A strike-slip fault slips at a long-term rate and releases an average of of slip in…

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

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

Problem

A strike-slip fault slips at a long-term rate

V = 20\,\mathrm{mm\,yr^{-1}}

and releases an average of

\Delta u = 4\,\mathrm{m}

of slip in each characteristic earthquake. The last such earthquake occurred

150\,\mathrm{yr}

ago. ((a)) Estimate the mean recurrence interval

T_r

and the slip deficit accumulated since the last earthquake. State in one sentence why this estimate does not fix the date of the next earthquake. ((b)) A nearby wastewater disposal well injects a fluid volume

\Delta V = 5\times10^{4}\,\mathrm{m^3}

into rock of shear modulus

\mu = 30\,\mathrm{GPa}

. Using McGarr's bound on the largest induced seismic moment, estimate the largest moment magnitude

M_w^{\max}

, using

M_w = \tfrac{2}{3}\log_{10}M_0 - 6.07

with

M_0

\mathrm{N\,m}

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