Towards a sequence stratigraphic solution set for autogenic processes and allogenic controls: Upper Cretaceous strata, Book Cliffs, Utah, USA

Upper Cretaceous strata exposed in the Book Cliffs of east–central Utah are widely used as an archetype for the sequence stratigraphy of marginal-marine and shallow-marine deposits. Their stratal architectures are classically interpreted in terms of accommodation controls that were external to the sediment routing system (allogenic), and that forced the formation of flooding surfaces, sequence boundaries, and parasequence and parasequence-set stacking patterns. Processes internal to the sediment routing system (autogenic) and allogenic sediment supply controls provide alternatives that can plausibly explain aspects of the stratal architecture, including the following: (1) switching of wave-dominated delta lobes, expressed by the internal architecture of parasequences; (2) river avulsion, expressed by the internal architecture of multistorey fluvial sandbodies and related deposits; (3) avulsion-generated clustering of fluvial sandbodies in delta plain strata; (4) ‘autoretreat’ owing to increasing sediment storage on the delta plain as it lengthened during progradation, expressed by progradational-to-aggradational stacking of parasequences; (5) sediment supply control on the stacking of, and sediment grain-size fractionation within, parasequence sets. The various potential allogenic controls and autogenic processes are combined to form a sequence stratigraphic solution set. This approach avoids anchoring of sequence stratigraphic interpretations on a specific control and acknowledges the non-unique origin of stratal architectures.

Sequence stratigraphy has developed over the last four decades through the integrated interpretation of stratal geometries (e.g. as imaged in seismic reflection data) and vertical facies successions (e.g. as interpreted in core and wireline-log data), typically with reference to conceptual models and case studies of well-exposed outcrops (e.g. Van Wagoner et al. 1990). The first generation of conceptual sequence stratigraphic models attributed key aspects of stratal architecture to eustatic sea-level changes (e.g. Vail et al. 1977;, and despite the recognition that other controls are important, subsequent generations of conceptual sequence stratigraphic models remain firmly anchored to relative variations in sea-level or base-level as the principal driver of stratal architecture (e.g. Catuneanu et al. 2009;). Additional controls on stratal architecture may include the following: hinterland tectonics and climate, which control the generation and release of siliciclastic sediment in upstream source regions (e.g. Castelltort & Van Den Driessche 2003;Armitage et al. 2011); the internal dynamics of sediment routing systems, which modify source-region signals during sediment transport (e.g. Jerolmack & Paola 2010); basin physiography, tectonic and compactional subsidence, sediment transport efficiency and sedimentological process regime, which control patterns of accommodation and sediment dispersal in downstream sink regions (e.g. Galloway 1989;Burgess et al. 2006;Madof et al. 2015) (Fig. 1). These various controls are challenging or impossible to disentangle. The most logical approach to interpreting stratal architecture is to acknowledge the likelihood of multiple controls, by developing a solution set that encompasses the plausible range of combinations of controls (Heller et al. 1993).
The most thorough examinations of multiple controls on stratal architecture have been conducted using numerical forward and inverse stratigraphic models (e.g. Kendall et al. 1991;Rivenaes 1997;Ritchie et al. 2004a,b;Burgess et al. 2006;Charvin et al. 2009a,b;Williams et al. 2011;Burgess & Prince 2015) and physical modelling experiments (e.g. Heller et al. 2001;Kim et al. 2006a,b;Muto et al. 2007;Martin et al. 2009). However, the results of numerical and physical stratigraphic modelling experiments are not straightforward to compare with outcrop and subsurface geological data, and have only sparingly been used as a basis to interpret observations made on such data (e.g. Muto & Steel 1992, 2002Van Heist et al. 2001;Paola & Martin 2012). In this paper, I re-examine the stratal architectures exposed in continuous, large-scale outcrops of marginal-marine and shallow-marine strata (late Cretaceous Star Point Sandstone, Blackhawk Formation, lower Castlegate Sandstone and related strata exposed in the Wasatch Plateau and Book Cliffs, Utah and Colorado, USA), from which widely applied conceptual models of high-resolution sequence stratigraphy that invoke a relative sea-level control were developed during the 1980s and 1990s (e.g. Balsley 1980;Van Wagoner et al. 1990, 1991. The aims of this paper are threefold: (1) to identify potential alternative controls to relative sea-level on stratal architecture; (2) to summarize the descriptive tools and interpretation approaches that allow multiple controls on stratal architecture to be considered without invoking sea-level-driven sequence stratigraphic conceptual models; (3) to outline a framework for a sequence stratigraphic solution set that encompasses multiple potential controls on stratal architecture.

Dataset
The Book Cliffs form a large continuous escarpment (>250 km) that is aligned WNW-ESE, oblique to regional depositional dip (Figs 2 and 3a). At their western limit, the Book Cliffs pass into the north-south-trending Wasatch Plateau, which is oriented oblique to regional depositional strike (Figs 2 and 3b). Sequence stratigraphic interpretations are tightly constrained along 2D cliff-faces, which are variably dissected by branching canyon networks that provide some 3D control. Interpretations away from outcrop control are based on wireline-log data from wells of variable spacing and quality (e.g. Hampson 2010) and sparse seismic data (Horton et al. 2004). Outcrops of the proximal part of the Star Point-Blackhawklower Castlegate sediment routing system are patchy and discontinuous to the west of the Book Cliffs and Wasatch Plateau outcrop belts, resulting in disputed and apparently contradictory correlations in these strata (e.g. compare correlations of the Castlegate Sandstone of Slingerland 1998, andArush 2001).

Geological context
The studied strata were deposited along the western margin of the Cretaceous Western Interior Seaway of North America, which lay within a wide (c. 1500 km), north-south-trending basin produced by short-wavelength thrust-sheet loading in the Sevier Orogen to the west and long-wavelength dynamic subsidence generated above the subducting Farallon Plate (inset map in Fig. 2; e.g. Kauffman & Caldwell 1993;Liu et al. 2014). The basin fill comprises mainly siliciclastic sediment that was eroded from the Sevier Orogen and transported eastward into the seaway (inset map in Fig. 2; e.g. Kauffman & Caldwell 1993;DeCelles & Coogan 2006). This sediment was deposited as a series of eastward-thinning wedges of coastal-plain and shallow-marine strata, whose location and age were controlled by thrust-sheet emplacement, erosion and sediment routing within the Sevier Orogen (Krystinik & DeJarnett 1995). The Star Point Sandstone, Blackhawk Formation and lower part of the Castlegate Sandstone form one such eastward-thinning wedge that passes basinward into coeval offshore deposits of the Mancos Shale ( Fig. 3a) (Young 1955). Interfingering of the Star Point-Blackhawklower Castlegate wedge with the Mancos Shale defines several tens of Fig. 1. Schematic illustration of the Star Point-Blackhawk-Castlegate sediment routing system and its deposits as preserved in a typical stratigraphic interval (after Hampson et al. 2014), with principal controls on stratal architecture of the deposits of the routing system and its segments listed underneath. The delta comprising the distal segments of the sediment routing system had a 'compound clinoform' geomorphology, in which an inner, sand-rich, wave-dominated clinofom was separated by a subaqueous topset from an outer clinofom containing sand-poor, 'shelf' or 'ramp' turbidites (Hampson 2010). shallow-marine sandstone tongues, which are grouped to define members of the Blackhawk Formation ( Fig. 3a) (Young 1955). These strata are late Santonian to middle Campanian in age and represent a duration of 5.0-6.0 myr (Krystinik & DeJarnett 1995). They were deposited at a subtropical palaeolatitude (c. 42°N) under a warm, humid climate (Kauffman & Caldwell 1993).
Sediment deposited in the Star Point-Blackhawk-lower Castlegate wedge was sourced from Precambrian and Palaeozoic basement rocks, most probably via erosional unroofing of the Canyon Range and Santaquin Culminations (Fig. 2b) Horton et al. 2004;Hampson 2010;Hampson et al. 2011Hampson et al. , 2012Hampson et al. , 2014. Interpreted major flooding surfaces and sequence boundaries (e.g. Castlegate Sequence Boundary, CSB) are labelled. The Star Point Sandstone, the Spring Canyon (SC), Aberdeen (A), Kenilworth (K), Sunnyside (S), Grassy (G) and Desert (D) shallow-marine members of the Blackhawk Formation, and the Castlegate Sandstone (C) are indicated. A variety of coal zones, major flooding surfaces and other labelled stratigraphic surfaces are used as datum surfaces for different parts of the correlation panels. Each surface is assigned the depositional dip of an ESE-dipping coastal plain or shelf profile where used as a datum. Locations of the panels are shown in Figure 2. (c) Ammonite biostratigraphy, radiometric dates (Obradovich 1993), estimated ammonite biozone durations (Krystinik & DeJarnett 1995) and schematic chronostratigraphic chart (modified from Hampson 2010) for the studied strata, showing the interpreted ages of major flooding surfaces (a and b). Chronostratigraphic relationships for parasequence sets are illustrated, but those for single parasequences and their bounding flooding surfaces are omitted for clarity. Condensed marine sedimentation in the eastern part of the study area is marked as hiatuses. Incised valleys, marked by erosion and sediment bypass, appear to be absent in alluvial-to-coastal-plain deposits of the Blackhawk Formation in the Wasatch Plateau (Hampson et al. 2012), which is consistent with nearly continuous sedimentation in the foredeep of the Sevier Orogenic Belt. Discontinuous sediment accumulation in Blackhawk Formation incised valleys and the Castlegate Sandstone is shown schematically (after Miall 2014).

