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==Conceptual framework for clinoform modeling==
 
==Conceptual framework for clinoform modeling==
[[File:BLTN13190fig2.jpg|thumb|300px|{{figure number|2}}Examples of clinoforms produced by the clinoform-modeling algorithm conditioned to different bounding surfaces and clinoform geometries. (A) Bounding surfaces represent postdepositional compaction and folding of the original (depositional) geometries of the clinoform and the top and base bounding surfaces. (B) Bounding surfaces represent a clinoform within a volume truncated at its top, for example, by a channel ([[:File:BLTN13190fig1.jpg|Figure 1]]). (C) Bounding surfaces represent a clinoform downlapping onto irregular sea-floor topography. (D) Height function, BLTN13190eq2 (equation 1; see Table 1 for nomenclature). (E) Shape function, BLTN13190eq3 (equation 7; Table 1), demonstrating that increasing the exponent, BLTN13190eq4, increases the dip angle of clinoforms.]]
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[[File:BLTN13190fig2.jpg|thumb|300px|{{figure number|2}}Examples of clinoforms produced by the clinoform-modeling algorithm conditioned to different bounding surfaces and clinoform geometries. (A) Bounding surfaces represent postdepositional compaction and folding of the original (depositional) geometries of the clinoform and the top and base bounding surfaces. (B) Bounding surfaces represent a clinoform within a volume truncated at its top, for example, by a channel ([[:File:BLTN13190fig1.jpg|Figure 1]]). (C) Bounding surfaces represent a clinoform downlapping onto irregular sea-floor topography. (D) Height function, ''h(r<sub>c</sub>)'' (equation 1; see Table 1 for nomenclature). (E) Shape function, ''s(r<sub>c</sub>)'' (equation 7; Table 1), demonstrating that increasing the exponent, ''P'', increases the dip angle of clinoforms.]]
    
Clinoforms occur at a wide range of spatial scales, from large, basinward-dipping surfaces at the shelf-slope margin, to smaller surfaces associated with progradation of deltaic and shoreface systems across the shelf (e.g., Helland-Hansen and Hampson, 2009). This study focuses on developing a surface-based approach to represent clinoforms at any lengthscale in reservoir models, with emphasis on clinoforms produced by the progradation of deltaic, barrier-island, and strandplain shorelines, which are typically up to a few tens of meters in height. The 3-D geometry and spatial arrangement of shoreline-scale clinoforms reflect in large part the process regime under which they were deposited (e.g., Galloway, 1975). Fluvial-dominated deltas exhibit a hierarchy of point-sourced, teardrop-shaped sediment bodies that are fed via a downstream branching network of distributary channels. From small to large lengthscales, this hierarchy consists of mouth bars, mouth-bar assemblages, and delta lobes (Bhattacharya, 2006; equivalent to the jet-plume deposits, jet-plume-complex deposits, and delta lobes of Wellner et al., 2005). Sediment-body geometry is modified by the action of waves and tides, which respectively tend to result in shoreline-parallel and shoreline-perpendicular sediment transport that suppresses branching and switching of distributary channels (e.g., Galloway, 1975; Willis, 2005; Bhattacharya, 2006; Plink-Björklund, 2012). Clinoforms exist as a preserved record of sediment-body morphologies at each of these hierarchical lengthscales (e.g., Gani and Bhattacharya, 2007) but are most commonly described at the scale of delta lobes in outcrop and high-resolution, shallow seismic data. For example, in Pleistocene fluvial-dominated delta deposits imaged in shallow-seismic data, Roberts et al. (2004, p. 185) comment that “each clinoform set represents rather continuous deposition from a distributary or related set of distributaries, resulting in the formation of a delta lobe.” Shale drapes and cemented concretionary layers occur along depositional surfaces at each hierarchical level but generally have greater continuity and extent at larger lengthscales of the hierarchy (e.g., Gani and Bhattacharya, 2007; Lee et al., 2007; Ahmed et al., 2014). Thus, delta lobes tend to be overlain across flooding surfaces by prodelta shales and distal-delta-front heteroliths, which may cause them to behave as distinct reservoir zones that can be correlated between wells, whereas clinoforms are associated with heterogeneity between wells and within reservoir zones (e.g., Ainsworth et al., 1999; Hampson et al., 2008).
 
