The sonic porosity is usually abbreviated SPHI or PHIS  on log panels and denoted as   in equations.

The key measurement is the p-wave velocity from sonic tool readings.

The key model parameter is rock matrix sonic velocity   which is calibrated for each facies individually and can be can be assessed as vertical axis cut-off on  cross-plot against the core-data porosity . 

The model also accounts for saturating rock fluids with p-wave velocity  value.

In overbalance drilling across permeable rocks the saturating fluid is usually mud filtrate. 

In underbalance drilling this the saturating fluid is identified from resistivity logs.  

WGG Equation (Wyllie)

The WGG sonic porosity  equation is :

\frac{1}{V_{p \ log}} = \frac{1-\phi_s \ C_p}{V_{p \ m}} + \frac{\phi_s \ C_p}{V_{p \ f}}

where   is compaction factor, accounting for the shaliness specifics and calculated as:

C_p = \frac{V_{shс}}{V_{sh}}

where 

 – p-wave velocity for adjacent shales,

 – p-wave velocity reference value for tight shales (usually 0.003 ft/μs).

GGG Equation (Gardner, Gardner, Gregory)

The GGG sonic porosity  equation is :

\frac{1}{V^{1/4}_{p \ log}} =  \frac{(1-\phi_s)}{V^{1/4}_{p \ m}} + \frac{\phi_s}{V^{1/4}_{p \ f}}

The above equation is based on the Gardner correlation for sonic density:

\rho_s = 171 \cdot V_{p \ m}^{1/4}

where  is measured in  and  is measured in  

and mass balance equation:

\rho_s = (1-\phi_s)\rho_m + \phi_s \rho_f

RHG Equation (Raymer, Hunt, Gardner)

The RHG sonic porosity  equation is :

V_{p \ log} = (1-\phi_s)^2 V_{p \ m} + \phi_s V_{p \ f}

and only valid for .