Gardner's relation
Encyclopedia
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/cc, 
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 
. 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.
P-wave
P-waves are a type of elastic wave, also called seismic waves, that can travel through gases , solids and liquids, including the Earth. P-waves are produced by earthquakes and recorded by seismographs...
velocity to the bulk density
Bulk density
Bulk density is a property of powders, granules and other "divided" solids, especially used in reference to mineral components , chemical substances, ingredients, foodstuff or any other masses of corpuscular or particulate matter. It is defined as the mass of many particles of the material...
of the lithology
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, such as colour, texture, grain size, or composition. It may be either a detailed description of these characteristics or be a summary of...
in which the wave travels. The equation reads:
where
is bulk density given in g/cc, is P-wave velocity given in ft/s, and and are empirically derived constants that depend on the geologyGeology
Geology is the science comprising the study of solid Earth, the rocks of which it is composed, and the processes by which it evolves. Geology gives insight into the history of the Earth, as it provides the primary evidence for plate tectonics, the evolutionary history of life, and past climates...
. Gardner et al. proposed that one can obtain a good fit by taking
and . 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 sonicSonic logging
Sonic logging shows a formation’s interval transit time, designated Dt. It is a measure of a formation’s capacity to transmit sound waves. Geologically, this capacity varies with lithology and rock textures, notably porosity....
and density
Density logging
Density logging is a well logging tool determining rock bulk density along a wellbore. This is the overall density of a rock including solid matrix and the fluid enclosed in pores. Geologically, bulk density is a function of the density of the minerals forming a rock Density logging is a well...
well log information but in the absence of these, Gardner's constants are a good approximation.