The seismic hazard associated with an individual fault can be assessed from the distributions of slip and recurrence times of earthquakes. However, seismic cycle models 1 that aim to predict rupture lengths and fault displacements of successive earthquakes on one fault remain poorly validated. It is therefore unknown whether individual fault segments rupture independently, producing earthquakes with a diverse range of magnitudes and recurrence times, or slip by characteristic amounts, with characteristic magnitudes. Here we use high-resolution satellite data to document the horizontal offsets of stream channels and terraces created by strike-slip motion on the Fuyun fault, Xinjiang, China, during five historical earthquakes. We find that the M s 7.9 11 August 1931 earthquake produced a surface rupture with a length of 160 km, dispersed over three different fault segments. The 290 measured stream channel and terrace offsets record an average slip of 6.3 m. We use the degree of preservation of geomorphological markers to assign relative ages to individual fault offsets and identify at least four distinct older earthquakes. We find that these older earthquakes also produced fault offsets with a similar distribution to the 1931 earthquake. As the slip distributions during five successive earthquakes were so similar, we conclude that ruptures on the Fuyun fault obey a characteristic slip model.

[1] We present a new 3-D cellular automaton model for bed form dynamics in which individual physical processes such as erosion, deposition, and transport are implemented by nearest neighbor interactions and a time-dependent stochastic process. Simultaneously, a lattice gas cellular automaton model is used to compute the flow and quantify the bed shear stress on the topography. Local erosion rates are assumed to be proportional to the shear stress in such a way that there is a complete feedback mechanism between flow and bed form dynamics. In the numerical simulations of dune fields, we observe the formation and the evolution of superimposed bed forms on barchan and transverse dunes. Using the same model under different initial conditions, we perform the linear stability analysis of a flat sand bed disturbed by a small sinusoidal perturbation. Comparing the most unstable wavelength in the model with the characteristic size of secondary bed forms in nature, we determine the length and time scales of our cellular automaton model. Thus, we establish a link between discrete and continuous approaches and open new perspectives for modeling and quantification of complex patterns in dune fields.

Earth's sand seas (dune fields) experience winds that blow with different strengths and from different directions in line with the seasons. In response, dune fields show a rich variety of shapes, from crescentic barchans to star and linear dunes. These dunes commonly exhibit complex and compound patterns with a range of length scales and various orientations, which up to now have remained difficult to relate to wind cycles. Here, we develop a model for dune orientation that explains the coexistence of bedforms with different alignments in multidirectional wind regimes. This model derives from subaqueous experiments, which show that a single bidirectional flow regime can lead to two different dune orientations depending on sediment availability, i.e., the erodibility of the bed. Sediment availability selects the overriding mechanism for the formation of dunes: increasing in height from the destabilization of a sand bed (with no restriction in sediment availability) or elongating in a finger on a nonerodible surface from a localized sand source. These mechanisms drive the dune orientation. Therefore, dune alignment maximizes dune orthogonality to sand fluxes in the bed instability mode, while dunes are aligned with the mean sand transport direction in the fingering mode. Applied to Earth's deserts, the model quantitatively predicts the orientation of rectilinear dunes and their superimposed patterns. This field study suggests that many linear dunes on Earth elongate from sources, and are simply aligned with the mean sand transport direction.

[1] We compare the aftershock decay rate in natural data with predictions from a stochastic analytical model based on a Markov process with stationary transition rates. These transition rates vary according to the magnitude of a scalar representing the state of stress and defined as the overload. Thus, the aftershock decay rate in the model is a sum of independent exponential decay functions with different characteristic times. From different shapes of the overload distribution and different expressions of the transition rates, we discuss the magnitude of the exponent of the power law aftershock decay rate and the time interval over which we can expect to observe this regime. Before and after this time interval, we show that the decay is linear and exponential, respectively. From our analytical solutions, we deduce a model of aftershock decay rate in which a power law scaling exponent and two characteristic rates emerge. One rate is a short-term linear decrease before the onset of the power law decay to account for a finite number of events at zero time, and the other one can be interpreted as an inverse correlation time, after which aftershocks no longer occur. Then, we interpret the empirical modified Omori law (MOL) and its parameters in the framework of our theoretical model. We suggest a technique to systematically estimate and interpret the temporal limits of the power law aftershock decay rate in real sequences. We approximate these temporal limits from data available from several well-known aftershock sequences and show from an Akaike Information Criteria (AIC) that, in almost all cases examined here, our model fits better the aftershock decay rate than the MOL despite a quantitative penalty for the extra parameter required. From this work, we conclude that the time delay before the onset of the power law decay may be related to the recurrence time of an earthquake. Finally, we suggest that the power law decay rates extend over longer times according to the concentration of the deformation along dominant major faults.INDEX TERMS: 3299 Mathematical Geophysics: General or miscellaneous; 5199 Physical Properties of Rocks: General or miscellaneous; 7230 Seismology: Seismicity and seismotectonics; 7260 Seismology: Theory and modeling Citation: Narteau, C., P. Shebalin, and M. Holschneider, Temporal limits of the power law aftershock decay rate,

