 " - S18 0.3 1992 5 1.3 0.33 1.4 " - S07 0.0 1992 9 0.64 0.11 0.72 " - S05 -0.1 1995 13 0.73 0.32 0.78 " - S01 -0.7 1995 9 0.95 0.40 1.0 " _