Magnetometer coordinate systems
Magnetometer coordinate systems

The strength and direction of the magnetic field describe a vector. The coordinate system used to order the magnetic field vector is usually one of two types -
  1. Cartesian or
  2. cylindrical polar

- and is usually orientated in one of two ways -

  1. geographically or
  2. geomagnetically
Figure 1a shows a local Cartesian system in which the magnetic field vector, F, has components, H, D, and Z. H is defined as positive northwards, D as positive eastwards, and Z as positive downwards. Here "north" can mean one of two things: Either, "north" can mean geographic north. This is defined as the direction of the great circle path to the geographic north pole. Alternatively, "north" can mean geomagnetic north. This is generally not the same as geographic north for reasons which will be apparent later. Geomagnetic north is usually defined as the direction that the local field points in the horizontal plane, either on average or on a "quiet" day when there is little short time scale (< 1 day) variation.

Figure 1b shows a local cylindrical polar coordinate system in which the magnetic field vector, F, has components, H, D, and Z. Here Z is the vertical component defined as positive downwards, as before, H is the component of the magnetic field in the horizontal plane, and D is the angle of the horizontal field component, H, from the eastward direction. D is referred to as the declination. (It is often to be seen on maps, indicating the angle between geographic and geomagnetic north.) Another angle that may be quoted is also shown in the figure. It is the inclination angle, I, between the vector, F, and the horizontal plane. We can see that (F, /2 -I , D) define a spherical polar coordinate system.

The various coordinate systems are often distinguished by using different letters for their orthogonal axes. For example, it is common to use (X, Y, Z) for a geographic coordinate system and (H, D, Z) for a geomagnetic coordinate system. However, there is no set standard and so any rules are made to be broken. For example, some people may prefer to use (X, Y, Z) and ( H, D, Z) to distinguish between Cartesian and cylindrical polar coordinates, respectively. You have been warned! At BAS we use (H, D, Z) to define a geomagnetic Cartesian coordinate system.

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