Abstract
Noise-contaminated data and prior information on model parameters are the basic elements of any inverse problem. Probability can be seen from two viewpoints: a purely mathematical perspective and a heuristic perspective. This chapter deals with Kolmogorov's mathematical definition of probability. In probabilistic, nonlinear inversion with complex priors, Monte Carlo methods are often the only method that is able to characterize distributions in high-dimensional model spaces. The idea is to attempt to produce independent realizations from the posterior, but the problem of generating such realizations may be difficult to solve. In some cases the computational burden of data inversion is so large that it is tempting, or even necessary, to use what is known as sparse methods. Inverse problem theory belongs to mathematical physics. It looks like a purely mathematical topic: Parameters are identified, probability densities are defined, and equations relating the individual parameters are used to solve the problem.
| Original language | English |
|---|---|
| Title of host publication | Integrated imaging of the earth : theory and applications |
| Publisher | Wiley |
| Publication date | 1 Apr 2016 |
| Pages | 9-28 |
| Chapter | 1 |
| ISBN (Print) | 978-1-118-92905-6 |
| DOIs | |
| Publication status | Published - 1 Apr 2016 |