Minimum number of stress magnitude data records for model calibration

Geomechanical-numerical modeling aims to provide a comprehensive characterization of the stress tensor within rock volumes by leveraging localized stress magnitude data for model calibration. This calibration involves optimizing boundary conditions to achieve the closest alignment with in-situ stress measurements from boreholes, which provides magnitudes of the minimum and maximum horizontal stress. However, the high cost of acquiring stress magnitude data often results in sparse and incomplete datasets, potentially hindering meaningful calibration.

In this study, we use a comprehensive dataset of 45 stress magnitude data records acquired for the geomechanical characterization of the candidate siting region Zürich Nordost, a potential site for a deep geological repository in northern Switzerland. We demonstrate how the number of available stress magnitude data records influences the accuracy of 3D total stress tensor predictions. To achieve this, we introduce a novel statistical approach that enables the analytical estimation of a large number of model simulations, each calibrated using different numbers of stress magnitude data records. This approach evaluates how the availability of data influences stress predictions across formations with varying rock stiffness by rapidly assessing the stress states associated with numerous combinations of stress magnitude data records.

By comparing the resulting stress fields with an increasing number of data records, it is possible to estimate the minimum number of calibration points required to achieve a prediction range comparable to the range expected due to inherent data uncertainties. The results indicate that for the region Zürich Nordost, fewer than 15 data records are sufficient to achieve the same model precision and accuracy, suggesting that additional data would not significantly improve model accuracy.

In addition, detailed analysis of the dataset revealed an outlier with respect to our model, linked to a local stiffness anomaly. While this outlier represents a physically valid measurement, it significantly impacts stress predictions when calibration data are limited. However, as the calibration dataset size increases, the influence of the outlier diminishes. Our statistical approach also allows the objective identification of clear outliers within the calibration dataset, which in turn affects the minimum number of data points required for model calibration.

These results highlight the importance of dataset size and composition in reducing uncertainties, and providing a framework for optimizing calibration strategies. This study provides valuable insights for subsurface projects, such as energy storage, CO₂ sequestration, deep geological repositories, and geothermal energy, where precise stress predictions are critical.