Earth: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:
- [math]\displaystyle{ \rho = \alpha V_p^{\beta} }[/math]
where [math]\displaystyle{ \rho }[/math] is bulk density given in g/cm3, [math]\displaystyle{ V_p }[/math] is P-wave velocity given in ft/s, and [math]\displaystyle{ \alpha }[/math] and [math]\displaystyle{ \beta }[/math] are empirically derived constants that depend on the geology. Gardner et al. proposed that one can obtain a good fit by taking [math]\displaystyle{ \alpha = 0.23 }[/math] and [math]\displaystyle{ \beta = 0.25 }[/math].[1] Assuming this, the equation is reduced to:
- [math]\displaystyle{ \rho = 0.23 V_p^{0.25}, }[/math]
where the unit of [math]\displaystyle{ V_p }[/math] is feet/s.
If [math]\displaystyle{ V_p }[/math] is measured in m/s, [math]\displaystyle{ \alpha = 0.31 }[/math] and the equation is:
- [math]\displaystyle{ \rho = 0.31 V_p^{0.25}. }[/math]
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 [math]\displaystyle{ \alpha }[/math] and [math]\displaystyle{ \beta }[/math] are usually calibrated from sonic and density well log information but in the absence of these, Gardner's constants are a good approximation.
References
- ↑ Gardner, G.H.F.; Gardner L.W.; Gregory A.R. (1974). "Formation velocity and density -- the diagnostic basics for stratigraphic traps". Geophysics 39: 770–780. doi:10.1190/1.1440465. Bibcode: 1974Geop...39..770G. http://www.ipt.ntnu.no/pyrex/stash/GPY00770.pdf.
![]() | Original source: https://en.wikipedia.org/wiki/Gardner's relation.
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