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BLTN13190fig3.jpg|{{figure number|3}}Generalized, first-order approximations of the plan-view geometry of clinoforms in different depositional environments: (A) Nayarit Coast, Mexico, representative of a wave-dominated strandplain (image modified after Google Earth and DigitalGlobe, 2013); (B) Nile Delta, Egypt, representative of a wave-dominated delta (image modified after Google Earth, 2013); and (C) Wax Lake Delta, Louisiana, representative of a fluvial-dominated delta (image modified after Google Earth and TerraMetrics, 2013). Solid white lines represent a first-order approximation of the shoreline at the clinoform top, whereas the dashed white lines represent first-order approximations of the likely maximum extent of the clinoform surface and its downlap termination on the underlying sea floor.

BLTN13190fig3.jpg|{{figure number|3}}Generalized, first-order approximations of the plan-view geometry of clinoforms in different depositional environments: (A) Nayarit Coast, Mexico, representative of a wave-dominated strandplain (image modified after Google Earth and DigitalGlobe, 2013); (B) Nile Delta, Egypt, representative of a wave-dominated delta (image modified after Google Earth, 2013); and (C) Wax Lake Delta, Louisiana, representative of a fluvial-dominated delta (image modified after Google Earth and TerraMetrics, 2013). Solid white lines represent a first-order approximation of the shoreline at the clinoform top, whereas the dashed white lines represent first-order approximations of the likely maximum extent of the clinoform surface and its downlap termination on the underlying sea floor.

BLTN13190fig4.jpg|{{figure number|4}}(A) A user specifies the length of the top (solid line) and base (dashed line) ellipses in depositional dip and strike directions (BLTN13190eq36, BLTN13190eq37, BLTN13190eq38, BLTN13190eq39; Table 1) relative to the clinoform origin. The surface representing the clinoform is created in the volume between the top and base ellipses. (B) At a point on the clinoform, the radius relative to the clinoform origin (black arrow, BLTN13190eq40, the radius of the base ellipse (black arrow, BLTN13190eq41 and the radius of the top ellipse (black arrow, BLTN13190eq42 are calculated. (C) Plan view of four adjacent clinoforms. The user specifies the overall progradation direction of the clinoforms relative to north, as well as the coordinates of the initial insertion point BLTN13190eq43. (D) Conceptual depositional-dip-oriented cross-section view of clinoforms. Clinoform spacing, BLTN13190eq44, is defined as the distance between the top truncation points of two adjacent clinoforms. Clinoform length, L, is defined as the distance between the top and base truncations by the user-specified bounding surfaces along a single clinoform.

BLTN13190fig4.jpg|{{figure number|4}}(A) A user specifies the length of the top (solid line) and base (dashed line) ellipses in depositional dip and strike directions (t_s, t_D, b_s, b_D; Table 1) relative to the clinoform origin. The surface representing the clinoform is created in the volume between the top and base ellipses. (B) At a point on the clinoform, the radius relative to the clinoform origin (black arrow, BLTN13190eq40, the radius of the base ellipse (black arrow, BLTN13190eq41 and the radius of the top ellipse (black arrow, BLTN13190eq42 are calculated. (C) Plan view of four adjacent clinoforms. The user specifies the overall progradation direction of the clinoforms relative to north, as well as the coordinates of the initial insertion point BLTN13190eq43. (D) Conceptual depositional-dip-oriented cross-section view of clinoforms. Clinoform spacing, BLTN13190eq44, is defined as the distance between the top truncation points of two adjacent clinoforms. Clinoform length, L, is defined as the distance between the top and base truncations by the user-specified bounding surfaces along a single clinoform.

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The depositional processes acting at the shoreline control the plan-view shape and abundance of clinoforms and their associated heterogeneity (Howell et al., 2008a). Maps, satellite images, and aerial photographs of modern systems are used to make a first-order approximation of the distinct plan-view shape of clinoforms in different depositional environments ([[:File:BLTN13190fig3.jpg|Figure 3]]), as described in the subsequent text, because there is a paucity of reliable data of this type from subsurface reservoirs and ancient analogs. This approximation assumes that the modern-day shape of a shoreline represents a snap-shot in time that mimics the geometry of clinoforms and associated depositional elements preserved in the stratigraphic record (Howell et al., 2008a). Mattson and Chan (2004) assumed a simple radial geometry in plan view for fluvial-dominated deltaic clinoforms in the Ferron Sandstone Member outcrop analog, but this geometry is not universally applicable even as a first-order approximation. For example, wave-dominated strandplains are nearly linear in plan view ([[:File:BLTN13190fig3.jpg|Figure 3A]]), wave-dominated deltas have broad arcuate forms ([[:File:BLTN13190fig3.jpg|Figure 3B]]), and fluvial-dominated deltaic shorelines form distinct, lobate protuberances ([[:File:BLTN13190fig3.jpg|Figure 3C]]) (e.g., Galloway, 1975).

