Interpolation of principal stress directions by nonparametric statistics: Global maps with confidence limits

We suggest a simple method for interpolation of data on the horizontal most compressive principal stress direction (<(sigma)over cap>(1h)) which makes no assumptions about their distribution, except that the probability of a given discrepancy is primarily a function of distance. Using the 6000 data of the World Stress Map, we obtain empirical two-point distributions of direction differences at a number of distances. Then, to find the probability distribution at an interpolation point, we form the product of the distributions implied by all the available data within the correlation horizon (with or without preaveraging of clustered data). It is then simple to select the most likely direction and 90% (or other) confidence bounds. The resulting global maps of <(sigma)over cap>(1h) directions have 90% confidence limits of less than +/-45 degrees over 20-65% of the globe, and small uncertainties of less than +/-10 degrees over 5-25% of the globe (depending on the method). Both maps illustrate how radial <(sigma)over cap>(1h) directions encircle high topography (or unusually shallow bathymetry), suggesting a generally low level of deviatoric stress in the lithosphere.