Calibration data and exploration programs

The tool FAST calibration

A key step in geomechanical modelling of the 3D in situ stress state is to find lateral displacement boundary conditions that result in a best fit with respect to the point-wise measurements of the minimum horizontal stress Shmin and the estimates of the maximum horizontal stress SHmax. In a linear system, i.e. when the stress-strain relationship is assumed to be based on linear elasticity, the best fit can be determined with a least square fit. The FAST calibration tool is performing this step automatically. The tool has been updated within this project phase (Ziegler et al., 2023a,b) and translated in addition to the Matlab version into a Python code (Zielger, 2023a,b). The figure below shows the basic principle with a pair of SHmax and Shmin stress magnitude data point. Repeating this for all available stress magnitude data records results in a best fit boundary condition.

Basic workflow of the tool FAST Calibration. a) Stress state from three model scenarios with arbitrary displacement boundary conditions is used to span the entire solution space. b) Measured and estimated stress magnitude data records c). A set of linear equations is formulated d) Estimation of the best-fit boundary condition with respect to the pair stress magnitudes.

Modeling for optimal localization of input and calibration data

Geomechanical models are tuned with point-wise stress magnitude measurements. However, acquiring such calibration data is costly and thus, a key question is how much data records are needed to achieve a robust model result. To examine how the number of calibration data influences the reliability of modeled stress we use a unique dataset from northern Switzerland. We identified the minimum number of calibration data records required, so that additional data does not increase model accuracy. The figure below explains the basic concept of our workflow. The results of this individual case study shows that 16 data records are sufficient and more calibration data do not improve the model accuracy. This finding allows for more efficient site investigations, helping reduce the cost and complexity of subsurface characterization without compromising confidence in model performance (Laruelle et al., in review). With this framework, we are also capable to identify stress measurements that, by coincidence, are acquired at a very local anomaly. These so-called outliers distort the quality of model predictions. To systematically identify such outliers in the calibration data, we developed and documented the Python tool DOuGLAS (Laruelle and Ziegler, 2025a;b).

Variability in observed values and modeling uncertainties. (a) Young’s Modulus within a rock unit, shown as a probability distribution (bell curve). The light blue region, representing 90% of the values, is bounded by red edges. The dark blue dashed line marks the median, and the light blue dashed lines indicate the 5th and 95th percentiles (P05 and P95, respectively). (b) Modeled stress magnitudes within a rock unit derived from rock properties variability, depicted as a probability distribution. The light orange region, representing 90% of the values, is bounded by red edges. The dashed dark red line marks the median, and the orange dashed lines indicate the 5th and 95th percentiles. (c) Evolution of the range of modeled stress magnitudes (gray area) with increasing percentages of the total set of stress magnitude data records used for model calibration. Dark red dashed line represents the stress prediction when all available calibration data records are used. This line corresponds to the P50 from panel (b). The P05 and P95 percentiles from (b) are shown by the orange dashed lines. The two red circles indicate the required percentage of calibration data records to achieve a P95 smaller than the P95 derived from rock properties (1), and a P05 larger than the P05 derived from rock properties (2).

Stress perturbations at faults and critical distance

For the prediction of the in-situ stress state in an undisturbed rock volume it is important to quantify at which distance stress perturbations due to faults are still resolvable in comparison to other stress perturbations and stress variability due to rock stiffness variability. We use two approaches: 1.) A series of generic 3-D models to investigate which component of the stress tensor is affected at which distance from the fault (Reiter et al., 2024) and 2.) A case study from the siting region of Zürich Nordost in Northern Switzerland where we have a unique stress magnitude data for model calibration (Velagala et al., in prep.). Both studies concentrate on the far field, located hundreds of meters from the fault zone. Both studies show that an influence on either the stress tensor orientation or principal stress magnitudes in the far field beyond 500 m from the fault is much smaller than e.g. the impact of rock stiffness variability, which is a key control of stress variability, or the uncertainties of the measurements and estimate of the stress magnitudes that are used for the model calibration. The figure below shows the impact of faults on the SHmax orientation. The differences are smaller than the resolution limit of SHmax stress indicator. The same holds for the stress magnitudes as the impact of faults a magnitude smaller at greater distance compared to the expected variability due to rock stiffness distribution and stress magnitude uncertainties.

Impact of faults along two cross sections : SHmax orientation changes along N-S cross section through borehole STA3‑1 (white line). Upper figure shows the best fit model with faults and a friction coefficient of µ=0.6. Lower figure shows the model results where the faults have been excluded. Horizontal black lines show top and bottom of the Opalinus Clay layer. 

References:

Laruelle, L. and Ziegler, M. O.: Manual of the Python Script DOuGLAS v1.0, WSM TR, 25-03, 33 pp., https://doi.org/10.48440/wsm.2025.003, 2025.

Laruelle, L. and Ziegler, M. O.: Python Script DOuGLAS v1.0, GFZ Data Services, https://doi.org/10.5880/wsm.2025.003, 2025.

Laruelle, L., Ziegler, M. O., Reiter, K., Heidbach, O., Desroches, J., Giger, S. B., Degen, D., and Cotton, F.: Minimum amount of stress magnitude data records for reliable geomechanical modeling, Rock Physics and Rock Engineering, https://doi.org/10.22541/essoar.175138827.77215704/v1, 2025 [preprint].

Reiter, K., Heidbach, O., and Ziegler, M. O.: Impact of faults on the remote stress state, Solid Earth, 15, 305–327, https://doi.org/10.5194/se-15-305-2024, 2024.

Velagala, L. S. A. R., Heidbach, O., Ziegler, M., Reiter, K., Henk, A., Rajabi, M., Hergert, T., and Giger, S.: Spatial Influence of Faults on the Far-field Stress State, in prep.

Ziegler, M., Heidbach, O., Morawietz, S., and Wang, Y.: Manual of the Matlab Script FAST Calibration v2.4, WSM TR, 23-02, 44 pp., https://doi.org/10.48440/wsm.2023.002, 2023a.

Ziegler, M. O., Heidbach, O., Morawietz, S., and Wang, Y.: Matlab Script FAST Calibration v2.4, GFZ Data Services, https://doi.org/10.5880/wsm.2023.002, 2023b.

Ziegler, M.: Manual of the Python Script FAST Estimation v1.0, WSM TR, 23-01, 17 pp., https://doi.org/10.48440/wsm.2023.001, 2023c.

Ziegler, M. O.: Python Script FAST Estimation v.1.0, GFZ Data Services, https://doi.org/10.5880/WSM.2023.001, 2023d.