Universal law for waiting internal time in seismicity and its implication to earthquake network

In their paper (Europhys. Lett., 71 (2005) 1036), Carbone, Sorriso-Valvo, Harabaglia and Guerra showed that "unified scaling law" for conventional waiting times of earthquakes claimed by Bak et al. (Phys. Rev. Lett., 88 (2002) 178501) is actually not universal. Here, instead of the conventional time, the concept of the internal time termed the event time is considered for seismicity. It is shown that, in contrast to the conventional waiting time, the waiting event time obeys a power law. This implies the existence of temporal long-range correlations in terms of the event time with no sharp decay of the crossover type. The discovered power-law waiting event-time distribution turns out to be universal in the sense that it takes the same form for seismicities in California, Japan and Iran. In particular, the parameters contained in the distribution take the common values in all these geographical regions. An implication of this result to the procedure of constructing earthquake networks is discussed.Comment: 21 pages, 5 figure

A renormalization group model for the stick-slip behavior of faults

A fault which is treated as an array of asperities with a prescribed statistical distribution of strengths is described. For a linear array the stress is transferred to a single adjacent asperity and for a two dimensional array to three ajacent asperities. It is shown that the solutions bifurcate at a critical applied stress. At stresses less than the critical stress virtually no asperities fail on a large scale and the fault is locked. At the critical stress the solution bifurcates and asperity failure cascades away from the nucleus of failure. It is found that the stick slip behavior of most faults can be attributed to the distribution of asperities on the fault. The observation of stick slip behavior on faults rather than stable sliding, why the observed level of seismicity on a locked fault is very small, and why the stress on a fault is less than that predicted by a standard value of the coefficient of friction are outlined

Development of anisotropic contiguity in deforming partially molten aggregates:2. Implications for the lithosphere‐asthenosphere boundary

In this article, we calculate the seismic anisotropy resulting from melt redistribution during pure and simple shear deformation. Deformation strongly modifies the geometry of melts initially occupying three grain junctions. The initially isotropic fractional area of intergranular contact, contiguity, becomes anisotropic due to deformation. Consequently, the component of contiguity evaluated on the plane parallel to axis of maximum compressive stress decreases. During both modes of deformation, the trace of the contiguity tensor remains nearly unchanged. In the companion article [labeled DHM], we outline the numerical methods and present the synthetic micrographs from our numerical deformation experiments. In pure shear deformation, the principal contiguity directions remain stationary while they rotate during simple shear. The ratio between the principal components of the contiguity tensor decrease from 1 in an undeformed aggregate to 0.1 after 45% shortening in pure shear and to 0.3 after a shear strain of 0.75 in simple shear. In both pure and simple shear experiments, anisotropy in the shear wave velocity increases with the strain in a strongly nonlinear fashion. In pure shear deformation, the steady state microstructure produces nearly 3% anisotropy between shear waves vibrating perpendicular and parallel to the planes of melt films

Network of recurrent events for the Olami-Feder-Christensen model

We numerically study the dynamics of a discrete spring-block model introduced by Olami, Feder and Christensen (OFC) to mimic earthquakes and investigate to which extent this simple model is able to reproduce the observed spatiotemporal clustering of seismicty. Following a recently proposed method to characterize such clustering by networks of recurrent events [Geophys. Res. Lett. {\bf 33}, L1304, 2006], we find that for synthetic catalogs generated by the OFC model these networks have many non-trivial statistical properties. This includes characteristic degree distributions -- very similar to what has been observed for real seismicity. There are, however, also significant differences between the OFC model and earthquake catalogs indicating that this simple model is insufficient to account for certain aspects of the spatiotemporal clustering of seismicity.Comment: 11 pages, 16 figure

Origin and thermal evolution of Mars

The thermal evolution of Mars is governed by subsolidus mantle convection beneath a thick lithosphere. Models of the interior evolution are developed by parameterizing mantle convective heat transport in terms of mantle viscosity, the superadiabatic temperature rise across the mantle, and mantle heat production. Geological, geophysical, and geochemical observations of the compositon and structure of the interior and of the timing of major events in Martian evolution are used to constrain the model computations. Such evolutionary events include global differentiation, atmospheric outgassing, and the formation of the hemispherical dichotomy and Tharsis. Numerical calculations of fully three-dimensional, spherical convection in a shell the size of the Martian mantle are performed to explore plausible patterns of Martian mantel convection and to relate convective features, such as plumes, to surface features, such as Tharsis. The results from the model calculations are presented