| Abstract: | The numerical method described in this paper enables the study in terms of stress of the kinematics of seismic faults provided by focal mechanisms. This method assumes a mean state of stress in the source region and is based on the simple mechanical model used for fault population analysis which supposes slip in the direction of the resolved shear stress acting on the fault plane. The proposed algorithm first defines compressional and tensional zones resulting from superimposition of the compressional and tensional quadrants limited by the nodal planes. This enables one to test the data homogeneity. Furthermore, this restricts the space where the principal stress axes have to be searched. Then, for each principal stress reference whose location is constrained by above confined zones, the R value (chosen equal to (σ2′ − σ1′)/(σ3′ − σ1′)) is computed which fits the slip vector on each nodal plane. This permits one to select a set of preferred seismic fault planes from a set of auxiliary planes. Finally, a state of stress is computed from the preferred seismic fault plane set using the non-linear simplex method already applied to fault populations. This algorithm is constructed so as to avoid two major difficulties: misleading estimation of the deviatoric stress tensor which may result from excessive emphasis by minimizing the residuals by a least squares method if some of the data are wrong and a lengthy prospection of the stress references over all the space of directions. This calculation does not take into account possible changes of the strike and dip of the nodal planes. However, we use rotations of nodal planes in agreement with the first arrival data to test the compatibility of these data with the computed state of stress. Tibetan teleseisms and southern Peruvian microseisms are analyzed and results are compared with kinematics of superficial recent and active faults measured in field in the same regions. This suggests that major seismic events may give a good evaluation of the regional (mean) state of stress. Focal mechanisms of the small events are also modelled by a mean stress deviator, but this differs significantly from the regional state of stress in southern Peru deduced from Quaternary faulting. This may be due to imprecise location of the small events. However, some movements are strongly different from those predicted by the computed mean stress deviator. This suggests that small fault kinematics surely depend on the regional state of stress but that local effects may control the small deformations. |
