Link between Elelctrical Resistivity and Seismic Velocity

The main inputs for forward seismic modeling are the P- and S-wave velocity and density. A common problem is poor quality or absence of sonic, dipole, and density logs. It is important to reconstruct these curves from reliable measurements, such as resistivity. In an early attempt, Faust empirically relates the velocity and resistivity to the geologic age, depth, and lithology. This relation links the sonic velocity to the depth and formation factor (resistivity) and does not have any apparent physical basis because the velocity depends on the elasticity of a material while the resistivity describes its electrical charge transport capability. The observed link is most likely due to the dependence of both material properties on porosity. We analyze this link by using recent rock physics transforms between the velocity, porosity, and mineralogy, with existing empirical and theoretical resistivity-porosity models. We also use a number of high-quality data sets to verify the results. We find that Faust’s equation is applicable to consolidated cemented sandstones with low clay content and porosity between 5 and 20%. It should not be used in shale or unconsolidated and/or uncemented rock. We derive a family of new resistivity-velocity equations appropriate for various textures of clastic sediment.