f Hume, popper, bayes and geophysical inverse problems

We distinguish two approaches to geophysical inverse problems. One is the opposite, or inverse, of the forward problem. Signature deconvolution and migration are examples of this kind of inversion. The data are inverted to arrive at the Barth model. The other approach is iterative forward modeping, in which we try to match the measured data with synthetic data created with a model and the given theory. In recent years Bayes's rule has been a popular way to measure the quality of the result obtained by iterative forward modelling. We focus on the philosophical arguments for the two approaches and on the difficulties in applying them to geophysical inverse problems.