CORRELATIONS OF EARTHQUAKE FOCAL MECHANISMS

We performed a statistical analysis of the Harvard catalogue of seismic moment tensor solutions. We investigated the distribution of hypocentres on focal spheres of earthquakes. The hypocentres are concentrated along fault planes; the hypocentre distribution does not significantly differ for earthquakes in different depth ranges. To study the rotation of focal mechanisms, we have solved an inverse problem of a 3-D rotation of double-couple earthquake sources, i.e., for each pair of focal mechanisms we find all four 3-D rotations which rotate one mechanism into another. The stochastic disorientation of focal mechanisms is well approximated by the rotational Cauchy distribution which has previously been identified through theoretical arguments and simulations as the result of stress perturbations caused by random defects in the medium. The Cauchy distribution is characterized by one parameter, kappa; kappa = 0 means no rotations, and kappa > 0. 5 corresponds to approximately random rotation. For earthquake focal mechanisms the value of kappa is between 0.05 and 0.1 in a fault zone, and it increases with distance between pairs of events. In directions other than a fault plane, kappa reaches the value 0.5; the Cauchy distribution is then close to completely random rotations. Although kappa increases slowly with depth, in general, disorientations of focal mechanisms in various depth ranges display the same dependence. Therefore, we can conclude that deep earthquakes are controlled by the same stress interaction regime as shallow events. The results of these measurements made us question the suitability of some terms and models that are commonly used in the theory of an earthquake source. For example, we argued that tectonic earthquakes rupture rock material which has large-scale defects (or faults), comparable in size with tectonic blocks in which they originate. Properties of the rocks should be significantly different from those of regular materials where the size of defects is typically much smaller than the scale of interest. These properties should strongly depend on the geometry (location and orientation) of major defects.