The depositional processes acting at the shoreline control the plan-view shape and abundance of clinoforms and their associated heterogeneity (Howell et al., 2008a). Maps, satellite images, and aerial photographs of modern systems are used to make a first-order approximation of the distinct plan-view shape of clinoforms in different depositional environments ([[:File:BLTN13190fig3.jpg|Figure 3]]), as described in the subsequent text, because there is a paucity of reliable data of this type from subsurface reservoirs and ancient analogs. This approximation assumes that the modern-day shape of a shoreline represents a snap-shot in time that mimics the geometry of clinoforms and associated depositional elements preserved in the stratigraphic record (Howell et al., 2008a). Mattson and Chan (2004) assumed a simple radial geometry in plan view for fluvial-dominated deltaic clinoforms in the Ferron Sandstone Member outcrop analog, but this geometry is not universally applicable even as a first-order approximation. For example, wave-dominated strandplains are nearly linear in plan view ([[:File:BLTN13190fig3.jpg|Figure 3A]]), wave-dominated deltas have broad arcuate forms ([[:File:BLTN13190fig3.jpg|Figure 3B]]), and fluvial-dominated deltaic shorelines form distinct, lobate protuberances ([[:File:BLTN13190fig3.jpg|Figure 3C]]) (e.g., Galloway, 1975).

As the algorithm is generic, the user can specify the shape of an ellipse that approximates the plan-view geometry of clinoforms ([[:File:BLTN13190fig4.jpg|Figure 4A]]). Using an ellipse, rather than a radial geometry, allows the user to specify a wide range of plan-view clinoform geometries using a simple function, depending on the interpreted environment of deposition and scale of shoreline curvature. Two ellipses are used: the top ellipse represents the shoreline at the clinoform top, and the base ellipse represents the maximum extent of the clinoform at its downlap termination on the underlying sea floor. The user defines the length of the top and base ellipses in depositional dip and strike directions (BLTN13190eq31, BLTN13190eq32, BLTN13190eq33, BLTN13190eq34; [[:File:BLTN13190fig4.jpg|Figure 4B]], Table 1) relative to the origin of the clinoform. The difference between the user-defined maximum extents of the top and base ellipses yields the clinoform length BLTN13190eq35 ([[:File:BLTN13190fig4.jpg|Figure 4D]]). The maximum extent of the top and base ellipses can then be defined as  

As the algorithm is generic, the user can specify the shape of an ellipse that approximates the plan-view geometry of clinoforms ([[:File:BLTN13190fig4.jpg|Figure 4A]]). Using an ellipse, rather than a radial geometry, allows the user to specify a wide range of plan-view clinoform geometries using a simple function, depending on the interpreted environment of deposition and scale of shoreline curvature. Two ellipses are used: the top ellipse represents the shoreline at the clinoform top, and the base ellipse represents the maximum extent of the clinoform at its downlap termination on the underlying sea floor. The user defines the length of the top and base ellipses in depositional dip and strike directions (t_s, t_D, b_s, b_D; [[:File:BLTN13190fig4.jpg|Figure 4B]], Table 1) relative to the origin of the clinoform. The difference between the user-defined maximum extents of the top and base ellipses yields the clinoform length L ([[:File:BLTN13190fig4.jpg|Figure 4D]]). The maximum extent of the top and base ellipses can then be defined as  

:<math>EQUATIONS/BLTN13190eqd2</math>

:<math>b_s = t_s + L \: \: \: \: \: \: \: \: (2)</math>

and  

and  

:<math>EQUATIONS/BLTN13190eqd3</math>

:<math>b_D = t_D + L \: \: \: \: \: \: \: \: (3)</math>

The clinoform is generated in the volume between the top and base ellipses ([[:File:BLTN13190fig4.jpg|Figure 4A, B]]). In this volume, the radius of each point on the clinoform, BLTN13190eq45 (Table 1), is calculated relative to the clinoform origin (BLTN13190eq46), using  

The clinoform is generated in the volume between the top and base ellipses ([[:File:BLTN13190fig4.jpg|Figure 4A, B]]). In this volume, the radius of each point on the clinoform, BLTN13190eq45 (Table 1), is calculated relative to the clinoform origin (BLTN13190eq46), using  

:<math>EQUATIONS/BLTN13190eqd4</math>

:<math>r_c(x,y) = \sqrt{(x_{\text{origin}} - x)^2 + (y_{\text{origin}} - y)^2} \: \: \: \: \: \: \: \: (4)</math>

 

At each point on the clinoform, the radius of the top ellipse relative to the clinoform origin is calculated using  

At each point on the clinoform, the radius of the top ellipse relative to the clinoform origin is calculated using  

:<math>EQUATIONS/BLTN13190eqd5</math>

:<math>EQUATIONS/BLTN13190eqd5</math>