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.