Dictionary:Gardner’s equation

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Term Gardner's equation
Pronunciation gard’ n∂r
Series Geophysical Reference Series
Author Robert E. Sheriff
DOI http://dx.doi.org/10.1190/1.9781560802969
ISBN 978-1-56080-118-4
Store SEG Online Store

Gardner's equation, or Gardner's relation, 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 is bulk density given in g/cm3, is P-wave velocity given in ft/s, and and are empirically derived constants that depend on the geology. Gardner et al. proposed that one can obtain a good fit by taking and .[1] Assuming this, the equation is reduced to:

If is measured in m/s, 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 and are usually calibrated from sonic and density well log information but in the absence of these, Gardner's constants are a good approximation.

The empirical relationship that density is proportional to the 1/4 power of P-wave velocity:

where a is 0.31 when V is in m/s, 0.23 when in ft/s[1].



  1. 1.0 1.1 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.
  2. Whaley, J., 2017, Oil in the Heart of South America, https://www.geoexpro.com/articles/2017/10/oil-in-the-heart-of-south-america], accessed November 15, 2021.
  3. Wiens, F., 1995, Phanerozoic Tectonics and Sedimentation of The Chaco Basin, Paraguay. Its Hydrocarbon Potential: Geoconsultores, 2-27, accessed November 15, 2021; https://www.researchgate.net/publication/281348744_Phanerozoic_tectonics_and_sedimentation_in_the_Chaco_Basin_of_Paraguay_with_comments_on_hydrocarbon_potential
  4. Alfredo, Carlos, and Clebsch Kuhn. “The Geological Evolution of the Paraguayan Chaco.” TTU DSpace Home. Texas Tech University, August 1, 1991. https://ttu-ir.tdl.org/handle/2346/9214?show=full.