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

the alternatives?David D. Jackson

Department of Earth and Space Sciences

UCLA

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;

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

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?

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.

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?

BSSA, August 1987; v. 77; no. 4; p. 1347-1358, 1987Quasi-periodic occurrence of earthquakes in the 1978-1986 Bishop-Mammoth Lakes sequence, eastern California J. C. SAVAGE and ROBERT S. COCKERHAM, USGSAbstract… 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.

A new probabilistic seismic hazard assessmentfor greater Tokyo,

BY ROSS S. STEIN, SHINJI TODA, TOM PARSONS, AND ELLIOT GRUNEWALDIn press, Phil. Trans. R. Soc. A.

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

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.

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

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

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

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).

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

JGR, VOL. 104, PAGES 23,111–23,126, 1999 Noncharacteristic behavior and complex recurrence of large

subduction zone earthquakesSusan Y. Schwartz, University of California, Santa Cruz

Abstract... plate boundary segments that failed in (1) 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.

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.

Stationarity of California Earthquakes

Coastal California

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1850 1875 1900 1925 1950 1975 2000

Year

Cu

m.

Fra

ctio

n

M5.25+

M5.75+

M6.25+

M6.75+

M7.25+

M7.75+

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

Mag 1850-1925 1926-2000 lower upper5.25+ 113 123 92 1345.75+ 83 62 65 1016.25+ 34 29 23 466.75+ 11 12 6 187.25+ 4 3 1 77.75+ 2 0 0 4

Fault Segment First Last Mc Mthd. Texp Present Elapsed since firstP130SAF North Coast 1906 1906 8 Dir 228 1990 84 0.002SAF SF Peninsula 1906 1906 7 Dir 136 1990 84 0.083SAF S. Sta Cruz Mtns 1906 1906 7 Dir 91 1989 83 0.231SAF S. Sta Cruz Mtns 1906 1989 7 Dir 91 1990 84 0.000SAF Parkfield 1857 1966 6 Hist 21 1988 131 0.604SAF Cholame 1857 1857 7 Dir 159 1988 131 0.459SAF Carrizo 1857 1857 8 Dir 296 1988 131 0.022SAF Mojave 1857 1857 7.5 Dir 162 1988 131 0.380SAF San Bern Mtns 1812 1812 7.5 Dir 198 1988 176 0.543SAF Coachella 1680 1680 7.5 Geol 256 1988 308 0.898Hwd. N. E. Bay 1836 1836 7 Dir 209 1990 154 0.500Hwd. S. E. Bay 1868 1868 7 Dir 209 1990 122 0.321SJF San Ber Val 1890 1890 7 Dir 203 1988 98 0.154SJF San Jac Valley 1918 1918 7 Dir 184 1988 70 0.047SJF Anza 1892 1892 7 Dir 142 1988 96 0.293SJF Borrego Mtn 1968 1968 6.5 Dir 189 1988 20 0.000Imp. Imperial 1940 1940 6.5 Dir 44 1979 39 0.487Imp. Imperial 1940 1979 6.5 Dir 44 1988 48 0.001R.C. Rodgers Creek 1808 1808 7 Dir 222 1990 182 0.333SAF Mid Peninsula 1906 1906 7 Dir 147 1990 84 0.145SAF N. Sta Cruz Mtns 1906 1906 6.5 Dir 95 1990 84 0.414

Expected number 5.917Poisson Probability 0.066

Quasi-prospective test of 1988 and 1990 WG estimates

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

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

Estimating Earthquake Probabilities

• Historical approach: f(m)future=f(m)past

• Moment balance approach– Tectonic moment in equals earthquake moment out

mmagnitudeofmomentseismicM

mmagnitudeoffrequencymf

rateslipV

widthfaultW

lengthfaultL

rigidity

dmmMmfLWV

o

o

____

___)(

_

_

_

)()(

Southern CaliforniaM>4

0

200

400

600

800

1000

1200

1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010

Date

Cu

mu

lati

ve

nu

mb

er

of

qu

ak

es

Seismic moment balanceLWvt = i(Aidi)

d = v * t

W

L

d1

d3

d4

d2

Bulletin of the Seismological Society of America, Vol. 78, No. 2, pp. 636-650, April 1988SPATIAL DISTRIBUTION OF TURN-OF-THE-CENTURY SEISMICITYALONG THE ALASKA-ALEUTIAN ARCBY THOMAS M. BOYD* AND ARTHUR L. LERNER-LAM

1938

1964

1946195719861965

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

Old #3

New #3

Fault Length Scaling, Global Earthquakes

1

10

100

1000

5.0 6.0 7.0 8.0

Mw

Le

ng

th,

km

Wells & Coppersmith

Pegler & Das