Abstract
Velocity and density measured in a well are crucial for synthetic seismic generation which is, in turn, a key to interpreting real seismic amplitude in terms of lithology, porosity, and fluid. Because velocity and density curves are sometimes of poor quality, or simply absent in older wells, it is important to be able to reconstruct these curves from reliable measurements, such as resistivity and gamma-ray (GR). A recent example of this approach is by Xu et al. (2003) where mechanical compaction curves and velocity-porosity relations are used to reconstruct a full suite of the needed log data. The earliest attempt to reconstruct a sonic curve from resistivity is by Faust (1953), where both the velocity and resistivity are empirically related to depth and lithology. From these two relations an equation follows that links the sonic velocity to the depth and formation factor, where the formation factor is defined, as usual, as the ratio of the resistivity of water-saturated rock to the resistivity of water. We revisit Faust's equation and use the currently available rock physics transforms between the velocity, porosity, and mineralogy together with existing empirical and theoretical resistivity-porosity models to determine the ranges of its applicability in terms of rock type and lithology. We offer extensions of this equation for rock types that apparently were not included in original analysis.
