Forecasting Magnitude from Fault Geometry Bill Ellsworth, USGS Menlo Park, CA

Magnitude – Area Relations M = 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 = log(A)(W&C) M = log(A)(Ellsworth) M = /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 Relations M = log(LWR) + k

M(A) and the Earthquake Cycle

Seismologists observe the coseismic rupture M = log(LW) + k

Forecast models must account for the total slip budget M = log(LWR) + k

In this example R = 0.7 or log(R) = -0.15

If the coseismic rupture is described by M = log(LW) the forecast rupture is M = log(LWR)

WG02 Approach to Determining W and R Define W as the depth of the brittle-ductile transition determined from seismicity and thermal 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 aseismic slip at the brittle-ductile transition If great earthquakes rupture into the brittle-ductile transition W and R will be incorrect

2002 Mw 7.9 Denali Fault, Alaska Earthquake

Denali Aftershocks Locations Rathkoviski et al.

Near-Fault Displacements from GPS Survey and Rupture Depth of a Uniform Dislocation Best model: 5.95 m slip from 0 to 11.6 km Fault displacement vectors along the Trans-Alaskan Pipeline

Comparing Depth of Rupture Estimates Obtained from Geodesy and Seismology Depth range of seismic rupture models Depth range of geodetic 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.