Large-scale hydraulic tomography and joint inversion of head and tracer data using the princial component geostatistical approach
Abstract/Contents
- Abstract
- The stochastic geostatistical inversion approach is widely used in subsurface inverse problems to estimate the unknown parameter field and corresponding uncertainty from noisy observations. However, the approach requires a large number of forward model runs to determine the Jacobian or sensitivity matrix, thus the computational and storage costs become prohibitive when the number of unknowns, m, and the number of observations, n increase. To overcome the challenges in the large-scale geostatistical inversion, the Principal Component Geostatistical Approach (PCGA) has been developed as a “matrix-free” geostatistical inversion strategy that avoids the direct evaluation of the Jacobian matrix through the principal components (low-rank approximation) of the prior covariance and the drift matrix with a finite-difference approximation. As a result, the proposed method requires about K runs of the forward problem in each iteration independently of m and n, where K can be much less than m and n for large-scale inverse problems. Furthermore, the PCGA is easily adaptable to different forward simulation models and various data types for which the adjoint-state method may not be implemented suitably. In this paper, we apply the PCGA to representative subsurface inverse problems to illustrate its efficiency and scalability. The low-rank approximation of the large-dimensional dense prior covariance matrix is computed through a randomized eigen-decomposition. A hydraulic tomography problem in which the number of observations is typically large is investigated first to validate the accuracy of the PCGA compared with the conventional geostatistical approach. Then the method is applied to a large-scale hydraulic tomography with 3 million unknowns and it is shown that underlying subsurface structures are characterized successfully through an inversion that involves an affordable number of forward simulation runs. Lastly, we present a joint inversion of head and tracer test data using MODFLOW and MT3DMS as coupled black-box forward simulation solvers. These applications demonstrate the advantages of the PCGA, i.e., the scalability to high-dimensional inverse problems and the ability to utilize multiple forward models as black boxes.
Description
| Type of resource | software, multimedia |
|---|---|
| Date created | February 21, 2014 |
Creators/Contributors
| Author | Lee, Jonghyun |
|---|---|
| Author | Kitanidis, Peter |
Subjects
| Subject | subsurface characterization |
|---|---|
| Genre | Dataset |
| Genre | Article |
Bibliographic information
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- User agrees that, where applicable, content will not be used to identify or to otherwise infringe the privacy or confidentiality rights of individuals. Content distributed via the Stanford Digital Repository may be subject to additional license and use restrictions applied by the depositor.
- License
- This work is licensed under an Open Data Commons Public Domain Dedication & License 1.0.
Preferred citation
- Preferred Citation
- Lee, Jonghyun and Kitanidis, Peter. (2014). Large-scale hydraulic tomography and joint inversion of head and tracer data using the princial component geostatistical approach. Stanford Digital Repository. Available at: http://purl.stanford.edu/zf668sp7224
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Stanford Research Data
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- cnilsen@stanford.edu
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