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The determination of confidence intervals of stress orientation is a crucialelement in the discussion of homogeneity or heterogeneity of the stress fieldunder study. The error estimates provided by the grid search method FocalMechanism Stress Inversion of Gephart and Forsyth (1984) have been shown to betoo wide but the reasons for this failure have escaped elucidation. Through theuse of directional statistics and synthetic focal mechanisms, I show that thegrid search methodology does yield appropriate uncertainty estimates. Thedirect perturbation of the synthetic focal mechanisms introduces bias whichleads to confidence intervals which become increasingly too wide as the amountof perturbation increases. The synthetic data also show at what point themethod fails to overcome this bias and when confidence intervals will be toowide. The indirect perturbation of the focal mechanisms by perturbing thegenerating deviatoric stress tensor generates synthetic data devoid of bias.Inversion of these data sets yields correct confidence intervals. The FocalMechanism Stress Inversion method is vindicated as a highly effective method,and with the use of appropriate directional statistics, its results can beassessed and homogeneity or heterogeneity of the stress field can be discussedwith confidence.

Stress Orientation Confidence Intervals from Focal Mechanism Inversion