Direct validation of dune instability theory.

Modern dune fields are valuable sources of information for the large-scale analysis of terrestrial and planetary environments and atmospheres, but their study relies on understanding the small-scale dynamics that constantly generate new dunes and reshape older ones. Here, we designed a landscape-scale experiment at the edge of the Gobi desert, China, to quantify the development of incipient dunes under the natural action of winds. High-resolution topographic data documenting 42 mo of bedform dynamics are examined to provide a spectral analysis of dune pattern formation. We identified two successive phases in the process of dune growth, from the initial flat sand bed to a meter-high periodic pattern. We focus on the initial phase, when the linear regime of dune instability applies, and measure the growth rate of dunes of different wavelengths. We identify the existence of a maximum growth rate, which readily explains the mechanism by which dunes select their size, leading to the prevalence of a 15-m wavelength pattern. We quantitatively compare our experimental results with the prediction of the dune instability theory using transport and flow parameters independently measured in the field. The remarkable agreement between theory and observations demonstrates that the linear regime of dune growth is permanently expressed on low-amplitude bed topography, before larger regular patterns and slip faces eventually emerge. Our experiment underpins existing theoretical models for the early development of eolian dunes, which can now be used to provide reliable insights into atmospheric and surface processes on Earth and other planetary bodies.

Depth dependent stress revealed by aftershocks.

Characterising the state of stress in the brittle upper-crust is essential in mechanics of faulting, industrial production processes, and operational earthquake forecasting. Nevertheless, unresolved questions concern the variation of pore-fluid with depth and the absolute strength on tectonically active faults. Here we show that, along the San Andreas fault system, the time-delay before the onset of the power-law aftershock decay rate (the c-value) varies by three orders of magnitude in the first 20 km below the surface. Despite the influence of the lithostatic stress, there is no continuous change in c-value with depth. Instead, two decay phases are separated by an abrupt increase at an intermediate depth range of 2-5 km. This transitional regime is the only one observed in fluid-injection-induced seismic areas. This provides strong evidence for the role of fluid and a porosity reduction mechanism at depth of few kilometres in active fault zones. Aftershock statistics can then be used to predict changes in differential shear stress with depth until the brittle-ductile transition is reached.

Unravelling raked linear dunes to explain the coexistence of bedforms in complex dunefields.

Raked linear dunes keep a constant orientation for considerable distances with a marked asymmetry between a periodic pattern of semi-crescentic structures on one side and a continuous slope on the other. Here we show that this shape is associated with a steady-state dune type arising from the coexistence of two dune growth mechanisms. Primary ridges elongate in the direction of the resultant sand flux. Semi-crescentic structures result from the development of superimposed dunes growing perpendicularly to the maximum gross bedform-normal transport. In the particular case of raked linear dunes, these two mechanisms produces primary and secondary ridges with similar height but with different orientations, which are oblique to each other. The raked pattern develops preferentially on the leeward side of the primary ridges according to the direction of propagation of the superimposed bedforms. As shown by numerical modelling, raked linear dunes occur where both these oblique orientations and dynamics are met.

Phase diagrams of dune shape and orientation depending on sand availability.

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.

Common dependence on stress for the statistics of granular avalanches and earthquakes.

Both earthquake size-distributions and aftershock decay rates obey power laws. Recent studies have demonstrated the sensibility of their parameters to faulting properties such as focal mechanism, rupture speed or fault complexity. The faulting style dependence may be related to the magnitude of the differential stress, but no model so far has been able to reproduce this behaviour. Here we investigate the statistical properties of avalanches in a dissipative, bimodal particulate system under slow shear. We find that the event size-distribution obeys a power law only in the proximity of a critical volume fraction, whereas power-law aftershock decay rates are observed at all volume fractions accessible in the model. Then, we show that both the exponent of the event size-distribution and the time delay before the onset of the power-law aftershock decay rate are decreasing functions of the shear stress. These results are consistent with recent seismological observations of earthquake size-distribution and aftershock statistics.

Common dependence on stress for the two fundamental laws of statistical seismology.

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.