Use of focal mechanisms to determine stress: A control study

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Abstract
To allow focal mechanisms to be inverted for the stress field requires a different inversion algorithm than for slickenside data because focal mechanisms do not represent fault slip data unless one can decide which nodal plane is the fault plane. If one can decide which nodal plane is the fault plane, then the focal mechanisms can be inverted with the slickenside inversion algorithm. This decision cannot always be made, so algorithms for inverting focal mechanisms for the stress field are studied. These algorithms either use both of the possible fault planes or attempt to choose the correct fault plane while determining the stress tensor. Simulated focal mechanisms are made from slickenside data and used to provide a control study for the focal mechanism inversion algorithms. The results of this control study show that focal mechanisms can be inverted to find the best stress tensor, but the resolution is decreased unless the fault planes can be picked a priori. The resolution can also be increased by including constraints on the magnitude of the tangential traction on the fault plane. Therefore, using focal mechanisms to study small variations in the stress field requires that other data (e.g., studies of the hypocenters, surface faulting, or structural information concerning the region) be introduced to pick which of the nodal planes is the fault plane. This study also introduces the method of bootstrap resampling to the statistics of this problem. The non‐Gaussian nature of the data makes the nonparametric formulation of the bootstrap approach ideal for this problem.