Definition
Bayesian inversion is a statistical method used in many geoscience applications to assess the probability distribution of the unknown variables conditioned on the available measurements, where the posterior model is uniquely defined by a prior model representing the knowledge of the variable before the data acquisition and a likelihood model linking the target variables and the measured data.
Introduction
Geophysics theories, such as seismology, electromagnetism, and poro-elasticity, include mathematical relations of the physical processes and properties of rock and fluid properties in the subsurface. If the rock and fluid physical properties are known, then it is possible to apply a forward operator to predict the geophysical response of the subsurface. For example, if the volumetric fractions of the mineral and fluid components of porous rocks are known, then their seismic response can be predicting by solving a set of poro-elastic equations. In practice, the...
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Bibliography
Aki K, Richards PG (1980) Quantitative seismology: theory and methods. W.H. Freeman, New York
Buland A, Omre H (2003) Bayesian linearized AVO inversion. Geophysics 68(1):185–198
de Figueiredo LP, Grana D, Roisenberg M, Rodrigues BB (2019) Multimodal Markov chain Monte Carlo method for nonlinear petrophysical seismic inversion. Geophysics 84(5):M1–M13
Grana D, Fjeldstad T, Omre H (2017) Bayesian Gaussian mixture linear inversion for geophysical inverse problems. Math Geosci 49(4):493–515
Mosegaard K, Tarantola A (1995) Monte Carlo sampling of solutions to inverse problems. J Geophys Res 100:12,431–12,447
Rimstad K, Avseth P, Omre H (2012) Hierarchical Bayesian lithology/fluid prediction: a North Sea case study. Geophysics 77(2):B69–B85
Sambridge M, Mosegaard K (2002) Monte Carlo methods in geophysical inverse problems. Rev Geophys 40(3):3–1
Scales JA, Tenorio L (2001) Prior information and uncertainty in inverse problems. Geophysics 66:389–397
Tarantola A (2005) Inverse problem theory. SIAM, Oxford
Ulrych TJ, Sacchi MD, Woodbury A (2001) A Bayes tour of inversion: a tutorial. Geophysics 66:55–69
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Grana, D., Mosegaard, K., Omre, H. (2021). Bayesian Inversion in Geoscience. In: Daya Sagar, B., Cheng, Q., McKinley, J., Agterberg, F. (eds) Encyclopedia of Mathematical Geosciences. Encyclopedia of Earth Sciences Series. Springer, Cham. https://doi.org/10.1007/978-3-030-26050-7_415-1
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DOI: https://doi.org/10.1007/978-3-030-26050-7_415-1
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