Changes

[[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_c)'' (equation 1; see Table 1 for nomenclature). (E) Shape function, ''s(r_c)'' (equation 7; Table 1), demonstrating that increasing the exponent, ''P'', increases the dip angle of clinoforms.]]

[[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_c)'' (equation 1; see Table 1 for nomenclature). (E) Shape function, ''s(r_c)'' (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<ref name=HHH>Helland-Hansen, W., and G. J. Hampson, 2009, Trajectory analysis: Concepts and applications: Basin Research, v. 21, no. 5, p. 454–483, doi: 10.1111/j.1365-2117.2009.00425.x.</ref>). 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<ref name=GB07>Gani, M. R., and J. P. Bhattacharya, 2007, Basic building blocks and process variability of a Cretaceous delta: Internal facies architecture reveals a more dynamic interaction of river, wave, and tidal processes than is indicated by external shape: Journal of Sedimentary Research, v. 77, no. 4, p. 284–302, doi: 10.2110/jsr.2007.023.</ref>) 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;<ref name=GB07 /> 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.,;<ref name=Answrth1999 /> Hampson et al.<ref name=Hmpsn2008 />).

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<ref name=HHH>Helland-Hansen, W., and G. J. Hampson, 2009, Trajectory analysis: Concepts and applications: Basin Research, v. 21, no. 5, p. 454–483, doi: 10.1111/j.1365-2117.2009.00425.x.</ref>). 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<ref name=Glwy>Galloway, W. E., 1975, Process framework for describing the morphological and stratigraphic evolution of deltaic depositional systems, in M. L. Broussard, ed., Deltas, models for exploration: Houston, Texas, Houston Geological Society, p. 87–98.</ref>). 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<ref name=Bhttchry2006>Bhattacharya, J. P., 2006, Deltas, inH. W. Posamentier, and R. Walker, eds., Facies models revisited: SEPM Special Publication 84, p. 237–292.</ref> (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;<ref name=Glwy /> Willis, 2005; Bhattacharya;<ref name=Bhttchry2006 /> Plink-Björklund, 2012). Clinoforms exist as a preserved record of sediment-body morphologies at each of these hierarchical lengthscales (e.g., Gani and Bhattacharya<ref name=GB07>Gani, M. R., and J. P. Bhattacharya, 2007, Basic building blocks and process variability of a Cretaceous delta: Internal facies architecture reveals a more dynamic interaction of river, wave, and tidal processes than is indicated by external shape: Journal of Sedimentary Research, v. 77, no. 4, p. 284–302, doi: 10.2110/jsr.2007.023.</ref>) 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;<ref name=GB07 /> 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.,;<ref name=Answrth1999 /> Hampson et al.<ref name=Hmpsn2008 />).

The clinoform-modeling algorithm developed here is simple to use, requiring specification of only a few input parameters: (1) the upper and lower surfaces that define the rock volume within which the clinoforms are to be modeled; (2) the plan-view geometry of clinoforms; (3) clinoform geometry in depositional-dip-oriented cross section; and (4) spacing and progradation direction of the clinoforms. The user can also use a stochastic component of the clinoform-modeling algorithm if there are uncertainties in the parameter values to be used.

The clinoform-modeling algorithm developed here is simple to use, requiring specification of only a few input parameters: (1) the upper and lower surfaces that define the rock volume within which the clinoforms are to be modeled; (2) the plan-view geometry of clinoforms; (3) clinoform geometry in depositional-dip-oriented cross section; and (4) spacing and progradation direction of the clinoforms. The user can also use a stochastic component of the clinoform-modeling algorithm if there are uncertainties in the parameter values to be used.

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The depositional processes acting at the shoreline control the plan-view shape and abundance of clinoforms and their associated heterogeneity.<ref name=Hwll2008a /> 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.<ref name=Hwll2008a /> 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.<ref name=Hwll2008a /> 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.<ref name=Hwll2008a /> 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<ref name=Glwy />).

