  The evolution of $V_\mathrm{P}/V_\mathrm{S}$ with increasing fluid-saturated
porosity is computed for isotropic rocks containing spheroidal pores.
$V_\mathrm{P}/V_\mathrm{S}$ is shown to either decrease or increase with
increasing porosity, depending on the aspect ratio $\alpha$ of the pores, fluid
to solid bulk modulus ratio $\zeta$, and initial Poisson's ratio $\nu_0$ of the
solid. A critical initial Poisson's ratio $\nu_\mathrm{0,crit}$ is computed,
separating cases where $V_\mathrm{P}/V_\mathrm{S}$ increases (if
$\nu_0<\nu_\mathrm{0,crit}$) or \emph{decreases} (if
$\nu_0>\nu_\mathrm{0,crit}$) with increasing porosity. For thin cracks and
highly compressible fluids, $\nu_\mathrm{0,crit}$ is approximated by
$0.157\,\zeta/\alpha$, whereas for spherical pores $\nu_\mathrm{0,crit}$ is
given by $0.2 + 0.8\zeta$. If $\nu_0$ is close to $\nu_\mathrm{0,crit}$, the
evolution of $V_\mathrm{P}/V_\mathrm{S}$ with increasing fluid-saturated
porosity is near neutral and depends on subtle changes in pore shape and fluid
properties. This regime is found to be relevant to partially dehydrated
serpentinites in subduction zone conditions (porosity of aspect ratio near 0.1
and $\zeta$ in the range 0.01--0.1), and makes detection of these rocks and
possibly elevated fluid pressures difficult from $V_\mathrm{P}/V_\mathrm{S}$
only.
