Saturated Sediment Properties

After having determined the dry properties of the solid phase, the saturated rock properties can be calculated at seismic frequencies using Gassman's equations. These equations relate the effective moduli of a dry rock with those containing fluid. The saturated bulk and shear moduli $\rm K_{\rm sat}$ and $\rm G_{\rm sat}$ are given by

$$\begin{eqnarray} &\rm K_{\rm sat}& =\:\rm K\:{{\phi\:\rm K_{\rm dry}\:-\:(1+\phi... ...m dry}/\rm K}}, \nonumber \\ &\rm G_{\rm sat}& =\:\rm G_{\rm dry},\end{eqnarray}$$ (13)

where $\rm K$ is the bulk modulus of the mineral making up the rock, $\rm K_{\rm dry}$ and $\rm G_{\rm dry}$ are the dry bulk and shear moduli of the rock, and $\rm K_{\rm f}$ is the bulk modulus of the saturating fluid. In the case of purely brine-saturated sediments, $\rm K_{\rm f}$ is identical to the bulk modulus of water. If the sediment is homogeneously saturated with free gas, $\rm K_{\rm f}$ becomes an average of the brine and gas fluid moduli:

$$\rm K_{\rm f}\:=\:\left[ \: {\rm S_{\rm w}\over \rm K_{\rm w}}\:+ {(1-\rm S_{\rm w})\over \rm K_{\rm g}} \right]$$ (14)

where $\rm K_{\rm w}$ and $\rm K_{\rm g}$ are the bulk moduli of water and gas, and $\rm S_{\rm w}$ is the water saturation.

The elastic velocities $\rm v_{\rm p}$ and $\rm v_{\rm s}$ and the bulk density $\rho_{\rm B}$ can then be determined with the following equations:

$$\begin{eqnarray} &\rho_{\rm B}& \:=\: (1-\phi)\: \rho_{\rm s} \: +\: \phi\:\rho_... ...mber \\ &\rm v_{\rm s}& \:=\: \sqrt{\rm G_{\rm sat}/\rho_{\rm B}};\end{eqnarray}$$ (15)

where $\rho_{\rm s}$ is the bulk density of the solid phase and $\rho_{\rm f}$ the density of the pore fluid. Both the solid density and the fluid density can be obtained as an arithmetic mean of the volumetric fractions of their components.