6, since 1973) Mean rate of M>9.5 = 10 ( ) = yr -1 (return period 23.4 years) Probability of zero M>9.5 earthquakes in 107 years P(N=0 | M>9.5,T=107) = exp( x 107) = 0.01 Conclusion: These probabilities are small. Mc = 9.5 is a useful estimate for the Global Mmax. Probability of zero M>9.5 events in 50 years exp( x 50) = 0.11 Figure A5–3">

# Mmax and the Maximum Catalog Magnitude Martin Chapman Department of Geosciences Virginia Tech Blacksburg, VA 24061 Mmax Workshop Golden, Colorado.

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Mmax and the Maximum Catalog Magnitude Martin Chapman Department of Geosciences Virginia Tech Blacksburg, VA 24061 mcc@vt.edu Mmax Workshop Golden, Colorado September 8-9, 2008 Figure A5–1

sources: NEIC PDE catalog M>6.0, since 1973 NEIC list of significant earthquakes, since 1900 Figure A5–2

Is the absence of events with M greater than 9.5 in the global catalog significant? (i.e., is the maximum catalog magnitude Mc = 9.5 a "useful" estimate for the global Mmax, in the context of our standard PSHA model?) Assumptions:1) Poisson Process 2) Log N = 8.13 - M, (data for M > 6, since 1973) Mean rate of M>9.5 = 10 (8.13-9.5) = 0.0427 yr -1 (return period 23.4 years) Probability of zero M>9.5 earthquakes in 107 years P(N=0 | M>9.5,T=107) = exp(-0.0427 x 107) = 0.01 Conclusion: These probabilities are small. Mc = 9.5 is a useful estimate for the Global Mmax. Probability of zero M>9.5 events in 50 years exp(-0.0427 x 50) = 0.11 Figure A5–3

Can we infer useful information about Mmax from Mc in sub-regions of the Earth? It depends on N, and the length of time over which the catalog for a given sub-region can be considered complete. Figure A5–4

mblg > 0.0, 1977 - 2005 Figure A5–5

source: SEUSSN catalog Figure A5–6

Eastern Tennessee Seismic Zone Maximum catalog magnitude M=4.6 (2003, Ft. Payne, AL) (mblg 4.8) Figure A5–7

Is mblg=5 a useful estimate for Mmax in the Eastern Tennessee Seismic Zone? Assume that the catalog is complete to 1870 ( T=138 years,) P (N=0|mblg>5.0,T=138) = exp(-0.00758 x 138) = 0.35 Complete to 1840: P = 0.28 Assume Log N = 3.23 - 1.07mblg: mean rate for mblg>5.0, N(5.0) = 0.00758 yr -1 return period = 132 years How long would the catalog have to be complete, for the absence of mblg>5.0 to be significant: i.e., P=0.1 or less (as in the case of M 9.5 for the Earth)? T = -ln(0.1) / 0.00758 = 303 years Conclusion: For the maximum catalog magnitude (mblg 5.0) to be a "useful" estimate of Mmax, the catalog would have to be complete for mblg > 5.0 to 1705. The earliest recorded shock in the region was in 1777. Figure A5–8

The maximum catalog magnitude Mc provides information on Mmax. In fact, given no other information, it provides the best estimate (under the assumptions made here). Unfortunately, unless the product of N(Mc), and T, the time period of catalog completeness, is such that e [-N(Mc) x T ] is a significantly small number, the estimate will not be reliable. Summary Figure A5–9

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