Geomagnetic Field / Geomagnetism
"Geomagnetic field" indicates magnetic field of the Earth (Geo-). You know that the Earth is a huge magnet itself since the N pole of a compass in your hand points the northward direction. Actually the Earth is a magnet with strength of 1020∼ 1025 times as strong as magnets around us.
The Earth is as a magnet, but it is not a lodestone (parmanent magnet) but an electric magnet. Very strong electric current is generated inside of the Earth and the current and the magnetic field is fluctuating anytime.
The Earth has some layers in itself.
There is rock ground shell with thickness of tens km, named "crust".
The Earth's radius is about 6,400km so that the crust is very thin skin of the Earth.
Below the crust, "mantle" whose depth is 2,900km lies. The mantle also composed almost entirely of rocks.
Inside the mantle, there are two layers of iron-nickel alloy, "outer core" and "inner core".
The inner core, which is the most lower layer in the Earth, is the just "core" of the Earth and has the radius of 1,200km. It is composed of solid state iron-nickel alloy. On the other hand, the outer core is in liquid state. Liquid metal in the outer core is convecting driven by the heat.
The geomagnetic field is generated in the outer core by dynamo process. Physical cycle in the dynamo process has two elements; "electric current occurs due to electric conductor moving in the magnetic field" and "magnetic field occurs around the electric current".
Geomagnetism is a field of academic study researching how the geomagnetic field is and has been, why it is generated, and how the geomagnetic field will be.
Geomagnetic field models
As menthoned above, magnetic field observed on the Earth's surface is almost origined in the core of the Earth. When we observe the field on the surface or in the space above the Earth by satellite, we can obtain the feature of almost whole geomagnetic field. Geomagnetic field model is a model representating the field at a time, made from these observations. The first construction of geomagnetic field model was by Gauss (). He introduced spherical harmonics functions and made an expansion with them for representating potential of the geomagnetic field. Now we call "Gauss coefficients" as the expansion coefficients of the field. Spherical harmonic functions are used for various applications in physics, e.g. quantum mechanics.
More details: "Earth's magnetic field" in Wikipedia
How about MAGE << Geomagnetic field >> Geodynamo