Monte Carlo Solution of Inverse Problems

With this document, a brief (so incomplete) review of the use of Monte Carlo methods in the solution of Inverse Problems is presented along with some examples of applications to Elastodynamics. The main examples are taken from the literature in Geophysics, e.g. in Explorative Seismology, but not only. A clear distinction is made between Inverse Problems treated as optimization prob-lems and a Bayesian approach to their theory. In the first case, Monte Carlo methods are used for random direct search in the model space of an Inverse Problem, while, in the second case, Monte Carlo sampling of probability density functions arises as the natural method for solving teh Inverse Problem, treated from a probabilistic point of view. This second approach to such Problems is relatively new and has been developed in recent years (mainly) within the Geophysics community. 1 Chapter