Earth's magnetic field

Definition

Earth's magnetic field is the magnetic field $B(x, t)$ at points $x$ in and near the Earth, at time $t$. It is the sum of an internal part and an external part. The internal part comes from sources inside the Earth, mainly the core and also the crust. The external part comes from currents in the ionosphere and magnetosphere. At a point of the surface, in the local frame with axes to geographic north, east and vertically down, write $B = (X, Y, Z)$. The elements of the field are:

1. the horizontal intensity $H = \sqrt{X^2 + Y^2}$ and the total intensity $F = \sqrt{X^2 + Y^2 + Z^2}$;
2. the declination $D$, the angle from geographic north to the horizontal component, measured eastward, so $(X, Y) = H (\cos D, \sin D)$;
3. the inclination $I$, the angle of $B$ below the horizontal, so $\tan I = Z / H$.