A local earthquake is recorded at epicentral distance

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Earth, Climate & Energy Physics · Seismology, tectonics and geodynamics

The Solid Earth, Ch The earthquake source: moment tensor, radiation and spectra

Problem

A local earthquake is recorded at epicentral distance r=50 kmr = 50\,\mathrm{km}. Its far-field S-wave displacement spectrum is flat at low frequency, with level Ω0=1.0×10−6 m s\Omega_0 = 1.0\times10^{-6}\,\mathrm{m\,s}, and falls above a corner frequency fc=5.0 Hzf_c = 5.0\,\mathrm{Hz}. The crust has density ρ=2700 kg m−3\rho = 2700\,\mathrm{kg\,m^{-3}} and shear speed vS=3.5 km s−1v_S = 3.5\,\mathrm{km\,s^{-1}}. Using Ω0=M0/(4πρvS3r)\Omega_0 = M_0/(4\pi\rho v_S^3 r) (taking the radiation-pattern coefficient 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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