Clinoforms occur at a wide range of spatial scales, from large, basinward-dipping surfaces at the shelf-slope margin, to smaller surfaces associated with progradation of deltaic and shoreface systems across the shelf (e.g., Helland-Hansen and Hampson, 2009). This study focuses on developing a surface-based approach to represent clinoforms at any lengthscale in reservoir models, with emphasis on clinoforms produced by the progradation of deltaic, barrier-island, and strandplain shorelines, which are typically up to a few tens of meters in height. The 3-D geometry and spatial arrangement of shoreline-scale clinoforms reflect in large part the process regime under which they were deposited (e.g., Galloway, 1975). Fluvial-dominated deltas exhibit a hierarchy of point-sourced, teardrop-shaped sediment bodies that are fed via a downstream branching network of distributary channels. From small to large lengthscales, this hierarchy consists of mouth bars, mouth-bar assemblages, and delta lobes (Bhattacharya, 2006; equivalent to the jet-plume deposits, jet-plume-complex deposits, and delta lobes of Wellner et al., 2005). Sediment-body geometry is modified by the action of waves and tides, which respectively tend to result in shoreline-parallel and shoreline-perpendicular sediment transport that suppresses branching and switching of distributary channels (e.g., Galloway, 1975; Willis, 2005; Bhattacharya, 2006; Plink-Björklund, 2012). Clinoforms exist as a preserved record of sediment-body morphologies at each of these hierarchical lengthscales (e.g., Gani and Bhattacharya, 2007) but are most commonly described at the scale of delta lobes in outcrop and high-resolution, shallow seismic data. For example, in Pleistocene fluvial-dominated delta deposits imaged in shallow-seismic data, Roberts et al. (2004, p. 185) comment that “each clinoform set represents rather continuous deposition from a distributary or related set of distributaries, resulting in the formation of a delta lobe.” Shale drapes and cemented concretionary layers occur along depositional surfaces at each hierarchical level but generally have greater continuity and extent at larger lengthscales of the hierarchy (e.g., Gani and Bhattacharya, 2007; Lee et al., 2007; Ahmed et al., 2014). Thus, delta lobes tend to be overlain across flooding surfaces by prodelta shales and distal-delta-front heteroliths, which may cause them to behave as distinct reservoir zones that can be correlated between wells, whereas clinoforms are associated with heterogeneity between wells and within reservoir zones (e.g., Ainsworth et al., 1999; Hampson et al., 2008).
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<sup>*N/A = not applicable.</sup>
 
<sup>*N/A = not applicable.</sup>
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This allows the clinoforms to adapt to the morphology of the bounding surfaces ([[:File:BLTN13190fig2.jpg|Figure 2A]]). For cases in which an overlying erosional bounding surface is interpreted to truncate clinoforms ([[:File:BLTN13190fig2.jpg|Figure 2B]]) and/or clinoforms are interpreted to downlap onto a bounding surface that reflects irregular sea-floor topography ([[:File:BLTN13190fig2.jpg|Figure 2C]]), a planar and horizontal dummy surface is used either above the erosional bounding surface or below the bounding surface, reflecting irregular sea-floor topography. The height function BLTN13190eq30 (equation 1), is applied to the planar dummy surfaces to insert clinoforms; and, in a final step, the bounding surface geometries are used to remove the upper and/or lower portions of the clinoforms, where appropriate, to match interpreted truncation ([[:File:BLTN13190fig2.jpg|Figure 2B]]) and/or down lap ([[:File:BLTN13190fig2.jpg|Figure 2C]]).
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This allows the clinoforms to adapt to the morphology of the bounding surfaces ([[:File:BLTN13190fig2.jpg|Figure 2A]]). For cases in which an overlying erosional bounding surface is interpreted to truncate clinoforms ([[:File:BLTN13190fig2.jpg|Figure 2B]]) and/or clinoforms are interpreted to downlap onto a bounding surface that reflects irregular sea-floor topography ([[:File:BLTN13190fig2.jpg|Figure 2C]]), a planar and horizontal dummy surface is used either above the erosional bounding surface or below the bounding surface, reflecting irregular sea-floor topography. The height function ''h(r<sub>c</sub>)'' (equation 1), is applied to the planar dummy surfaces to insert clinoforms; and, in a final step, the bounding surface geometries are used to remove the upper and/or lower portions of the clinoforms, where appropriate, to match interpreted truncation ([[:File:BLTN13190fig2.jpg|Figure 2B]]) and/or down lap ([[:File:BLTN13190fig2.jpg|Figure 2C]]).
    
===Plan-View Clinoform Geometry===
 
===Plan-View Clinoform Geometry===
 
<gallery mode=packed heights=400px widths=400px>
 
<gallery mode=packed heights=400px widths=400px>
 
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 (t<sub>s</sub>, t<sub>D</sub>, b<sub>s</sub>, b<sub>D</sub>; 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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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<sub>s</sub>, t<sub>D</sub>, b<sub>s</sub>, b<sub>D</sub>; 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, ''r<sub>c</sub>(x, y)'', the radius of the base ellipse (black arrow, ''r<sub>max</sub>(x, y)'' and the radius of the top ellipse (black arrow, ''r<sub>min</sub>(x, y)'' 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 ''P<sub>O<sub>''. (D) Conceptual depositional-dip-oriented cross-section view of clinoforms. Clinoform spacing, ''S'', 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.
 
</gallery>
 
</gallery>
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:<math>b_D = t_D + L</math>
 
:<math>b_D = t_D + L</math>
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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  
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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, ''r<sub>c</sub>(x, y)'' (Table 1), is calculated relative to the clinoform origin (''x<sub>origin</sub>, y<sub>origin</sub>''), using  
 
:<math>r_c(x,y) = \sqrt{(x_{\text{origin}} - x)^2 + (y_{\text{origin}} - y)^2}</math>
 
:<math>r_c(x,y) = \sqrt{(x_{\text{origin}} - x)^2 + (y_{\text{origin}} - y)^2}</math>
  

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