Velocity dispersion due to anelasticity; implications for seismology and mantle composition

TLDR

A relaxation spectrum framework is employed to calculate absorption and dispersion in linear anelastic solids. The authors solve the Boltzmann after‑effect equation for a standard linear solid with a distribution of relaxation times chosen to produce an almost constant quality factor across seismic frequencies, examining both discrete and continuous spectra. The model yields a broad absorption band that can be viewed as a superposition of individual relaxation‑mechanism peaks.

Abstract

The concept of a relaxation spectrum is used to compute the absorption and dispersion of a linear anelastic solid. The Boltzmann after-effect equation is solved for a solid having a linear relationship between stress and strain and their first time derivatives, the ‘standard linear solid’, and having a distribution of relaxation times. The distribution function is chosen to give a nearly constant Q over the seismic frequency range. Both discrete and continuous relaxation spectra are considered. The resulting linear solid has a broad absorption band which can be interpreted in terms of a superposition of absorption peaks of individual relaxation mechanisms.