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Sequence stratigraphic solution set Hampson et al. 2012). The Castlegate Sandstone comprises predominantly braided fluvial sandstones (Miall 1993;Van Wagoner 1995;Yoshida 2000;Miall & Arush 2001). The Mancos Shale contains isolated sandstones and sandy intervals that were deposited as river-fed, storm-wave-modified gravity flows supplied from the west (e.g. Cole & Young 1991;Pattison 2005;Pattison et al. 2007) and as nearshore deposits that were reworked towards the south by tides and waves (e.g. Boyles & Scott 1982;Hampson et al. 2008). Sediment transport in the Star Point-Blackhawk-lower Castlegate sediment routing system was predominantly towards the east, transverse to the basin margin (e.g. Fig. 4a), but additional southward-directed, longshore sediment transport occurred in shallow-marine sandstone tongues (e.g. Hampson 2010;Hampson et al. 2014). This latter, southward-directed component of sediment transport is more pronounced in the upper part of the Star Point-Blackhawk-lower Castlegate wedge (e.g. Fig. 4b) (Hampson 2010).

Previously interpreted controls on sequence stratigraphic architecture
Most sequence stratigraphic studies have focused on shallowmarine and marginal-marine components of the Star Point-Blackhawk-lower Castlegate wedge, to develop observational criteria to diagnose sequence stratigraphic units and surfaces in sparse, subsurface well data (e.g. Van Wagoner et al. 1990;Kamola & Van Wagoner 1995). These studies have developed or applied facies models for sequence stratigraphic units (e.g. shoreface parasequences, fluvio-estuarine valley fills) and diagnostic criteria for 'non-Waltherian' facies dislocations across sequence stratigraphic surfaces (e.g. flooding surfaces, sequence boundaries). Typically, sequence stratigraphic architecture has been explained in terms of relative sea-level variations that implicitly combine eustasy with tectonic and compactional subsidence (e.g. Van Wagoner et al. 1990;Kamola & Van Wagoner 1995;Howell & Flint 2003). Interpreted tectonic controls, where specified, include differential subsidence across basement structures, giving rise to localized sequence boundaries (Yoshida et al. 1996), and tectonic reorganization of the thrust-sheet load in the Sevier Orogen, giving rise to distinctive parasequence stacking patterns (Kamola & Huntoon 1995;Houston et al. 2000). Unroofing and erosion of the Santaquin Culmination is interpreted to have formed a sub-regional angular unconformity and change in provenance at or near a sequence boundary that is interpreted to mark the base of the Castlegate Sandstone (Miall & Arush 2001;Horton et al. 2004).
The entire Star Point-Blackhawk-lower Castlegate wedge exhibits an overall upward increase in the abundance and degree of erosional amalgamation of channelized fluvial sandbodies in coastal-plain strata (Adams & Bhattacharya 2005;Hampson et al. 2012Hampson et al. , 2013, and a corresponding overall upward increase in the degree of shallow-marine progradation ( Fig. 3a and c) (e.g. Balsley 1980;Hampson 2010). These trends are generally interpreted to record a progressive decrease in tectonic subsidence and associated accommodation development (e.g. Howell & Flint 2003;Hampson et al. 2012). These large-scale patterns do not extend along the entire western margin of the seaway, implying that they were forced by a tectonic control at the spatial scale of a single thrust sheet or structural culmination (Krystinik & DeJarnett 1995).
Ammonite biozones define a biostratigraphic framework of c. 0.3-0.7 myr resolution (Krystinik & DeJarnett 1995;Cobban et al. 2006) that can be linked to major flooding surfaces within the Mancos Shale and shallow-marine strata of the Star Point Sandstone and Blackhawk Formation (Hampson 2010). In this paper, we follow the nomenclature of Hampson (2010) and Hampson et al. (2014), who subdivided the Star Point-Blackhawk-lower Castlegate wedge into eight parasequence sets or genetic sequences (sensu Galloway 1989) bounded by major flooding surfaces (Fig. 3). Each parasequence set has an estimated duration of c. 0.3-1.0 myr , although there is considerable uncertainty in the accuracy of these estimates because radiometric dates that constrain the duration of ammonite biozones are sparse. The major flooding surfaces that bound each parasequence set correspond to major, laterally extensive coal zones in lower coastal-plain strata of the Blackhawk Formation (Flores et al. 1984;Dubiel et al. 2000;Hampson et al. 2012), and these coal zones can be projected updip into alluvial-plain deposits to provide a provisional stratigraphic framework in these strata (Hampson et al. 2012).

Analysis of internal controls on stratal architecture
The components of a sediment routing system (e.g. rivers, deltas, submarine fans), and even the whole system itself, exhibit behaviours that result from processes internal to the system (autogenic processes) rather than from external (allogenic) controls. These autogenic behaviours may be preserved as stratal patterns that are intrinsic to the sediment routing system and its component deposits. Such patterns arise because sediment routing systems and their components lack an equilibrium configuration over relatively short time scales (typically less than several million years for an entire sediment routing system, and of shorter duration for its components). Autogenic stratal patterns therefore represent a 'norm' that is inherent to a particular sediment routing system and its constituent depositional environments ('autostratigraphy' sensu Muto et al. 2007). At least some of these autogenic stratal patterns result from the internal response of sediment routing systems to steady external forcing (e.g. uniformly increasing or uniformly decreasing relative sea-level or sediment supply) (e.g. Muto 2001;Muto & Steel 2002;Muto et al. 2007).

