Analysis of near-source strong-motion recordings along the Mexican subduction zone

Near-source strong motions of 64 earthquakes (3 ≦ M ≦ 8.1; 10 ≦ R ≦ 54 km) recorded above the Mexican subduction zone are analyzed to study the scaling of peak horizontal acceleration, a_max, and Fourier acceleration amplitude spectra, a(f), as a function of magnitude M. The a_max data reduced to 16 km shows clear dependence on M for M ≦ 6. For M > 6, the existing data suggests that for such events a_max does not depend on M. Observation points 16 km above the source are in the far field for earthquakes with M > 6 for the frequencies (>1 Hz) of interest here, so that for such events a(f) is easily explained in terms of Brune's source spectra modified by attenuation. The same spectra explain the a_max data when Parseval's theorem is used to obtain a_rms and the expected a_max is computed using random vibration theory (RVT). For larger earthquakes, we modify the point-source model to estimate Fourier amplitude spectra from finite sources, ignoring possible directivity effects. These spectra along with rupture duration T_d is used to compute a_rms and to estimate a_max by applying RVT. The character of the near-source recordings of 6 ≦ M ≦ 8.1 earthquakes in Mexico suggests that the assumption of stationarity over T_d is reasonable. The results from the model show that beyond M ≅ 6, the dependence of a_max on M decreases; for M > 7.5 a_max becomes essentially independent of M. The a_max and a(f) observed for M ≦ 6.5 may be interpreted in terms of this finite-source model with stress drops Δσ of 40 to 100 bars and an appropriate site attenuation parameter. From a possible M = 7.5 to 8 earthquake in the Guerrero gap the expected a_max from the finite-source model in Acapulco, corresponding to Δσ = 100 bars and κ = 0.023s, is roughly $12$ g.