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  

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>c(r_c) = h_{\text{min}}(r_c) + \left ( \frac{(r_{\text{max}}(x, y) - r_c(x, y))^P}{r_{\text{max}}(x, y) - r_{\text{min}}(x, y))^P} h(r_c) \right )</math>

:<math>c(r_c) = h_{\text{min}}(r_c) + \left ( \frac{(r_{\text{max}}(x, y) - r_c(x, y))^P}{r_{\text{max}}(x, y) - r_{\text{min}}(x, y))^P} h(r_c) \right )</math>

By varying the exponent in the clinoform shape function, ''P'', the user can increase or decrease the dip angle and change the shape of the clinoform ([[:File:BLTN13190fig2.jpg|Figure 2E]], Table 1). If a similar geometry is interpreted for each clinoform within a parasequence, because they are inferred to have formed under the influence of similar hydrodynamic and sedimentologic processes, then the same value of ''P'' (equation 7) can be applied to each clinoform modeled in the parasequence. Different values of ''P'' can be applied to distinct geographic regions of a parasequence in which clinoforms are interpreted to have different geometries (e.g., on different flanks of an asymmetric wave-dominated delta; Bhattacharya and Giosan, 2003;<ref>Charvin, K., G. J. Hampson, K. L. Gallagher, and R. Labourdette, 2010, High-resolution stratigraphic architecture within an interpreted asymmetrical wave-dominated deltaic parasequence: Sedimentology, v. 57, no. 3, p. 760–785, doi: 10.1111/j.1365-3091.2009.01118.x.</ref>), provided that the bounding surfaces of these geographic regions have been defined (in the initial step of the method).

By varying the exponent in the clinoform shape function, ''P'', the user can increase or decrease the dip angle and change the shape of the clinoform ([[:File:BLTN13190fig2.jpg|Figure 2E]], Table 1). If a similar geometry is interpreted for each clinoform within a parasequence, because they are inferred to have formed under the influence of similar hydrodynamic and sedimentologic processes, then the same value of ''P'' (equation 7) can be applied to each clinoform modeled in the parasequence. Different values of ''P'' can be applied to distinct geographic regions of a parasequence in which clinoforms are interpreted to have different geometries (e.g., on different flanks of an asymmetric wave-dominated delta;<ref>Bhattacharya, J. P., and L. Giosan, 2003, Wave-influenced deltas: Geomorphological implications for facies reconstruction: Sedimentology, v. 50, no. 1, p. 187–210, doi: 10.1046/j.1365-3091.2003.00545.x.</ref><ref>Charvin, K., G. J. Hampson, K. L. Gallagher, and R. Labourdette, 2010, High-resolution stratigraphic architecture within an interpreted asymmetrical wave-dominated deltaic parasequence: Sedimentology, v. 57, no. 3, p. 760–785, doi: 10.1111/j.1365-3091.2009.01118.x.</ref>), provided that the bounding surfaces of these geographic regions have been defined (in the initial step of the method).

===Spacing and Progradation Direction of Clinoforms===

===Spacing and Progradation Direction of Clinoforms===

Construction and fluid-flow simulation of models based on outcrop analogs is an established method for investigating geologic controls on subsurface reservoir performance (e.g., Ciammetti et al., 1995; White and Barton, 1999; White et al., 2004; Jackson et al.;<ref name=Jckson2009 /> Sech et al.;<ref name=Sch09 /> Enge and Howell<ref name=EH2010 />). Here, the clinoform-modeling algorithm is used to build a reservoir model utilizing a high-resolution outcrop data set from the Ferron Sandstone Member, Utah, at a scale that is comparable to the interwell spacing (750 × 3000 m [2461 × 9843 ft] areally) in a typical hydrocarbon reservoir and captures several tens of clinoforms and their associated heterogeneities. Previously, Forster et al. <ref name=Frstr2004 /> constructed 2-D flow-simulation models of the same outcrop analog via data-intensive, deterministic mapping of clinoforms and facies boundaries in cliff-face exposures. In contrast, our aim is to verify that the clinoform-modeling algorithm can produce realistic 3-D stratigraphic architectures that mimic rich outcrop data sets when conditioned to sparse input data that are typical in the subsurface. The scale of the model fills the gap between detailed but sparse 2-D core and well-log data and low-resolution but extensive 3-D seismic data.

