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Appendix A: Methodology for estimating sediment flux
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The persistent and repetitive nature of clinoform profiles within shelf-margin successions
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suggest that these profiles can be treated as migrating sediment waves in a fashion analogous to
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bedforms such as dunes. We can therefore use the wave equation (sensu Paola, 2000) to relate
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the depositional rate (∂/∂t) at any point x along the clinoform profile to the speed (P) at which
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the profiles advance basinward and the local topographic slope at the given point on the profile (-
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∂/∂x)
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where x denotes a downbasin coordinate originating at the proximal pinchout of the clinothem
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(i.e. the coastal onlap), and  denotes the clinoform elevation measured from a datum. Here we
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define the datum at the underlying surface over which the profiles migrate (i.e. the downlap
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surfaces). The migration rate (P) is the progradation rate of the clinoforms. To account for the
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effects of subsidence, sea-level change, and sediment loading, we can add a source/sink term (A)
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to equation 1:
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The source/sink term incorporates the depositional response to vertical movement of the
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basement and sea level. Equation 2 shows us that deposition on a clinoform succession (Fig. 1) is
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a function of both horizontal accretion of a migrating inclined surface (i.e. clinoform
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progradation) as well as vertical accretion in response to relative sea-level rise. As an
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approximation, A can be taken as the time-normalized vertical component of the shelf-edge
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trajectory and considered constant across the clinothem. Such an approximation would disregard
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the spatial variability of subsidence (such as fore- or back-tilting) and depositional loading.
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This concept can be applied to estimate spatial profiles of sediment flux across clinoform
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profiles. To do so, we must consider the Exner equation for the law of conservation of sediment
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mass (Paola and Voller, 2005)
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Equation 4 relates the depositional rate to the spatial change in sediment flux (∂qs/∂x) factored by
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a bed sediment concentration term (bed, equal to 1-porosity). Since equations 2 and 3 share the
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same left-hand side (deposition rate), we can rearrange (equation 4) and integrate (equation 5)
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them with respect to x for obtaining sediment flux (qs) at any point x along the clinoform profile
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where L is the downdip location of the distal clinothem pinchout, L and x are the clinoform
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elevations at L and x, respectively, and qs(L) is the sediment flux at the distal pinchout. Since L
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is the downlap location, the elevation at this point is zero. Sediment is assumed to be entirely
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conserved within the clinothem, and therefore, qs(L) is also equal to zero. Solving for qs(x)
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gives
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Sediment flux is a function of the sediment necessary to prograde the clinoform (the first set of
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terms within the bracket) as well as the sediment required to overcome subsidence and sea-level
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changes (the second set of terms within the bracket). The distal clinothem pinchouts were
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extrapolated using basinward thinning rates of the seismic packages.
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Total sediment fluxes for the model were calculated at the landward pinchouts of the
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seismic packages (i.e. the inferred position of coastal onlap). Since coastal onlap was not
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observed in the available seismic data, the landward thinning rates of the seismic packages were
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extrapolated to the proximal pinchout position.
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References
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PAOLA, C. (2000) Quantitative models of sedimentary basin filling. Sedimentology, 47 (Suppl.
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1), 121-178.
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PAOLA, C., & VOLLER, V.R. (2005) A generalized Exner equation for sediment mass balance.
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Journal of Geophysical Research, 110, F04014, doi:10.1029/2004JF000274.
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Figure captions
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Figure 1. Parameters used for sediment-flux estimation and their relationship to clinothem
geometries.