Variogram Map and Rose Diagram for Spatial Continuity Modeling
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Solution Overview
Problem
Conventional methods for computing variogram models in geostatistics require domain expertise and involve trial and error, with automated methods often relying on blind curve fitting that is not user-friendly or accurate.
Innovation Solution
The use of a variogram map and rose diagram to compute semi-variograms, allowing for non-linear fitting and user interaction through graphical interfaces, enabling alignment of the maximum direction of spatial continuity and adjustment of model parameters for improved accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional trial and error methods are used for semi-variogram fitting, then domain expertise can be utilized to guide the process, but the process becomes time-consuming and requires considerable manual intervention
Solution Approach 1:
The system performs preliminary computation of experimental semi-variograms along multiple azimuths and automatically generates a variogram map before user interaction, preparing the foundation for rapid iterative fitting without requiring users to manually set up each calculation
Solution Approach 2:
The system provides visual feedback through the variogram map and rose diagram that immediately shows users how their parameter adjustments affect the fitting quality, allowing rapid iteration without waiting for complex computational results
2Extent of automation
If automated least squares curve fitting is used, then the process becomes faster and more automated, but the fitting becomes blind to user input and less accurate for rigorous cases
Solution Approach 1:
The system transitions from static automated fitting to a dynamic interactive process where users can adjust parameters in real-time based on visual feedback from the variogram map, combining automation with user control
Solution Approach 2:
The variogram map and rose diagram serve as intermediary visual representations that translate complex fitting results into intuitive graphical feedback, enabling users to make informed adjustments without needing deep domain expertise
3Loss of information
If multiple experimental semi-variograms are computed along different azimuths, then the spatial continuity can be better analyzed, but the complexity of the interface and number of parameters increases
Solution Approach 1:
The system merges multiple experimental semi-variograms from different azimuths into a single integrated variogram map and rose diagram, preserving spatial information while simplifying the interface into unified visual representations
Solution Approach 2:
The system transforms the analysis from examining multiple separate 2D semi-variogram plots to a single 3D variogram map with azimuth as the third dimension, allowing comprehensive spatial analysis in a unified view
Data Source
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AI summary
Systems and methods for computing a variogram model, which utilize a variogram map and a rose diagram to compute the model.