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en>MikiBOB in CFG set N and T are disjoint, so Alpha cannot be member of empty set! There is mistake, see CFG definition, Alpha is member of union of N and T |
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'''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>\rho = \alpha V_p^{\beta}</math> | |||
where <math>\rho </math> is bulk density given in g/cm<sup>3</sup>, <math>V_p</math> is P-wave velocity given in ft/s, 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 fit by taking <math>\alpha = 0.23</math> and <math>\beta = 0.25</math>.<ref name="Gardner">{{cite journal|last=Gardner|first=G.H.F.|coauthors=Gardner L.W. & Gregory A.R.|url=http://www.ipt.ntnu.no/pyrex/stash/GPY00770.pdf|year=1974|title=Formation velocity and density -- the diagnostic basics for stratigraphic traps|journal=Geophysics|volume=39|pages=770–780|bibcode = 1974Geop...39..770G |doi = 10.1190/1.1440465 }}</ref> Assuming this, the equation is reduced to: | |||
:<math>\rho = 0.23 V_p^{0.25}.</math> | |||
This equation is very popular in [[Hydrocarbon exploration|petroleum exploration]] because it can provide information about the lithology from interval velocities obtained from seismic data. The constants <math>\alpha</math> and <math>\beta</math> are usually calibrated from [[Sonic logging|sonic]] and [[Density logging|density]] well log information but in the absence of these, Gardner's constants are a good approximation. | |||
==References== | |||
{{Reflist}} | |||
{{geophysics-stub}} | |||
[[Category:Seismology]] | |||
Latest revision as of 07:41, 24 July 2013
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:
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:
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.
References
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