Global datasets of the mean orientation of maximum horizontal stress S_Hmax on regular grids

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).

世界应力图（World Stress Map, WSM）是全球地壳现今应力场信息的汇编数据集。当前的2025版WSM数据库（Heidbach等，2025）包含100,842条数据记录，但数据分布不均且存在聚集现象。为分析最大水平主应力（maximum horizontal stress, SHmax）方向的地壳应力场波长，我们采用了所谓的平滑应力图，该图展示了规则网格上的平均SHmax方向。平均SHmax方向的估算基于WSM 2025版数据库中的77,365条A-C类数据记录，通过Matlab®脚本stress2grid v.1.1（Ziegler与Heidbach，2019）完成，该脚本基于轴向数据的圆形统计方法实现。我们为每个网格点设定搜索半径，若搜索半径内至少包含5条数据记录，则计算该点的平均SHmax方向。

通过对输入数据采用三种不同参数进行加权，进一步提升了结果的显著性。1. 数据质量加权：A类数据的权重wQ=1/15，B类数据的权重wQ=1/20，C类数据的权重wQ=1/25。2. 反距离加权：该加权方式基于“数据点距网格点越近，其对应地壳应力状态对网格点应力场的影响越强”的假设，因此单条数据记录对SHmax方向的贡献随其与网格点距离的减小而增大。3. 最小距离阈值：若网格点附近的数据记录过近，会因距离加权被过度代表。为避免该问题，我们设置了最小距离阈值：所有处于搜索半径10%范围内的数据记录将被赋予相同的加权系数。固定搜索半径可有效从SHmax数据记录中筛选出由所选搜索半径定义的应力场波长，无法解析更小空间尺度上的SHmax方向旋转现象。

我们提供了13套全球SHmax数据集，分别采用500 km、250 km、100 km及50 km的搜索半径计算得到。其中，500 km与250 km搜索半径对应的数据集均使用了2°、1°、0.5°及0.2°四种网格分辨率；100 km搜索半径对应的数据集使用1°、0.5°及0.2°三种网格分辨率；50 km搜索半径对应的数据集仅采用0.5°与0.2°两种网格分辨率。关于包含平均SHmax方向的数据文件格式细节，可参见随附的Readme文件。有关WSM 2025版数据库的更多细节，可查阅WSM技术报告25-01（Rajabi等，2025）。