Bayesian Inversion of Time-lapse Seismic Data using Bimodal Prior Models
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The objective of the current study is to make inference about reservoir properties from seismic reflection data. The inversion problem is cast in a Bayesian framework, and we compare and contrast three prior model settings; a Gaussian prior, a mixture Gaussian prior and a generalized Gaussian prior. A Gauss-linear likelihood model is developed and by the convenient properties of the family of Gaussian distributions, we obtain the explicit expressions for the posterior models. The posterior models define computationally efficient inversion methods that can be used to make predictions of the reservoir variables while providing an uncertainty assessment. The inversion methodologies are tested on synthetic seismic data with respect to porosity, water saturation, and change in water saturation between two time steps. The mixture Gaussian and generalized Gaussian posterior models show encouraging results under realistic signal-noise ratios.