Modeling Sonic and Density From Neutron and Gamma Ray

 Logs
One log that is relatively unaffected by noise and bad hole effects is the neutron log. It is a good source of total porosity (PHIt) and can be used in the time average equation to generate a sonic log:
      1: DTCsyn = DTCMA + (CTCW - DTCMA) * PHIN

This can be rewritten in its more usual form as:
      2: DTCsyn = DTCMA * (1 - PHIN) + DTCW * PHIN

Neutron logs can be run through casing and many are available in well files where no sonic or a poor sonic is present. Because neutron and sonic logs respond similarly to shale, no special shale compensation is needed with this method.

The density log is not as strongly affected by shale, so it requires more attention to detail:
      3: Vshg = (GR - GR0) / (GR100 - GR0)
      4: Vshs = (SP - SP0) / (SP100 - SP0)
      5: Vsh = Min (Vshg, Vshs)
      6: PHIe = PHIN - (Vsh * PHINSH)
      7: DENSsyn = (1 - Vsh - PHIe) * DENSMA + DENSW * PHIe + Vsh * DENSSH

If there is no neutron log to use as a guide, the following will give reasonable results for seismic purposes:
      8: Vsh = (GR - GR0) / (GR100 -GR0)
      9: DELTmod = DELTMA * (1 - Vsh - PHIMAX) + DELTW * PHIMAX + DELTSH * Vsh
      10: DENSmod = DENSMA * (1 - Vsh - PHIMAX) + DENSW * PHIMAX + DENSSH * Vsh

Where:
  PHIMAX is determined from offset well data (zoned according to lithology).

PHIN is too low in gas zones, giving DELTmod too low and DENSmod too high.