Inverse methods: problem formulation and probabilistic solutions

TY - CHAP

T1 - Inverse methods

T2 - problem formulation and probabilistic solutions

AU - Mosegaard, Klaus

AU - Hansen, Thomas Mejer

PY - 2016/4/1

Y1 - 2016/4/1

N2 - 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.

AB - 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.

U2 - 10.1002/9781118929063.ch2

DO - 10.1002/9781118929063.ch2

M3 - Book chapter

SN - 978-1-118-92905-6

SP - 9

EP - 28

BT - Integrated imaging of the earth

PB - Wiley

ER -