Statistical properties of seismicity of fault zones at different evolutionary stages

We perform a systematic parameter space study of the seismic response of a large fault with different levels of heterogeneity, using a 3-D elastic framework within the continuum limit. The fault is governed by rate-and-state friction and simulations are performed for model realizations with frictional and large scale properties characterized by different ranges of size scales. We use a number of seismicity and stress functions to characterize different types of seismic responses and test the correlation between hypocenter locations and the employed distributions of model parameters. The simulated hypocenters are found to correlate significantly with small L values of the rate-and-state friction. The final sizes of earthquakes are correlated with physical properties at their nucleation sites. The obtained stacked scaling relations are overall self-similar and have good correspondence with properties of natural earthquakes.     

Accelerated Seismic Release and Related Aspects of Seismicity Patterns on Earthquake Faults

—Observational studies indicate that large earthquakes are sometimes preceded by phases of accelerated seismic release (ASR) characterized by cumulative Benioff strain following a power law time-to-failure relation with a term (t _f?t) ^m , where t _f is the failure time of the large event and observed values of m are close to 0.3. We discuss properties of ASR and related aspects of seismicity patterns associated with several theoretical frameworks. The subcritical crack growth approach developed to describe deformation on a crack prior to the occurrence of dynamic rupture predicts great variability and low asymptotic values of the exponent m that are not compatible with observed ASR phases. Statistical physics studies assuming that system-size failures in a deforming region correspond to critical phase transitions predict establishment of long-range correlations of dynamic variables and power-law statistics before large events. Using stress and earthquake histories simulated by the model of Ben-Zion (1996) for a discrete fault with quenched heterogeneities in a 3-D elastic half space, we show that large model earthquakes are associated with nonrepeating cyclical establishment and destruction of long-range stress correlations, accompanied by nonstationary cumulative Benioff strain release. We then analyze results associated with a regional lithospheric model consisting of a seismogenic upper crust governed by the damage rheology of Lyakhovsky et al. (1997) over a viscoelastic substrate. We demonstrate analytically for a simplified 1-D case that the employed damage rheology leads to a singular power-law equation for strain proportional to (t _f?t)^?1/3, and a nonsingular power-law relation for cumulative Benioff strain proportional to (t _f?t)^1/3. A simple approximate generalization of the latter for regional cumulative Benioff strain is obtained by adding to the result a linear function of time representing a stationary background release. To go beyond the analytical expectations, we examine results generated by various realizations of the regional lithospheric model producing seismicity following the characteristic frequency-size statistics, Gutenberg-Richter power-law distribution, and mode switching activity. We find that phases of ASR exist only when the seismicity preceding a given large event has broad frequency-size statistics. In such cases the simulated ASR phases can be fitted well by the singular analytical relation with m = ?1/3, the nonsingular equation with m = 0.2, and the generalized version of the latter including a linear term with m = 1/3. The obtained good fits with all three relations highlight the difficulty of deriving reliable information on functional forms and parameter values from such data sets. The activation process in the simulated ASR phases is found to be accommodated both by increasing rates of moderate events and increasing average event size, with the former starting a few years earlier than the latter. The lack of ASR in portions of the seismicity not having broad frequency-size statistics may explain why some large earthquakes are preceded by ASR and other are not. The results suggest that observations of moderate and large events contain two complementary end-member predictive signals on the time of future large earthquakes. In portions of seismicity following the characteristic earthquake distribution, such information exists directly in the associated quasi-periodic temporal distribution of large events. In portions of seismicity having broad frequency-size statistics with random or clustered temporal distribution of large events, the ASR phases have predictive information. The extent to which natural seismicity may be understood in terms of these end-member cases remains to be clarified. Continuing studies of evolving stress and other dynamic variables in model calculations combined with advanced analyses of simulated and observed seismicity patterns may lead to improvements in existing forecasting strategies.     

Testing tidal-torque theory – I. Spin amplitude and direction

We evaluate the success of linear tidal-torque theory (TTT) in predicting galactic-halo spin using a cosmological N -body simulation with thousands of well-resolved haloes. The protohaloes are identified by tracing today's haloes back to the initial conditions. The TTT predictions for the protohaloes match, on average, the spin amplitudes of the virialized haloes of today, if linear growth is assumed until ∼ t ₀/3, or  55–70  per cent of the halo effective turn-around time. This makes it a useful qualitative tool for understanding certain average properties of galaxies, such as total spin and angular momentum distribution within haloes, but with a random scatter of the order of the signal itself. Non-linear changes in spin direction cause a mean error of ∼50° in the TTT prediction at t ₀, such that the linear spatial correlations of spins on scales ≥1  h ⁻¹ Mpc are significantly weakened by non-linear effects. This questions the usefulness of TTT for predicting intrinsic alignments in the context of gravitational lensing. We find that the standard approximations made in TTT, including a second-order expansion of the Zel'dovich potential and a smoothing of the tidal field, provide close-to-optimal results.     

The dispersive flux in transport phenomena in porous media

Employing the principles of continuum mechanics and a volumetric averaging approach to the derivation of the macroscopic balance equation of an extensive quantity of a fluid phase in a porous medium, the paper derives a macroscopic expression for the dispersive flux that appears in the latter as a result of averaging. It is shown that the dispersive flux obeys a Fickian type law, i.e., it is proportional to the macroscopic density gradient of the considered extensive quantity. The nature of the coefficient of dispersion that appears in the expression of the dispersive flux is analyzed and interpreted.     

The stages of ionization of oxygen and helium in the solar wind

In this paper we attempted to relate the relative abundance measurements of the solar wind at the earth's orbit to conditions in the solar corona. We followed the distribution of ionization stages of oxygen and helium by integrating the coupled rate equations outward from the corona to the earth's orbit. We concluded that the material observed in the solar wind at the earth's orbit must be a superposition of contributions from hotter and cooler regions of the corona.Supported in part by the National Science Foundation [GP-7976, formerly GP-5391] and the Office of Naval Research [Nonr-220(47)].