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Experimental Measurement of the Relative Importance of Controls on Shoreline Migration

¹ St. Anthony Falls Laboratory, University of Minnesota, Minneapolis, Minnesota 55414, U.S.A.; National Center for Earth-surface Dynamics, University of Minnesota, Minneapolis, Minnesota 55414, U.S.A.; Department of Geology and Geophysics, University of Minnesota, Minneapolis, Minnesota 55455, U.S.A.; kimx0826{at}umn.edu
² St. Anthony Falls Laboratory, University of Minnesota, Minneapolis, Minnesota 55414, U.S.A.; National Center for Earth-surface Dynamics, University of Minnesota, Minneapolis, Minnesota 55414, U.S.A.; Department of Geology and Geophysics, University of Minnesota, Minneapolis, Minnesota 55455, U.S.A.
³ St. Anthony Falls Laboratory, University of Minnesota, Minneapolis, Minnesota 55414, U.S.A.; National Center for Earth-surface Dynamics, University of Minnesota, Minneapolis, Minnesota 55414, U.S.A.; Department of Civil Engineering, University of Minnesota, Minneapolis, Minnesota 55455, U.S.A.
⁴ Department of Geological Sciences and Large Lakes Observatory, University of Minnesota, Duluth, Minnesota 55812, U.S.A.

Shoreline position in sedimentary rocks is a sensitive recorder of the interplay of several controlling factors. The most important of these are thought to be the "stratigraphic trinity:" eustatic sea level, subsidence, and sediment supply. In ancient rock sequences, it is generally difficult to disentangle the effects of these variables. Here we analyze the relative influence of sea level, subsidence, sediment supply, and other controlling variables on shoreline migration in an experimental basin equipped with a subsiding floor. The experiment used a linear-hinge type subsidence profile for which the rate was kept constant in time, constant overall sediment supply, and base-level variation on two time scales that were first applied separately and then superimposed. Although base level was the only controlling variable that was externally varied in time, the base-level changes induced changes in other variables indirectly (e.g., by changing the partitioning of sediment between the fluvial and offshore segments of the system).

We examine the relative importance of measured direct and indirect changes in all the governing variables through the use of a moving-boundary equation for shoreline migration. When measured values are used for all the variables in the equation, shoreline migration rate throughout the run can be predicted with a maximum R² of > 0.92. Starting with this optimal prediction of the observed shoreline behavior, we successively replace variables in the equation with their run-averaged values, degrading the prediction. The relative loss of prediction accuracy as each variable is replaced is a measure of the importance of that variable in accounting for the observed shoreline migration. By this measure, base level is the most important variable, followed in turn by sediment supply to the foreset, geometry of the foreset, and the average subsidence rate over the foreset. From the shoreline migration equation, we also derive a quantitative version of the "A/S ratio" often applied in sequence stratigraphy. The new formulation reduces to a form comparable to the traditional descriptive A/S ratio if changes in foreset slope, gain or loss of sediment to the fluvial system, and spatial variation in subsidence rate are all negligible.

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