The fourth slope: A fundamental new classification of continental margins

Continental margins develop long submarine slopes, linking the shallow shelves along the continental landmasses to the deep abyssal plain. They are the results of a complex interaction between destructive and constructive processes, although by and large they are sites of deposition. There is a great amount of variation between the length, height, smoothness, gradient and variation thereof between the slope profiles; however, there is also recurring similarity in their shape. The similitude has suggested systematic relationships between the shape and the processes forming them, and led to studies on geomorphological categorisation based on curvatures. The potential for prediction of along-strike variations and connection between morphology and sedimentary process is herein approached through broadening the mathematical functions used, detailed measurement, observation and curve-fitting of over 150 passive continental margins. Previously, three functions have been used to categorise submarine slopes. The present study finds that four mathematical functions closely match the slopes: Linear, Gaussian, exponential and quadratic (positive and negative/inverse), and reveals that the fourth slope, the quadratic, is by far the most common. While exponential and quadratic slopes are similar there is a crucial difference in the way in which the angle of the slope changes. This study suggests that quadratic slopes represent systematically decreasing sediment deposition with distance, previously attributed to exponential slopes. Exponential slopes meanwhile, represent slope readjustment profiles with upper sediment bypass and lower slope aggradation. Linear slopes, which form the longest low-angle slopes, form in response to high sediment input. Abrupt shelf-edges form in shallower water and develop longer slope aprons, suggesting formation from erosional processes. This implies that the quintessential sigmoidal (s-shaped, Gaussian function) slope, with a smooth rollover, represents the fundamental depositional slope profile.