Sparse Bayesian Learning for NMR Inversion
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Current NMR logging technologies face challenges in accurately characterizing subterranean formations by obtaining multi-dimensional property distributions, such as T1-T2 and D-T2 distributions, due to limitations in data processing and inversion methods, which can lead to incomplete fluid analysis and characterization of reservoirs.
Innovation Solution
The implementation of sparse Bayesian learning (SBL) for processing NMR data to determine multi-dimensional property distributions, utilizing an overcomplete dictionary and Monte-Carlo resampling to refine the distributions, thereby improving the accuracy and resolution of NMR measurements.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional NMR data processing and inversion methods are used, then the logging process is simpler, but the accuracy and resolution of multi-dimensional property distributions are insufficient
Solution Approach 1:
The patent transforms the NMR inversion problem by changing the parameter representation from conventional continuous distributions to sparse discrete representations using overcomplete dictionaries. This allows accurate recovery of multi-dimensional property distributions (T1-T2, D-T2) by representing them as linear combinations of dictionary atoms with sparse coefficients, improving measurement precision while managing computational complexity through sparsity constraints
Solution Approach 2:
The patent replaces conventional mechanical iterative inversion methods with a statistical learning approach based on sparse Bayesian learning. By substituting the traditional mechanical optimization process with a probabilistic framework that leverages sparsity priors and overcomplete dictionary representations, the method achieves higher accuracy in recovering multi-dimensional property distributions without requiring complex iterative mechanical adjustments
2Measurement precision
If conventional inversion methods are used, then computational resources are reduced, but the resolution and accuracy of NMR measurements are insufficient
Solution Approach 1:
The patent changes the parameter space by representing multi-dimensional property distributions in terms of sparse coefficients over an overcomplete dictionary. This parameter transformation enables high-resolution NMR measurements because the sparse representation concentrates information in fewer coefficients, improving resolution while the structured sparsity pattern reduces the effective computational burden compared to full-dimensional inversion
Solution Approach 2:
The patent extracts only the essential information from the NMR data by representing the multi-dimensional property distributions as sparse linear combinations of dictionary atoms. By taking out and retaining only the significant coefficients (those with non-negligible magnitudes) and discarding the rest, the method achieves high measurement resolution while reducing computational burden through selective information extraction
3Measurement precision
If sparse Bayesian learning with overcomplete dictionaries is used, then accuracy of property distribution recovery is improved, but computational complexity increases
Solution Approach 1:
The patent manages computational complexity by changing the parameter representation to sparse coefficients. Although the overcomplete dictionary increases the dimensionality of the parameter space, the sparsity constraint effectively reduces the number of active parameters that need to be computed, balancing accuracy improvement with computational tractability through efficient sparse optimization algorithms
Solution Approach 2:
The patent applies partial action by using an overcomplete dictionary where only a subset of dictionary atoms are actually needed to represent the property distributions. By providing more dictionary atoms than strictly necessary (excessive action) but relying on sparsity to select only the relevant ones (partial action), the method improves accuracy through richer representation while keeping computational complexity manageable through selective usage
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach enables the efficient recovery of sparse representations of NMR data, allowing for more accurate characterization of subterranean formations and reduced waiting times during logging processes, with improved resolution and reduced computational burden.
Implementation Method 1
The tool performs a nuclear magnetic resonance (NMR) measurement and obtains NMR data for a local region of the subterranean formation adjacent the tool
Data Source
AI summary
Methods and systems for characterizing a subterranean formation using nuclear magnetic resonance (NMR) measurements are described herein. One method includes locating a downhole logging tool in a wellbore that traverses the subterranean formation, and performing NMR measurements to obtain NMR data for a region of the subterranean formation. The NMR data is processed by employing sparse Bayesian learning (SBL) to determine a multi-dimensional property distribution of the NMR data (e.g., T1-T2, D-T2, and D-T1-T2 distributions). The sparse Bayesian learning can utilize Bayesian inference that involves a prior over a vector of basis coefficients governed by a set of hyperparameters, one associated with each basis coefficient, whose most probable values are iteratively estimated from the NMR data. The sparse Bayesian learning can achieve sparsity because posterior distributions of many of such basis coefficients are sharply peaked around zero.