# Difference between revisions of "Gardner's equation"

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:<math>\rho = \alpha V_\mathrm{P}^\beta</math> | :<math>\rho = \alpha V_\mathrm{P}^\beta</math> | ||

− | where <math>\rho </math> is bulk density, <math>V_\mathrm{P}</math> is P-wave velocity and <math>\alpha</math> and <math>\beta</math> are empirically derived constants that depend on the geology. Gardner et al. proposed that one can obtain a good estimate of density in g/cc, given velocity in ft/s, by taking <math>\alpha = 0.23</math> and <math>\beta = 0.25</math>. | + | where <math>\rho </math> is bulk density, <math>V_\mathrm{P}</math> is P-wave velocity and <math>\alpha</math> and <math>\beta</math> are empirically derived constants that depend on the geology. Gardner et al. proposed that one can obtain a good estimate of density in g/cc, given velocity in ft/s, by taking <math>\alpha = 0.23</math> and <math>\beta = 0.25</math>. |

− | + | Assuming this, and using units of g/cc, the equation is reduced to the following for a velocity log in ft/s: | |

− | If <math> | + | :<math>\rho = 0.23\ V_\mathrm{P}^{\,0.25}\ \ \mathrm{kg}/\mathrm{m}^3</math> |

+ | |||

+ | If <math>V_\mathrm{P}</math> is measured in m/s and you want density in kg/m<sup>3</sup>, then <math>\alpha = 310</math> and the equation is: | ||

:<math>\rho = 310\ V_\mathrm{P}^{\,0.25}\ \ \mathrm{kg}/\mathrm{m}^3</math> | :<math>\rho = 310\ V_\mathrm{P}^{\,0.25}\ \ \mathrm{kg}/\mathrm{m}^3</math> |

## Latest revision as of 17:43, 29 January 2018

Gardner's equation is an empirical equation that relates P-wave velocity to bulk density. It is a pseudo-velocity relationship commonly used in estimating sonic or density logs when only one of them is available (both are required for a synthetic when performing a well tie).

Gardner showed that^{[1]}:

where is bulk density, is P-wave velocity and and are empirically derived constants that depend on the geology. Gardner et al. proposed that one can obtain a good estimate of density in g/cc, given velocity in ft/s, by taking and .

Assuming this, and using units of g/cc, the equation is reduced to the following for a velocity log in ft/s:

If is measured in m/s and you want density in kg/m^{3}, then and the equation is:

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

## Inverse Gardner equation from density in g/cc

Sometimes you need to estimate density from velocity, if is in ft/s and ** is in g/cc**:

Or, if velocity is in m/s:

If is in kg/m^{3}, the factors are much smaller: and respectively.

## External links

- Gardner's relation — Wikipedia entry
- Gardner's equation — SEG Wiki

## References

- ↑ Gardner, G, L Gardner & A Gregory, 1974. Formation velocity and density—the diagnostic basis for stratigraphic traps. Geophysics 39, 770–780. A PDF is available online.