Uncertainty quantification of groundwater (GW) aquifer parameters is critical for efficient management and sustainable extraction of GW resources. These uncertainties are introduced by the data, model, and prior information on the parameters. Here, we develop a Bayesian inversion framework that uses Interferometric Synthetic Aperture Radar (InSAR) surface deformation data to infer the laterally heterogeneous permeability of a transient linear poroelastic model of a confined GW aquifer. The Bayesian solution of this inverse problem takes the form of a posterior probability density of the permeability. Exploring this posterior using classical Markov chain Monte Carlo (MCMC) methods is computationally prohibitive due to the large dimension of the discretized permeability field and the expense of solving the poroelastic forward problem. However, in many partial differential equation (PDE)‐based Bayesian inversion problems, the data are only informative in a few directions in parameter space. For the poroelasticity problem, we prove this property theoretically for a one‐dimensional problem and demonstrate it numerically for a three‐dimensional aquifer model. We design a generalized preconditioned Crank‐Nicolson (gpCN) MCMC method that exploits this intrinsic low dimensionality by using a low‐rank‐based Laplace approximation of the posterior as a proposal, which we build scalably. The feasibility of our approach is demonstrated through a real GW aquifer test in Nevada. The inherently two‐dimensional nature of InSAR surface deformation data informs a sufficient number of modes of the permeability field to allow detection of major structures within the aquifer, significantly reducing the uncertainty in the pressure and the displacement quantities of interest.
A comprehensive model for the kyr and Myr timescales of Earth's axial magnetic dipole field
Abstract. We consider a stochastic differential equation modelfor Earth's axial magnetic dipole field.Our goal is to estimate the model's parametersusing diverse and independent data sources that had previously been treated separately,so that the model is a valid representation of an expanded paleomagnetic recordon kyr to Myr timescales.We formulate the estimation problem within the Bayesian frameworkand define a feature-based posterior distributionthat describes probabilities of model parameters givena set of features derived from the data.Numerically, we use Markov chain Monte Carlo (MCMC)to obtain a sample-based representation of the posterior distribution.The Bayesian problem formulation and its MCMC solutionallow us to study the model's limitations and remaining posterior uncertainties.Another important aspect of our overall approach is thatit reveals inconsistencies between model and data or within the various data sets.Identifying these shortcomings is a first and necessary step towards building more sophisticated models or towards resolving inconsistencies within the data.The stochastic model we derive representsselected aspects of the long-term behavior of the geomagnetic dipole fieldwith limitations and errors that are well defined.We believe that such a model is useful (besides its limitations) for hypothesis testing and give a few examples of how the model can be used in this context.
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- Award ID(s):
- 1644644
- NSF-PAR ID:
- 10131454
- Date Published:
- Journal Name:
- Nonlinear Processes in Geophysics
- Volume:
- 26
- Issue:
- 3
- ISSN:
- 1607-7946
- Page Range / eLocation ID:
- 123 to 142
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.5194/npg-26-123-2019