Switching of wave-dominated delta lobes expressed within parasequences
Over relatively small temporal and spatial scales, autogenic stratal patterns have long been recognized in delta systems in the form of 'autocyclic' delta-lobe switching (e.g. Coleman & Gagliano 1964). Such lobe switching is less pronounced in wave-dominated delta systems, because waves and storms act to suppress deltaic distributaries and lobes reaching the geomorphological threshold(s) required to switch their positions by redistributing river-supplied sediment offshore and alongshore (e.g. Coleman & Wright 1975).
Detailed architectural analysis of selected parasequences in the Blackhawk Formation suggests that they contain evidence for deltalobe switching during progradation of a wave-dominated deltaic shoreline (Hampson & Storms 2003;Hampson & Howell 2005;Charvin et al. 2010). In each case, a wave-dominated shoreface succession that records eastward progradation of a north-southtrending shoreline is onlapped by a southward-prograding fluvialdominated delta-front succession near the downdip pinchout of the parasequence (e.g. Fig. 5; Charvin et al. 2010). Both the wavedominated shoreface succession and fluvial-dominated delta-front succession are capped by the same coal seam (e.g. Fig. 5a), indicating that the changes in local depositional process regime and shoreline orientation between them were not forced by a rise in relative sealevel (Charvin et al. 2010). Instead, the recurring stratal architectural pattern is interpreted to record the southward advance of a fluvialdominated delta front that lay on the downdrift flank of a strongly deflected, asymmetrical wave-dominated delta (e.g. Fig. 5b; Charvin et al. 2010). The spatially and temporally restricted advance of the fluvial-dominated delta-front successions is attributed to avulsion of a trunk distributary channel, which is also inferred to have caused abandonment and wave-reworking of older delta lobes (Charvin et al. 2010). Such delta-lobe switching may also have driven temporal variations in wave-generated, alongshore sediment supply and in localized shoreline palaeogeography, which are subtly expressed in wave-dominated shoreface successions within parasequences (e.g. Sømme et al. 2008). Thus, shallow-marine strata of the Blackhawk Formation contain a subtle but pervasive architectural motif that probably records autogenic processes over time scales significantly shorter than parasequence duration (i.e. <100 kyr). The spatiotemporal development of this architectural motif is characterized by rapid but localized (10 0 -10 2 km 2 ) increments of delta-lobe deposition (c. 1-10 kyr) alternating with longer hiatuses during subregional to regional (10 2 -10 5 km 2 ) parasequence deposition (Miall 2014(Miall , 2015. In the absence of data that fully document key architectural relationships (e.g. Fig. 5) and a conceptual framework that encompasses autogenic stratal patterns, the architectural motif may be incorrectly attributed to an allogenic control such as cyclical variations in relative sea-level (e.g. the wave-dominated shoreface and fluvial-dominated delta-front successions may be assigned to different parasequences).

River avulsion expressed within multistorey fluvial sandbodies and associated floodplain strata
Rivers switch position via avulsion on their floodplains, to generate channel belts that are spatially distinct from each other in plan view

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Sequence stratigraphic solution set (e.g. Slingerland & Smith 2004). Avulsion typically results from a river exceeding a geomorphological threshold(s) related to local topographic gradients, such that it relocates to a topographic low on the floodplain or reoccupies a previously abandoned channel location (Mohrig et al. 2000;Slingerland & Smith 2004). Avulsion is common in delta plain settings, which are characterized by high and spatially variable sedimentation rates and low regional slopes, such that localized topographic gradients accumulate rapidly and are exaggerated. Avulsion is commonly regarded as an 'autocyclic' process, although it may be modulated by external controls (e.g. Stouthamer & Berendsen 2007), and distributary channel avulsion on the delta plain is a common trigger for delta-lobe switching (e.g. Edmonds et al. 2009).
Detailed analysis of selected channelized fluvial sandbodies and associated non-channelized floodplain deposits indicates that avulsion was the predominant control on local floodplain sedimentation and stratal architecture in alluvial-to-coastal-plain strata of the Blackhawk Formation (Hampson et al. 2013;Flood & Hampson 2014). Multistorey sandbodies record vertical stacking of channel-belt deposits but generally are not confined above a deep, 'master' erosion surface (e.g. within a palaeovalley), and are therefore interpreted to record repeated occupation of the same site on the floodplain after avulsion (e.g. Fig. 6; Hampson et al. 2013). These avulsion-generated multistorey sandbodies have irregular boundaries across which single channel storeys and belts interfinger with, and correlate to, coeval floodplain deposits (see Chamberlin & Hajek 2015). In addition to avulsion by reoccupation, stratigraphicarchitectural relationships between channelized fluvial sandbodies and non-channelized floodplain deposits indicate that avulsion also took place via the progradation of crevasse splays (to produce 'stratigraphically transitional avulsion deposits' sensu Jones & Hajek 2007), and by incision (to produce 'stratigraphically abrupt avulsion deposits' sensu Jones & Hajek 2007) (Flood & Hampson 2014). There is no apparent temporal or spatial trend in avulsion style in the Blackhawk Formation, implying that avulsions occurred in a similar manner for a range of distances from the coeval shoreline (c. 0-100 km) and a range of long-term tectonic subsidence rates (80-700 m Ma −1 ) (Flood & Hampson 2014). Given their apparent insensitivity to a wide range of boundary conditions, avulsions were probably autogenic in origin.

Avulsion-generated clustering of fluvial sandbodies in delta plain strata
Autogenic stratal patterns have been interpreted at larger spatial and temporal scales in alluvial and coastal plain strata (Straub et al. 2009;Hajek et al. 2010;Wang et al. 2011). In the apparent absence of an external stratigraphic or palaeogeographical control, clustering and regular spacing of channelized fluvial sandbodies are attributed to autogenic processes. For example, channelized sandbodies may be clustered owing to localized avulsion within a depositional system that maintains a relatively uniform position (e.g. channels downstream of an avulsion node; Mackey & Bridge 1995). In contrast, regular spacing of channelized sandbodies (or clusters of such sandbodies) may reflect compensational stacking owing to relocation of the depositional system to a palaeo-topographic low (Bridge & Leeder 1979).
Clustering and regular spacing of channelized fluvial sandbodies have been interpreted via spatial statistical analysis of sandbody distributions in alluvial and coastal plain strata of the Blackhawk Formation in exposures of the eastern Wasatch Plateau (Figs 2 and 3b) . Sandbody distributions were analysed in six well-exposed, nearly 2D cliff faces from the Wasatch Plateau outcrop belt (Fig. 7). Two descriptive spatial statistical measures, lacunarity and Ripley's K function, were used to characterize sandbody distribution patterns (Fig. 8). Lacunarity is a pixel-based method that describes patterns of spatial dispersion (Allain & Cloitre 1991). Low values of lacunarity (minimum = 0) are obtained from regular patterns containing evenly distributed gaps of similar size between sandbodies, whereas high values of lacunarity (maximum = 1) characterize complex patterns that contain unevenly distributed gaps of heterogeneous size between sandbodies. Values of lacunarity are not dependent on interpretation of sandbody type or hierarchy. Ripley's K function is a spatial point process method for detecting deviations from spatial homogeneity (Ripley 1976). The method determines how point pattern distributions change over different length scales within a dataset (Ripley 1977). Ripley's K function was used to identify clustering, random spacing and regular spacing of sandbody centroids. The results are sensitive to interpretation of sandbody type and hierarchy; channelized fluvial sandbodies in the Blackhawk Formation largely represent channel belts, but a minority of sandbodies represent channel storeys and vertically amalgamated channel belts (Hampson et al. 2013;. Further details of the statistical methods, their application to the Blackhawk Formation, and associated errors and limitations have been given by  and Villamizar et al. (2015).
The overall proportion of channelized fluvial sandbodies increases from the base (c. 10%) to the top (c. 30%) of the Blackhawk Formation exposures in the eastern Wasatch Plateau, coincident with progressively increasing distance from the coeval shoreline as it advanced farther east (e.g. Fig. 3a and c), and progressively decreasing tectonic subsidence rate (Hampson et al. 2012). However, there is much localized variation around this overall trend (e.g. Marley et al. 1979;Rittersbacher et al. 2014a). Channelized sandbodies broadly increase in width and decrease in abundance per unit area from the base to the top of the Blackhawk Formation (e.g. Fig. 7) . Clustering of channelized sandbodies is relatively common in coal-rich, lower coastal plain strata (<50 km from the coeval shoreline) ) (e.g. green-and-grey and blue-and-grey bars in Fig. 8), implying avulsion and bifurcation of deltaic distributary channels downstream of delta-apex avulsion nodes (see Karssenberg & Bridge 2008). A small number of unusually large (up to 25 m thick, 1-6 km wide), multistorey, multilateral, fluvial sandbodies that occur at distinct stratigraphic levels in these lower coastal plain strata are interpreted as fluvial incised valley fills (Hampson et al. 2012;Gani et al. 2015). Spatial regularity of channelized sandbody spacing is apparent in coal-poor, upper coastal plain and alluvial strata (>50 km from the coeval shoreline) ) (e.g. red-and-grey and yellow-and-grey bars in Fig. 8), implying the predominance of avulsion-generated compensational stacking (see Bridge & Leeder 1979). Thus, the spatial distribution of channelized fluvial sandbodies in alluvial-tocoastal-plain strata of the Blackhawk Formation can be explained largely by autogenic processes that are determined by distance from the coeval shoreline.

