A New Approach to Nonlinear Inverse Uncertainty Using Model Compression and Sparse Posterior Sampling (Invited)
Abstract
We outline a scalable uncertainty estimation method that allows for the broad search of model posterior space while maintaining computational efficiencies on the order of deterministic inverse solutions and requiring minimal storage. We accomplish this by combining an efficient model compression method, a parameter constraint mapping routine, a sparse geometric sampling scheme, and an efficient forward solver. While our method requires model space reduction to produce both a reduced and orthogonal model basis, we show that computationally burdensome methods, which factorize the model covariance matrix, can be replaced with a fast and storage-efficient compression method which acts on training models, directly. We present model-based Singular Value Decomposition as a “covariance-free” model reduction alternative, which is able to represent large correlated model spaces, equivalently, by only a few decorrelated basis vectors. We then map parameter constraints, in the original model space, to this reduced space in order to define a bounded subregion in feasible model space. We show that optimally sparse grids can be employed to sample this feasible model region, while forward evaluations determine which samples are likely. The result is an ensemble of equivalent models, consistent with general training model structures, that is used to infer nonlinear inverse solution uncertainty. We demonstrate, with a 2D field marine CSEM example, that this method reduces the parameter space by orders of magnitude, can require less than one forward solve per parameter, and results in an optimally-sparse representation of the posterior model space. We also present a set of uncertainty statistics, which quantify physical properties probabilistically, and result in potentially more robust reservoir scale interpretations.
- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2010
- Bibcode:
- 2010AGUFM.H41L..01F
- Keywords:
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- 0560 COMPUTATIONAL GEOPHYSICS / Numerical solutions;
- 0629 ELECTROMAGNETICS / Inverse scattering;
- 3225 MATHEMATICAL GEOPHYSICS / Numerical approximations and analysis;
- 3275 MATHEMATICAL GEOPHYSICS / Uncertainty quantification