PHYSICS · Multi-part · Fermi University Physics · Earth, Climate & Energy Physics · Seismology, tectonics and geodynamics · Seismology, tectonics and geodynamics
The Solid Earth, Ch The earthquake source: moment tensor, radiation and spectra
Problem
A strike-slip fault ruptures unilaterally, breaking northward from its southern end over a length L=250km at a rupture speed vr=0.75vS, with vS=3.5kms−1 in the surrounding crust. Town P lies at bearing 010∘ from the hypocentre, an angle θP=10∘ from the rupture direction (due north); town Q lies at bearing 200∘, an angle θQ=160∘ from the rupture direction. Both towns are far enough from the fault that the point-source directivity formula applies to each, with the same L and vr; take their distances and radiation-pattern factors to be equal.
((a)) Find the apparent S-wave duration tapp at each town, and the ratio of the two.
((b)) The same moment arrives at each town however it is spread out in time. Find the ratio of peak shaking amplitude at P to that at Q.
((c)) For a station exactly ahead of (θ=0∘) and exactly behind (θ=180∘) a rupture with this vr/vS, the idealised duration ratio is (1+vr/vS)/(1−vr/vS). Compute it and explain why the ratio found in (a) is smaller.
((d)) The fault is confined to a seismogenic layer W=15km wide (Chapter 7's brittle layer), has rigidity μ=32GPa and average slip D=4.0m. Estimate its moment and moment magnitude, and say whether directivity changes this estimate.