ABSTRACT
Backus and Gilbert, in a series of three articles,1 discuss the following method of solving inverse problems that arise in studies of the structure of the earth. Their articles are quite long and involve some rather advanced mathematics. I suspect that relatively few people have read them, although it would be well worth the effort. The first one cited starts, “Any single number which describes some property of the whole Earth will be called a gross datum of the Earth….” They look like heavy reading: it is tempting to rely on secondary sources in cases like these. However, having read the original papers in preparation for writing this chapter, I have come to see that the secondary sources that I am familiar with do not really do them justice. While Backus and Gilbert do describe another way to invert remote-sensing data, they also provide some important mathematical insight into necessary limitations of any inversion method. The secondary authors that I know of who describe Backus and Gilbert’s method either do not give the solution, or they simply state the result without proof, claiming that it is obvious. While I would encourage the reader to consult the original papers for themselves, I will explain the method, demonstrate the solution, and discuss some of its implications.
