Role of autoretreat and A/S changes in the understanding of deltaic shoreline trajectory: a semi‐quantitative approach

There is continued interest in how the rate of relative sea-level rise [A ( > 0)] and the rate of sediment supply [S] function during the growth and evolution of deltaic shorelines. The theory of shoreline autoretreat, recently corroborated in flume experiments, claims that (1) A( > 0) and S can never be in equilibrium, and (2) shoreline or shelf-edge progradation inevitably turns to retrogradation, when relative sea level is rising even modestly and even if A/S = const (> 0). Autoretreat arises because the area of the clinoform surface of the delta (or shelf edge) per kilometer of shoreline must increase as the relative sea level rises, and the delta (or shelf edge) progrades into deeper water. A finite sediment supply rate is thus liable to become inadequate to sustain progradation. The problem increases further as a rising sea level also greatly increases the delta-plain volume that needs to be filled, further limiting the progradation of the system. The fundamental trajectory of shoreline migration is thus one characterized by a concave-landward shape, even under the steady forcing of the basin. The magnitudes of A (> 0) and S, or A/S do not determine whether the landward turnaround of the shoreline is realized or not, but affect merely the length and height of the fundamental trajectory curve. Thus, any attempt to detect and interpret temporal changes in A and S from the observed stratigraphic record of shoreline trajectory needs first to take full account of the inbuilt autoretreat mechanism. We develop here a simple, semi-quantitative method of reconstructing the basin conditions (A and S) from the stratigraphic record of prograding deltaic shorelines (or prograding shelf-margin clinoforms) on the basis of the theory of shoreline autoretreat. The deterministic nature of the autoretreat theory is advantageous in managing this latter issue, because any expected or unexpected change emerges as some discrepancy from a trajectory that was predicted for the initial conditions. The autoretreat theory also provides a convenient graphical method of dealing with the uncertainty of the field data, and with evaluating the accuracy of any reconstruction. Our methodology has been developed to deal with the behaviour of deltaic shorelines, but is basically applicable to any clinoform system, the development of which is affected by relative sea level. The suggested method is applied to an Early Eocene (Ypresian) regressive shoreline succession in the Central Tertiary Basin on Spitsbergen. The studied regressive wedge developed as a delta-driven, progradational shelf-margin system under a regime of overall (i.e. long-term) rise of relative sea level, but also suffered short-term sea-level falls associated with valley incisions on the coastal plain and shelf. On the assumption that S was constant or was steadily decreasing, the analysis of field data obtained from three sites within the basin suggests that the initial water depth in the basin was around 0.45 km, and that the overall relative sea-level rise (c. 0.80 km) happened largely during an early time period and was followed by a longer period of much lower rate of rise. This pattern of relative sea-level rise is consistent with the Palaeogene tectonic subsidence trend of the basin which was determined independently through a geohistory analysis. The uncertainty of the field data does not negate our reconstruction. The combined effects of autoretreat and A/S changes on a deltaic shoreline trajectory are confirmed through the development of an autoretreat-based methodology. Conventional sequence stratigraphic models that assume a possible equilibrium condition between A and S are both conceptually misleading and insufficient to analyse basin conditions quantitatively. Sequence stratigraphic analyses of shorelines need to incorporate the autoretreat concept.