Autogenic controls on generation and stacking of wave-dominated deltaic parasequences
Under conditions of steady relative sea-level rise, lengthening and aggradation of the fluvial profile occur during shoreline progradation, which leads to increased sediment storage on the coastal plain. This effect limits the extent of progradation under conditions of steady forcing, and eventually results in autogenic retreat of the shoreline ('autoretreat' sensu Muto & Steel 1992). The maximum depositional length (see Fig. 1) of a fluvio-deltaic sediment routing system, developed just prior to autoretreat, is described by a characteristic length scale (D): for a constant rate of sediment supply per unit of basin width (S) and a constant absolute rate of accommodation increase or decrease (A) (Muto 2001). D represents the maximum depositional length of a sediment routing system that can be attained under the steady external forcing described by S and A. Shoreline trajectories that arise from autoretreat are concave landward (e.g. Muto & Steel 1992;Muto et al. 2007), and reflect a decreasing rate of progradation during aggradation.   Hampson et al. 2011, and references therein). D is estimated for each of the parasequence sets (or genetic sequences) bounded by major flooding surfaces in the same dip-oriented cross-section (Fig. 9b). This cross-section extends farther palaeo-landward of the data used previously for similar analysis, with the result that estimates of D presented in this paper differ slightly from those Fig. 8. Plot of lacunarity v. inhomogeneity in spatial positioning of sandbody centroids, as identified using Ripley's K function, in stratigraphic subdivisions of the cliff-face sections (A1, B1 and B2, C1-3, D1-3, E1-3 and F1-4; Fig. 7) (after . Grey bars represent the spatial extent of data for each stratigraphic subdivision of the cliff-face sections, and superimposed coloured bars show the length scales of sandbody-centroid clustering or regular spacing. Length scales not represented by coloured portions of the grey-andcoloured bars correspond to random spacing of sandbody centroids. Length scales are expressed as multiples of mean apparent sandbody dimensions. Lacunarity is dimensionless. Sandbody clustering is common in stratigraphic subdivisions representing lower coastal plain deposits (green-and-grey and blueand-grey bars), whereas regular spacing occurs mainly in stratigraphic subdivisions representing upper coastal plain and alluvial strata (red-and-grey and yellow-and-grey bars). There is no systematic palaeogeographical variation in sandbody clustering or lacunarity (e.g. from (a) to (f )) in any of the four stratigraphic subdivisions.  Figure 3a. The trajectories are not corrected for post-depositional compaction. Shoreline trajectories for parasequences (between neighbouring black data points) and parasequence sets (between blue lines) are illustrated, but those within parasequences are omitted for clarity. (b) Estimates of the characteristic lengthscale (D) of the linked depositional segments of the sediment routing system for parasequence sets bounded by major flooding surfaces (Figs 3c and 9a), compared against their maximum depositional length (see Fig. 1) observed in the study dataset (Fig. 3a). The stratal architecture of parasequence sets that exhibit an overall concave-landward shoreline trajectory, and for which the estimated value of D coincides with the observed maximum depositional length, can be attributed plausibly to autoretreat.

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Sequence stratigraphic solution set previously published ( fig. 16 of Hampson 2010). The estimates of D presented herein assume that S, which combines fluvial sediment flux (Q fl in Fig. 1) and net shallow-marine sediment flux into or out of the section (Q shin and Q shout in Fig. 1), and A were constant, decreased at a constant rate, or increased at a constant rate during deposition of any particular parasequence set. S is taken to be the product of mean sediment accumulation rate per unit of basin width and the depositional length of the sediment routing system (based on the cross-sectional area and duration of each parasequence set; Fig. 3a and c). A is taken to be the vertical component of the shoreline migration path (Fig. 9a) divided by the duration of each stratigraphic interval (Fig. 3c). Uncertainties in the up-dip and down-dip pinchout locations, thickness variations and duration of each parasequence set were used to derive a range of rates for S and A, and thus a range of values for D (red bars in Fig. 9b, with red points representing the 'best estimates' within each range). Undecompacted sediment thicknesses are used in the calculations.
Four of the eight parasequence sets exhibit an overall concavelandward shoreline trajectory (FS050-FS075, FS075-FS100, FS100-FS200 and FS250-FS400; Fig. 9a). In three of these parasequence sets, the maximum depositional length of the sediment routing system coincides with the estimated value of D (FS050-FS075, FS075-FS100 and FS100-FS200; Fig. 9b). This coincidence indicates that autoretreat is a plausible mechanism to explain the overall concave-landward shoreline trajectory and associated pattern of parasequence stacking in each of these three latter parasequence sets. Three parasequence sets have nearly linear overall shoreline trajectories (FS200-FS250, FS400-FS500 and FS500-FS600; Fig. 9a), and the estimated value of D is greater than the maximum depositional length of the sediment routing system in two of these parasequence sets (FS400-FS500 and FS500-FS600; Fig. 9b). Autoretreat cannot explain the shoreline trajectory and parasequence stacking in these parasequence sets. There are insufficient data to constrain the shoreline trajectory and to estimate D in one parasequence set (FS050-FS075; Fig. 9a). In summary, these results indicate that parasequence stacking patterns and shoreline trajectories within parasequence sets in the lower part of the Star Point-Blackhawk-lower Castlegate wedge may record autogenic behaviour (autoretreat) at the scale of the sediment routing system, under conditions of steady external forcing. The internal architecture of parasequence sets in the middle and upper parts of the Star Point-Blackhawk-lower Castlegate wedge are instead likely to record unsteady external forcing of accommodation and/or sediment supply.
Furthermore, it is possible that parasequences within all parasequence sets in the Star Point-Blackhawk-lower Castlegate wedge may have been generated by autogenic pulses of sediment storage and release on the alluvial-to-coastal plain during its aggradation (Kim et al. 2006a). Minor localized steepening (by 1-4%) of the fluvial gradient may have driven sediment storage in upstream locations, which resulted in shoreline retreat. Subsequent shallowing of the fluvial gradient to its original values then drove release of the stored sediment, which resulted in shoreline advance. Small, repeated variations in upstream fluvial gradient may thus have generated quasi-cyclical transgressive-to-regressive patterns of shoreline trajectory that are comparable in scale with parasequences (Kim et al. 2006a) (compare trajectories between neighbouring black data points in Fig. 9a) or localized pulses of progradation that are comparable with delta-lobe deposits within parasequences (e.g. within Ab1 parasequence in Fig. 5). Such minor variations (by 1-4%) in fluvial gradient lie well within the error range for palaeohydraulic estimates of river channel slope that are calculated from outcrop data (e.g. table 16 of Hampson et al. 2013), such that they are probably impossible to detect from field observations.

Analysis of external controls on stratal architecture
A wide variety of external forcing parameters may be invoked to influence the stratal architecture of sediment routing systems, but these can be combined into two allogenic controls, accommodation and sediment supply. Accommodation combines eustasy, tectonic and compactional subsidence, and antecedent bathymetry to define the space available for potential sediment accumulation (Jervey 1988). Siliciclastic sediment supply is a product of tectonic uplift of hinterland source regions, climatic influence on hinterland weathering, and sediment routing and transport from the catchments that drain the hinterland to the margin of a depositional basin (e.g. Tucker & Slingerland 1997;Allen 2008;Armitage et al. 2011). Accommodation can generally be estimated from sediment thicknesses combined with palaeo-geomorphological and/or palaeontological indicators of water depth during deposition. Sediment supply cannot be estimated independently of accommodation using classical sequence stratigraphic interpretation methods, but instead requires mass-balance analysis of sediment budgets within a sediment routing system (e.g. Michael et al. 2013). The ratio of accommodation to sediment supply ('A/S ratio') can be qualitatively interpreted from observed stratal architectures (e.g. Muto & Steel 1997).
Accommodation control on parasequence formation, parasequence stacking, parasequence-set stacking and sequence boundary formation The influence of accommodation on stratal architecture is typically interpreted from patterns in the vertical accumulation of coastal deposits, which are characterized in the context of 2D cross-sections and 3D volumes that capture palaeo-bathymetry prior to and during deposition (e.g. Van Wagoner et al. 1990). These vertical patterns define a relative sea-level curve, which some researchers deconvolve into multiple superimposed sinusoidal curves of different frequency and amplitude, attributed to cyclical changes in basinwide or eustatic sea-level, and a linear trend, attributed to slow and steady tectonic subsidence (e.g. ).
The approach described above has been applied by various researchers to parts or all of the succession of shallow-marine strata in the Star Point-Blackhawk-lower Castlegate wedge (Taylor & Lovell 1995;Van Wagoner 1995;Howell & Flint 2003). These strata were deposited on a broad, gently dipping shelf or ramp that had little antecedent bathymetry and underwent little differential subsidence, as evident in the rather uniform thickness of parasequence sets bounded by major flooding surfaces (Figs 3a and 10). Within this context, thickening towards the western basin margin reflects increased flexural subsidence in the foredeep of the Sevier Orogen (e.g. 0-100 km in Fig. 10b), basinward thickening in more distal locations reflects the influence of an antecedent platform-and-slope bathymetry constructed by the stacking of underlying parasequence sets (e.g. 180-220 km in Fig. 10a), and basinward thinning towards the down-dip pinchout of the parasequence sets reflects incomplete filling of accommodation in offshore settings (e.g. 220-430 km in Fig. 10a, 290-430 km in Fig. 10b). An accommodation control on stratal architecture can be plausibly interpreted at three spatial scales: (1) formation of single parasequences and high-frequency sequence boundaries; (2) parasequence stacking within a parasequence set (or genetic sequence); (3) stacking of parasequence sets and low-frequency sequence boundary formation within the entire Star Point-Blackhawk-lower Castlegate wedge. Each of these three spatial scales is discussed in turn below.
Detailed reconstructions of stratal architecture within several wavedominated deltaic parasequences of the Blackhawk Formation imply Over multiple episodes of delta-lobe switching during the progradation represented by a parasequence, these processes resulted in a relatively linear shoreline palaeogeography and in deposition of a nearshore sandbody that is continuous along depositional strike (Hampson & Howell 2005). The formation of a parasequence-bounding flooding surface cannot therefore be attributed to autogenic delta-lobe switching or river avulsion, but instead requires an allogenic relative sea-level rise (e.g. Kamola & Van Wagoner 1995) and/or reduction in regional sediment supply. Given the age model for parasequence sets presented in Figure 3c, the inferred allogenic control(s) operated over c. 50-300 kyr periods. High-frequency glacio-eustatic sea-level cycles are thus a plausible allogenic accommodation control (see Plint 1991;Plint & Kreitner 2007), particularly because they can also readily account for periods of falling sea-level required for rivers to cut incised valleys during progradation of a parasequence (e.g. unnamed sequence boundaries represented by thin red lines in Fig. 3a and b; see Plint & Wadsworth 2003). Milankovitch cyclicity has been tentatively proposed for the inferred glacio-eustatic sea-level cycles (Plint 1991), but spectral analysis of cycle periodicity calibrated to high-resolution absolute age data, which would test this hypothesis, has not yet been attempted. The small palaeo-landward displacements of the shoreline across parasequence-bounding flooding surfaces (<20 km; Fig. 9a) indicate that any formative relative sea-level cycles had only modest amplitudes (<30 m), consistent with current estimates of Cretaceous glacio-eustasy (Miller et al. 2003 Between two and seven parasequences are stacked in a progradational-to-aggradational (concave-landward shoreline trajectory) or progradational pattern (linear shoreline trajectory) within each parasequence set (Fig. 9a), and most parasequence sets are documented to contain one or two fluvio-estuarine bodies, interpreted as incised valley fills that mark sequence boundaries and occur at or near the position of maximum regression within the parasequence set ( Fig. 3a) (Howell & Flint 2003;Hampson 2010, and references therein). Although autoretreat is a plausible mechanism to explain parasequence stacking in some but not all parasequence sets, as explained above (see also Fig. 9), relative sea-level variations owing to allogenic accommodation mechanisms have also been proposed (Taylor & Lovell 1995;Van Wagoner 1995;Howell & Flint 2003). Changes in tectonic subsidence rate linked to thrust-sheet emplacement in the hinterland (Kamola & Huntoon 1995;Houston et al. 2000) and/or relatively low-frequency eustatic sea-level fluctuations (Plint 1991) both appear reasonable, and would need to have operated in a quasi-cyclical manner over periods of c. 0.3-1.0 myr.
The overall shoreline trajectory of the Star Point-Blackhawklower Castlegate wedge has a concave-seaward path (Fig. 9a), indicating a progressive change from aggradational to increasingly progradational stacking of parasequence sets (Fig. 3a). Similar patterns are noted in other clastic wedges, but they are not laterally persistent along the western margin of the Cretaceous Western Interior Seaway and instead only extend along the strike of thrust sheets that were active during their deposition (i.e. the Charleston, Nebo and Paxton thrusts in Fig. 2) (Krystinik & DeJarnett 1995). The overall concave-seaward shoreline trajectory is attributed to a progressive decrease in tectonic subsidence rate during the c. 5.0-6.0 myr duration of the Star Point-Blackhawk-lower Castlegate wedge (Taylor & Lovell 1995;Howell & Flint 2003;Hampson 2010). This mechanism can also account for the observed overall upward increase in the size and proportion of channelized fluvial sandbodies in Blackhawk Formation coastal plain deposits in the Wasatch Plateau outcrop belt, assuming that river avulsion rate remained approximately constant (Hampson et al. 2012). The base of the Castlegate Sandstone is marked in palaeo-landward locations (within c.    Fig. 1), assuming that a reference case of zero net along-strike sediment import or export (i.e. Q shin = Q shout ) is provided by (c) the three parasequence sets between the 'base Mancos B' surface and FS100, and by (d) the four parasequence sets between FS100 and FS500. The net-depositional mass fluxes shown in (c) and (d) represent end-member scenarios of along-strike sediment transport. Error ranges in net-depositional mass fluxes are not shown for clarity; errors associated with sediment masses are comparable with those shown in (a) (±21%), whereas potential errors in parasequence set durations are much greater (×0.5 to ×2). Details of the methods and their associated assumptions and limitations have been given by Hampson et al. (2014).

Sediment supply control on parasequence-set stacking
The volume, grain-size characteristics, timing and location of sediment supply control the filling of accommodation, and sediment supply combines with accommodation to determine trends in the landward or seaward movement of the shoreline and shelf edge (e.g. Vail et al. 1977;Muto & Steel 1997). Despite the longstanding recognition of sediment supply as a fundamental control on stratal architecture, it has proved difficult to extract a clear record of sediment supply from the stratigraphic record of ancient siliciclastic depositional systems. In part, this reflects the buffering or modification of an upstream sediment supply signal during sediment transport (e.g. Jerolmack & Paola 2010), such that high-frequency (<100 kyr) sediment supply signals are unlikely to be preserved in the stratigraphic record of all but the smallest sediment routing systems (Castelltort & Van Den Driessche 2003). However, recent outcrop studies demonstrate that the construction of sediment volume or mass budgets within the source-to-sink context of a sediment routing system can provide a powerful tool to quantitatively estimate the volume and grain size of sediment supply (e.g. Duller et al. 2010;Whittaker et al. 2011;Carvajal & Steel 2012;Michael et al. 2013). The results are particularly useful if analysed in a mass-balance framework, in which the cumulative deposited volume of sediment in the downsystem direction is normalized by the total sediment volume (e.g. Paola et al. 1992;Strong et al. 2005;Paola & Martin 2012), because this dimensionless framework allows the stratigraphic record of different sediment routing systems to be readily compared. Downsystem variation in grain-size distributions may also be characterized in the context of sediment volume or mass budgets for a sediment routing system (Allen et al. 2016).
Mass-balance analysis of a regional depositional dip-oriented cross-section through the Star Point-Blackhawk-lower Castlegate wedge was carried out by Hampson et al. (2014), and their key results are presented and extended below. Details of the methods and their associated assumptions and limitations have been given by Hampson et al. (2014). Estimates of sediment mass within different stratigraphic intervals of the Star Point-Blackhawk-lower Castlegate wedge are shown in Figure 11a. These estimates are based on assigning a width of 1 km to a representative, depositionaldip-oriented cross-section (Fig. 3a) to generate specific sediment volumes, which are then multiplied by bulk-density values for conglomerates, sandstones and shales derived from geophysical density logs. The fractions of total sediment mass by the grain-size components corresponding to these three siliciclastic lithologies are shown in Figure 11b for each stratigraphic interval, based on using facies (e.g. as shown in Figs 3 and 4) as a textural proxy for grain size. The resulting estimates of sediment mass and its fractionation into grain-size components are combined with an age model for the Star Point-Blackhawk-lower Castlegate wedge (Fig. 3c) to generate estimates of net-depositional sediment mass fluxes ( Fig. 11c and d). The sediment mass fluxes are considered in terms of fluvial supply down depositional dip, along the axis of the sediment routing system (Q fl ; Fig. 1), and shallow-marine supply along depositional strike, perpendicular to the axis of the sediment routing system (Q shin , Q shout ; Fig. 1). The mass fluxes are estimated in relative terms, and require calibration to a reference case to generate absolute values. Two reference cases for end-member scenarios are shown herein, assuming zero net along-strike sediment import or export (i.e. Q shin = Q shout ; Fig. 1) in either the three stratigraphic intervals between the 'base Mancos B' surface and FS100 (as shown in fig. 11 of Hampson et al. 2014) (Fig. 11c) or the four stratigraphic intervals between FS100 and FS500 (Fig. 11d). The entire deposited sediment mass was derived from fluvial sediment supply (Q fl ; Fig. 1) in stratigraphic intervals for which there is assumed to have been zero net along-strike sediment import or export ( Fig. 11c and d). Downsystem variations in the combined proportion of conglomerate and sandstone mass fractions are shown in Figure 12, for fluvial, shoreline-shelf and shelf-turbidite segments of the Star Point-Blackhawk-lower Castlegate sediment

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Sequence stratigraphic solution set routing system. Errors in the estimated mass fluxes arise from uncertainty in definition of stratigraphic intervals, facies volume estimation, characterization of grain-size fractions within facies, conversion of sediment volumes to masses and the duration of stratigraphic intervals (table 1 of Hampson et al. 2014). This last parameter is particularly poorly constrained, because the assumed age model is constructed from sparse biostratigraphic data of limited age resolution, and it constitutes the principal uncertainty in the estimated net-depositional mass fluxes.
Fluvial sediment supply (Q fl ) generally increased in successive parasequence sets in the lower and then the upper parts of the studied succession (from 'base Mancos B' surface to FS200, and from FS250 to FS600; red curves in Fig. 11c and d). Shallowmarine sediment supply (Q shin , Q shout ) supplemented fluvial sediment supply during deposition of most parasequence sets in the middle and upper parts of the studied succession (from FS100 to FS500) by either net import of silt and mud (blue curve in Fig. 11c) or no net export of sediment (blue curve in Fig. 11d). The youngest parasequence set is the exception, as there was net shallow-marine export of silt and mud (from FS500 to FS600; blue curves in Fig. 11c and d). These temporal trends in sediment supply are broadly consistent with the interpretation of an increased influence of basinal oceanographic circulation on shallow-marine sediment dispersal during deposition of the upper part of the Star Point-Blackhawk-lower Castlegate wedge (Hampson 2010).
There is a relatively uniform downsystem decrease in the thickness of fluvial conglomerate and sandstone for most parasequence sets in the studied succession, within the context of a mass-balance framework (from 'base Mancos B' surface to FS500; Fig. 12a). The youngest parasequence set (from FS500 to FS600; Fig. 12a) is the exception, irrespective of the correlation used to define this interval (correlations A and B; Fig. 12a). The difference between the trend of downsystem decrease in fluvial conglomerate and sandstone thickness for this youngest parasequence set and those of all older parasequence sets can be considered as a 'residual' deviation from the baseline for the Star Point-Blackhawk-lower Castlegate wedge (see Paola & Martin 2012). The 'residual' deviation represents a pronounced increase in the sand-to gravelgrade mass fraction of fluvial sediment supply (Q fl ) across the upstream-unconformable base of the Castlegate Sandstone (labelled CSB in Fig. 3). This marked increase can be attributed to hinterland unroofing and/or cannibalization of wedge-top basins , consistent with observations of an angular unconformity and change in sandstone provenance across the base of the Castlegate Sandstone (Robinson & Slingerland 1998;Miall & Arush 2001;Horton et al. 2004) and also with net along-strike export of silt and mud in shallow-marine segments of the routing system (from FS500 to FS600; blue curves in Fig. 11c and d).

Unlikely Unlikely
Distribution of channelized fluvial sandbodies in alluvial-to-coastal-plain strata Probable: local to sub-regional (10 1 -10 4 km 2 ) variations in avulsion frequency (density of sandbody stacking) and pattern (sandbody clustering downstream of avulsion nodes on delta plain, regular sandbody distribution owing to compensational stacking) Probable: progressive sub-regional (10 3 -10 5 km 2 ) decrease in tectonic subsidence rate (upward increase in proportion of sandbodies) and regional (10 4 -10 6 km 2 ), high-frequency (c. 50-300 kyr), moderate-amplitude (c. 30 m) relative sea-level variations (dense, localized sandbody stacking in coastal incised valleys) Possible (but indirect): variations in avulsion frequency potentially affected by variations in local to subregional (10 1 -10 4 km 2 ) fluvial sediment supply Angular unconformity at base of multistorey, sheet fluvial sandbody (Castlegate Sandstone) Unlikely Probable: sub-regional (10 3 -10 5 km 2 ) tectonic uplift of hinterland (including wedge-top basins) Unlikely (but fluvial sediment supply increased owing to tectonically forced hinterland unroofing) ( Fig. 12c) in the mass-balance framework, which is consistent with net along-strike sediment import or export by shallow-marine processes (Q shin , Q shout ) (see Parrish et al. 1984;Swift et al. 1987;Hampson et al. 2008;Hampson 2010). The shoreline thus represents a key moving boundary within the Star Point-Blackhawk-lower Castlegate sediment routing system. The importance of basinal process regime in sediment dispersal from the shoreline and across the shelf is provided by the distribution of gravity flow siltstones and sandstones, which occur only in strata corresponding to the lower four parasequence sets (from the 'base Mancos B' surface to FS200; Fig. 3). During their deposition, the shelfal segment of the sediment routing system lay within a broad embayment ('Utah Bight') and was somewhat sheltered from interaction with oceanographic circulation in the centre of the Western Interior Seaway, such that shelfal gravity flows could accumulate as fan bodies (e.g. Fig. 4a). Progradation of the shoreline farther basinward in the upper four parasequence sets (from FS200 to FS600; Fig. 3) is interpreted to have resulted in reworking and dispersal of shelfal sediment toward the south by basinal oceanographic currents (Hampson 2010), as indicated by the occurrence of large, southward-prograding, tidedominated deltas that lay north of the Book Cliffs outcrops (e.g. Fig. 4b) (Mellere & Steel 1995;Hampson et al. 2008).
Although it can be plausibly argued that changes in the volume and grain-size characteristics of sediment supply played a major role in the stacking of parasequence sets, as outlined above , numerical modelling of sediment transport suggests that upstream controls on sediment supply (sediment flux, precipitation rate) are unlikely to have formed the cyclical patterns of shoreline migration that characterize parasequence sets and their parasequences (Armitage et al. in preparation). Model results indicate that upstream controls on sediment supply affect all moving boundaries in the sediment routing system, including the downsystem limit of alluvial conglomerates ('gravel front' of Paola et al. 1992) and the shoreline, whereas downstream controls such as relative sea-level affect only the downsystem boundaries such as the shoreline. The gravel front does not change its position significantly during deposition of the Blackhawk Formation, implying that periodic upstream variations in sediment supply did not force parasequence-scale or parasequence-set-scale cycles of shoreline regession and transgression (Armitage et al. in preparation).

