Percolation theory applied to simulated meander belt sandbodies

The evolution of meander belts is simulated using a single-channel model of freely meandering dynamics with constant discharge and no avulsion. This means that lateral migration of the river is not confined by a valley (i.e., it takes place on a sloping plain), and that chute cutoffs and avulsions do not occur. The meander belt undulates within a relatively narrow tract roughly 50 channel width units wide. This limited width is caused by a river planform fractal geometry in the form of self-affine scale covariance of meanders. The simulated meander belt pattern compares well with actual meander belts of free meandering rivers, suggesting that the assumptions of the model are reasonably realistic for freely meandering rivers in nature. The spatial sandbody distribution in deposits from this system is an outcome of the processes of isolation of point-bars from the active river by neck cutoffs, and vertical attenuation by subsidence and/or deposition. For a constant total subsidence and deposition (tsd) rate, the vertical spatial distribution is well described by percolation theory. This was demonstrated by analysis of a simulated spatial distribution of point-bar sandbodies. The tsd rate controls the density of single sandbodies and amalgamated sandbody clusters within the formation, and is therefore equivalent to the inverse of the probability of site occupation in site percolation models. Percolation theory predicts the existence of a critical tsd rate in the vertical direction, and that sandbody clusters follow a power-law size distribution over a large scale range at the critical value. These predictions were confirmed. The analysis indicates that a scaling law of composite and single sandbodies exists at the percolation threshold (the threshold of sandbody connectivity at a given scale): N ( M > m ) = a m − 1 where N(M > m) is the number of single or amalgamated sandbodies larger than size m (area of point-bar enclosed by an oxbow lake, or area of amalgamated cluster of point-bars). The exponent is the scaling exponent D, and a is a constant of proportionality. Both parameters go to a minimum value at the critical threshold.