Comment on “Models of Stochastic, Spatially Varying Stress in the Crust Compatible with Focal‐Mechanism Data, and How Stress Inversions Can Be Biased toward the Stress Rate” by Deborah Elaine Smith and Thomas H. Heaton

Abstract

Smith and Heaton (2011) propose a model in which stress in the crust is fractal‐like and highly variable on a range of length scales, including short length‐scales of ∼1 km. Smith and Heaton (2011) motivate the need for stress heterogeneity on short length‐scales by citing observations such as short length‐scale changes in stress directions inferred from borehole breakouts, short length‐scale changes in earthquake slip, and the success of numerical models that include short‐wavelength stress heterogeneity. The heterogeneous part of the stress field in their model is more than twice as large as the homogeneous part. The stress field in this model frequently reverses itself over short distances, as can be seen in figure 14a of Smith and Heaton (2011). The modeled stress field contains at least 10 areas of reversed shear stress direction over the length of a 100 km long profile, with the length of the reversed areas ranging from <1 to ∼5 km. This model makes specific predictions about the orientations and heterogeneity of earthquake focal mechanisms. Smith and Heaton (2011) attempt to validate this heterogeneous stress model using observations of earthquake focal‐mechanism variability from Hardebeck (2006). They then demonstrate that the model predicts a bias in the orientations of earthquake focal mechanisms, which are biased away from the background stress and toward the stressing rate. They suggest the focal‐mechanism bias in this model invalidates the large body of work over the last several decades, that has inferred stress orientations from the inversion of earthquake focal mechanisms. The question of whether or not the Smith and Heaton (2011) model is applicable to the real Earth is therefore important not only for understanding spatial stress variability but also for evaluating the numerous studies that have inferred crustal stress orientations from earthquake focal mechanisms (e.g., as compiled by Heidbach et al. , 2008 …