Discussion
In the following discussion, the various internal and external controls on stratal architecture are synthesized into a framework for a stratigraphic solution set (sensu Heller et al. 1993). A key aspect of constructing the various components of this solution set is the use of descriptive tools that characterize stratal architecture without implicit reference to relative sea-level. The solution set encompasses multiple interpretations that account for observed stratal architecture. Sequence stratigraphy was developed principally as a tool for hydrocarbon exploration (Vail et al. 1977;Van Wagoner et al. 1990), and the final section of the discussion considers the added value of the solution set approach for predicting the distribution of reservoir, source and seal lithologies. Table 1 summarizes the various internal (autogenic) and external (allogenic) controls that may have generated the stratal architectures observed in the Star Point-Blackhawk-lower Castlegate wedge, based on the analysis presented above. More than one plausible causative mechanism can be proposed for most aspects of stratal architecture, and these mechanisms can be considered to act in isolation or, more probably, in combination. Indeed, there are clear links between various causative mechanisms. Three examples of such links are given below. First, a localized (10 0 -10 2 km 2 ) autogenic variation in sediment flux or transport capacity through a distributary river channel may have caused an internal threshold in differential floodplain topography to be exceeded, thus triggering delta-lobe switching and shoreline reorganization, which in turn modified local wave climate (e.g. within parasequences in Aberdeen and Sunnyside members of the Blackhawk Formation; Sømme et al. 2008;Charvin et al. 2010). Second, the distribution of channelized fluvial sandbodies in alluvial-to-coastal-plain strata of the Blackhawk Formation reflects river avulsion across a wide range of boundary conditions , but variations in avulsion-generated patterns of sandbody distribution are modified or overprinted by temporal variations in tectonic subsidence rate and the location of valleys cut during relative sea-level falls (Hampson et al. 2012). Finally, generation of an angular unconformity at or near the base of the Castlegate Sandstone reflects tectonically forced changes in accommodation and hinterland uplift (e.g. Robinson & Slingerland 1998;Miall & Arush 2001), which in turn influenced the provenance and volume of fluvial sediment supply (Horton et al. 2004;Hampson et al. 2014). Sheet sandstones bounded by hiatuses within the Castlegate Sandstone (as shown schematically in Fig. 3c after Miall 2014) may be coincident with parasequence-scale increments of shoreline progradation (e.g. Pattison 2010; fig. 18 of Bhattacharya 2011), which are not portrayed in Figure 3c, even though the base of the Castlegate Sandstone is everywhere marked by a composite erosion surface. Attempting to distinguish between the various causative mechanisms is impossible given the available data. A more useful approach is to define a stratigraphic solution set that places limits on the potential contributions of the multiple causative mechanisms to the observed stratal architectures (Heller et al. 1993).

Synthesis of framework for a sequence stratigraphic solution set
The various autogenic and allogenic mechanisms listed in Table 1 operated across a wide range of spatial and temporal scales. In combination with linkages between the mechanisms, this wide range of scales places the generation of a comprehensive, quantitative solution set for the stratal architecture of the Star Point-Blackhawk-lower Castlegate wedge beyond the scope of this paper. Instead, the paper is intended to identify the range of likely potential mechanisms that may have caused the observed stratal architectures, as a framework for future data collection and quantitative analysis. However, quantitative limits have been placed on the range of values required for some controls. For example, end-member scenarios for the sediment supply parameters required to account for parasequence-set stacking are presented in Figure 11c and d. Numerical inverse modelling experiments have also demonstrated that solution sets can be generated for sediment-supply, relative sealevel and wave-climate histories for parasequences and parasequence sets (compare within Aberdeen Member of the Blackhawk Formation; Charvin et al. 2011). Currently, the largest uncertainty in these components of a stratigraphic solution set for the Star Point-Blackhawk-lower Castlegate wedge results from the small number and poor accuracy of available age data. Future work should give priority to the collection of accurate and high-resolution age data (e.g. zonal ammonites from the Book Cliffs outcrops, and radiometric ages that are tied to the ammonite biozonation scheme of Cobban et al. 2006), and the development of approaches for estimating the partitioning of time within a sequence stratigraphic framework (e.g. incorporating characterization of stratigraphic completeness across different temporal and spatial scales; Sadler 1981). The latter is already under way (e.g. Miall 2014Miall , 2015.

Use of objective tools for description of stratal architecture
Classical sequence stratigraphic methods and terminology emphasize relative sea-level as a control on stratal architecture (e.g.

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Sequence stratigraphic solution set through interpretation of systems tracts tied to a sinusoidal relative sea-level curve; Van Wagoner et al. 1990;Catuneanu et al. 2009). A broader and more objective frame of reference is required to develop a sequence stratigraphic solution set that includes other controls, and this in turn requires the use of descriptive tools to characterize stratal architecture. Several such descriptive tools are available.
Characterization of stratal architectures can be based on patterns of aggradation and progradation (e.g. Neal & Abreu 2009), which allows interpretation of the relative balance between accommodation and sediment supply (see the 'A/S ratio'; Muto & Steel 1997). A similar descriptive tool is provided by tracking the position of topographic breaks in slope (e.g. at a shoreline or shelf edge), to define trajectories for such palaeo-geomorphological features (Helland-Hansen & Martinsen 1996;Helland-Hansen & Hampson 2009). These two approaches do not anticipate a fixed succession of stratal architectures (in contrast to the succession of systems tracts associated with a sinusoidal relative sea-level curve), and they allow aspects of stratal architecture to be quantitatively estimated if due care is exercised in choosing a reference datum surface(s) and accounting for compaction (Løseth et al. 2006;Helland-Hansen & Hampson 2009;Prince & Burgess 2013). The application of shoreline trajectory to characterize shallow-marine stratigraphic patterns (e.g. parasequence definition and stacking) in the Star Point-Blackhawk-lower Castlegate wedge is shown in Figure 9a (after Hampson 2010; Hampson et al. 2011). Spatial statistical tools such as lacunarity and Ripley's K function allow subtle spatial patterns to be objectively identified, including those describing the distribution of channelized fluvial sandbodies (e.g. Fig. 8) (Hajek et al. 2010;. Construction of sediment budgets and mass-balance frameworks, within which sediment supply can be quantitatively estimated, also requires the consistent application of an objective approach without presumption of an underlying control (e.g. Carvajal & Steel 2012;Michael et al. 2013). The application of this approach to the Star Point-Blackhawk-lower Castlegate wedge has been documented by Hampson et al. (2014), and results are shown in Figures 11 and 12. Quantitative estimation of sediment budgets and other objective descriptors allows errors and uncertainties to be appraised, which is a prerequisite for numerical modelling studies that define stratigraphic solution sets and explore their sensitivity to underlying controls.

