Chapter 4: The SFBR Chapter 4: The SFBR Earthquake Source Model: Earthquake Source Model: Magnitude and Long-Term Magnitude and Long-Term

RatesRates

Ahyi Kim 2/23/07 EQW

SFBR Earthquake Source ModelSFBR Earthquake Source Model

SFBR earthquake model SFBR earthquake model

SizeSize

LocationsLocations

MagnitudeMagnitude

Long-term recurrence rateLong-term recurrence rate

Earthquake: fixed, floating and back groundEarthquake: fixed, floating and back ground

Constructed from variety of geologic, Constructed from variety of geologic, geodetic and seismic datageodetic and seismic data

OutlineOutline

Compute rate of characterized earthquake, γCompute rate of characterized earthquake, γcharchar

Long-term occurrence rate and intervalLong-term occurrence rate and interval Evaluating the SFBR modelEvaluating the SFBR model

iochar

charioichar

M

FM

Introduction: Calculating Rupture Source Rates Introduction: Calculating Rupture Source Rates in Complex Modelin Complex Model

If each segment act as independent rupture source, the rate of earthquaIf each segment act as independent rupture source, the rate of earthquake, γwill be ke, γwill be

Long-term moment Long-term moment release rate of segmentrelease rate of segment

Mean moment of Mean moment of earthquakesearthquakes

However, SFBR model allows segments to fail in combinationHowever, SFBR model allows segments to fail in combination

Char: characterized rupture sourceChar: characterized rupture source

Fchar: fraction of seismogenic momFchar: fraction of seismogenic moment rate expended in characterized ent rate expended in characterized eq eq

Steps in the calculation sequenceSteps in the calculation sequence

Eq. 4-2aEq. 4-2a

Estimating the magnitudes and moments of Estimating the magnitudes and moments of earthquakesearthquakes

Mean characteristic Magnitude: M-logA relationsMean characteristic Magnitude: M-logA relations

Wells and Coppersmith(1994)Wells and Coppersmith(1994)

Regression of 83 continental eqRegression of 83 continental eq

WG99 4-5a and 4-5c: 95% bound WG99 4-5a and 4-5c: 95% bound of 4-5bof 4-5b

Hanks and Bakun(2001) : based on constant stress drop soHanks and Bakun(2001) : based on constant stress drop source scaling. For 7<M, L-model scaling of average fault slip Uurce scaling. For 7<M, L-model scaling of average fault slip U=αL, α=2E-5=αL, α=2E-5

4-6a4-6a

4-6b4-6b

4.44.4

4-5a4-5a

4-5b4-5b

4-5c4-5c

Comparison of candidate M-logA relationshipsComparison of candidate M-logA relationships

1906 San Francisco event1906 San Francisco event

(1)The 1906 eq is one instance in a global (1)The 1906 eq is one instance in a global dataset dataset

(2)1906 eq is the one of the event which is (2)1906 eq is the one of the event which is relevant to SFBRrelevant to SFBR

Weight of M-logA modelsWeight of M-logA models

Calculating mean momentCalculating mean moment

approximationapproximation

Estimating rupture source moment rates Estimating rupture source moment rates

Fault segment moment rateFault segment moment rate

μ=3E11dyne/cm^2μ=3E11dyne/cm^2

νν ： ： long-term slip rate (Table long-term slip rate (Table 3.8)3.8)

Regional slip rate constraintRegional slip rate constraint

Prescott et al. (2001): GPS data between 1992 and 2000 in central CaliforPrescott et al. (2001): GPS data between 1992 and 2000 in central California nia 39.8+-1.2mm/yr 39.8+-1.2mm/yr

Argus and Gordon (2001): GPS and VBLI Argus and Gordon (2001): GPS and VBLI 39+-2m/yr 39+-2m/yr

Long-term estimatesLong-term estimates

DeMets and Dixon (1999) and Prescott et al.(2001):global plate-motion moDeMets and Dixon (1999) and Prescott et al.(2001):global plate-motion models. 41+-1mm/yr dels. 41+-1mm/yr

Defining relative likelihoods of ruptureDefining relative likelihoods of rupture

Moment rate for each rupture source: product of Moment rate for each rupture source: product of available moment rate and the moment-balanced available moment rate and the moment-balanced factors, summed across all rupture scenariosfactors, summed across all rupture scenarios

Partitioning moment rate across earthquake Partitioning moment rate across earthquake typestypes FcharFchar

characteristic earthquake Fcharcharacteristic earthquake Fchar

Fractions of seismogenic moment rate aftershocks FafterFractions of seismogenic moment rate aftershocks Fafter

small earthquake Fsmallsmall earthquake Fsmall

Fchar + Fafetr + Fsmall = 1Fchar + Fafetr + Fsmall = 1

Seismic moment rate in aftershocksSeismic moment rate in aftershocks

Summed moment of aftershock=10% of main shock momentSummed moment of aftershock=10% of main shock moment

ButBut

This is because of some of very large aftershocksThis is because of some of very large aftershocks

If the large aftershocks are removed,If the large aftershocks are removed,

3+-2%3+-2%

Fafter = 0 Fafter = 0

Seismic moment rate in smaller earthquakesSeismic moment rate in smaller earthquakes

Magnitude-frequency distributions for faultsMagnitude-frequency distributions for faults

Pi(M>Mτ) is the probability that the Pi(M>Mτ) is the probability that the magnitude of rupture i is greater thamagnitude of rupture i is greater than the threshold valuen the threshold value

fmi(m) is the magnitude pdf for the fmi(m) is the magnitude pdf for the ith rupture sourceith rupture source

Background earthquakesBackground earthquakes

Based on Gutenberg-Richter distributionBased on Gutenberg-Richter distribution

For the 1951-1998(M>3)For the 1951-1998(M>3)

a=3.67(3.6-3.74 at 95% confidence)a=3.67(3.6-3.74 at 95% confidence)

b=0.89b=0.89

For the 1836-2001(M>5.5)For the 1836-2001(M>5.5)

a=3.94(3.62-4.3 at 95% confidence)a=3.94(3.62-4.3 at 95% confidence)

b=0.89b=0.89

Wesson et al.Wesson et al.

Results: Long-term earthquake rates in the SFBRResults: Long-term earthquake rates in the SFBR

Evaluating the SFBR Model (Regional comparisons)

M>6.7 0.031eq/yr b=1.02M>6.7 0.031eq/yr b=1.02

M<6.7 b=0.9M<6.7 b=0.9

Timing of Large EQ on SFBR faultsTiming of Large EQ on SFBR faults

Evaluating the SFBR Model (Fault-specific comparisons)

Comparison of SFBR model to other modelsComparison of SFBR model to other models

Frequency of events (6.7>M)Frequency of events (6.7>M)

Andrews and Schwere(2000) 0.0378/yrAndrews and Schwere(2000) 0.0378/yr

1 B=(2/3)b1 B=(2/3)b

SFBR model 0.031/yrSFBR model 0.031/yr

using eq1 in Andrews and Schwere(2000): 0.028/yrusing eq1 in Andrews and Schwere(2000): 0.028/yr

Using roll-off model: 0.043/yrUsing roll-off model: 0.043/yr