Dummies guide to robust inversion
(This is part of a series of documents I created during the PhD, with no intention to submit or reproduce them anywhere else. If you find it helpful, that's great. The formatting was butchered in the upload so there's a link to original document here: https://drive.google.com/open?id=1HJthXFj5Vta8cNSOtWFSJSN84yXQX012) Introduction to Norms A ‘norm’ is an expression of the size, or length, of a vector. These are typically expressed with a single bar ( ) for vectors, or a double-bar ( ) for matrices. They are used in conjunction with misfit to restrict the rate-of-change of model values during successive iterations of a deterministic numerical inversion process. Geophysical inversion presents an under-determined, or ill-posed, linear problem. The under-determined problem is easily surmised as a system where more variables than data are present. A mathematically infinite number of solutions exist to solve this problem