Failure of Newtonian viscosity

Also remarkable is the failure of basic textbook seismology to explain the observed frequency-dependence of the dissipation parameter Q. The simplest theoretical approach to dissipation is to add a strain-rate term to Hooke's stress-strain law. This predicts stronger relative dissipation of high frequencies than of low frequencies. Experimentally, relative dissipation is observed to be roughly constant over many decades of frequency. Other simple Newtonian theories yield polynomial ratios in $-i \omega$ for the stress/strain ratio. These theories contain scale lengths and characteristic frequencies. They do not predict constant Q. The heterogeneity of the rock at all scales seems to be an essential attribute of a successful theory.