A regional earthquake is recorded at epicentral distance

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 regional earthquake is recorded at epicentral distance r=200 kmr = 200\,\mathrm{km}. Its far-field S-wave displacement spectrum has flat low-frequency level Ω0=5.0×10−4 m s\Omega_0 = 5.0\times10^{-4}\,\mathrm{m\,s} and corner frequency fc=0.20 Hzf_c = 0.20\,\mathrm{Hz}. The surrounding rock has density ρ=2800 kg m−3\rho = 2800\,\mathrm{kg\,m^{-3}} and shear speed vS=3.7 km s−1v_S = 3.7\,\mathrm{km\,s^{-1}}. Using Ω0=M0/(4πρvS3r)\Omega_0 = M_0/(4\pi\rho v_S^3 r) (radiation-pattern coefficient taken as 11), the Brune relation fc=0.37vS/af_c = 0.37v_S/a, and Δσ=7M0/16a3\Delta\sigma = 7M_0/16a^3, estimate: ((a)) the seismic moment M0M_0; ((b)) the source radius aa; ((c)) the static stress drop Δσ\Delta\sigma.

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