Construction and fluid-flow simulation of models based on outcrop analogs is an established method for investigating geologic controls on subsurface reservoir performance (e.g., Ciammetti et al., 1995; White and Barton, 1999; White et al., 2004; Jackson et al.;<ref name=Jckson2009 /> Sech et al.;<ref name=Sch09 /> Enge and Howell<ref name=EH2010 />). Here, the clinoform-modeling algorithm is used to build a reservoir model utilizing a high-resolution outcrop data set from the Ferron Sandstone Member, Utah, at a scale that is comparable to the interwell spacing (750 × 3000 m [2461 × 9843 ft] areally) in a typical hydrocarbon reservoir and captures several tens of clinoforms and their associated heterogeneities. Previously, Forster et al. <ref name=Frstr2004 /> constructed 2-D flow-simulation models of the same outcrop analog via data-intensive, deterministic mapping of clinoforms and facies boundaries in cliff-face exposures. In contrast, our aim is to verify that the clinoform-modeling algorithm can produce realistic 3-D stratigraphic architectures that mimic rich outcrop data sets when conditioned to sparse input data that are typical in the subsurface. The scale of the model fills the gap between detailed but sparse 2-D core and well-log data and low-resolution but extensive 3-D seismic data.

The Ferron Sandstone Member of the Mancos Shale is located in east-central Utah. The unit was deposited during the Late Cretaceous (Turonian–Coniacian) on the western margin of the Western Interior Seaway and, in the study area, records the progradation of the Last Chance delta system from southwest (paleolandward) to northeast (paleoseaward) (Cotter, 1976) ([[:File:BLTN13190fig5.jpg|Figure 5A]]). These deltaic deposits form a basinward-thinning wedge that passes eastward into the offshore deposits of the Mancos Shale. The wedge contains either seven (Ryer, 1991; Gardner, 1993; Barton et al., 2004) or eight sandstone tongues (Anderson and Ryer, 2004; Garrison and Van den Bergh, 2004), such that one tongue is equivalent to a parasequence set of Deveugle et al.<ref name=Dvgl2011 /> ([[:File:BLTN13190fig5.jpg|Figure 5B]]). A single delta-lobe deposit within the lowermost sandstone tongue is the focus of the study (bedset Kf-1-Iv[a] of Anderson et al., 2004; parasequence 1h of Garrison and Van den Bergh, 2004; parasequence 1.6 of Deveugle et al.<ref name=Dvgl2011 />) ([[:File:BLTN13190fig5.jpg|Figure 5C, D]]). The delta-lobe deposit is fluvial dominated with low-to-moderate wave influence (Gardner, 1993; Garrison and Van den Bergh, 2004; Ryer and Anderson, 2004) and contains numerous, well-documented clinoforms in the exposures of the Ivie Creek amphitheater (Anderson et al., 2002, 2003, 2004; <ref name=Frstr2004 /><ref name=EH2010 /> ([[:File:BLTN13190fig5.jpg|Figure 5D]]). Clinoform-related bedding geometries and facies distributions imply that clinoforms mapped by previous workers, and used as input data for the models presented below ([[:File:BLTN13190fig6.jpg|Figure 6A]], after Forster et al. <ref name=Frstr2004 />), bound clinothems equivalent to mouth bars (sensu Bhattacharya, 2006). Subtle, apparently cyclic variations in clinoform spacing and dip angle probably define mouth-bar assemblages (sensu Bhattacharya, 2006; “bedsets” sensu Enge et al., 2010). Smaller-scale lithologic variation at the scale of individual beds occurs between the mapped clinoforms and records incremental growth of a mouth bar because of varying water and sediment discharge through the feeder distributary channel. Deveugle et al.<ref name=Dvgl2011 /> used a high-resolution outcrop data set to build a reservoir-scale (7200 × 3800 × 50 m [23622 × 12467 × 164 ft]), surface-based model of the lower two tongues (parasequence sets) of the Ferron Sandstone Member. Clinoforms were not represented in the delta-lobe deposits (cf. parasequences) of the Deveugle et al.<ref name=Dvgl2011 /> model, and their surface-based model is used here as the context in which the clinoform-modeling algorithm should be applied.

