The World Stress Map (WSM) is the global compilation of information on the present-day stress field in the Earth's crust. The current WSM database release 2025 (Heidbach et al., 2025) has 100,842 data records, but the data are unevenly distributed and clustered. To analyse the wavelength of the crustal stress pattern of the orientation of maximum horizontal stress SHmax, we use so-called smoothed stress maps that show the mean SHmax orientation on regular grids. The mean SHmax orientation is estimated using the 77,365 A-C data records from the WSM database release 2025 in the Matlab® script stress2grid v.1.1 (Ziegler and Heidbach, 2019) which is based on the circular statistics of axial data. We use a search radius around the grid point and compute the mean SHmax orientation if at least five data records are within the search radius. The significance of the results is further improved by the weighting of the input data by three different parameters. 1.) Data quality weighting with wQ=1/15 for A-, wQ=1/20 for B-, and wQ = 1/25 for C-quality data. 2.) Inverse distance weighting relative to the grid point. This is based on the assumption that the closer a data record is to a grid point, the more strongly the stress state at the grid point influences that data record. Consequently, the contribution of an individual data record to the SHmax orientation increases with decreasing distance to the grid point. 3.) Minimum distance threshold: Data records located very close to a grid point would be overrepresented by the distance weight. To avoid this, a minimum distance threshold is applied such that all data records within 10% of the search radius are assigned the same weighting coefficient. Using a fixed search radius effectively filters from the SHmax data records the wavelength defined by the chosen search radius and does not resolve rotations of SHmax at smaller spatial scales. We provide 13 global datasets for SHmax calculated with search radii of 500 km, 250km, 100km, and 50 km. For the 500 km and 250 km search all four grids are used on 2°, 1°, 0.5°, and 0.2°. For the 100 km search radius the 1°, 0.5°, and 0.2° grids are used and for the 50 km search radius only the 0.5° and 0.2° grids are applied. Details on the format of the data files with the mean SHmax orientation are provided in the accompanying Readme file. Further details on the WSM database release 2025 are available in the WSM Technical Report 25-01 (Rajabi et al., 2025).
This open access database compiles stress magnitude information from various sources. It currently includes 568 data records in the area of Germany and adjacent regions (latitude: 47 - 55.5 N; longitude: 5.8 - 15.1 E). The data records are ranked after a newly developed quality scheme for stress magnitude data. The data are provided in two formats: Excel-file (stressmagdata_germany_2020.xlsx), comma separated fields (stressmagdata_germany_2020.csv). Additional files include a) an overview over the compiled parameters including the abbreviation keys for stress magnitude indicators and stress regimes (List_of_parameters.pdf); b) the key for the referenced data sources (Key_for_ref_labels.pdf); and c) the applied quality ranking scheme (Quality_ranking_scheme.pdf).
For the visualization and analysis of the stress field from 4D thermo-hydro-mechanical (THM) numerical model results two main technical steps are necessary. First, one has to derive from the six independent components of the stress tensor scalar and vector values such as the ori-entation and magnitude of the maximum and minimum horizontal stress, stress ratios, differential stress. It is also of great interest to display e.g. the normal and shear stress with respect to an arbitrarily given surface. Second, an appropriate geometry has to be given such as cross sections, profile e.g. for borehole pathways or surfaces on which the model results and further derived values are interpolated. This includes the three field variables temperature, pore pressure and the displacement vector. To facilitate and automate these steps the add-on GeoStress for the professional visualization software Tecplot 360 EX has been programmed. Besides the aforementioned values derived from the stress tensor the tool also allows to calculate the values of Coulomb Failure Stress (CFS), Slip and Dilation tendency (ST and DT) and Fracture Potential (FP). GeoStress also estimates kinematic variables such as horizontal slip, dip slip, rake vector of faults that are implemented as contact surfaces in the geomechanical-numerical model as well as the true vertical depth. Furthermore, the add-on can export surfaces and polylines and map on these all available stress values. The technical report describes the technical details of the visualization tool, its usage and exemplifies its application using the results of a 3D example of a geomechanical-numerical model of the stress field. The numerical solution is achieved with the finite element software Abaqus version 2019. It also presents a number of special features of Tecplot 360 EX in combination with GeoStress that allow a professional and efficient analysis.
