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
Seismology (; from Ancient Greek σεισμός (''seismós'') meaning "earthquake" and -λογία (''-logía'') meaning "study of") is the scientific study of earthquakes (or generally, quakes) and the generation and propagation of elastic ...
P-wave
A P wave (primary wave or pressure wave) is one of the two main types of elastic body waves, called seismic waves in seismology. P waves travel faster than other seismic waves and hence are the first signal from an earthquake to arrive at any ...
velocity to the
bulk density
In materials science, bulk density, also called apparent density, is a material property defined as the mass of the many particles of the material divided by the bulk volume. Bulk volume is defined as the total volume the particles occupy, includ ...
of the
lithology
The lithology of a rock unit is a description of its physical characteristics visible at outcrop, in hand or core samples, or with low magnification microscopy. Physical characteristics include colour, texture, grain size, and composition. Lit ...
in which the wave travels. The equation reads:
:
where
is bulk density given in g/cm
3,
is P-wave velocity given in ft/s, and
and
are empirically derived constants that depend on the
geology
Geology (). is a branch of natural science concerned with the Earth and other astronomical objects, the rocks of which they are composed, and the processes by which they change over time. Modern geology significantly overlaps all other Earth ...
. Gardner et al. proposed that one can obtain a good fit by taking
and
.
Assuming this, the equation is reduced to:
:
where the unit of
is feet/s.
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
Density (volumetric mass density or specific mass) is the ratio of a substance's mass to its volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' (or ''d'') can also be u ...
well log information but in the absence of these, Gardner's constants are a good approximation.
References
Seismology
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