Bounds on low-frequency seismic velocities in partially saturated rocks

The most common technique for estimating seismic velocities in rocks with mixed pore fluid saturations is to use Gassmann's relations with an effective fluid whose density and compressibility are averages of the individual pore fluid properties. This approach is applicable only if the gas, oil: and brine phases are mixed uniformly at a very small scale, so the different wave-induced increments of pore pressure in each phase have time to diffuse and equilibrate during a seismic period. In contrast, saturations that are heterogeneous over scales larger than the characteristic diffusion length, i.e., patchy saturation, will always lead to higher seismic velocities than if the same fluids are mixed uniformly at a fine scale. Critical saturation scales separating uniform from patchy behavior are typically of the order 0.1-1 cm for laboratory measurements acid tens of centimeters for field seismic frequencies. For low seismic frequencies, velocities corresponding to patchy and homogeneous saturations represent approximate upper and lower bounds for given saturations and dry rock properties. For well-consolidated rocks, both bounds can be estimated easily using Gassmann's relations with Voigt and Reuss average effective fluids, respectively.