Reverse magnetic dating
This mathematical tool was invented by the ubiquitous German mathematician, Carl Freidrich Gauss, circa 1835, for the purpose of evaluating the Earth's magnetic field.
This ingenious method uses an infinite sum of trigonometric functions to evaluate a field, on the surface of a sphere embedded in the field.
This is a poor idea, as it is very hard to reconcile with the spatial extent of these higher order components, as illustrated by figure 2.5 in [1, page 25].
It is very hard to imagine a field of magnetic rocks, or a coherent telluric current, either of which is as large as one half or one quarter of the Earth.
All of my comments and arguments are therefore directed only towards the first edition, cited at the top of the page.
At this time I have not seen the second edition of the book, though I know that one exists.
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.
So far as I know the second edition is out of print at this time.
Since any surface can be evaluated, then the complete three dimensional shape of the field can be returned by extending the analysis to an integration over a family of nested, concentric spheres, which fills the space of interest.
Of course, in practice, real computers cannot carry out an infinite sum, and have to stop summing after a finite number of terms.
But, as you might imagine, modern computers can add a lot of numbers together very fast, so while this may have been a fundamental problem for Gauss, it is no longer all that bothersome.
One can approximate the true shape of the field by extending the sum to an arbitrarily large number of terms, the only limitation being the practicalities involved.
One way, which I will call the physical model, is to derive the form of the field directly from the equations that govern the physical processes by which the field is generated.