Quantifying the heterogeneity of the tectonic stress field using borehole data

The heterogeneity of the tectonic stress field is a fundamental property which influences earthquake dynamics and subsurface engineering. Self-similar scaling of stress heterogeneities is frequently assumed to explain characteristics of earthquakes such as the magnitude-frequency relation. However, observational evidence for such scaling of the stress field heterogeneity is scarce. We analyze the local stress orientations using image logs of two closely spaced boreholes in the Coso Geothermal Field with subvertical and deviated trajectories, respectively, each spanning about 2km in depth. Both the mean and the standard deviation of stress orientation indicators (borehole breakouts, drilling-induced fractures, and petal-centerline fractures) determined from each borehole agree to the limit of the resolution of our method although measurements at specific depths may not. We find that the standard deviation in these boreholes strongly depends on the interval length analyzed, generally increasing up to a wellbore log length of about 600m and constant for longer intervals. We find the same behavior in global data from the World Stress Map. This suggests that the standard deviation of stress indicators characterizes the heterogeneity of the tectonic stress field rather than the quality of the stress measurement. A large standard deviation of a stress measurement might be an expression of strong crustal heterogeneity rather than of an unreliable stress determination. Robust characterization of stress heterogeneity requires logs that sample stress indicators along a representative sample volume of at least 1km. Plain Language Summary The forces in the Earth's crust are important for earthquake processes and underground structures, yet we lack a deep understanding of how these forces change from one point to another. Here we use observations in deep boreholes to describe how these forces change. We find that the degree of variability of these forces is a property of each location in the Earth. In order to describe the variability well enough, we need to take measurements over sections of boreholes at least about 1 km long.