Estimation of True Horizontal Stress Directions From Seismically Resolvable Stress Tensor Parameters

To fully describe the state of stress in the crust requires six independent parameters, most commonly represented as either the six components of the symmetric stress tensor or the magnitudes and orientations of the three corresponding principal stresses. It is common, however, to work with a subset of these parameters, either because not all of them can be measured or because of difficulty in visualizing the complete stress tensor. A common and geologically plausible presumption is that one of the principal stresses is vertical (an "Andersonian" state of stress), in which case it often suffices to know only which of the principal stresses that is --- S1 (normal), S2 (strike-slip), or S3 (reverse) --- and the azimuth of maximum horizontal compressive stress (SHmax). Focal mechanism stress inversions yield only the three principal stress directions and a single stress magnitude parameter (e.g. R = (S11 - S2)/(S1 - S3)), but these four parameters are sufficient to calculate SHmax even when the Andersonian condition is not met. This can be demonstrated by considering the normal stress acting on a vertical fault plane, which is a maximum when the plane's strike is SHmax+90°. It is important to emphasize that when none of the principal stresses is strictly vertical, the azimuth of SHmax does not generally coincide with the trend of S1 (in reverse- or strike-slip-faulting conditions) or S2 (in normal-faulting conditions), as SHmax depends on R as well as the principal stress orientations. The distinction between SHmax and the trend of S1 or S2 can amount to tens of degrees, which is of great importance when assessing fault stability or when spatial or temporal differences in stress are under consideration. We present an algorithm for computing SHmax from routine focal mechanism stress inversion results, and demonstrate its application in case studies from Iceland, California, and Japan.