Multivariate Well Log Normalization via Covariance Preservation
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Solution Overview
Problem
Univariate normalization of well logs fails to accurately capture subsurface properties due to neglecting covariance between logs and introducing artifacts, leading to petrophysically inconsistent results.
Innovation Solution
A multivariate linear transformation method that differentiates between mutable and context logs, using reference logs to adjust the transformation parameters and reweight probability distribution components, ensuring that only mutable logs are changed during normalization while maintaining context logs' integrity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Object-affected harmful factors
If univariate normalization (histogram matching) is applied to well logs, then noise removal is achieved, but geologically significant signals are removed and petrophysical consistency is lost
Solution Approach 1:
The patent transitions from univariate normalization (handling each log independently in one dimension) to multivariate normalization (handling multiple logs together in multidimensional space). This is achieved by representing well logs as vectors in a high-dimensional space and applying linear transformations that preserve the covariance structure among different log types, thereby maintaining petrophysical relationships while removing noise.
Solution Approach 2:
The patent combines multiple well logs into a unified multivariate framework where the covariance matrix captures the relationships between different log types. By treating the logs as interconnected rather than independent, the normalization process preserves the joint statistical properties and petrophysical consistency across all logs simultaneously.
2Device complexity
If univariate normalization is applied to well logs, then processing simplicity is maintained, but covariance between logs is neglected and artifacts are introduced
Solution Approach 1:
The patent moves from one-dimensional univariate processing to multidimensional multivariate processing. Each well log becomes a dimension in a high-dimensional space, and the covariance matrix provides the structural framework. This dimensional expansion enables capture of inter-log relationships while the linear transformation approach keeps the methodology computationally tractable.
Solution Approach 2:
The patent transforms the normalization approach by changing from individual log statistics (mean, variance of single logs) to joint statistics (covariance matrix of multiple logs). This parameter change enables the system to account for correlations between different log types, improving measurement precision without excessive complexity.
3Reliability
If multivariate linear transformation is applied to normalize well logs, then petrophysical consistency is maintained, but differentiation between mutable and context logs is required
Solution Approach 1:
The patent segments the set of well logs into two categories: mutable logs (those to be transformed for normalization) and context logs (those to remain unchanged). This segmentation is implemented through a selection mechanism that identifies which logs should undergo transformation based on their role in the normalization process, allowing the system to preserve reference logs while transforming target logs.
Solution Approach 2:
The patent applies different treatment to different subsets of logs within the same dataset. Mutable logs receive the full multivariate linear transformation to achieve normalization, while context logs are preserved in their original form to maintain reference integrity. This local differentiation enables selective normalization that maintains overall petrophysical consistency.
Data Source
AI summary
Application logs to be normalized may be grouped into (1) mutable logs to be changed through normalization, and (2) context logs that remain constant. Reference logs may be grouped into same types of logs. Multivariate linear transformation may be performed on the application logs using the reference logs, with the parameters of the multivariate linear transformation adjusted based on comparison of the probability distribution of reference logs with the probability distribution of normalized application logs.