The Ferron Sandstone Member of the Mancos Shale is located in east-central Utah. The unit was deposited during the Late Cretaceous (Turonian–Coniacian) on the western margin of the Western Interior Seaway and, in the study area, records the progradation of the Last Chance delta system from southwest (paleolandward) to northeast (paleoseaward) (Cotter, 1976) ([[:File:BLTN13190fig5.jpg|Figure 5A]]). These deltaic deposits form a basinward-thinning wedge that passes eastward into the offshore deposits of the Mancos Shale. The wedge contains either seven (Ryer, 1991; Gardner, 1993; Barton et al., 2004) or eight sandstone tongues (Anderson and Ryer, 2004; Garrison and Van den Bergh, 2004), such that one tongue is equivalent to a parasequence set of Deveugle et al.<ref name=Dvgl2011 /> ([[:File:BLTN13190fig5.jpg|Figure 5B]]). A single delta-lobe deposit within the lowermost sandstone tongue is the focus of the study (bedset Kf-1-Iv[a] of Anderson et al., 2004; parasequence 1h of Garrison and Van den Bergh, 2004; parasequence 1.6 of Deveugle et al.<ref name=Dvgl2011 />) ([[:File:BLTN13190fig5.jpg|Figure 5C, D]]). The delta-lobe deposit is fluvial dominated with low-to-moderate wave influence (Gardner, 1993; Garrison and Van den Bergh, 2004; Ryer and Anderson, 2004) and contains numerous, well-documented clinoforms in the exposures of the Ivie Creek amphitheater (Anderson et al., 2002, 2003, 2004; <ref name=Frstr2004 /><ref name=EH2010 /> ([[:File:BLTN13190fig5.jpg|Figure 5D]]). Clinoform-related bedding geometries and facies distributions imply that clinoforms mapped by previous workers, and used as input data for the models presented below ([[:File:BLTN13190fig6.jpg|Figure 6A]], after Forster et al. <ref name=Frstr2004 />), bound clinothems equivalent to mouth bars (sensu Bhattacharya<ref name=Bhttchry2006 />). Subtle, apparently cyclic variations in clinoform spacing and dip angle probably define mouth-bar assemblages (sensu Bhattacharya;<ref name=Bhttchry2006 /> “bedsets” sensu Enge et al., 2010). Smaller-scale lithologic variation at the scale of individual beds occurs between the mapped clinoforms and records incremental growth of a mouth bar because of varying water and sediment discharge through the feeder distributary channel. Deveugle et al.<ref name=Dvgl2011 /> used a high-resolution outcrop data set to build a reservoir-scale (7200 × 3800 × 50 m [23622 × 12467 × 164 ft]), surface-based model of the lower two tongues (parasequence sets) of the Ferron Sandstone Member. Clinoforms were not represented in the delta-lobe deposits (cf. parasequences) of the Deveugle et al.<ref name=Dvgl2011 /> model, and their surface-based model is used here as the context in which the clinoform-modeling algorithm should be applied.

===Model Construction===

===Model Construction===

The top and base flooding surfaces of parasequence 1.6 were extracted from the model of Deveugle et al.<ref name=Dvgl2011 /> and served as the bounding surfaces used in the clinoform algorithm ([[:File:BLTN13190fig2.jpg|Figure 2]]). The surfaces were cropped to cover a model area of 750 × 3000 m (2461 × 9843 ft) in the Ivie Creek amphitheater ([[:File:BLTN13190fig5.jpg|Figure 5D]]). Additional surfaces representing the boundaries between facies associations from the model of Deveugle et al.<ref name=Dvgl2011 /> were also extracted and similarly cropped; these define the distribution of facies associations present in each rock volume bounded by two clinoforms (i.e., clinothem) (cf. table 1 in Deveugle et al.<ref name=Dvgl2011 />). From distal to proximal, the modeled facies associations are prodelta mudstone (PD), distal delta-front heteroliths (dDF), proximal delta-front sandstones (pDF), and stream-mouth-bar sandstones (SMB) ([[:File:BLTN13190fig5.jpg|Figure 5D]]). Where facies associations pinch out, the facies association boundary surfaces were adjusted to coincide throughout the remainder of the model volume with either the top or base parasequence bounding surface. This ensures that the surface is defined across the entire model volume and is suitable for gridding.<ref name=Jckson2009 /> There are no faults within the model volume of 750 × 3000 × 6 m (2461 × 9843 × 20 ft). In a final step, isochore maps were generated between the top and base flooding surfaces and between facies association boundary surfaces and the base flooding surface. The base bounding surface was flattened, to mimic clinoform progradation over a flat, horizontal sea floor, and isochore maps were used to modify the geometries of the top bounding surface and facies association boundary surfaces above this horizontal base surface. As a result of flattening on the base bounding surface, the bounding surfaces from the existing model of Deveugle et al.<ref name=Dvgl2011 /> have been modified.

