# Encyclopedia of Solid Earth Geophysics

Living Edition
| Editors: Harsh K. Gupta

# Inverse Theory, Monte Carlo Method

• Malcolm Sambridge
• Kerry Gallagher
Living reference work entry
DOI: https://doi.org/10.1007/978-3-030-10475-7_192-1

## Definition

Monte Carlo method. A computational technique making use of random numbers to solve problems that are either probabilistic or deterministic in nature. Named after the famous Casino in Monaco.

Monte Carlo inversion method. A method for sampling a parameter space of variables representing unknowns, governed by probabilistic rules.

Markov chain Monte Carlo (McMC). A probabilistic method for generating vectors or parameter variables whose values follow a prescribed density function.

## Introduction

Because geophysical observations are made at (or very near) the Earth’s surface, all knowledge of the Earth’s interior is based on indirect inference. There always exists an inverse problem where models of physical properties are sought at depth that are only indirectly constrained by the available observations made at the surface. Geophysicists have been dealing with such problems for many years and in doing so have made substantial contributions to the understanding of inverse problems.

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## Notes

### Acknowledgments

We would like to thank FAST (French-Australia Science and Technology exchange program) for their support during the preparation of this entry. This project is supported by the Commonwealth of Australia under the International Science Linkages program.

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