Chapter 7 Earthquake prediction and hazard analysis

San Francisco 1906 - George R. Lawrence

Earthquake prediction

Is earthquake prediction possible?

Short-term prediction: 1. A system in a state of self-

organized criticality. Earthquake occurrence is too random and chaotic to be predictable on the short timescale.

2. Misunderstands the nature of chaos and complexity, which does not imply complete unpredictablity or randomness, but that predictability will eventually be lost over long enough timescales, just as in weather prediction.

Canonical sandpile model of self-organized criticality (SOC)

Earthquake prediction

1.Rethinking Earthquake Prediction. ""Sykes, L.R., Shaw, B.E. and Scholz, C.H., 1999. Pure Appl. Geophys., 155: 207-232.2. ?Christopher Scholz, March 1997, Geotimes, pp. 16-193. 3. Earthquake Prediction in China: From Haicheng to Wenchuan (:)4. Working Group Approach to Modeling Earthquake Probabilities

Precursory phenomena

1. Preinstrumental observations2. Intermediate-term precursors

a. Seismicity patternsb. Crustal deformationc. Seismic wave propagationd. Hydrological and geochemicale. Electrical and magnetic

3. Short-term precursorsa. Seismicity (foreshocks)b. Crustal deformation

Crustal uplift that preceded earthquakes in Japan

1. the Adigasawa earthquake of 1793, in which the land rose 1 m 4 h before the earthquake;

2. the Sado earthquake of 1802, in which there was also a 1-m uplift 4 h prior to the earthquake;

3. the earthquake at Hamada in 1872, where a 2-m uplift preceded the earthquake by 1520 min;

4. the Tango earthquake of 1927, preceded by a 1.5-m uplift h before the earthquake.

Imamura, 1937

Various patterns of seismicity during the seismic cycle

Mogi, 1985; Scholz, 1988

Aftershocksequence A

Principal rupture

Postseismic period of quiescence Q1

5070% of the recurrence period T Increase in

background seismicity B

intermediate-term quiescence Q2

short-term quiescence Q 3.

Short-term precursors: F and Q3Intermediate-term precursors: patterns B, D, and Q2

doughnut pattern D

Seismicity of the Oaxaca, Mexico, region

Ohtake et al., 1981

quiescence

Seismic quiescence before 1999 Chi-Chi

earthquake

Wu and Chiao, BSSA, 2006

Seismic quiescence before 1999 Chi-Chi earthquake

Wu and Chiao, BSSA, 2006

ZMAP method (Wiemerand Wyss, 1994)

Rall, Rcal: mean seismicity ratenall, ncal: number of samples in these periods

Z-value ranges from -3.37 to 6.75

Z-value ranges from -2.42to 4.92

positive Z-value: decreasein seismicity

negative Z-value: rise in seismicity.

Duration ofintermediate-term

quiescencesplotted as a

function of themagnitude of the

shock that followed

Open symbols:Kanamori, 1981

Solid symbols:Wyss and Habermann, 1988

Crustal deformationNiigata () earthquake of 1964 (M7.5): west-dipping reverse faultSea of Japan earthquake of1983 (M 7.7)

uplift

Mogi, 1985

2007 Chuetsu-okiearthquake()

Nishimura et al. EPS, 2008

2007 Niigata-ken Chuetsu-oki Earthquake (NCOE) () and Kashiwazaki-Kariwa nuclear power plant (-)

http://www.jsm.or.jp/ejam/

Tokyo Electric Power Company , Tepco

Slow uplift prior to the Sea of Japan earthquake of 1983

May 26

Mogi, 1985

Tide gauges

Oga Peninsula

The May 26, 1983, Japan Sea Earthquake (Ms7.8)

Leveling surveys indicated 2 cm uplift on the Ogapeninsula during the periods 19691977 and 19771981, and 4 cm uplift on the Fukaura peninsula between 1975 and 1981.

GJM recorded 86 anomalous strain events, with amplitudes of 1030 nanostrain and durations of about 3 h, in the 6 months remaining before the mainshock (Linde et al. 1988).

Roeloffs, 2006, Annu. Rev. Earth Planet. Sci.

