A shallow earthquake occurs on a fault with strike

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 shallow earthquake occurs on a fault with strike ϕf=210∘\phi_f=210^\circ, dip δ=58∘\delta=58^\circ and rake λr=−80∘\lambda_r=-80^\circ, at depth h=12 kmh=12\,\mathrm{km} in crust with vP=6.3 km s−1v_P=6.3\,\mathrm{km\,s^{-1}}. ((a)) Using Anderson's classification of faulting regimes (Chapter 4), say which regime this event belongs to and which principal stress was vertical. ((b)) A teleseismic P arrival has ray parameter p=7.20 s deg−1p=7.20\,\mathrm{s\,deg^{-1}} (Chapter 5). Taking the source radius as rh=6371 kmr_h=6371\,\mathrm{km} minus the depth, find the take-off angle ihi_h at the source. ((c)) The source spectrum has a flat low-frequency level giving M0=5.0×1018 N mM_0=5.0\times10^{18}\,\mathrm{N\,m} and a corner frequency fc=0.045 Hzf_c=0.045\,\mathrm{Hz}. Using Brune's relation with local shear speed vS=3.6 km s−1v_S=3.6\,\mathrm{km\,s^{-1}}, find the source radius aa that this corner implies for a circular crack. ((d)) Chapter 7's strength envelope confines earthquakes on a continental normal fault to a brittle layer about 15 km15\,\mathrm{km} thick. Compare this with the radius found in (c), and explain what the comparison says about the true shape of the rupture. Then compute the stress drop implied by the circular-crack formula and say why its value is a further sign of the same problem.

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