Handling zero standard deviation in adaptive localization for field parameters in ERT

[sondreso]

During updates in ERT with adaptive localization for both facies and petrophysical field parameters (such as permeability and porosity), a recurring issue with zero standard deviation values for certain grid cells has been observed. These values usually arise from fixed geological zones with no variance or due to the presence of inactive grid cells at the edge of the defined areas. As a consequence, there may be misleading cross-correlations or divide by zero errors during the update step after the initial forecast. The current extrapolation methods for undefined grid cell values can result in multiple grid cells having the same fixed value across all realizations, thereby leading to a zero std.dev.

The problem is not easily solvable by users as it requires implementing additional algorithms or injecting noise into the values, which is impractical. Users are also unable to discern whether error messages arising from this issue can be safely ignored or entail critical malfunctions.

Proposed Solutions

1. Early Error Reporting and Input Validation: ERT should conduct early checks for zero std.dev values:

   • If all grid cell values have a std.dev of zero, the field parameters in question should not be included in updates, and users should be notified to remove these parameters since they cannot be updated.
   • If only some of the grid cells exhibit a std.dev of zero, filtering should be applied to update only those cells with a positive std.dev, while maintaining the initial value of cells with a zero std.dev across all realizations.

2. Adaptive Localization Processing Optimization:

   • The process should be optimized to skip the processing of grid cell values that cannot be updated due to a zero std.dev. This would not only prevent unnecessary computations but also reduce support queries and confusion arising from erroneous cross-correlations and divide by zero errors during adaptive localization.

3. Documentation and User Guidance:

   • Provide clear documentation and feedback mechanisms informing users about the detection of suspicious values (e.g., a zero std.dev) and advising on correct procedures or automated handling by ERT.

Screenshot of error messages: