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Each set of shoreline clinoforms is contained within a distinct, upward-shallowing, regressive succession, or parasequence (sensu Van Wagoner et al., 1990; Hampson et al., 2008), that is bounded at its base and top by flooding surfaces. Multiple clinoforms exist within each parasequence. Because the algorithm is generic, any top and base bounding surfaces can be used; the only requirement is that the top bounding surface is entirely above, or coincident with, the base bounding surface across the model volume ([[:File:BLTN13190fig1.jpg|Figure 1A–C]]). By using the flooding surfaces at the top and/or base of a parasequence as reference surfaces, the algorithm can produce clinoforms that are modified by postdepositional folding and faulting ([[:File:BLTN13190fig2.jpg|Figure 2A]]), truncation by overlying erosion surfaces ([[:File:BLTN13190fig2.jpg|Figure 2B]]), and/or progradation over irregular sea-floor topography ([[:File:BLTN13190fig2.jpg|Figure 2C]]). The parasequence-bounding flooding surfaces are first read into the clinoform-modeling algorithm, using a standard gridded format exported from a reservoir modeling software package. Clinoforms created by the algorithm adapt to the morphology of either (or both) bounding surfaces, using a height function, BLTN13190eq1 ([[:File:BLTN13190fig2.jpg|Figure 2D]]), that calculates the height of the clinoform relative to the length along the clinoform surface and the height difference between the top and base bounding surfaces (see Table 1 for nomenclature):  
 
Each set of shoreline clinoforms is contained within a distinct, upward-shallowing, regressive succession, or parasequence (sensu Van Wagoner et al., 1990; Hampson et al., 2008), that is bounded at its base and top by flooding surfaces. Multiple clinoforms exist within each parasequence. Because the algorithm is generic, any top and base bounding surfaces can be used; the only requirement is that the top bounding surface is entirely above, or coincident with, the base bounding surface across the model volume ([[:File:BLTN13190fig1.jpg|Figure 1A–C]]). By using the flooding surfaces at the top and/or base of a parasequence as reference surfaces, the algorithm can produce clinoforms that are modified by postdepositional folding and faulting ([[:File:BLTN13190fig2.jpg|Figure 2A]]), truncation by overlying erosion surfaces ([[:File:BLTN13190fig2.jpg|Figure 2B]]), and/or progradation over irregular sea-floor topography ([[:File:BLTN13190fig2.jpg|Figure 2C]]). The parasequence-bounding flooding surfaces are first read into the clinoform-modeling algorithm, using a standard gridded format exported from a reservoir modeling software package. Clinoforms created by the algorithm adapt to the morphology of either (or both) bounding surfaces, using a height function, BLTN13190eq1 ([[:File:BLTN13190fig2.jpg|Figure 2D]]), that calculates the height of the clinoform relative to the length along the clinoform surface and the height difference between the top and base bounding surfaces (see Table 1 for nomenclature):  
 
:<math>EQUATIONS/BLTN13190eqd1</math>
 
:<math>EQUATIONS/BLTN13190eqd1</math>
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 +
{| class=wikitable
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|+ Table 1. Nomenclature for Parameters Used in the Clinoform-Modeling Algorithm*
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|-
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! Parameter || Description || Units || Stochastic Modeling Component
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|-
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| b<sub>D</sub> || Length of base ellipse in depositional dip direction || m || ✓
 +
|-
 +
| bS || Length of base ellipse in depositional strike direction || m || ✓
 +
|-
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| c(rc) || Clinoform shape function || m || N/A
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|-
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| h(rc) || Height function, to give height of clinoform at rc(x, y) || m || N/A
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|-
 +
|}
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hmaxðrcÞ Maximum height of top bounding surface at rcðx; yÞ hminðrcÞ Minimum height of top bounding surface at rcðx; yÞ
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L Clinoform length
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P Shape function exponent
 +
pO Axis of progradation relative to bounding surfaces
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rcðx;yÞ Radius from clinoform origin to point on surface rmaxðx;yÞ Radius of base ellipse relative to clinoform origin rminðx;yÞ Radius of top ellipse relative to clinoform origin
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S Clinoform spacing
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sðrcÞ Shape function (power law for concave-upward geometry) θ Clinoform progradation angle relative to north
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tD Length of top ellipse in depositional dip direction
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tS Length of top ellipse in depositional strike direction
 +
x x coordinate on surface
 +
xorigin x coordinate of clinoform origin on surface
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y y coordinate on surface
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yorigin y coordinate of clinoform origin on surface
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*N/A = not applicable.
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m ✓ m ✓ m N/A m N/A m N/A m N/A m ✓
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None ✓ None ✓
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m N/A m N/A m N/A m ✓
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None N/A ° ✓ m ✓ m ✓
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None N/A None N/A None N/A None N/A
    
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]]).
 
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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