### Declustering, Rates, and b

```Decustering, Rates, and b-values
or
Declustering: the Necessary Evil of Statistical Seismology
Andy Michael
Gardner and Knopoff Declustering
Method:
Gardner and Knopoff (BSSA, 1974):
Magnitude-dependent spatial circles and time windows
Problem: Spatial circles too small for large earthquakes
Solution: Use radii based on fault rupture lengths from
Wells and Coppersmith (BSSA, 1994)
Christophersen et al. Declustering Radii Choices
SCSN M≥2 1984-2010 Radii = Uhrhammer ΔT = 1 day
Nmain=32490, p=0
SCSN M≥2 1984-2010 Radii = G-K ΔT = 1 day
Nmain=26992, p=3*10^-7
SCSN M≥2 1984-2010 Radii = G-K ΔT = 3 days
Nmain=19494, p=0.002
SCSN M≥2 1984-2010 Radii = G-K ΔT = 7 days
Nmain=12892, p=0.56
SCSN M≥2 1984-2010 Radii = G-K ΔT = 100 days
Nmain=1185, p=0.89
N=79661
N=13529
N=8124
Issues for UCERF3:
Decluster and then estimate rates or
Estimate rates using an ETAS model directly.
If declustering then which method or how many methods?
National Maps use Gardner-Knopoff which lowers b-value
ETAS uses the same b-value for background and clusters
Could decluster with a stochastic ETAS approach and maintain
the same b-value, good for ETAS but bad for National Maps
Could decluster with Gardner-Knopoff and then do ETAS
with a different magnitude-frequency distribution
that combines to the correct total distribution.
```