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Software Documentation

Baseline Calculator - Equations Magnetic Directions.

A general understanding of the Earth’s magnetic field will aid you in understanding the functionality of the Baseline Calculator. The Baseline Calculator exists within the MagDisplay program as well as on its own.

General Info
The U.S.Geological Survey measures H, D, Z and F.
  F2 = X2 + Y2 + Z2 = H2 + Z2
  H2 + X2 + Y2
  X = H*cos(D)
  Y = H*sin(D) = X*tan(D)
  Z = F*sin(I) = H*tan(I)
  D = arctan(Y/X)
  I = arctan(Z/H)

Observatory
  - The Geomagnetic observatory where the data was gathered.
Instrument Number
  - The instrument number of the Magnetometer that was used to take the absolutes.
Observer
  - Specifies who conducted the absolutes.
Set Number
  - Absolutes are always done in sets of 4 to help eliminate measurement errors.
Pier
  - Each pier at each observatory has a measured Pier Correction associated with it.
Temperature
  - The temperature reading from the temperature probe at the Pier.
Date/Year Day
  - Date the absolutes were taken (the year day is used in the file name).
Mark
  - Each Pier can have one or more Pier Marks associated with it. These Marks have a measured True Azimuth of Mark.

Red = Theodolite Measured Values
Green = Calculated Values
Blue = Given Values and Constants
Baseline Program - Set 1.


Mark Up 1* (10.3428°)
  - Telescope pointing at Mark, magnetometer sensor up.
Mark Down 1* (10.3425°)
  - Telescope pointing at Mark, magnetometer sensor down.

West Down* (270.8147°)
  - Telescope pointing West, magnetometer sensor down.
East Down* (90.7233°)
  - Telescope pointing East, magnetometer sensor down.
West Up* (90.7825°)
  - Telescope pointing West, magnetometer sensor up.
East Up* (270.8417°)
  - Telescope pointing East, magnetometer sensor up.

South Down* (246.8156°)
  - Telescope pointing South, magnetometer sensor down.
North Up* (66.8233°)
  - Telescope pointing North, magnetometer sensor up.
South Up* (113.1547°)
  - Telescope pointing South, magnetometer sensor up.
North Down* (293.1483°)
  - Telescope pointing North, magnetometer sensor down.

Mark Up 2* (10.3433°)
  - Telescope pointing at Mark, magnetometer sensor up.
Mark Down 2* (10.3428°)
  - Telescope pointing at Mark, magnetometer sensor down.
   (* The time is in UTC when the measurement is taken. Degree, Minute and Second values are read from the Magnetometer after it is zeroed.)

  The Sensor readings follow a Cosine wave.
cosine wave      

Declination

  • The Magnetic Meridian is the average of the entered declination values. This averaging helps compensate for any errors.
    The Null Point Method
    When the sensor is perpendicular to H, or facing Magnetic East-West, the reading will be 0.
    Null Point Method
    This addition/subtraction will give you the
    Magnetic Meridian.

    Magnetic S. Meridian =
     (West Down + East Down + West Up + East Up) / 4
    = (270.8147° + 90.7233° + 90.7825° + 270.8417°) / 4
    = 180.7906°

  • The Offset is based on the 4 entered offset values.
      Offset Correction (EW) = 180 * PI * (-West Down + East Down - West Up + East Up) / (4 * 20900)

  • The Corrected Meridian value is the Offset added to the Meridian.
      Magnetic S. Meridian Corrected = Magnetic S. Meridian + Offset Correction (EW)

  • The Mean Mark is the average of all 4 Mark values.
      Mean Mark = (Mark Up 1 + Mark Down 1 + Mark Up 2 + Mark Down 2) / 4
                       = (10.3428° + 10.3425° + 10.3433° + 10.3428°) / 4 = 10.3428°

  • Magnetic Azimuth of Mark = Mean Mark + 90° - Magnetic S. Meridian
                                          = 10.3428° + 90° - 180.7906° = -80.4478°