The top and base flooding surfaces of parasequence 1.6 were extracted from the model of Deveugle et al.<ref name=Dvgl2011 /> and served as the bounding surfaces used in the clinoform algorithm ([[:File:BLTN13190fig2.jpg|Figure 2]]). The surfaces were cropped to cover a model area of 750 × 3000 m (2461 × 9843 ft) in the Ivie Creek amphitheater ([[:File:BLTN13190fig5.jpg|Figure 5D]]). Additional surfaces representing the boundaries between facies associations from the model of Deveugle et al.<ref name=Dvgl2011 /> were also extracted and similarly cropped; these define the distribution of facies associations present in each rock volume bounded by two clinoforms (i.e., clinothem) (cf. table 1 in Deveugle et al.<ref name=Dvgl2011 />). From distal to proximal, the modeled facies associations are prodelta mudstone (PD), distal delta-front heteroliths (dDF), proximal delta-front sandstones (pDF), and stream-mouth-bar sandstones (SMB) ([[:File:BLTN13190fig5.jpg|Figure 5D]]). Where facies associations pinch out, the facies association boundary surfaces were adjusted to coincide throughout the remainder of the model volume with either the top or base parasequence bounding surface. This ensures that the surface is defined across the entire model volume and is suitable for gridding.<ref name=Jckson2009 /> There are no faults within the model volume of 750 × 3000 × 6 m (2461 × 9843 × 20 ft). In a final step, isochore maps were generated between the top and base flooding surfaces and between facies association boundary surfaces and the base flooding surface. The base bounding surface was flattened, to mimic clinoform progradation over a flat, horizontal sea floor, and isochore maps were used to modify the geometries of the top bounding surface and facies association boundary surfaces above this horizontal base surface. As a result of flattening on the base bounding surface, the bounding surfaces from the existing model of Deveugle et al.<ref name=Dvgl2011 /> have been modified.

The parameters used to insert clinoforms into the model volume are summarized in Table 2. The delta lobe in parasequence 1.6 is approximately 8.1 km (5.03 mi) wide and 12.2 km (7.58 mi) long, giving a plan-view aspect ratio of 0.7,<ref name=Dvgl2011 /> comparable to values for lobes of the Pleistocene Lagniappe delta (after data in Kolla et al., 2000; Roberts et al., 2004) and the modern Wax Lake Delta lobe (after data in Wellner et al., 2005) ([[:File:BLTN13190fig3.jpg|Figure 3C]]). These dimensions were likely smaller during the growth of the delta lobe, and it is assumed here that the lobe initiated with dimensions (''t_D'', ''t_s'') that were a third of those of the final preserved delta lobe, consistent in areal proportions to a single mouth-bar assemblage or jet-plume complex in the modern Wax Lake Delta lobe (after data in Wellner et al., 2005). The length, ''L'', and spacing, ''S'', of clinoforms in depositional dip cross section were extracted from the bedding-diagram interpretations of Forster et al. <ref name=Frstr2004 /> ([[:File:BLTN13190fig6.jpg|Figure 6A]]), clinoform length and dip statistics of Enge et al. (2010), and the LIDAR data used to create the model of Enge and Howell.<ref name=EH2010 /> A database of clinoform lengths, dips, and spacings was compiled from these data sources, yielding frequency distributions from which the geometry or spatial arrangement of clinoforms that bound mouth-bar clinothems (sensu Bhattacharya, 2006), or a trend in these parameters, can be extracted ([[:File:BLTN13190fig6.jpg|Figure 6B, C]]). The clinoform-modeling algorithm was used to build 31 clinoforms in the modeled volume of parasequence 1.6 ([[:File:BLTN13190fig7.jpg|Figure 7]]). For simplicity, clinoform spacing is fixed at 25 m (82 ft), which is the average value observed at outcrop ([[:File:BLTN13190fig6.jpg|Figure 6C]]). Heterogeneity at bed scale is recognized to be present but is not explicitly captured by surfaces in the model; rather, the effective petrophysical properties assigned to the facies associations (particularly the ratio of vertical-to-horizontal permeability) are modified to account for these.<ref name=Jckson2009 /><ref name=Dvgl2011 /><ref name=Grhm2015 /> A constant value of 2 was assigned to the clinoform shape-function exponent, ''P'' ([[:File:BLTN13190fig2.jpg|Figure 2E]]), to ensure that the clinoform dip angle is always in the range extracted from the data of Enge et al. (2010). The initial clinoform insertion point, ''P_o'' ([[:File:BLTN13190fig4.jpg|Figure 4C]]), was qualitatively matched with a plan-view map of facies association belts at the top of parasequence 1.6 ([[:File:BLTN13190fig5.jpg|Figure 5D]]). The overall progradation direction for the clinoforms (''θ'') was assigned an azimuth of 274° relative to north, which corresponds to the interpreted progradation direction of the delta lobe in parasequence 1.6.<ref name=Dvgl2011 /> In a subsequent step, the facies association boundary surfaces extracted from the model of Deveugle et al.<ref name=Dvgl2011 /> were used to create facies association zones within each clinothem. Application of the clinoform-modeling algorithm yields a surface-based model measuring 750 × 3000 × 6 m (2461 × 9843 × 20 ft), which contains 95 surfaces: the top- and base-parasequence bounding surfaces, 31 clinoforms, and 62 facies-association boundary surfaces ([[:File:BLTN13190fig8.jpg|Figure 8]]).

