[CEUS-earthquake-hazards] CEUS earthquake hazards

[Wang, Zhenming]

Ellis,

Your concern on the b-value is actually the same as the ergodic assumption of Anderson and Brune (1999). The b-value is used to determine the temporal measure, the annual rate of earthquake exceeding a specific magnitude (M).  For a single characteristic earthquake (M7.7) with 500 years recurrence interval in the New Madrid seismic zone, the rate is fixed at 0.002 (1/500). But PSHA could derive a range of rate, 0.002 to infinite small, for the ground motions generated by this single M7.7 earthquake. The rate of ground motion exceeding (annual probability of exceedance) is equal to 0.002 (earthquake rate) times the exceeding probability of ground motion (P, ranging from 1.0 to infinite small). The ground motion uncertainty is a spatial measure. The return period is defined as the reciprocal of the annual probability of exceedance in PSHA. This example demonstrates that it is not the b-value being projected to a larger magnitude, but exceeding probability of ground motion being used to extrapolate the rate for ground motion.

Unfortunately, the return period of ground motion has been interpreted as "the mean (average) time between occurrences of a seismic hazard - for example, a certain ground motion at a site" (McGuire, 2004). Art also had a similar interpretation on the PSHA ground motion "the ground motion with 2% PE in 50 years is exceeded once, on average over 2,500 years, so that it has a 1/2500 annual probability of being exceeded" (Frankel, 2005).  These interpretations are clearly wrong.

Similarly, PSHA can derive a design M7 earthquake from two faults with M6 and M8 earthquakes by mixing temporal and spatial measures or so-called de-aggregation.

Thank

Zhenming

___________________________________
Zhenming Wang, PhD, PE
Head, Geologic Hazards Section
Kentucky Geological Survey
228 Mining and Mineral Resources Building
University of Kentucky
Lexington, Kentucky 40506
Phone:(859)257-5500x142
Email: zmwang at uky.edu<mailto:zmwang at uky.edu>
Website: www.uky.edu/KGS/geologichazards<http://www.uky.edu/KGS/geologichazards>
____________________________________

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