Gardner's relation

Gardner's relation, or Gardner's equation, named after G. H. F. Gardner and L. W. Gardner, is an empirically derived equation that relates seismic P-wave velocity to the bulk density of the lithology in which the wave travels. The equation reads:

where ρ is bulk density given in g/cm³, V p is P-wave velocity given in ft/s, and α and β are empirically derived constants that depend on the geology. Gardner et al. proposed that one can obtain a good fit by taking α = 0.23 and β = 0.25 . Assuming this, the equation is reduced to:

where the unit of V p is feet/s.

If V p is measured in m/s, α = 0.31 and the equation is:

This equation is very popular in petroleum exploration because it can provide information about the lithology from interval velocities obtained from seismic data. The constants α and β are usually calibrated from sonic and density well log information but in the absence of these, Gardner's constants are a good approximation.