The parameters used to insert clinoforms into the model volume are summarized in Table 2. The delta lobe in parasequence 1.6 is approximately 8.1 km (5.03 mi) wide and 12.2 km (7.58 mi) long, giving a plan-view aspect ratio of 0.7,<ref name=Dvgl2011 /> comparable to values for lobes of the Pleistocene Lagniappe delta (after data in Kolla et al., 2000; Roberts et al., 2004) and the modern Wax Lake Delta lobe (after data in Wellner et al., 2005) ([[:File:BLTN13190fig3.jpg|Figure 3C]]). These dimensions were likely smaller during the growth of the delta lobe, and it is assumed here that the lobe initiated with dimensions (''t_D'', ''t_s'') that were a third of those of the final preserved delta lobe, consistent in areal proportions to a single mouth-bar assemblage or jet-plume complex in the modern Wax Lake Delta lobe (after data in Wellner et al., 2005). The length, ''L'', and spacing, ''S'', of clinoforms in depositional dip cross section were extracted from the bedding-diagram interpretations of Forster et al. <ref name=Frstr2004 /> ([[:File:BLTN13190fig6.jpg|Figure 6A]]), clinoform length and dip statistics of Enge et al. (2010), and the LIDAR data used to create the model of Enge and Howell.<ref name=EH2010 /> A database of clinoform lengths, dips, and spacings was compiled from these data sources, yielding frequency distributions from which the geometry or spatial arrangement of clinoforms that bound mouth-bar clinothems (sensu Bhattacharya<ref name=Bhttchry2006 />), or a trend in these parameters, can be extracted ([[:File:BLTN13190fig6.jpg|Figure 6B, C]]). The clinoform-modeling algorithm was used to build 31 clinoforms in the modeled volume of parasequence 1.6 ([[:File:BLTN13190fig7.jpg|Figure 7]]). For simplicity, clinoform spacing is fixed at 25 m (82 ft), which is the average value observed at outcrop ([[:File:BLTN13190fig6.jpg|Figure 6C]]). Heterogeneity at bed scale is recognized to be present but is not explicitly captured by surfaces in the model; rather, the effective petrophysical properties assigned to the facies associations (particularly the ratio of vertical-to-horizontal permeability) are modified to account for these.<ref name=Jckson2009 /><ref name=Dvgl2011 /><ref name=Grhm2015 /> A constant value of 2 was assigned to the clinoform shape-function exponent, ''P'' ([[:File:BLTN13190fig2.jpg|Figure 2E]]), to ensure that the clinoform dip angle is always in the range extracted from the data of Enge et al. (2010). The initial clinoform insertion point, ''P_o'' ([[:File:BLTN13190fig4.jpg|Figure 4C]]), was qualitatively matched with a plan-view map of facies association belts at the top of parasequence 1.6 ([[:File:BLTN13190fig5.jpg|Figure 5D]]). The overall progradation direction for the clinoforms (''θ'') was assigned an azimuth of 274° relative to north, which corresponds to the interpreted progradation direction of the delta lobe in parasequence 1.6.<ref name=Dvgl2011 /> In a subsequent step, the facies association boundary surfaces extracted from the model of Deveugle et al.<ref name=Dvgl2011 /> were used to create facies association zones within each clinothem. Application of the clinoform-modeling algorithm yields a surface-based model measuring 750 × 3000 × 6 m (2461 × 9843 × 20 ft), which contains 95 surfaces: the top- and base-parasequence bounding surfaces, 31 clinoforms, and 62 facies-association boundary surfaces ([[:File:BLTN13190fig8.jpg|Figure 8]]).

