GARDNER'S EQUATION
There are many wells that have sonic logs in the well files, but the density log is missing over all or part of the well. This occurred mainly in older wells where the operator had financial constraints or thought the uphole potential was limited. Times change, and today the density log is run, often in preference to the sonic over the entire hole. In either case, geophysicists would like both logs over the entire borehole so they can make reasonable calculations of acoustic impedance and generate realistic synthetic seismograms.

 

 


 

Gardner proposed a model in 1974 that is widely used to transform acoustic velocity (inverse of travel time or slowness) and vice versa. The relationship is shown graphically at the right (dotted line), and follows the equation:

      1: DENS = A * (Vp^B)
 
Where:
  DENS =  density (g/cc)
  A = 0.31 when Vp is in m/s
  A = 0.23 when Vp is in ft/s
  B = 0.25

Note that this relationship is a relatively crude approximation to the sandstone, limestone, dolomite, and shale lines on the graph. It does not fit salt or anhydrite data and these layers must be handled separately. The log response equation works better in mixed lithology and in shaly sands, and with the available computer software, is no extra work.
 
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