The stress field in Europe: optimal orientations with confidence limits

Abstract

In this study, we modify and extend a data analysis technique to determine the stress orientations between data clusters by adding an additional constraint governing the probability algorithm. We apply this technique to produce a map of the maximum horizontal compressive stress (S_Hmax) orientations in the greater European region (including Europe, Turkey and Mediterranean Africa). Using the World Stress Map dataset release 2008, we obtain analytical probability distributions of the directional differences as a function of the angular distance, θ. We then multiply the probability distributions that are based on pre-averaged data within θ<3° of the interpolation point and determine the maximum likelihood estimate of the S_Hmax orientation. At a given distance, the probability of obtaining a particular discrepancy decreases exponentially with discrepancy. By exploiting this feature observed in the World Stress Map release 2008 dataset, we increase the robustness of our S_Hmax determinations. For a reliable determination of the most likely S_Hmax orientation, we require that 90% confidence limits be less than ±60° and a minimum of three clusters, which is achieved for 57% of the study area, with small uncertainties of less than ±10° for 7% of the area. When the data density exceeds 0.8×10^-3 data/km2, our method provides a means of reproducing significant local patterns in the stress field. Several mountain ranges in the Mediterranean display 90° changes in the S_Hmax orientation from their crests (which often experience normal faulting) and their foothills (which often experience thrust faulting). This pattern constrains the tectonic stresses to a magnitude similar to that of the topographic stresses.