Vast fields of linear dunes have been observed in the equatorial regions of Titan, Saturn's largest moon. As the Cassini mission, in orbit around Saturn since July 2004 and extended until May 2017, carries on, the high-resolution coverage of Titan's surface increases, revealing new dune fields and allowing refinements in the examination of their properties. In this paper, we present the joint analysis of Cassini's microwave and infrared global scale observations of Titan. Integrating within an up-to-date global map of Titan all the Cassini RADAR and VIMS (Visual and Infrared Mapping Spectrometer) images-the latter being empirically corrected for atmospheric scattering and surface photometry, from July 2004 through July 2013 and June 2010 respectively, we found very good qualitative and quantitative spatial matching between the geographic distribution of the dune fields and a specific infrared spectral unit (namely the ''dark brown'' unit). The high degree of spatial correlation between dunes and the ''dark brown'' unit has important implications for Titan's geology and climate. We found that RADAR-mapped dunes and the ''dark brown'' unit are similarly confined within the equatorial belt (±30°in latitudes) with an equivalent distribution with latitude, suggesting an increasing sediment availability and mobility at Titan's tropics relative to higher latitudes, compatible with the lower ground humidity predicted in equatorial regions by General Circulation Models. Furthermore, the strong correlation between RADAR-mapped dunes and the VIMS ''dark brown'' unit (72%) allows us to better constrain the total surface area covered by dune material, previously estimated from the extrapolation of the RADAR observations alone. According to our calculations, dune material cover 17.5 ± 1.5% of Titan's surface area, equivalent to a total surface area of 14.6 ± 1.2 million km 2 ($1.5 times the surface area of Earth's Sahara desert). The VIMS ''dark brown'' coloration of the dune material is here confirmed at large spatial scale. If the sand particle composition is dominated by solid organics produced in and settling from the atmosphere, as supported by our spectral modeling and by previous spectral analysis, microwave radiometric data and atmospheric modeling, dune fields are one of the major surface hydrocarbon reservoirs on Titan. Assuming two possible scenarios for the sand distribution (either the sand is (1) entirely trapped in dune landforms, or (2) trapped in dunes at places where dune landforms are firmly observed and in sand sheets elsewhere), we estimate the volume of hydrocarbons trapped in the dune sediment to be comprised between 1.

New evidence indicates that sand availability does not only control dune type but also the underlying dune growth mechanism and the subsequent dune orientation. Here we numerically investigate the development of bedforms in bidirectional wind regimes for two different conditions of sand availability: an erodible sand bed or a localized sand source on a non-erodible ground. These two conditions of sand availability are associated with two independent dune growth mechanisms and, for both of them, we present the complete phase diagrams of dune shape and orientation. On an erodible sand bed, linear dunes are observed over the entire parameter space. Then, the divergence angle and the transport ratio between the two winds control dune orientation and dynamics. For a localized sand source, different dune morphologies are observed depending on the wind regime. There are systematic transitions in dune shape from barchans to linear dunes extending away from the localized sand source, and vice-versa. These transitions are captured fairly by a new dimensionless parameter, which compares the ability of winds to build the dune topography in the two modes of dune orientation.

Two of the long-standing relationships of statistical seismology are power laws: the Gutenberg-Richter relation describing the earthquake frequency-magnitude distribution, and the Omori-Utsu law characterizing the temporal decay of aftershock rate following a main shock. Recently, the effect of stress on the slope (the b value) of the earthquake frequency-magnitude distribution was determined by investigations of the faulting-style dependence of the b value. In a similar manner, we study here aftershock sequences according to the faulting style of their main shocks. We show that the time delay before the onset of the power-law aftershock decay rate (the c value) is on average shorter for thrust main shocks than for normal fault earthquakes, taking intermediate values for strike-slip events. These similar dependences on the faulting style indicate that both of the fundamental power laws are governed by the state of stress. Focal mechanisms are known for only 2 per cent of aftershocks. Therefore, c and b values are independent estimates and can be used as new tools to infer the stress field, which remains difficult to measure directly.

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