The May 26, 1983, Japan Sea Earthquake (Ms7.8)

Foreshocks (M > 5) occurred 612 days prior to the mainshock, near the hypocenter (Mogi 1985).

entailing 5.7 m total preseismic slip on downdipextensions of the coseismicrupture planes, 4 m of this within a few minutes prior to the earthquake.

Slip accelerated from 25mm/year, 7.8 years prior tothe earthquake, to 10 mm/sin the last few minutesbefore the earthquake,

Roeloffs, 2006, Annu. Rev. Earth Planet. Sci.

Anomalies Vp/Vs prior to the earthquakes

Aggarwal et al., 1973

A reductionin the ratio VP/VS of compressional and shear velocities prior to anumber of earthquakes near Garm, in Tadjikistan (Semenov, 1969).

VP/VS ratio decreased by1015% within a zone surrounding the rupture

Magnitude of hydrological precursors as a function of epicentral distance

Roeloffs, 1988

Radon Anomaly: A Possible Precursor,1978 IzuOshima-kinkai earthquake

Wakati et al., Science,1980

Records of intermediate to short-term precursors to the 1978 IzuOshima-kinkai

earthquake

Wakita, PNAC, 1988

Foreshock swarms followed by short-term quiescences before three

earthquakes in the Izu Peninsula

1978 IzuOshima-kinkai earthquake

(Sagami Bay)

Synopsis of the short-term tilt: Leveling just prior to the 1944 Tonankai

earthquake on the Nankai trough, Japan

Mogi, 1985

Mechanisms of precursory phenomena

Physical models of precursory phenomena, two broad categories:(a) Nucleation models & Lithospheric loading models: fault

constitutive relations, which predict fault slip behavior but no change in properties in the material surrounding the fault;

(b) Dilatancy models: based on bulk rock constitutive relations, which predict physical property changes in a volume surrounding the fault.

Nucleation models Nucleation: The growth of the slipping patch up to the point of

instability This process is therefore a potential mechanism for generating

earthquake precursory phenomena Crack and friction models both predict that instability will not

occur until slip has occurred over a fault patch of a critical radius, which is a function of the fault strength, state of stress, and elastic constants of the surrounding rock

21

2( )

cc

f

L

021

( )( )

y fc

f

L d

Expressions for this critical radius: Equations (4.13), (2.34), and (4.15) for crack, friction-slider, and hybrid crackmodels, respectively

Nucleation models: friction-slider (2.34) For a 2- or 3-dimensional case:

Stiffness is inversely proportional to a length scale

If slipping region is treated as an elliptical crack

22 1EK

L

Stability transition takes

place at a critical value of L

22 1c

cn

EDLb a

Stable sliding: occur in a nucleation stage until the slipping region grows to Lc & the instability occurs

Nucleation process is of considerable interest in earthquake prediction theory

E: Youngs modulus: Poissons ratioL: length of the slipping region

Nucleation models: Crack radius as a function of time

Stress-corrosion mechanism: The crack is found to extend, subcritically, at stress intensity factors much below KIc, with a well-defined relationship between K & v, the crack-tip velocity

Assumption: under slow loading conditions, a crack first begins to propagate subcritically because of a stress-corrosion-type process

Instability: because K increases with crack length, & the crack-tip velocity increases exponentially with K

nIAK

0 exp( )Iv bK

n is called the stress-corrosion index

Crack-tip Velocity & Stress Intensity Factor I area, 0: (crack blunting or healing)stress corrosion limit: very hard to

demonstrate experimentally because ofthe very low crack velocities involved

(typically < 10-9 m s-1).1. Atkinson (1984): 0.2 c II area:1. -v relation: 2. Rate of crack-tip advance: controlled by

the rate of a stress-enhanced chemical reaction at the crack tip (e.g., hydration of the SO bond)

III area:1. Rate is controlled by diffusion of the

reactive species to the crack

nIAK

2 2Si O Si H O x SiOH

Nucleation models

Slip as a function of time, from a friction slider model of nucleation

Very strong accelerationo f fault slip just prior to instability: possibility of detecting precursory phenomena resulting from nucleation will be significant only for a short period before the earthquake.