The distribution of data records for the maximum horizontal stress orientation S_Hmax in the Earth’s crust is sparse and very unequally. To analyse the stress pattern and its wavelength and to predict the mean S_Hmax orientation on regular grids, statistical interpolation as conducted e.g. by Coblentz and Richardson (1995), Müller et al. (2003), Heidbach and Höhne (2008), Heidbach et al. (2010) or Reiter et al. (2014) is necessary. Based on their work we wrote the Matlab® script Stress2Grid that provides several features to analyse the mean S_Hmax pattern. The script facilitates and speeds up this analysis and extends the functionality compared to the publications mentioned before. This script is the update of Stress2Grid v1.0 (Ziegler and Heidbach, 2017). It provides two different concepts to calculate the mean S_Hmax orientation on regular grids. The first is using a fixed search radius around the grid points and computes the mean S_Hmax orientation if sufficient data records are within the search radius. The larger the search radius the larger is the filtered wavelength of the stress pattern. The second approach is using variable search radii and determines the search radius for which the standard deviation of the mean S_Hmax orientation is below a given threshold. This approach delivers mean S_Hmax orientations with a user-defined degree of reliability. It resolves local stress perturbations and is not available in areas with conflicting information that result in a large standard deviation. Furthermore, the script can also estimate the deviation between plate motion direction and the mean S_Hmax orientation. The script is fully documented by the accompanying WSM Technical Report 19/02 (Ziegler and Heidbach, 2019) which includes a changelog in the beginning.
In geosciences 3D geomechanical-numerical models are used to estimate the in-situ stress state. In such a model each geological unit is populated with the rock properties Young’s module, Poisson ratio, and density. Usually, each unit is assigned a single set of homogeneous properties. However, variable rock properties are observed and expected within the same geological unit. Even in small volumes large variabilities may. The Python script HIPSTER (Homogeneous to Inhomogeneous rock Properties for Stress TEnsor Research) provides an algorithm to include inhomogeneities in geomechanical-numerical models that use the solver Abaqus®. The user specifies the mean values for the rock properties Young's module, Poisson ratio and density, and their variability for each geological unit. The variability of the material properties is individually defined for each of the three rock properties in each geological layer. For each unit HIPSTER generates a normal or uniform distribution for each rock property. From these distri-butions for each single element HIPSTER draws individual rock properties and writes them to a separate material file. This file defines different material properties for each element. The file is included in the geomechanical-numerical analysis solver deck and the numerical model is solved as usual.HIPSTER is fully documented in the associated data report (Ziegler, 2019, http://doi.org/10.2312/WSM.2019.003) and can also be accessed at Github (http://github.com/MorZieg/hipster)
The 3D geomechanical-numerical modelling of the in-situ stress state requires observed stress information at reference locations within the model area to be compared to the modelled stress state. This comparison of stress states and the ensuing adaptation of the displacement boundary conditions provide a best fit stress state in the entire model region that is based on the available stress information. This process is also referred to as calibration. Depending on the amount of available information and the complexity of the model the calibration is a lengthy process of trial-and-error modelling and analysis.The Fast Automatic Stress Tensor Calibration (FAST Calibration) is a method and a Matlab script that facilitates and speeds up the calibration process that has been developed in the framework of the World Stress Map (WSM, Heidbach et al., 2010; 2016). The method requires only three model scenarios with different boundary conditions. The modelled stress states at the locations of the observed stress state are extracted. Then they are used to compute the displacement boundary conditions that are required in order to achieve the best fit of the modelled to the observed stress state. Furthermore, the influence of the individual observed stress information on the resulting stress state can be weighted.The FAST-Calibration (Fast Automatic Stress Tensor Calibration) is a Matlab tool that controls the statistical calibration of a 3D geomechanical-numerical model of the stress state following the approach described by Reiter and Heidbach (2014), Hergert et al. (2015), and Ziegler et al. (2016). It is mainly designed to support the multi-stage modelling procedure presented by Ziegler et al. (2016). However, it can also be used for the calibration of a single-stage model. The tools run in Matlab 2017a and higher and are meant to work with the visualization software Tecplot 360 EX 2015 R2 and higher (https://www.tecplot.com/products/tecplot-360/) in conjunction with the Tecplot 360 Add-on GeoStress (Stromeyer and Heidbach, 2017). The user should be familiar with 3D geomechanical-numerical modelling, Matlab, Tecplot 360 EX, including a basic knowledge of Tecplot 360 EX macro functions, and the Tecplot 360 EX Add-on GeoStress. This FAST Calibration manual provides an overview of the scripts and is designed to help the user to adapt the scripts for their own needs.
