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Bayesian Inversion of Time-lapse Seismic Waveform Data Using an Integral Equation Method
- Publisher: European Association of Geoscientists & Engineers
- Source: Conference Proceedings, IOR 2017 - 19th European Symposium on Improved Oil Recovery, Apr 2017, Volume 2017, cp-511-00120
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Abstract
In the last couple of decades, we have witnessed an increased use of time-lapse seismic data. Interpretation of time-lapse seismic data can give a better understanding of the oil saturation in the reservoir, leading to identification of the water-flooded areas and pockets of remaining oil, and an improved understanding of compartmentalization of the reservoir. Within the context of dynamic reservoir characterization or seismic history matching, where one performs a quantitative integration of time-lapse seismic and production data, the covariance matrix (quantifying the uncertainty) of the seismic data needs to be specified. Usually, this is done in a very ad-hoc manner, for example by using a diagonal covariance matrix where the uncertainty is given in percentage of the measurement values. Eikrem et al. (2016) has recently demonstrated that a more accurate and complete dynamic reservoir characterization can be obtained if one performs a Bayesian seismic waveform inversion for the seismic parameters and use the full covariance matrix when updating permeability and porosity. In that paper a simple linear Born inversion was used, and it is of interest to investigate whether similar results hold for a more advanced seimic inversion method. The present work will focus on Bayesian nonlinear full waveform inversion (FWI) to get an estimate of the uncertainty in the seismic inversion. In contrast with the main stream of researchers within the FWI community, we develop a direct iterative nonlinear Bayesian inversion method based on an explicit representation of the data sensitivity function in terms of Green functions, rather than the indirect optimization approach based on the adjoint state method. Our method is based on the T-matrix approach by Jakobsen and Ursin (2015).