Gardner's relation

Gardner's relation,orGardner's equation,named after G. H. F. Gardner and L. W. Gardner, is an empirically derived equation that relatesseismicP-wavevelocity to thebulk densityof thelithologyin which the wave travels. The equation reads:

$\rho =\ Alpha V_{p}^{\beta }$

where$\rho$is bulk density given in g/cm³,$V_{p}$is P-wave velocity given in ft/s, and$\ Alpha$and$\beta$are empirically derived constants that depend on thegeology.Gardner et al. proposed that one can obtain a good fit by taking$\ Alpha =0.23$and$\beta =0.25$.Assuming this, the equation is reduced to:

$\rho =0.23V_{p}^{0.25},$

where the unit of$V_{p}$is feet/s.

If$V_{p}$is measured in m/s,$\ Alpha =0.31$and the equation is:

$\rho =0.31V_{p}^{0.25}.$

This equation is very popular inpetroleum explorationbecause it can provide information about the lithology from interval velocities obtained from seismic data. The constants$\ Alpha$and$\beta$are usually calibrated fromsonicanddensitywell log information but in the absence of these, Gardner's constants are a good approximation.