The reflectivity method for the computation of synthetic seismograms, as devised by Fuchs, is extended to include the elastic transmission losses and time shifts due to a stack of layers on top of the reflecting medium. Numerical details of this method are described, and a comparison with the ray-theoretical method, as devised by Miiller, is given. The results of both methods agree well if the models are not too complicated. The field of application of these methods is the comparison with observed seismograms obtained from refraction studies of the Earth's crust and upper mantle.

Knowledge of the present-day crustal in-situ stress field is a key for the understanding of geodynamic processes such as global plate tectonics and earthquakes. It is also essential for the management of geo-reservoirs and underground storage sites for energy and waste. Since 1986, the World Stress Map (WSM) project has systematically compiled the orientation of maximum horizontal stress (). For the 30th anniversary of the project, the WSM database has been updated significantly with 42,870 data records, which is double the amount of data in comparison to the database release in 2008. The update focuses on areas with previously sparse data coverage to resolve the stress pattern on different spatial scales. In this paper, we present details of the new WSM database release 2016 and an analysis of global and regional stress pattern. With the higher data density, we can now resolve stress pattern heterogeneities from plate-wide to local scales. In particular, we show two examples of 40°-60° rotations within 70 km. These rotations can be used as proxies to better understand the relative importance of plate boundary forces that control the long wave-length pattern in comparison to regional and local controls of the crustal stress state. In the new WSM project phase IV that started in 2017, we will continue to further refine the information on the orientation and the stress regime. However, we will also focus on the compilation of stress magnitude data as this information is essential for the calibration of geomechanical-numerical models. This enables us to derive a 3-D continuous description of the stress tensor from point-wise and incomplete stress tensor information provided with the WSM database. Such forward models are required for safety aspects of anthropogenic activities in the underground and for a better understanding of tectonic processes such as the earthquake cycle.

Abstract. For many years, in situ stress in the brittle crust has been measured at relatively shallow depth and related to the mechanical behavior of the crust as inferred from laboratory studies and faulting theory. A continuous profile of the magnitudes and orientations of the three principal stresses has been estimated to depths of 7.7 km and 8.6 km in the German Continental Deep Drilling Program (KTB). This was achieved by hydraulic fracturing tests at relatively shallow depth (1-3 km), estimates of the magnitude of the least horizontal principal stress provided by modified hydraulic fracturing experiments at 6 km and 9 km depths, and analysis of compressional (breakouts) and tensile (drilling-induced tensile wall fractures) failures of the borehole wall over nearly the entire depth of the KTB borehole. The orientation of the maximum horizontal principal stress was found to be uniform with depth with an orientation of N160ø+10øE, which is consistent with the average orientation found throughout western Europe. The only significant change in stress orientation was observed directly below a major fault zone crosscutting the borehole. The profile of stress magnitudes we have obtained demonstrates that to a depth of 8 km, the state of stress in the brittle crust in southern Germany is in frictional equilibrium. That is, the ratio of shear to normal stress as resolved on preexisting faults which are well-oriented to the in situ stress field is comparable to their frictional strength based on predictions of Coulomb faulting theory for a coefficient of friction of about 0.7 and nearhydrostatic pore pressure.

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Nearly 1500 stress orientation determinations are now available for Europe. The data come from earthquake focal mechanisms, overcoring measurements, well bore breakouts, hydraulic fracturing measurements, and young fault slip studies and sample the stress field from the surface to seismogenic depths. Three distinct regional patterns of maximum compressive horizontal stress (SHmax) orientation can be defined from these data: a consistent NW to NNW SHmax stress orientation in western Europe; a WNW‐ESE SHmax orientation in Scandinavia, similar to western Europe but with a larger variability of SHmax orientations; and a consistent E‐W SHmax orientation and N‐S extension in the Aegean Sea and western Anatolia. The different stress fields can be attributed to plate‐driving forces acting on the boundaries of the Eurasian plate, locally modified by lithospheric properties in different regions. On average, the orientation of maximum stress in western Europe is subparallel to the direction of relative plate motion between Africa and Europe and is rotated 17° clockwise from the direction of absolute plate motion. The uniformly oriented stress field in western Europe coincides with thin to medium lithospheric thickness (approximately 50–90 km) and high heat flow values (>80 m W/m2). In western Europe a predominance of strike‐slip focal mechanisms implies that the intermediate principal stress is vertical. The more irregular horizontal stress orientations in Scandinavia coincide with thick continental lithosphere (110–170 km) and low heat flow (<50 m W/m2). The cold thick lithosphere in this region may result in lower mean stresses associated with far‐field tectonic forces and allow the stress field to be more easily perturbed by local effects such as déglaciation flexure and topography. The stress field of the Aegean Sea and western Anatolia is consistent with N‐S extension in a back arc setting behind the Hellenic trench subduction zone. The stress field is influenced in places by regional geologic structures, e.g., in the Western Alps, where SHmax directions show a slight tendency toward a radial stress pattern. Not all major geologic structures, however, appear to affect the SHmax orientation, e.g., in the vicinity of the Rhine rift system horizontal stress orientations are continuous.

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The World Stress Map Project compiles a global database of contemporary tectonic stress information of the Earth's crust. Early releases of the World Stress Map Project demonstrated the existence of first‐order (plate‐scale) stress fields controlled by plate boundary forces and second‐order (regional) stress fields controlled by major intraplate stress sources such as mountain belts and zones of widespread glacial rebound. The 2005 release of the World Stress Map Project database provides, for some areas, high data density that enables us to investigate third‐order (local) stress field variations, and the forces controlling them such as active faults, local inclusions, detachment horizons, and density contrasts. These forces act as major controls on the stress field orientations when the magnitudes of the horizontal stresses are close to isotropic. We present and discuss examples for Venezuela, Australia, Romania, Brunei, western Europe, and southern Italy where a substantial increase of data records demonstrates some of the additional factors controlling regional and local stress patterns.

Tectonic stress is one of the fundamental data sets in Earth sciences comparable with topography, gravity, heat flow and others. The importance of stress observations for both academic research (e.g. geodynamics, plate tectonics) and applied sciences (e.g. hydrocarbon production, civil engineering) proves the necessity of a project like the World Stress Map for compiling and making available stress data on a global scale. The World Stress Map project offers not only free access to this global database via the Internet, but also continues in its effort to expand and improve the database, to develop new quality criteria, and to initiate topical research projects. In this paper we present (a) the new release of the World Stress Map, (b) expanded quality ranking schemes for borehole breakouts and geological indicators, (c) new stress indicators (drilling-induced fractures, borehole slotter data) and their quality ranking schemes, and (d) examples for the application of tectonic stress data.