# Magnetic components

The Earth's magnetic field is a vector quantity; at each point in space it has a strength and a direction. To completely describe it we need three quantities. These may be:

- three orthogonal strength components (
**X**,**Y**, and**Z**); - the total field strength and two angles (
**F**,**D**,**I**); or - two strength components and an angle (
**H**,**Z**,**D**)

The relationship between these 7 elements is shown in the diagram.

Component | Description |
---|---|

F | the total intensity of the magnetic field vector |

H | the horizontal intensity of the magnetic field vector |

Z | the vertical component of the magnetic field vector; by convention Z is positive downward |

X | the north component of the magnetic field; X is positive northward |

Y | the east component of the magnetic field; Y is positive eastward |

D | magnetic declination, defined as the angle between true north (geographic north) and the magnetic north (the horizontal component of the field). D is positive eastward of true North. |

I | magnetic inclination, defined as the angle measured from the horizontal plane to the magnetic field vector; downward is positive |

**D** and **I** are measured in degrees. All other elements are measured in nanotesla (nT; 1 nT = 10^{-9} Tesla).

The seven elements are related through the following simple expressions.

$\begin{array}{cc}\text{Declination (D)}& D={\mathrm{tan}}^{-1}\left(\frac{Y}{X}\right)\\ \text{Inclination (I)}& I={\mathrm{tan}}^{-1}\left(\frac{Z}{H}\right)\\ \text{Horizontal (H)}& H=\sqrt{{X}^{2}+{Y}^{2}}\\ \text{North (X)}& X=H\mathrm{cos}\left(D\right)\\ \text{East (Y)}& Y=H\mathrm{sin}\left(D\right)\\ \text{Intensity (F)}& F=\sqrt{{X}^{2}+{Y}^{2}+{Z}^{2}}\end{array}$