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This problem, so far as I know, still does not have a completely general analytical solution, though some special cases do.The complex cases are invariably modeled numerically with high speed computers.The first thing I want to try to do is to introduce the reader to the basic concepts needed to, hopefully, make sense of the various arguments.However, of necessity I cannot embark on a detailed and technical explication of the physics involved. Jacobs , do treat the technical details, but also carry enough more general material that the less mathematically inclined readers should be able to get something out of them.However, the mathematical equations which govern the physics of the problem are frightfully complicated, and may well constitute the single most difficult mathematical problem in all of geophysics.MHD models require the simultaneous solution of a full set of coupled non-linear vector differential equations. In 1950, the re-named Hardin-Simmons University awarded Barnes the honorary degree, D. He is emeritus professor of physics, University of Texas at El Paso, where he joined the faculty in 1936.I just stuck them into the numbered sequence with little letters; it's a lot easier than going through and renumbering all those references each time I find something.
There are two primary methods by which one can generate a mathematical description of the Earth's magnetic field, or any other field for that matter. I have inserted a few additional references that came to my attention only after this article was essentially finished. So far as I know the second edition is out of print at this time.In practice, the magnetic field is measured constantly at a number of official magnetic observatories all over the world, as well as at universities, or by other scientific teams and expeditions, and now several spacecraft measure the field well above the Earth, and out into deep space.These data are then fed into computer programs which use spherical harmonics to create a model for the field everywhere on the Earth.