A cornerpoint gridding scheme in which variations in facies architecture are represented by variations in grid architecture was used (White and Barton, 1999; Jackson et al., 2005; <ref name=Sch09 />). The grid has vertical pillars with a constant spacing of 20 m (66 ft) in x and y (horizontal) directions. Grid layering in the z (vertical) direction within each facies-association zone conforms to the underlying clinoform surface, so layers are parallel to, and build up from, the underlying clinoform. Grid layers have a constant thickness of 0.2 m (0.66 ft); however, each facies-association zone is gridded separately, and the grid layers pinch out against facies-association boundaries and parasequence-bounding flooding surfaces. This gridding approach was used by Sech et al.;<ref name=Sch09 /> it ensures that the grid layering conforms to the architecture of the clinoform surfaces, preserving their dip and geometry, and captures facies association boundaries ([[:File:BLTN13190fig9.jpg|Figure 9]]). Where a grid layer pinches out, the grid cells have zero thickness and are set to be inactive in flow simulations. These zero-thickness cells are bridged using nonneighbor connections so that they do not act as barriers to flow. The chosen cell size of 20 × 20 × 0.2 m (66 × 66 × 0.66 ft) yields a total of approximately 5 million cells, of which 140,000 (2.6%) are active. Because the number of active grid cells is small, fluid-flow simulations can be performed on the grid without upscaling.

A cornerpoint gridding scheme in which variations in facies architecture are represented by variations in grid architecture was used (White and Barton, 1999; Jackson et al., 2005; <ref name=Sch09 />). The grid has vertical pillars with a constant spacing of 20 m (66 ft) in x and y (horizontal) directions. Grid layering in the z (vertical) direction within each facies-association zone conforms to the underlying clinoform surface, so layers are parallel to, and build up from, the underlying clinoform. Grid layers have a constant thickness of 0.2 m (0.66 ft); however, each facies-association zone is gridded separately, and the grid layers pinch out against facies-association boundaries and parasequence-bounding flooding surfaces. This gridding approach was used by Sech et al.;<ref name=Sch09 /> it ensures that the grid layering conforms to the architecture of the clinoform surfaces, preserving their dip and geometry, and captures facies association boundaries ([[:File:BLTN13190fig9.jpg|Figure 9]]). Where a grid layer pinches out, the grid cells have zero thickness and are set to be inactive in flow simulations. These zero-thickness cells are bridged using nonneighbor connections so that they do not act as barriers to flow. The chosen cell size of 20 × 20 × 0.2 m (66 × 66 × 0.66 ft) yields a total of approximately 5 million cells, of which 140,000 (2.6%) are active. Because the number of active grid cells is small, fluid-flow simulations can be performed on the grid without upscaling.

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# Barton, M. D., E. S. Angle, and N. Tyler, 2004, Stratigraphic architecture of fluvial-deltaic sandstones from the Ferron Sandstone outcrop, east-central Utah, inT. C. Chidsey, Jr., R. D. Adams, and T. H. Morris, eds., Regional to wellbore analog for fluvial-deltaic reservoir modeling: The Ferron Sandstone of Utah: AAPG Studies in Geology 50, p. 193–210.

# Barton, M. D., E. S. Angle, and N. Tyler, 2004, Stratigraphic architecture of fluvial-deltaic sandstones from the Ferron Sandstone outcrop, east-central Utah, inT. C. Chidsey, Jr., R. D. Adams, and T. H. Morris, eds., Regional to wellbore analog for fluvial-deltaic reservoir modeling: The Ferron Sandstone of Utah: AAPG Studies in Geology 50, p. 193–210.

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# Ciammetti, G., P. S. Ringrose, T. R. Good, J. M. L. Lewis, and K. S. Sorbie, 1995, Waterflood recovery and fluid flow upscaling in a shallow marine and fluvial sandstone sequence: SPE Paper 30783, 14 p.

# Ciammetti, G., P. S. Ringrose, T. R. Good, J. M. L. Lewis, and K. S. Sorbie, 1995, Waterflood recovery and fluid flow upscaling in a shallow marine and fluvial sandstone sequence: SPE Paper 30783, 14 p.

# Dilib, F. A., M. D. Jackson, A. Mojaddam Zadeh, R. Aasheim, K. Årland, A. J. Gyllensten, and S. M. Erlandsen, 2015, Closed-loop feedback control in intelligent wells: Application to a heterogeneous, thin oil-rim reservoir in the North Sea: SPE Reservoir Evaluation and Engineering, v. 18, no. 1, 15 p., doi: 10.2118/159550-PA.

