What is regularization?
In the broadest sense, “regularisation” is whatever it takes to get a unique solution to an “ill-posed” inverse problem – that is, to a problem where we are trying to estimate more parameters than we have information to do so. When do we do this? All the time really, for the earth is a complicated place and our models have to be parameter-simple so that parameters can be individually estimated. How do we regularise? We can do it ourselves through reducing the number of parameters that we try to estimate. Or we can use a simple lumped-parameter model rather than a complex physically-based model. Or we can let PEST do the regularisation for us. If done properly, the latter alternative has the following advantages. • we get maximum information out of the data, thereby achieving something that is close to a parameter set of minimum error variance; • by retaining many parameters in the model, we have the ability to explore the extent to which parameters, and any prediction that we make usin
