Linear inverse theory

In mathematical statistics is a well-established theory called ``linear inverse theory.'' ``Geophysical inverse theory'' is similar, with the additions that (1) variables can be sample points from a continuum, and (2) physical problems are often intractable without linearization. Once I imagined a book that would derive techniques used in industry from general geophysical inverse theory. After thirty years of experience I can report to you that very few techniques in routine practical use arise directly from the general theory! There are many reasons for this, and I have chosen to sprinkle them throughout discussion of the applications themselves rather than attempt a revision to the general theory. I summarize here as follows: the computing requirements of the general theory are typically unrealistic since they are proportional to the cube of a huge number of variables, which are sample values representing a continuum. Equally important, the great diversity of spatial and temporal aspects of data and residuals (statistical nonstationarity) is impractical to characterize in general terms.