A two‐diffusion model of fluvial stratigraphy in closed depositional basins

Abstract

Fundamental to interpreting the stratigraphic architecture within a basin is understanding the relationship between a basin's external conditions and its stratigraphic response. Here we present a model of fluvial basin filling that is based on two field observations. Firstly, natural fluvial systems commonly have an upstream region dominated by gravel transport and a downstream region dominated by sand transport with the transition between the two being relatively abrupt. Second, gravel bed and sand bed systems operate at nearly constant but different mean Shields stresses. Our model is based on a single, linear diffusion equation but is unique in that we use distinct transport (diffusion) coefficients for the two dominant fluvial regimes: a proximal gravel region and a distal sand region. This problem is complicated by the existence of two moving boundaries: the position of the distal fluvial toe and the position of the gravel-sand transition. We present a rigorous numerical treatment of both of these moving boundaries and verify our numerical formulation by comparing the model results to a semianalytical solution technique.We use the model to examine the stratigraphic response to perturbations in four external boundary conditions: sediment supply, water supply, rate of subsidence and gravel fraction. The response is analysed in terms of the phase relation between forcing and the position of the gravel front, the position of the fluvial toe, proximal accumulation rate and distal accumulation rate. The model supports the results of earlier single-diffusion models suggesting that the form of the response is dependent on the period of the perturbation relative to the intrinsic basin response time. For forcing periods less than the intrinsic basin response time, basin response is nearly constant and independent of the forcing period, suggesting that the transport system controls basin response. For forcing periods greater than the intrinsic response time of the basin the response time of the basin increases directly with the forcing period, suggesting that the transport system plays no role in limiting basin response. For gravel-sand systems we show that the intrinsic response time is a function of the ratio of gravel to sand entering the basin. Forcing of the above external boundaries, both slowly and rapidly relative to the basin response time, produces both distal and proximal unconformities. We present a nondimensional 'unconformity number' that constrains the amplitude and period of forcing necessary to generate proximal unconformities. These external (allogenic) forcings are communicated to Correspondence: J. G. Marr, St. Anthony Falls Laboratory, of external forcing is spatial variation in sediment grain Mississippi River at 3rd Ave. SE, University of Minnesota, size, which is easily observed at the outcrop scale and Minneapolis, MN 55414, USA.

The Permian–Triassic transition and the onset of Mesozoic sedimentation at the northwestern peri-Tethyan domain scale: Palaeogeographic maps and geodynamic implications

“…The similar evolution observed in these two domains leads to the conclusion that this trend was controlled by allocyclic factors independent of the basin location, such as intraplate tectonics or climate change. It could be explained by either an increase in sediment supply and/or a decrease in the subsidence of the depositional area, as demonstrated by numerical modelling (Heller and Paola, 1992;Marr et al, 2000;Paola, 2000;Paola et al, 1992). A strong clastic influx is well documented in the area of the Viki ng-Central Graben area (Geluk, 2005;Ziegter, 1990).…”

Advance, Retreat, and Halt of Abrupt Gravel‐Sand Transitions in Alluvial Rivers

“…A GST can halt in systems governed by subsidence, delta progradation, or base level rise (Parker, 2004) due to the creation of accommodation space for the gravel supply in the gravel reach (Dingle et al, 2017;Marr et al, 2000;Paola, Heller, et al, 1992).…”

“…An increase of the characteristic flow rate reduces the gravel and sand reach slopes (Blom et al, 2016), which enhances GST advance (Marr et al, 2000) as the relative effect of the sand reach slope on GST migration is almost negligible compared to the gravel reach slope. If the stable GST position is known, equation (2) can aid in constraining the gravel flux (Dingle et al, 2017).…”

Modelling the effect of form and profile adjustments on channel equilibrium timescales

“…width) adjustments in affecting timescales of adjustment following disturbance Simon and Darby, 1997). Specifically, Simon (1992) used a pair of contrasting field sites responding to disturbance and showed that channels with coarse sediment available for transport, and channels with adjustable banks equilibrated more rapidly than those with only fine sediment in transport or those Simons and Li (1980) Wallace (1977) Mosley (1984) Marr et al (2000) Marr et al (2000) that were only able to adjust via bed adjustments. He suggested that increasing channel width and/or increased downstream deposition of sediment caused more rapid reduction in the imposed energy grade.…”