# Dilib, F. A., M. D. Jackson, A. Mojaddam Zadeh, R. Aasheim, K. Årland, A. J. Gyllensten, and S. M. Erlandsen, 2015, Closed-loop feedback control in intelligent wells: Application to a heterogeneous, thin oil-rim reservoir in the North Sea: SPE Reservoir Evaluation and Engineering, v. 18, no. 1, 15 p., doi: 10.2118/159550-PA.

# Dreyer, T., M. Whitaker, J. Dexter, H. Flesche, and E. Larsen, 2005, From spit system to tide-dominated delta: Integrated reservoir model of the Upper Jurassic Sognefjord Formation on the Troll West field, inA. G. Doré, and B. A. Vining, eds., Petroleum geology: From mature basins to new frontiers—Proceedings of the 6th Petroleum Geology Conference: Petroleum Geology Conference Series 6: London, Geological Society, p. 423–448.

# Dreyer, T., M. Whitaker, J. Dexter, H. Flesche, and E. Larsen, 2005, From spit system to tide-dominated delta: Integrated reservoir model of the Upper Jurassic Sognefjord Formation on the Troll West field, inA. G. Doré, and B. A. Vining, eds., Petroleum geology: From mature basins to new frontiers—Proceedings of the 6th Petroleum Geology Conference: Petroleum Geology Conference Series 6: London, Geological Society, p. 423–448.

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# Enge, H. D., J. A. Howell, and S. Buckley, 2010, The geometry and internal architecture of stream mouth bars in the Panther Tongue and the Ferron Sandstone Members, Utah, U.S.A.: Journal of Sedimentary Research, v. 80, no. 11, p. 1018–1031, doi: 10.2110/jsr.2010.088.

# Enge, H. D., J. A. Howell, and S. Buckley, 2010, The geometry and internal architecture of stream mouth bars in the Panther Tongue and the Ferron Sandstone Members, Utah, U.S.A.: Journal of Sedimentary Research, v. 80, no. 11, p. 1018–1031, doi: 10.2110/jsr.2010.088.

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# Fraser, S. I., A. M. Robinson, H. D. Johnson, J. R. Underhill, D. G. A. Kadolsky, R. Connell, P. Johanessen, and R. Ravnås, 2003, Upper Jurassic, inD. Evans, C. Graham, A. Armour, and P. Bathurst, eds., The millennium atlas: Petroleum geology of the central and northern North Sea: London, The Geological Society, p. 158–189.

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# Gardner, M. H., 1993, Sequence stratigraphy and facies architecture of the Upper Cretaceous Ferron Sandstone Member of the Mancos Shale, east-central Utah: Ph.D. dissertation, Colorado School of Mines, Golden, Colorado, 528 p.

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# Jackson, M. D., G. J. Hampson, J. H. Saunders, A. El Sheikh, G. H. Graham, and B. Y. G. Massart, 2014, Surface-based reservoir modelling for flow simulation, in A. W. Martinius, J. A. Howell, and T. R. Good, eds., Sediment-body geometry and heterogeneity: Analogue studies for modelling the subsurface: Geological Society, London, Special Publication 387, p. 271–292, doi: 10.1144/SP387.2.

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# Willis, B. J., 2005, Deposits of tide-influenced river deltas, inL. Giosan, and J. P. Bhattacharya, eds., River deltas—Concepts, models, and examples: SEPM Special Publication 83, p. 87–129.

# Willis, B. J., 2005, Deposits of tide-influenced river deltas, inL. Giosan, and J. P. Bhattacharya, eds., River deltas—Concepts, models, and examples: SEPM Special Publication 83, p. 87–129.

# Willis, B. J., J. P. Bhattacharya, S. L. Gabel, and C. D. White, 1999, Architecture of a tide-influenced river delta in the Frontier Formation of central Wyoming, USA: Sedimentology, v. 46, no. 4, p. 667–688, doi: 10.1046/j.1365-3091.1999.00239.x.

# Willis, B. J., J. P. Bhattacharya, S. L. Gabel, and C. D. White, 1999, Architecture of a tide-influenced river delta in the Frontier Formation of central Wyoming, USA: Sedimentology, v. 46, no. 4, p. 667–688, doi: 10.1046/j.1365-3091.1999.00239.x.