Development of multiple hypotheses for interpretation of non-unique stratal architectures
The most valuable aspect of a sequence stratigraphic solution set is its emphasis on multiple different controls, which may generate similar stratal architectures. The non-uniqueness of stratal architectures is not explicit in classical sequence stratigraphic methods and models, which are invariably illustrated with reference to a sinusoidal relative sea-level curve Van Wagoner et al. 1990;Catuneanu et al. 2009). Instead, a sequence stratigraphic solution set provides a conceptual framework that promotes the construction and appraisal of multiple hypotheses, and is honest and pragmatic in acknowledging the limits of sequence stratigraphic interpretation (Heller et al. 1993). The solution set calls attention to the notion that stratal architectures are non-unique (Burgess et al. 2006;Burgess & Prince 2015), and challenges sedimentologists and stratigraphers to think broadly and inclusively about controls on stratal architecture.
In the Star Point-Blackhawk-lower Castlegate wedge, multiple hypotheses to explain aspects of observed stratigraphic architecture are developed (Table 1). Many of these hypotheses invoke autogenic processes or an allogenic sediment supply control, in contrast to interpretations of an allogenic accommodation control.
Three examples are listed below. First, several parasequence sets contain parasaequences that are arranged with a landward-concave shoreline trajectory (i.e. progradational-to-aggradational stacking pattern) in which the depositional length of the sediment routing system (Fig. 1) coincides with its characteristic length scale (D) (FS050-FS075, FS075-FS100, FS100-FS200; Fig. 9). Autoretreat (sensu Muto & Steel 1992) is a plausible alternative to moderatefrequency (c. 500 kyr), moderate-amplitude (c. 30 m) relative sealevel variations as an explanation for these patterns. Second, two end-member scenarios of sediment supply, based on using different parasequence sets as reference cases, are also presented ( Fig. 11c  and d). In combination with spatial and temporal trends in accommodation inferred from observed sediment thicknesses (e.g. Fig. 10), both of these sediment supply scenarios can account for the observed aggradational-to-progradational stacking of parasequence sets. Finally, the implications of two different correlations of the upsystem part of the lower Castlegate Sandstone (CSB; Fig. 3) are appraised: 'correlation A' after Robinson & Slingerland (1998) and McLaurin & Steel (2000), and 'correlation B' after Yoshida et al. (1996) and Miall & Arush (2001), in Figures 10b, 11 and 12a. Both correlations require an increase in the sand-to gravel-grade mass fraction of fluvial sediment supply (Q fl ) across the base of the Castlegate Sandstone (Fig. 12a), which emphasizes the sequence stratigraphic significance of this surface.

Added value for prediction of hydrocarbon play elements
The fuller consideration of multiple controls, use of new descriptive tools and acknowledgement of non-unique stratal architectures may at first sight appear problematic for sequence stratigraphy, at least as currently practised. The development of sequence stratigraphic solution sets certainly challenges the uncritical application of classical sequence stratigraphic models, which implicitly assume a predominant accommodation control on stratal architecture. More time and effort is required to develop and investigate multiple hypotheses, and then to synthesize the plausible hypotheses into a solution set. What then is the 'added value' of the solution set approach to sequence stratigraphic interpretation?
First, the solution set approach reduces the dependence of sequence stratigraphic interpretation on an implicit accommodation control, which is generally expressed in terms of relative sea-level. A broader range of geological information, including that regarding sediment supply and sediment routing system behaviour, can potentially be incorporated into a sequence stratigraphic solution set. Second, a solution set will probably contain a wider range of predictions for the distribution of reservoir, source and seal lithologies than a single sequence stratigraphic interpretation. One example from the Star Point-Blackhawk-lower Castlegate wedge concerns the distribution of gravity flow siltstones and sandstones, which occur in the distal, shelfal segment of the sediment routing system deposits (Fig. 3). These deposits occur only in strata corresponding to the lower four parasequence sets (from the 'base Mancos B' surface to FS200; Fig. 3), which are characterized by aggradational stacking of parasequence sets, rather than in the upper four parasequence sets (from FS200 to FS600; Fig. 3), which are characterized by more progradational parasequence-set stacking and the development of a major unconformity at the base of the Castlegate Sandstone (CSB; Fig. 3). This distribution contradicts the predictions of an accommodation-driven sequence stratigraphic model, but is instead consistent with increased interaction with the basinal hydrodynamic regime during progradation (Hampson 2010). This latter interpretation implies net import (FS200-FS500) or net export (FS500-FS600) of silt and mud by alongshelf, shallow-marine currents (Fig. 11c), which constitutes a sediment supply-and dispersal-driven interpretation that can be encompassed within a sequence stratigraphic solution set. In a broad sense, the development of solution sets allows judicious application of sequence stratigraphic methods to provide a deep understanding of the stratigraphic record. Just as importantly, numerical forward and inverse models now provide the means to turn the multiple hypotheses contained within a solution set into a probabilistic range of predictions for lithology distributions in a hydrocarbon exploration or production context (e.g. Burgess et al. 2006;Falivene et al. 2014).

Conclusions
The framework for a sequence stratigraphic solution set, and its components, is presented for an archetypal succession of marginalmarine and shallow-marine deposits exposed in the Book Cliffs of east-central Utah. Stratigraphic architectural patterns across a range of spatial scales can be attributed to various internal (autogenic) processes and external (allogenic) accommodation and sediment supply controls. Characterization of these architectures requires the use of descriptive tools that do not make implicit reference to relative sea-level, including shoreline trajectory, spatial statistics, sediment budgets and sediment mass balance. The solution set encompasses multiple, non-unique interpretations that account for observed stratigraphic architectural motifs. Aspects of the multiple interpretations and their underlying controls can be quantified, such that errors and uncertainty can be estimated.
Recurring stratigraphic architectural motifs and their potential controls in the studied strata are listed below, from small to large scale: (1) intra-parasequence architecture records autogenic switching of wave-dominated delta lobes, allogenic low-amplitude (c. 1 m) relative sea-level variations and/or allogenic wave-climate variations affecting sediment dispersal, all of which operated over short temporal scales (<10 kyr); (2) the dimensions and internal architecture of channelized fluvial sandbodies on the alluvial and coastal plain record autogenic river channel migration and avulsion history; (3) formation of wave-dominated deltaic and strandplain parasequences records allogenic variations in regional shallowmarine sediment supply and/or relative sea-level (c. 30 m amplitude) that operated at high frequency (c. 50-300 kyr); (4) stacking of parasequences into sets records autogenic shoreline retreat in response to lengthening of the alluvial-to-coastal plain ('autoretreat') and/or allogenic variations in relative sea-level of moderate frequency (c. 0.3-1.0 myr); (5) distributions of channelized fluvial sandbodies record autogenic avulsion dynamics that vary according to upstream-to-downstream position on the alluvial and coastal plain, allogenic tectonic subsidence rate and/or allogenic fluvial sediment supply; (6) stacking of parasequence sets records allogenic variations in long-term (5.0-6.0 myr) tectonic subsidence rate and/or allogenic variations in fluvial and shallowmarine sediment supply of moderate frequency (c. 0.3-1.0 myr); (7) formation of an angular unconformity at the base of a multistorey sheet fluvial sandstone records allogenic tectonic uplift and linked sediment supply controls. Combining these various controls within a sequence stratigraphic solution set provides a conceptual framework that promotes the construction and appraisal of multiple, non-unique hypotheses. The solution set approach therefore encompasses a wider range of predictions for the distribution of reservoir, source and seal lithologies than a single sequence stratigraphic interpretation, and is honest and pragmatic in acknowledging the limits of sequence stratigraphic interpretation.