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Published on: November 1, 2024
The generalized Phillips-Twomey method for NMR relaxation time inversion
Yang Gao1, Lizhi Xiao2, Yi Zhang3
1State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum, Beijing 102249, China; College of Science, China University of Petroleum, Beijing 102249, China.
This study introduces a robust method for Nuclear Magnetic Resonance (NMR) relaxation time inversion. The generalized Phillips-Twomey regularization effectively solves ill-posed integral equations, improving accuracy in NMR data analysis.
Area of Science:
- Nuclear Magnetic Resonance (NMR) spectroscopy
- Applied mathematics
- Geophysics
Background:
- NMR relaxation time inversion is crucial for analyzing subsurface properties.
- The problem is mathematically ill-posed, often leading to inaccurate numerical solutions.
- A well-posed method for this problem has been sought since the 1950s.
Purpose of the Study:
- To introduce and validate the generalized Phillips-Twomey regularization method for NMR relaxation time inversion.
- To mathematically prove the method's existence, uniqueness, stability, and convergence.
- To demonstrate the method's effectiveness using numerical simulations and core analyses.
Main Methods:
- Application of the generalized Phillips-Twomey regularization method.
- Mathematical proofs for existence, uniqueness, stability, and convergence.
- Numerical simulations of NMR transverse relaxation time inversion.
- Analysis of real-world NMR core data.
Main Results:
- The generalized Phillips-Twomey method is proven to be well-posed for NMR inversion.
- Numerical simulations show the method's high accuracy and reliability.
- Core analyses confirm the method's effectiveness and agreement with physical realities.
Conclusions:
- The generalized Phillips-Twomey regularization method offers an effective solution for the ill-posed problem of NMR relaxation time inversion.
- This method provides accurate and stable results, validated by both simulations and real-world data.
- The study advances NMR data processing techniques for geophysical and other applications.
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