Principal Investigator

Christoph H Arns Applied Mathematics, RSPhysSE, Australian National University

Project Title

Data Analysis for NMR in Porous Media

Brief Description for General Publications

Nuclear Magnetic Resonance is in porous media frequently employed for fluid typing and estimation of flow properties. The associated fundamental relationships between experimental noise, model bias, regularisation and resolution, are poorly understood, even for standard one-dimensional inverse Laplace experiments. The proposed project addresses theses questions not only in one, but up to four Laplace dimensions, a world first. Understanding above relationships will allow the development of optimal data acquisition techniques, making higher-dimensional NMR measurements faster and potentially applicable in well-logging applications or routine laboratory analysis. This would be a huge benefit to applications like fluid-typing, as current experiments take on the order of 2 days on very expensive experimental hardware. The main computational challenge is the repeated inversion of discretised Fredholm integrals of the first kind, in particular in higher dimensions, which is an extremely ill-conditioned and ill-posed problem. The best inversion algorithms involve positivity constraints, but are slowest. Repeated solutions are needed to find the optimal number and distribution of data acquisition points required for a desired resolution in a spectral domain of interest. A further issue with the inversion of high-dimensional transforms is that kernel bias and separability of the kernel can become an issue. We test these assumptions in an iterative forward modelling framework.