GNSS receivers straddle a locked strike-slip fault

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

GNSS receivers straddle a locked strike-slip fault. Far from the fault the fault-parallel velocity relative to a fixed reference block approaches a plateau of

\pm 25\,\mathrm{mm\,yr^{-1}}

on the two sides of the fault (a total relative motion of

50\,\mathrm{mm\,yr^{-1}}

across the boundary). At a perpendicular distance

x = 20\,\mathrm{km}

from the fault trace the measured fault-parallel velocity is

v_y = 12.5\,\mathrm{mm\,yr^{-1}}

. ((a)) Using the arctangent model of interseismic strain accumulation,

v_y(x) = (V/\pi)\arctan(x/D)

, find the long-term slip rate

V

and the locking depth

D

. ((b)) A seismic source zone along this fault lies at distance

R = 20\,\mathrm{km}

from a town. Its Gutenberg-Richter law is

\log_{10}N(\ge M) = 3.0 - M

(annual rate,

M

the moment magnitude), valid for

5 \le M \le 7.5

. Shaking at the town follows the illustrative ground-motion model

\log_{10}(y/g) = -2.5 + 0.5M - \log_{10}(R/\mathrm{km})

, where

y

is peak ground acceleration in units of

g

. Find the magnitude

M^{*}

and ground motion

y^{*}

for which the annual rate of exceeding

y^{*}

equals

1/475\,\mathrm{yr^{-1}}

, the return period used in building codes.

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