A continental strike-slip fault system ruptures along a length with average coseismic…
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 continental strike-slip fault system ruptures along a length L=80km with average coseismic slip Dˉ=3m and seismic moment M0=1.24×1020Nm. The crust hosting the rupture has density ρ=2800kgm−3 and S-wave speed vS=3.5kms−1. The rupture is treated as a uniform rectangular patch, elastic and homogeneous, with the down-dip width W (its seismogenic depth) unknown; below W the rock deforms by power-law creep rather than seismic slip.
((a)) Find the shear modulus μ of the crust.
((b)) Using M0=μLWDˉ for a rectangular rupture, find the seismogenic depth W.
((c)) Approximating the rupture as an equivalent circular crack of the same area, a=LW/π, and using the circular-crack static stress-drop relation, find the static stress drop Δσ on the source fault.
((d)) Static-stress-change modelling of this rupture shows that, at the closest point of a parallel receiver fault, the shear stress increases by 2.5 per cent of Δσ found in (c), and the fault-normal stress unclamps (decreases) by half of that shear increase. Taking an effective friction coefficient μ′=0.4, find the Coulomb stress change ΔCFS on the receiver fault.
((e)) The receiver fault has effective normal stress σn′=100MPa, b−a=0.005 and a field-scale characteristic slip distance Dc=1cm, the order estimated for natural fault gouge rather than a bare laboratory surface. Using the shear modulus from (a), find its nucleation length Lc, and state whether a 200m patch of elevated Coulomb stress on that fault is large enough to nucleate an instability on its own.