SIO 230 Geophysical Inverse Theory 2009
Prolog
The key factor that makes inverse theory different from simple
parameter estimation (a classical statistical problem) is that the
number of observations we can make is finite, while the unknowns are
functions (usually of position)
which require infinitely variables for their full
description. Thus finding a model solution involves a choice from an
infinitely large collection of alternative solutions. The approach
taken in the class is to apply mathematical optimization to select the
simplest models which avoids the introduction of exciting features that
are in fact unnecessary. To discover reliable properties of the Earth,
independent on any particular model, we can calculate upper and lower
bounds on functionals that represent those properties; that involves
optimization again.
A list of potential topics can be found
here.
We probably will not have the time in one Quarter to
cover them all.