[1] Earthquakes and the faults upon which they occur interact over a wide range of spatial and temporal scales. In addition, many aspects of regional seismicity appear to be stochastic both in space and time. However, within this complexity, there is considerable self-organization. We argue that the occurrence of earthquakes is a problem that can be attacked using the fundamentals of statistical physics. Concepts of statistical physics associated with phase changes and critical points have been successfully applied to a variety of cellular automata models. Examples include sandpile models, forest fire models, and, particularly, slider block models. These models exhibit avalanche behavior very similar to observed seismicity. A fundamental question is whether variations in seismicity can be used to successfully forecast the occurrence of earthquakes. Several attempts have been made to utilize precursory seismic activation and quiescence to make earthquake forecasts, some of which show promise. INDEX

The development of most unconventional oil and gas resources relies upon subsurface injection of very large volumes of fluids, which can induce earthquakes by activating slip on a nearby fault. During the last 5 years, accelerated oilfield fluid injection has led to a sharp increase in the rate of earthquakes in some parts of North America. In the central United States, most induced seismicity is linked to deep disposal of coproduced wastewater from oil and gas extraction. In contrast, in western Canada most recent cases of induced seismicity are highly correlated in time and space with hydraulic fracturing, during which fluids are injected under high pressure during well completion to induce localized fracturing of rock. Furthermore, it appears that the maximum-observed magnitude of events associated with hydraulic fracturing may exceed the predictions of an often-cited relationship between the volume of injected fluid and the maximum expected magnitude. These findings have far-reaching implications for assessment of inducedseismicity hazards.

SUMMARY The anelastic deformation of solids is often treated using continuum damage mechanics. An alternative approach to the brittle failure of a solid is provided by the discrete fibre‐bundle model. Here we show that the continuum damage model can give exactly the same solution for material failure as the fibre‐bundle model. We compare both models with laboratory experiments on the time‐dependent failure of chipboard and fibreglass. The power‐law scaling obtained in both models and in the experiments is consistent with the power‐law seismic activation observed prior to some earthquakes.

[1] Earthquake aftershock sequences have been found to approximately satisfy three empirical scaling relations: i) the Gutenberg-Richter frequency-magnitude scaling, ii) Båth's law for the difference in the magnitude of a mainshock and its largest aftershock, and iii) the modified Omori's law for the temporal decay of aftershock rates. The three laws are incorporated to give a generalized Omori's law for aftershock decay rates that depend on several parameters specific for each given seismogenic region. It is shown that the characteristic time c, first introduced in the modified Omori's law, is no longer a constant but scales with a lower magnitude cutoff and a mainshock magnitude. The generalized Omori's law is tested against earthquake catalogs for the aftershock sequences of the Landers, Northridge, Hector Mine, and San Simeon earthquakes.

The statistical properties of aftershock sequences are associated with three empirical scaling relations: (1) Gutenberg-Richter frequency-magnitude scaling, (2) Ba˚th's law for the magnitude of the largest aftershock, and (3) the modified Omori's law for the temporal decay of aftershocks. In this paper these three laws are combined to give a relation for the aftershock decay rate that depends on only a few parameters. This result is used to study the temporal properties of aftershock sequences of several large California earthquakes. A review of different mechanisms and models of aftershocks are also given. The scale invariance of the process of stress transfer caused by a main shock and the heterogeneous medium in which aftershocks occur are responsible for the occurrence of scaling laws. We suggest that the observed partitioning of energy could play a crucial role in explaining the physical origin of Ba˚th's law. We also study the stress relaxation process in a simple model of damage mechanics and find that the rate of energy release in this model is identical to the rate of aftershock occurrence described by the modified Omori's law.

In this work the distribution of interoccurrence times between earthquakes in aftershock sequences is analyzed and a model based on a nonhomogeneous Poisson (NHP) process is proposed to quantify the observed scaling. In this model the generalized Omori's law for the decay of aftershocks is used as a time-dependent rate in the NHP process. The analytically derived distribution of interoccurrence times is applied to several major aftershock sequences in California to confirm the validity of the proposed hypothesis.

[1] Correlations between topography, gravity, and areoid on Mars are used to constrain the crustal and lithospheric thicknesses on the planet. Assuming that the Hellas basin is in isostatic equilibrium with Airy compensation, point correlations between areoid anomalies and topography are used to obtain the mean crustal density and the crustal thickness. We find that the crustal thickness at the reference zero elevation is 90 ± 10 km. We also find that the mean crustal density is 2960 ± 50 kg m À3 . We have also used several approaches to constrain the thickness of the elastic lithosphere. Using the spherical harmonic coefficients of the gravity potential and topography as a function of degrees, a relatively weak constraint on the globally averaged thickness of the elastic lithosphere is obtained. An improved constraint is obtained using wavelet transform analyses of great circle tracks of gravity and topography. The gravity-topography admittance as a function of wavelet wavelength constrains the globally averaged thickness of the elastic lithosphere to be in the range 90 ± 10 km. The observation that the mean thicknesses of the crust and elastic lithosphere are likely to be equal suggests that a rheologically tougher crust is the elastic lithosphere.

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