  • The True Mark Azimuth is a constant at observatories for each Pier and Mark pair. (The Pier and Mark being used are listed at the top of the form.)
        True Azimuth of Mark = 199.1383°

  • Magnetic Declination should be between 0° and 180°, if not, subtract 180° until it is.
      Magnetic Declination = True Azimuth of Mark – Magnetic Azimuth of Mark
                                     = 199.1383° – -80.4478° = 279.5861° - 180° = 99.5861° pier

  • N, S, E, and W values are used as a comparison from day to day at the observatories.
      (West Up – East Down) * 60 = (90.7825° – 90.7233°) * 60 = 3.55 min.
      (East Up – West Down) * 60 = (270.8417° – 270.8147°) * 60 = 1.62 min.
      (South Down – North Up – 180°) * 60 = (246.8156° – 66.8233° - 180°) * 60 = -0.46 min.
      (North Down – South Up – 180°) * 60 = (293.1483° – 113.1547° - 180°) * 60 = -0.38 min.

  • The Mean F is obtained from the specified data file.
      F Mean = 53153.61 nT

  • The Pier Correction is a constant at observatories for each Pier and Mark pair. (The Pier and Mark being used are listed at the top of the form.)
        Pier Correction = -23.1 nT

  • Corrected F = F Mean + Pier Correction = 53153.61 + -23.1 = 53130.51 nT

Inclination

  • The Offset is based on the 4 entered offset values.
      Offset Correction (NS) = 180 * PI * (-South Down + North Up - South Up + North Down) / (4 * 53400)

  • Inclination (deg) = (South Down + North Up - South Up - North Down + 360°) / 4
                            = (246.8156° + 66.8233° - 113.1547° - 293.1483° + 360°) / 4 = 66.8340°

  • The Corrected Inclination value is the Offset added to the Inclination.
      Corrected Inclination = Inclination + Offset Correction (NS)

  • Horizontal Component = Corrected F * COS( Corrected Inclination )
                                      = 53130.51 * COS( 66.8340° ) = 20901.35 nT

  • Vertical Component = Corrected F * SIN( Corrected Inclination )
                                  = 53130.51 * SIN( 66.8340 ) = 48846.54 nT

PCDCP Magnetometer Ordinates

The Mean values are the averages of the 4 values pulled from the data files for the specified times.

  • H Mean Value = average of H values for the South Down, North Up, South Up and North Down times
                         = 20869.10 nT
  • D Mean Value = average of D values for the West Down, East Down, West Up and East Up times
                         = -64.70 nT
  • Z Mean Value = average of Z values for the South Down, North Up, South Up and North Down times
                         = 48293.68 nT
  • F Mean Value = average of F values for the South Down, North Up, South Up and North Down times
                         = 53153.61 nT

  • Abs. D (min) = 60 * Magnetic Declination = 60 * 99.5861 = 5975.16 min.
  • Abs. H (nT) = Horizontal Component = 20901.35 nT
  • Abs. Z (nT) = Vertical Component = 48846.54 nT

  • Scale Value = 3437.7468 / Abs. H = 3437.7468 / 20901.35 nT = 0.1645
  • H Computed Value = H Mean Value = 20869.10 nT
  • D Computed Value = D Mean Value * Scale Value = -64.70 * 0.1645 = -10.64 min.
  • Z Computed Value = Z Mean Value = 48293.68 nT
  • F Computed Value = F Mean Value = 53153.61 nT

  • D Baseline = Magnetic Declination * 60 – D Computed Value = 99.5861 * 60 – -10.64 = 5985.81 min.
  • H Baseline = Abs. H – H Computed Value = 20901.35 – 20869.10 = 32.25 nT
  • Z Baseline = Abs. Z – Z Computed Value = 48846.54 – 48293.68 = 552.86 nT
  • D (nT) = D Baseline / Scale Value = 5985.81 / 0.1645 = 36387.90

Some of the numbers on this page are slightly different than pictured due to rounding errors.


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