Nucleation modelsDependence of time to instability on the stress (friction) jump

Nucleation models Nucleation is an essential part of the instability, if it can be detected by

geophysical means, short-term earthquake prediction may become a reliable possibility.The crucial questions: how large is the nucleation zone & what is the slip in it.

Dieterichs model indicates that both the nucleation slip & the critical patch radius depend linearly on Dc, the critical slip distance, & so the nucleation moment depends on its cube.

Dc cannot exceed a value of about 100 mm or the fault behavior will become stable

Dc will decrease with depth, & will be in the range 110 mm at seismogenic depths

Summary: Nucleation models Very strong acceleration of fault slip just prior to instability:

possibility of detecting precursory phenomena resulting from nucleation; only for a short period before the earthquake.

Timescales are such that nucleation is a potential mechanism for short-term precursors, but not for those of intermediate term.

If a fault has a uniform value of Dc, then it could not produce earthquakes smaller than the nucleation moment corresponding to that value of Dc.

Such a lower cutoff in earthquake size is not observed, so Dcmust be spatially variable

If Dc is variable, then nucleation sizes will also be variable, which makes their detection, & predictions less reliable.

Dilatancy models: velocity anomalies

saturated fraction

crack density

Dilatancy models: velocity anomalies

a, b: Westerly granite, triaxial compression at a constant strain rate c: San Marcos gabbro (lower hydraulic diffusivity)d: Westerly granite with CO2 as the pore fluid

Various phenomena predicted by the dilatancy diffusion model

Scholz et al., 1973

Lithospheric loading models

Rudnicki, 1988

Simple slip-weakening constitutive laws was used to describe the fault behavior in these modelsInstability: but unlike the ratestate-variable friction laws they do not contain a mechanism for the rehealing of the fault

Lithospheric loading models

Rudnicki, 1988

(c) Stiffness line: intersecting the constitutive law at B, is marched along at the rate of imposedslip at the load point L

(d) A case where motion is always stable

(e) An instability point I is reached

(f) Why slip of the block, B, ccelerates as L increases steadily

Lithospheric loading models

Stuart, 1988

Lithospheric loading model employing ratestate-variablefrictions

Crustal deformation predictedthrough a seismic cycle at various sites adjacent to a thrust boundary

X is distance from the surface outcrop of the thrust

Instability 1 represents the prior EQ

Empirical precursor time magnitude relation

Scholz et al., 1973

The line through the data is consistent with the precursor timebeing diffusion controlled with adiffusivity of 104 cm2 s-1.

Earthquake hazard analysis

1. Straightforward goal of earthquake prediction research is to estimate the hazard presented by earthquakes.

2. Related to long-term prediction: when carried out thoroughly for a region, provides a basis upon which seismic hazard can be assessed and expressed in probabilistic terms.

Traditional methods1. Seismic hazard maps: Representations of the past historic

and/or instrumentally recorded seismicity of a region, which may be indicated by maps of intensity distributions or contours of elastic energy release.

2. Assumption: Future seismicity will be the same as past activity3. Problem: incompleteness of geographical & temporal

coverage in the record & a lack of identification of a time datum upon which to base the hazard estimation

4. Giving an erroneous picture of present-day hazard: (a) A quiet zone on such a map, representing low hazard, may

delineate a seismic gap & be a place of high present hazard.(b) A region experienced a damaging earthquake: is represented

as high hazard on the map, actually may be a region of low hazard in the near future because it is now at an early stage in a new seismic cycle

Frequencymagnitude relation

1. Attempts to mitigate the effects of incomplete data coverage.2. Recording small earthquakes in a region, and then

extrapolated to calculate the recurrence time of potentially damaging earthquakes of larger magnitude.

3. Problem: large potentially damaging earthquakes belong to a different fractal set than small earthquakes & cannot be predicted with this extrapolation

4. Improvement: It is only for a very large region that contains many active faults that this extrapolation will give accurate results.

Remediation of incompleteness of the historic record

Incorporation of geological data on fault slip rates bolstered with dates of paleoseismic events determined by the excavation of faults.

