Mmax and the Maximum Catalog Magnitude

Martin Chapman

Department of GeosciencesVirginia Tech

Blacksburg, VA 24061

mcc@vt.edu

Mmax WorkshopGolden, Colorado

September 8-9, 2008

Figure A5–1

sources:

NEIC PDE catalogM>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 Process2) 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 yearsexp(-0.0427 x 50) = 0.11

Figure A5–3

Can we infer useful information about Mmax from Mcin sub-regions of the Earth?

It depends on N, and the length of time over which thecatalog 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 magnitudeM=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 tobe 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, givenno other information, it provides the best estimate (under the assumptions madehere).

Unfortunately, unless the product of N(Mc), and T, the time period of catalogcompleteness, is such that e [-N(Mc) x T ] is a significantly small number, theestimate will not be reliable.

SummaryFigure A5–9