MANUAL Dipmeter Calculations
Although it is seldom done anymore, manual dipmeter calculations with a scientific calculator is quite practical and instructive. The technique given below was presented by R. Bateman and C. Konen in "The Log Analyst and the Programmable Calculator" in The Log Analyst, Jan 1978. The method is based on hand measurements of curve offsets from the raw dipmeter curves and readings from the hole direction data. These equations are for the four arm dipmeter and ignore closure and planarity errors. The position of the angles in space is shown below.

 

 


                        Definitions for dipmeter calculations

For low angle dipmeter:
      1: PAZ = AZ1 + MD
      2: HAZ = AZ1 - RBR + MAGD

For high angle dipmeter:
      3: PAZ = AHD + RBR + MAGD
      4: HAZ = AHD + MD

Adjust angles to fit between 0 and 360 degrees:
      5: PAZ = 360 * Frac ((PAZ +360) / 360)
      6: HAZ = 360 * Frac ((HAZ +360) / 360)

Note: All azimuth angles are measured positive clockwise, with north at zero (if appropriate).

The curve offsets are measured in inches or millimeters of log paper and translated into dip angles across orthogonal pad pairs:
      7: ANGLA = Arctan (SCALE * H13 / D13)
      8: ANGLB = Arctan (SCALE * H24 / D24)

Note: Curve offsets are positive measuring upward from pad 1 to pad 3 and from pad 2 to pad 4. 

Note: SCALE is the scale of the log film, ie. a 1:20 scale log (60 inches = 100 feet) has SCALE = 20. For example an offset of 0.25 inches of paper is really 20 * 0.25 = 5 inches of borehole.

Project these two dips onto the dip plane to find apparent dip and azimuth:
      9: ADM = Arctan (((Tan ANGLA)^2 + (Tan ANGLB)^2)^0.5)
      10: ANGLD = Arccos (Tan ANGLA / Tan ADM)
      11: IF H24 < 0
      12: THEN ANGLD = 360 - ANGLD
      13: ANGLD = ANGLD + PAZ
      14: ADAZ = 360 * Frac ((ANGLD + 360) / 360)

Translate apparent dip to true dip:
      15: DIP = Arccos(Cos WD * Cos ADM + Sin WD * Sin ADM * Cos(ADAZ - HAZ))
      16: ANGLG = Arccos ((Cos ADM - Cos WD * Cos DIP) / (Sin WD * Sin DIP))
      17: IF Sin (ADAZ - HAZ) >= 0
      18: THEN AZM = HAZ + 180 - ANGLG
      19: OTHERWISE AZM = HAZ - 180 + ANGLG
      20: AZM = 360 * Frac ((AZM + 360) / 360)

In a July 2017 email, Charles Berg at ResDip pointed out that DIP could exceed 90 degrees and that we usually do not report dips this way. An additional step provided by Charles corrects this problem:
      21: IF DIP > 90
      22: THEN DIP = 180 - DIP
      23: AND AZM = 180 + AZM

Note: All dip angles are measured from horizontal, down to the dipping plane.

Where:
  ADAZ = apparent dip azimuth from true north
  ADM = apparent dip magnitude
  AHD = azimuth of hole deviation relative to magnetic north
  ANGLA = dip angle between pads 1 and 3
  ANGLB = dip angle between pads 2 and 4
  ANGLD = apparent dip azimuth from pad 1
  ANGLG = apparent dip azimuth before tool orientation
  AZ1 = azimuth of pad 1 relative to high side of hole
  AZM = true azimuth of dip direction
  DIP = true dip angle
  D13 = hole diameter between pads 1 and 3 (inches or mm)
  D24 = hole diameter between pads 2 and 4 (inches or mm)
  HAZ = azimuth of hole direction relative to true north
  H13 = offset between events on dip curves 1 and 3 (inches or mm)
  H24 = offset between events on dip curves 2 and 4 (inches or mm)
  MAGD = magnetic declination (East is positive, West is negative)
  PAZ = azimuth of pad 1 relative to true north
  RBR = relative bearing
  WD = well deviation angle
 

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