The importance of nodal plane orientation diversity for earthquake focal mechanism stress inversions

Inversions of earthquake focal mechanisms are among the most accessible and reliable methods for determining crustal stress. However, the use of this method varies widely, and assumptions that underpin it are often violated, potentially compromising stress estimates. We investigate the consequences of violating the little-studied assumption that the focal mechanisms have diverse orientations. Our approach is to employ data-informed synthetic mechanisms, with nodal plane orientations defined by recent earthquake lineaments in the Midland Basin, western Texas, and rakes consistent with slip in the mapped stress field. Using both the traditional stress inversion method that assumes constant shear stress magnitudes on the causative faults as well as a recently published variable shear stress method, we show that low fault plane diversity can cause maximum horizontal stress (S_Hmax) orientation and relative principal stress magnitude (faulting regime) estimates to differ markedly from the true values. This problem is compounded for catalogs with even modest amounts of noise (≤15°) or few (e.g., 20) mechanisms. Significantly, traditional approaches for quantifying uncertainty such as the bootstrap can severely underestimate the true uncertainty under these circumstances. To remedy this, we provide simple tools to quantify nodal plane orientation diversity and stress inversion reliability.