Nonstationary Maximum Likelihood Method for Sonic Logging Dispersion
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Solution Overview
Problem
Current methods for estimating dispersion spectra in full waveform sonic (FWS) logging, such as the stationary maximum likelihood method, face challenges with over-estimation and inaccurate representations due to the need for partial linear moveout correction and pseudo-ensemble averaging, leading to high computational costs and reduced resolution.
Innovation Solution
A nonstationary maximum likelihood method is introduced, which uses nonstationary predictive error filtering within the Burg algorithm to estimate local matrices, eliminating the need for partial linear moveout correction and pseudo-ensemble averaging, thereby reducing computational costs and improving resolution.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If partial linear moveout correction and pseudo-ensemble averaging are used in stationary maximum likelihood method, then computational stability is improved, but computational cost increases and resolution decreases
Solution Approach 1:
The patent transitions from stationary to nonstationary maximum likelihood method, changing the fundamental assumption about signal stationarity. This parameter change allows the method to adapt to local variations in the data without requiring pseudo-ensemble averaging, thereby reducing computational cost while maintaining stability through the nonstationary framework's ability to handle local covariance structures.
Solution Approach 2:
The nonstationary method segments the signal analysis into local regions with their own covariance matrices, rather than applying a global stationary assumption. This segmentation allows computational stability to be achieved locally without the need for pseudo-ensemble averaging across the entire dataset, reducing overall computational cost.
2Reliability
If partial linear moveout correction and pseudo-ensemble averaging are used in stationary maximum likelihood method, then computational stability is improved, but measurement precision deteriorates
Solution Approach 1:
By changing from stationary to nonstationary assumptions, the method accurately captures local variations in dispersion characteristics without the blurring effect of pseudo-ensemble averaging. This improves measurement precision while the nonstationary framework's rigorous local covariance estimation maintains computational stability.
Solution Approach 2:
The nonstationary method applies local quality by estimating separate covariance matrices for different segments of the data, allowing each local region to be analyzed with its own characteristics. This eliminates the need for pseudo-ensemble averaging and improves dispersion spectra estimation accuracy while maintaining stability through local adaptation.
3Ease of operation
If conventional stationary method is used, then processing simplicity is maintained, but resolution in characterizing velocity dispersion decreases
Solution Approach 1:
The transition to nonstationary method changes the processing framework to accommodate local variations, which improves velocity dispersion resolution. While the processing becomes more complex, the patent implements efficient algorithms that compute local covariance matrices and apply nonstationary maximum likelihood estimation, achieving high resolution with manageable computational effort.
4Measurement precision
If nonstationary method is used, then resolution in characterizing velocity dispersion is improved, but device complexity increases
Solution Approach 1:
The nonstationary method improves resolution by changing the stationarity parameter, but the patent manages complexity through efficient implementation strategies including localized covariance matrix computation and systematic application of the nonstationary maximum likelihood framework, making the increased complexity tractable.
Solution Approach 2:
By segmenting the data into local regions for separate covariance estimation, the patent manages algorithmic complexity through modular processing. Each segment is handled independently with its own covariance matrix, making the overall nonstationary analysis more manageable while maintaining high resolution.
Data Source
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AI summary
The present disclosure describes methods and systems for estimating dispersion spectra for full waveform sonic (FWS) logging. One computer-implemented method includes receiving FWS data, performing frequency-spatial (FX) transform on the FWS data, using a nonstationary predictive error filtering (PEF) inversion on the transformed FWS data to estimate local matrix L and matrix P, calculating an inverse covariance matrix based on the estimated local matrix L and matrix P, and obtaining a nonstationary maximum likelihood method (MLM) spectra based on the inverse covariance matrix.