Frequency-dependent effects on travel times and waveforms of long-period S and SS waves

Abstract

The spectral properties of upper-mantle velocity perturbations are dominantly determined from regional and global tomographic models. In this paper we study frequency-dependent effects of l3ng-period S and SS waves of SH-type through random upper-mantle models with specified spectral properties. In particular, we investigate the information content of the power spectra of travel time perturbations as a function of model spectrum and frequency band. Wave propagation is simulated by a finite-difference (FD) approximation to the axi-symmetric wave equation in spherical coordinates. For global models with cylindrical symmetry and constant angular increment Δθ, the use of spherical coordinates leads to an effective lateral grid spacing (arc length) decreasing with depth. This is contrary to the requirements of global models with low velocities at the top of the mantle, which necessitate a dense grid spacing at small depths and a wider grid spacing at the base of the mantle. We introduce a grid with depth-dependent lateral grid spacing to overcome this inconsistency. Our main findings are that (1) the properties of spatial power spectra of travel time fluctuations are frequency-dependent; (2) power spectra of models obtained from long-period tomography may underestimate the power at intermediate scales; (3) frequency-dependent effects on the waveform are sensitive to the scales and amplitudes of perturbations present in the upper mantle.