A deconvolution-based method for nuclear magnetic resonance T₁-T₂ inversion

Area of Science:

• Geophysics
• Petroleum Geoscience
• Analytical Chemistry

Background:

• Nuclear Magnetic Resonance (NMR) relaxation data analysis commonly uses multi-exponential fitting or linear inversion.
• Traditional methods struggle with short T2 components in materials like organic matter and bitumen due to signal decay.
• This leads to incomplete recovery of short T2 components in 2D Laplace inversion, impacting accuracy.

Purpose of the Study:

• To develop an improved method for analyzing NMR relaxation data, specifically addressing short T2 component recovery.
• To enhance the accuracy of T1-T2 inversion, particularly for samples with complex relaxation behaviors.
• To mitigate the ill-conditioned nature of conventional inversion methods and improve computational efficiency.

Main Methods:

• Conversion of multi-exponential nonlinear fitting to a linear inversion problem.
• Further transformation of the linear inversion problem into a deconvolution problem.
• Development and application of a uniform logarithmic fitting and regularized deconvolution (LFD) algorithm.
• Reconstruction of echo data and inversion kernel using uniform logarithmic fitting.

Main Results:

• The LFD algorithm significantly improves the accuracy of short T2 component inversion in T1-T2 maps.
• Demonstrated substantial error reduction in kerogen saturation (20.20% to 2.60%), bitumen (14.97% to 1.90%), and clay bound water saturation (5.85% to 0.90%) in a shale model.
• The method mitigates ill-conditioning and enhances computational efficiency compared to traditional algorithms.

Conclusions:

• The proposed LFD algorithm effectively addresses the incomplete and inaccurate recovery of short T2 components.
• This method offers a significant advancement for T1-T2 inversion, particularly in complex geological samples.
• The study provides insights into the applicable conditions for the LFD algorithm in NMR relaxation analysis.