Robust Empirical Time–Frequency Relations for Seismic Spectral Amplitudes, Part 1: Application to Regional S Waves in Southeastern Iran

Abstract

ABSTRACT Empirical models of geometrical-, Q-, t-star, and kappa-type attenuation of seismic waves and ground-motion prediction equations (GMPEs) are viewed as cases of a common empirical standard model describing variation of wave amplitudes with time and frequency. Compared with existing parametric and nonparametric approaches, several new features are included in this model: (1) flexible empirical parameterization with possible nonmonotonous time or distance dependencies; (2) joint inversion for time or distance and frequency dependencies, source spectra, site responses, kappas, and Q; (3) additional constraints removing spurious correlations of model parameters and data residuals with source–receiver distances and frequencies; (4) possible kappa terms for sources as well as for receivers; (5) orientation-independent horizontal- and three-component amplitudes; and (6) adaptive filtering to reduce noise effects. The approach is applied to local and regional S-wave amplitudes in southeastern Iran. Comparisons with previous studies show that conventional attenuation models often contain method-specific biases caused by limited parameterizations of frequency-independent amplitude decays and assumptions about the models, such as smoothness of amplitude variations. Without such assumptions, the frequency-independent spreading of S waves is much faster than inferred by conventional modeling. For example, transverse-component amplitudes decrease with travel time t as about t−1.8 at distances closer than 90 km and as t−2.5 beyond 115 km. The rapid amplitude decay at larger distances could be caused by scattering within the near surface. From about 90 to 115 km distances, the amplitude increases by a factor of about 3, which could be due to reflections from the Moho and within the crust. With more accurate geometrical-spreading and kappa models, the Q factor for the study area is frequency independent and exceeds 2000. The frequency-independent and Q-type attenuation for vertical-component and multicomponent amplitudes is somewhat weaker than for the horizontal components. These observations appear to be general and likely apply to other areas.