0M

Youngs & Coppersmith, 1985

Remediation of incompleteness of the historic record

Schwartz & Coppersmith, 1984

Long-term hazard analysis

Open symbols: observed; Closed symbols: predicted from active fault data using the M0 max model;Stippled: predicted by the b value model Wesnousky et al., 1983

Seismicity of SW Japan for the last 400 y

Analysis of instantaneous hazard Long-term hazard analysis gives the average probability of shaking for

some arbitrary time interval T. Giving the last date of rupture of each fault segment, then a time-

dependent assessment of hazard can be made that takes into account the cyclicity of rupture

Assume a probability density function for recurrence time, f(T). The probability that an earthquake will occur at some time t in some

interval (T, T+T) is then:

If the date of the previous earthquake is known, we can determine the conditional probability that the earthquake will occur in the next interval (T, T+T), provided that it has not occurred in the time T since the last earthquake

|

Survivor function:T()

(Conditional probability):T,(T)/

(hazard function):t,t( f(t)/ )

T T+T

Long-term seismic hazard of Japan

The maps give the probability of shaking at JMA intensity 3V, from all sources, during the next 20, 50, 100, and 200 y.

Wesnousky et al., 1984

Probabilistic Seismic Hazard Maps (PSHM)

Exceedance probability within 30 years considering all earthquakes (JMA seismic intensity: 6 Lower or more; average case; period starting Jan. 2010)

Illustration of instantaneous seismic hazard analysis

The conditional probability of rupture of various segments of the San Andreas and other major faults in California. (From Working Group on California Earthquake Probabilities, 1988.)

Working Groups on California Earthquake Probabilities

They generally segmented faults and applied elastic-rebound-theory-motivated (quasi-periodic) renewal models to define time-dependent earthquake probabilities

(WGCEP, 1988, 1990, 1995, 2002)

EQ

Time

EQ EQEQ

Reids (1910) Elastic Rebound Hypothesis:

Ned Field, USGS

Reids (1910) Elastic Rebound Hypothesis

PerfectlyPeriodic

Lognormalor

BPT distribution

Ned Field, USGS

WGCEP 1988

They divided the San Andreas, San Jacinto, Hayward, and Imperial Faults into segments and assumed each ruptures only in a single-magnitude (characteristic) earthquake.

Ned Field, USGS

WGCEP 1988

COVI = 0.2Mean Recurrence Interval from:(1) Ave. of those observed previously.(2) Slip in last event divided by slip rate.(3) Ave. slip divided by slip rate.

Ned Field, USGS

UCERF: Map of Earthquake Probabilities, Major California Faults

The bar graph compares the 30-year probabilities of magnitude 6.7 or greater quakes for seven of the faults with the best data (numbered on the map).

The fault with the highest probability is the southern San Andreas (59% in the next 30 years).

For northern California, the most likely source of such earthquakes is the Hayward-Rodgers Creek Fault (31% in the next 30 years).

http://www.scec.org/ucerf2/

UCERF report assigns individual probabilities to major faults

Global seismic hazard map

Shedlock et al. (2000)

Global map of brittle strain rate in intraplate regions. (From Triep and Sykes, 1997.)

This map shows the peak ground acceleration, in meters per second squared with a 10% chance of exceedance in 50 y.

Future prospects & problems

1. Intrinsic standard deviation D: reflects the basic aperiodicity of earthquake recurrence, is a fundamental barrier to precise longtermprediction

2. Fault segmentation models are presently rules of thumb, & the models of fault segmentation that go into such ISHA analyses are little more than enlightened scenarios

3. The application of ISHA degenerates when applied to intraplateregions. Because the standard deviation of recurrence time scales with recurrence time, probabilities will be reduced and the prediction windows lengthened for the slower-moving faults in those regions

4. Fate of intermediate- and short-term earthquake prediction remains far from certain: to detect immediateterm precursors one needs to identify a soon-to-rupture gap & to make close-in measurements.

5. If short-term prediction depends entirely on detecting nucleation, then the probable nucleation zone within the gap also needs to be identified & instrumented, a far more exacting requirement