The two-point correlation function of the seismic moment tensor

Summary. We use the invariants of the two-point correlation function of the seismic moment to investigate the degree of irregularity of an earthquake fault, i.e. to study the rapidity with which a complex fault changes its direction of orientation. The two-point correlation function is a fourth-order tensor which has three scalar invariants in the isotropic case. Although the accuracy of present-day catalogues of fault plane solutions is rather low for our purpose, nevertheless the invariants of these correlation tensors confirm the generally     

On the consistency of earthquake moment release and space geodetic strain rates: Europe

In this paper, approximately 100 VLBI/SLR/GPS velocities map European strain rates from <0.09 × 10⁻⁸ to >9.0 × 10⁻⁸ yr⁻¹ with regional uncertainties of 20 to 40 per cent. Kostrov's formula translates these strain-rate values into regional geodetic moment rates M¯˙ _geodetic . Two other moment rates, M¯˙ _seismic , extracted from a 100-year historical catalogue and M¯˙ _plate , taken from plate-tectonic models, contrast the geodetic rates. In Mediterranean Europe, the ratios of M¯˙ _seismic to M¯˙ _geodetic are between 0.50 and 0.71. In Turkey the ratio falls to 0.22. Although aseismic deformation may contribute to the earthquake deficit ( M¯˙ _seismic values less than M¯˙ _geodetic ), the evidence is not compelling because the magnitudes of the observed shortfalls coincide with the random variations expected in a 100-year catalogue. If the lack of aseismic deformation inferred from the 100-year catalogue holds true for longer periods, then much of Europe's strain budget would have to be accommodated by more frequent or larger earthquakes than have been experienced this century to raise the ratios of M¯˙ _seismic to M¯˙ _geodetic to unity. Improved geological fault data bases, longer historical earthquake catalogues, and densification of the continent's space geodetic network will clarify the roles of aseismic deformation versus statistical quiescence.     

Cluster analysis of seismic moment tensor orientations

This paper demonstrates that well-known methods of cluster analysis and multivariate data analysis are useful for geodynamic interpretation of seismic moment tensors. To use these methods, moment tensors are expressed as vectors in a 6-D space. These are vectors in a rigorous sense, rather than an arbitrary set of ordered numbers, because a dot product can be defined that is independent of the coordinate system. In this vector space, non-isotropic moment tensors are a 5-D linear subspace and normalized moment tensors are unit vectors, or points on a unit sphere. Distance along a great circle of the unit sphere satisfies reasonable requirements for any measure of the difference between normalized moment tensors. In regions with a few isolated sets of orientations, cluster analysis based on the great circle distance identifies the same groups of earthquakes that a seismologist would. Figures based on principal component analysis and discriminant analysis illustrate orientation clustering better than equal area projections of moment tensor principal axes. In one case where clusters have been claimed to exist, orientations appear to be continuously distributed and no evidence is found for separate populations of moment tensors.     

A test of the precursory accelerating moment release model on some recent New Zealand earthquakes

The proposal that the moment release rate increases in a systematic way in a large region around a forthcoming large earthquake is tested using three recent, large New Zealand events. The three events, 1993–1995, magnitudes 6.7–7.0, occurred in varied tectonic settings. For all three events, a circular precursory region can be found such that the moment release rate of the included seismicity is modelled significantly better by the proposed accelerating model than by a linear moment release model, although in one case the result is dubious. The 'best' such regions have radii from 122 to 167 km, roughly in accord with previous observations world-wide, but are offset by 50–60 km from the associated main shock epicentre. A grid-search procedure is used to test whether these three earthquakes could have been forecast using the accelerating moment release model. For two of the earthquakes the result is positive in terms of location, but the main shock times are only loosely constrained.