Gardner's relation

Last updated October 31, 2024

Gardner's relation, or Gardner's equation, named after Gerald 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:

\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 the geology. Gardner et al. proposed that one can obtain a good fit by taking $\alpha =0.23$ and $\beta =0.25$ .^[1] 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 in petroleum exploration because it can provide information about the lithology from interval velocities obtained from seismic data. The constants $\alpha$ and $\beta$ are usually calibrated from sonic and density well log information but in the absence of these, Gardner's constants are a good approximation.

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References

↑ Gardner, G.H.F.; Gardner L.W.; Gregory A.R. (1974). "Formation velocity and density -- the diagnostic basics for stratigraphic traps" (PDF). Geophysics. 39: 770–780. Bibcode:1974Geop...39..770G. doi:10.1190/1.1440465. Archived from the original (PDF) on 2017-08-09. Retrieved 2010-03-07.

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[Gardner-1] Gardner, G.H.F.; Gardner L.W.; Gregory A.R. (1974). "Formation velocity and density -- the diagnostic basics for stratigraphic traps" (PDF). Geophysics. 39: 770–780. Bibcode:1974Geop...39..770G. doi:10.1190/1.1440465. Archived from the original (PDF) on 2017-08-09. Retrieved 2010-03-07.

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