Models of sedimentary fans and alluvial plains and how they propagate sedimentary, climatic and tectonic signals

The large-scale and long-term transport and deposition of sediment is commonly represented by one of two reduced-complexity models, namely the transport limited (or T-L) model or the under-capacity (or ξ−q) model more recently developed by Davy and Lague (2009). Using both models, I investigated the behavior of a sedimentary continental system fed by a fixed sedimentary flux from a nearby active orogen though which sediments transit to a fixed base level representing a large river, a lake or an ocean.

Firstly, I will show that the two models share the same steady-state solution, for which a simple 1D analytical solution exists that reproduces the major features of many orogenic sedimentary systems: a steep fan adjacent to the mountain front that connects to a shallower alluvial plain. The resulting fan geometry obeys basic observational constraints on fan size and slope with respect to the upstream drainage area, A0. I will also show that the solution is strongly dependent on the size of the system, L, in comparison to a distance L0 that is determined by the size of A0. This gives rise to two fundamentally different types of sedimentary systems: constrained systems where L < L0 and open systems where L > L0. Constrained systems contain only a steep, conical fan that connects directly to the base level, whereas open systems are made of a steep fan connecting to a broad, low slope alluvial plain.

Secondly, I will present simple expressions that show the dependence of the system response time on the system characteristics, such as its length, the size of the upstream catchment area, the amplitude of the incoming sedimentary flux and the respective rate parameters (diffusivity or erodibility) for each of the two models. The ξ−q model predicts significantly longer response times, which I relate to its greater efficiency at propagating signals through its entire length. I will also demonstrate that, although the manner in which signals propagates through the sedimentary system differs greatly between the two models, they both predict that perturbations that last longer than the response time of the system can be recorded in the stratigraphy of the sedimentary system and in particular of the fan.  Interestingly, the ξ−q model predicts that all perturbations (regardless of their period) in incoming sedimentary flux will be transmitted through the system whereas the T-L model predicts that rapid perturbations cannot. I will finally discuss why and under which conditions these differences are important and propose observational ways to determine which of the two models is most appropriate to represent natural systems.

Reference: Davy P. and Lague D., JGR-Earth Surface, 2009.