A town lies from a fault source whose earthquakes of concern all have magnitudes…

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Earth, Climate & Energy Physics · Seismology, tectonics and geodynamics

The Solid Earth, Ch Faults, the earthquake cycle and seismic hazard

Problem

A town lies

R=20\,\mathrm{km}

from a fault source whose earthquakes of concern all have magnitudes close to

M=6.5

; treat them as a single magnitude, occurring at an annual rate

\lambda_M=4\times10^{-3}\,\mathrm{yr^{-1}}

. Shaking at the town follows the illustrative ground-motion model of the worked hazard example,

\ln Y_{\rm med}=-4.0+0.9M-\ln(R+10\,\mathrm{km})

for the median peak ground acceleration in units of

g

, with

R

in kilometres and lognormal scatter of standard deviation

\sigma=0.6

\ln Y

. ((a)) Find the median peak ground acceleration

Y_{\rm med}

at the town. ((b)) Find the annual rate

\lambda(y)

of exceeding

y=Y_{\rm med}

and

y=2Y_{\rm med}

. ((c)) Find

\lambda(2Y_{\rm med})

again with the scatter switched off,

\sigma=0

. With the scatter kept, find the chance that

2Y_{\rm med}

is exceeded at least once in

50\,\mathrm{yr}

, and say what the scatter does to the rate of strong shaking.

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