HS LOWER This is a theoretical bound of 'cores' surrounding by a 'shell'. In case of the lower bound, the stiffest material forms the core, and the softest material forms the shell. This is geologically plausible, and therefore we see that the reality is often well described by the H/S lower bound, especially when the grains are in suspension (above critical orosity) and the matrix does not yet provide an excess stiffness. As such this bound does a better job than Reuss (unless we plot Mu as a function of porosity; if MuFluid = 0 - always the case except for heavy oils - then the H/S lower bound is the same as the Reuss bound). Where the soft material is a fluid, then the model may be plotted as a function of porosity (where the porosity is 1 - Volume Fraction Stiff). Where the soft material is a mineral then the porosity output is effectively the volume fraction of the soft material rather than an actual porosity)
HS UPPER This is a theoretical bound of 'cores' surrounded by a 'shell'. In case of the upper bound, the stiffest material forms the shell, and the softest material forms the core. This is geologically implausible, and therefore we see that the reality is often quite a bit softer than the H/S upper bound. Nevertheless, this bound does a better job than Voigt. Where the soft material is a fluid, then the model may be plotted as a function of porosity (where the porosity is 1 - Volume Fraction Stiff). Where the soft material is a mineral where the porosity output is effectively the volume fraction of the soft material rather than an actual porosity.