The distribution of data records for the maximum horizontal stress orientation SHmax in the Earth’s crust is sparse and very unequally. In order to analyse the stress pattern and its wavelength or to predict the mean SHmax orientation on a regular grid, statistical interpolation as conducted e.g. by Coblentz and Richardson (1995), Müller et al. (2003), Heidbach and Höhne (2008), Heidbach et al. (2010) or Reiter et al. (2014) is necessary. Based on their work we wrote the Matlab® script Stress2Grid that provides several features to analyse the mean SHmax pattern. The script facilitates and speeds up this analysis and extends the functionality compared to aforementioned publications. The script is complemented by a number of example and input files as described in the WSM Technical Report (Ziegler and Heidbach, 2017, http://doi.org/10.2312/wsm.2017.002).The script provides two different concepts to calculate the mean SHmax orientation on a regular grid. The first is using a fixed search radius around the grid point and computes the mean SHmax orientation if sufficient data records are within the search radius. The larger the search radius the larger is the filtered wavelength of the stress pattern. The second approach is using variable search radii and determines the search radius for which the variance of the mean SHmax orientation is below a given threshold. This approach delivers mean SHmax orientations with a user-defined degree of reliability. It resolves local stress perturbations and is not available in areas with conflicting information that result in a large variance. Furthermore, the script can also estimate the deviation between plate motion direction and the mean SHmax orientation.
The stress map of Germany shows the orientation of the current maximum horizontal stress (SHmax) in the earth's crust. Assuming that the vertical stress (SV) is a principal stress, SHmax defines the orientation of the 3D stress tensor; the minimum horizontal stress Shmin is than perpendicular to SHmax. In the stress map the SHmax orientations are represented as lines of different lengths. The length of the line is a measure of the quality of data and the symbol shows the stress indicator and the color the stress regime. Data with E-Quality are shown without additional information as dots on the map. The stress data are freely available and part of the World Stress Map (WSM) project. For more information about the data and criteria of data analysis and quality mapping are plotted along the WSM website at http://www.world-stress-map.org.The German version of the World Stress Map Germany is available via http://doi.org/10.5880/WSM.Germany2016.
Die Spannungskarte Deutschland zeigt die Orientierung der gegenwärtigen maximalen horizontalen Spannung (SHmax) in der Erdkruste. Unter der Annahme, dass die vertikale Spannung (SV) eine Hauptspannung ist, legt SHmax die Orientierung des 3D Spannungstensors festgelegt; die minimale horizontale Spannung Shmin ist entsprechend senkrecht zu SHmax. In der Spannungskarte sind die SHmax Orientierungen als Linien unterschiedlicher Länge dargestellt. Die Länge der Linie ist dabei ein Maß für die Datenqualität und das Symbol zeigt die Methode und die Farbe das Spannungsregime an. Daten mit E-Qualität sind ohne weitere Information als Punkte in der Karte dargestellt. Die Spannungsdaten sind frei zugänglich und Bestandteil des World Stress Map (WSM) Projektes. Weitere Informationen zu den Daten und Kriterien der Datenanalyse und Qualitätszuordnung befinden sich auf der WSM Internetseite unter http://www.world-stress-map.org. The English version of the World Stress Map Germany is available via http://doi.org/10.5880/WSM.Germany2016_en.
The World Stress Map (WSM) is the global repository for contemporary tectonic stress data from the Earth's crust. Its uniformity and quality is guaranteed through quality ranking of the data according to international standards and a standardized regime assignment. The WSM merges data which otherwise would be fragmented in separate, often inaccessible archives. It provides the long-term preservation of tectonic stress data from physical loss of data carriers or organizational problems of data storage. The data are provided as Excel table (xlsx) and tab-delimited text.
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