Forecasting Magnitude from Fault Geometry

Bill Ellsworth, USGS Menlo Park, CA

Magnitude – Area RelationsM = log(A) + k

• Wells and Coppersmith (W&C, 1994) widely used in hazard analysis.

• Good agreement between W&C and kinematic rupture models derived from seismic waves.

• Application of W&C to WG02 fault model overpredicts historical seismicity rate.

• WG02 adopted 3 relations for large earthquakes:

M = 3.98 + 1.02 log(A) (W&C) M = 4.2 + log(A) (Ellsworth) M = 3.03 + 4/3 log(A) (Hanks & Bakun)

where A = Length x Width x R (seismic coupling factor)

• Length (L): easy• Width (W): difficult;

disagreement between seismic and geodetic rupture models

• Aseismic slip factor (R): shallow creep – do-able; brittle-ductile transition – hard

• Trade-off between W and R: M = log(L) + log(WR) + k

Magnitude – Area RelationsM = log(LWR) + k

M(A) and the Earthquake Cycle

Seismologists observethe coseismic rupture

M = log(LW) + k

Forecast modelsmust account for the

total slip budget

M = log(LWR) + k

In this exampleR = 0.7

orlog(R) = -0.15

If the coseismic ruptureis described by

M = log(LW) + 4.0

the forecast rupture is

M = log(LWR) + 4.15

WG02 Approach to Determining W and R

Define W as the depth of the brittle-ductiletransition determinedfrom seismicity andthermal data

Use geodetic data to determine R given W

Depth of Seismicity and Depth to Brittle-Ductile transition in the San Francisco Bay Area

Colin Williams USGS, Menlo Park

WG02 Fault L, W and R Values

R factor accounts for creep but not for aseismicslip at the brittle-ductile transition

If great earthquakes rupture into the brittle-ductiletransition W and R will be incorrect

2002 Mw 7.9 Denali Fault, Alaska Earthquake

Denali Aftershocks LocationsRathkoviski et al.

East (km)

No

rth (

km

)

-20 -10 0 10 20

-20

-10

010

20

1 m

Near-Fault Displacements from GPS Surveyand Rupture Depth of a Uniform Dislocation

Distance to Denali Fault (km)

Fau

lt P

ara

lle

l S

lip

(m

)

-20 -15 -10 -5 0 5 10 15

-3-2

-10

12

3

Displacement (m)

De

pth

of

Fau

ltin

g (

km

)

3 4 5 6 7 8 9

51

015

20

0.90.99

Best model: 5.95 m slip from 0 to 11.6 km

Fault displacement vectors along the

Trans-Alaskan Pipeline

Comparing Depth of Rupture EstimatesObtained from Geodesy and Seismology

Depth range ofseismic rupture models

Depth range ofgeodetic models

Concluding Remarks

• Different approaches to the definition of W lead to different M(A) relations.

• The trade-off between W and R will be difficult to resolve with available data.

• The discrepancy between M(A) relations derived from earthquake slip models and those derived from earthquake cycle considerations can be explained by the R-factor.

• If rupture in large magnitude earthquakes routinely extends below the depth of complete locking the R-value in the current Working Group model will need to be modified if the W&C relation is used.