High energy gamma-rays and hadrons at Mount Fuji

The energy spectra of high energy gamma-rays and hadrons were obtained by the emulsion chamber with 40 c.u. thickness at Mt. Fuji (3750 m). These results are compared with the Monte Carlo calculation based on the same model which is used in a family analysis. Our data are compatible with the model of heavy-enriched primary and scaling in the fragmentation region

Particle interactions at energies over 1000 TeV inferred from gamma-families observed at Mount Fuji

Scaling, mean P sub t, high P sub t jets and others at energies over 1000 TeV are discussed on the basis of gamma-family data with sigma E sub gamma 100 TeV, observed at Mt. Fuji (3750 m). These quantities were examined in connection with the primary composition

Composition of primary cosmic rays at energies 10(15) to approximately 10(16) eV

The sigma epsilon gamma spectrum in 1 approx. 5 x 1000 TV observed at Mt. Fuji suggests that the flux of primary protons 10 to the 15 approx 10th eV is lower by a factor of 2 approx. 3 than a simple extrapolation from lower energies; the integral proton spectrum tends to be steeper than around to the power V and the spectral index tends to be steeper than Epsilon to the -17th power around 10 to the 14th power eV and the spectral index becomes approx. 2.0 around 10 to the 15th power eV. If the total flux of primary particles has no steepening up to approx 10 to the 15th power eV, than the fraction of primary protons to the total flux should be approx 20% in contrast to approx 45% at lower energies

Relation between stress heterogeneity and aftershock rate in the rate-and-state model

We estimate the rate of aftershocks triggered by a heterogeneous stress change, using the rate-and-state model of Dieterich [1994].We show that an exponential stress distribution Pt(au) ~exp(-tautau_0) gives an Omori law decay of aftershocks with time ~1/t^p, with an exponent p=1-A sigma_n/tau_0, where A is a parameter of the rate-and-state friction law, and \sigma_n the normal stress. Omori exponent p thus decreases if the stress "heterogeneity" tau_0 decreases. We also invert the stress distribution P(tau) from the seismicity rate R(t), assuming that the stress does not change with time. We apply this method to a synthetic stress map, using the (modified) scale invariant "k^2" slip model [Herrero and Bernard, 1994]. We generate synthetic aftershock catalogs from this stress change.The seismicity rate on the rupture area shows a huge increase at short times, even if the stress decreases on average. Aftershocks are clustered in the regions of low slip, but the spatial distribution is more diffuse than for a simple slip dislocation. Because the stress field is very heterogeneous, there are many patches of positive stress changes everywhere on the fault.This stochastic slip model gives a Gaussian stress distribution, but nevertheless produces an aftershock rate which is very close to Omori's law, with an effective p<=1, which increases slowly with time. We obtain a good estimation of the stress distribution for realistic catalogs, when we constrain the shape of the distribution. However, there are probably other factors which also affect the temporal decay of aftershocks with time. In particular, heterogeneity of A\sigma_n can also modify the parameters p and c of Omori's law. Finally, we show that stress shadows are very difficult to observe in a heterogeneous stress context.Comment: In press in JG

The mechanisms of spatial and temporal earthquake clustering

The number of earthquakes as a function of magnitude decays as a power law. This trend is usually justified using spring-block models, where slips with the appropriate global statistics have been numerically observed. However, prominent spatial and temporal clustering features of earthquakes are not reproduced by this kind of modeling. We show that when a spring-block model is complemented with a mechanism allowing for structural relaxation, realistic earthquake patterns are obtained. The proposed model does not need to include a phenomenological velocity weakening friction law, as traditional spring-block models do, since this behavior is effectively induced by the relaxational mechanism as well. In this way, the model provides also a simple microscopic basis for the widely used phenomenological rate-and-state equations of rock friction.Comment: 7 pages, 10 figures, comments welcom

Fractal Dynamics of Earthquakes

Many objects in nature, from mountain landscapes to electrical breakdown and turbulence, have a self-similar fractal spatial structure. It seems obvious that to understand the origin of self-similar structures, one must understand the nature of the dynamical processes that created them: temporal and spatial properties must necessarily be completely interwoven. This is particularly true for earthquakes, which have a variety of fractal aspects. The distribution of energy released during earthquakes is given by the Gutenberg-Richter power law. The distribution of epicenters appears to be fractal with dimension D {approx} 1--1.3. The number of after shocks decay as a function of time according to the Omori power law. There have been several attempts to explain the Gutenberg-Richter law by starting from a fractal distribution of faults or stresses. But this is a hen-and-egg approach: to explain the Gutenberg-Richter law, one assumes the existence of another power-law--the fractal distribution. The authors present results of a simple stick slip model of earthquakes, which evolves to a self-organized critical state. Emphasis is on demonstrating that empirical power laws for earthquakes indicate that the Earth`s crust is at the critical state, with no typical time, space, or energy scale. Of course the model is tremendously oversimplified; however in analogy with equilibrium phenomena they do not expect criticality to depend on details of the model (universality)