Geometric spreading and apparent anelastic attenuation of response spectral accelerations

Abstract

This paper discusses apparent anelastic (combination of intrinsic and scattering) attenuation of 5% damped response spectral accelerations (SA) associated with the geometric spreading of surface waves. In contrast to the “seismological” Q(f) factor measured using Fourier spectra of S-, Lg- or coda-waves SA quality factor QSA(f) represents apparent anelastic attenuation of response spectral accelerations first introduced in Graizer (2017) [1]. In the recent ground motion prediction equations (GMPE) models for the stable continental regions (SCR) (Graizer, 2017) [1] and active crustal regions (ACR) (Graizer, 2018) [2] I assumed large-distance geometric spreading of SA to be of the order of Ggeom ~ R-0.5. Multiple inversions performed to estimate QSA(f) demonstrated the best fit to be ∼ QSAA(f)=120f0.96 for the ACR for frequencies between 0.1 and 100 Hz and the best fit to be ∼ QSAS(f)=186f0.99 for the SCR for frequencies between 0.1 and 40 Hz. Apparent anelastic attenuation was found to be magnitude dependent with QSA factor increasing with magnitude. Resulting apparent attenuations of response spectral amplitudes at rupture distances of more than 50 km for the ACR and more than 70 km for the SCR are practically linearly dependent upon frequency demonstrating significantly different behavior from the “seismological” Q-factor.