One of the goals of sequence stratigraphy is to model the conditions that generate stratigraphic architecture at outcrop to basin scales. Accommodation and sedimentation are the principal variables included in sequence-stratigraphic models that describe facies architecture in marine successions. Similar models exist to describe wholly nonmarine architecture. Distinct models are commonly applied to basins containing predominantly lacustrine or predominantly fluvial facies, which can make it difficult to apply models to the entire history of a basin that may include both lacustrine-dominated or fluvial-dominated phases, depending on climatic and tectonic conditions. To account for these changing conditions over the history of nonmarine basins, we present a conceptual three-dimensional model that describes the potential architectural patterns under specific combinations of accommodation, sediment flux, and water balance. Sectors of the model delineate where basins are underfilled or overfilled with respect to accommodation and limited with respect to sediment and water, creating eight zones with different implications for the development of facies architecture. Different types of basins (e.g., foreland, extensional, pull-apart, intracratonic) show broadly different trends in architecture through time. Subtle changes in accommodation, sedimentation, and water balance in the model correspond to shifts in facies architecture between lithostratigraphic units, but architectural transitions within individual basins are more important indicators of evolving basin conditions than comparisons among all basins. This model may serve as a guide for comparing the influence of distinct drivers of architecture among different types of basins as well as identifying important intervals of change during the history of basin filling. The availability of commensurate data on the history of accommodation, sedimentation, and water balance is, however, an ongoing challenge to reconstructing complete basin histories. Future analyses will test how well predicted facies stacking patterns compare to observed nonmarine stratigraphic successions resulting from the combination of accommodation, sediment flux, and water balance during the history of basin filling.

Sequence stratigraphy provides a framework for evaluating facies architecture in relation to the controls on sediment accumulation. This framework allows changes in accommodation to be inferred from observed stratal stacking and architecture to be described from facies trends. The ability to model the expected responses of strata to changing accommodation revolutionized oil and gas exploration (Van Wagoner et al., 1988; Catuneanu, 2006), in addition to establishing a broader understanding of large-scale controls on stratigraphic architecture (Kraus and Middleton, 1987; Currie, 1997; Yang, 2011; McCarthy and Plint, 2013). This in turn has had broader applications, such as for evaluating patterns in the fossil record (Peters and Heim, 2011; Patzkowsky and Holland, 2012) and chemostratigraphy (Prave et al., 2022). Most sequence-stratigraphic models have been applied to marine strata (Jervey, 1988; Posamentier et al., 1988; Galloway, 1989; Hunt and Tucker, 1992), where the drivers of accommodation and the facies models are well characterized. In nonmarine strata, facies development in relation to accommodation is less understood, and it is expected to vary with factors including basin type, position within the basin, and climate—all of which may be poorly constrained or even unknown. For this reason, most nonmarine sequence-stratigraphic frameworks are based on stacking patterns of easily discernable but broadly defined channel and floodplain facies (Wright and Marriott, 1993; Currie, 1997; Martinsen et al., 1999).

Although many nonmarine stratigraphers use fluvial stacking patterns to interpret changes in accommodation, they have tended to use different approaches to characterizing the generation of fluvial deposits and major surfaces. Differences in these approaches and their methods have produced several sequence-stratigraphic models that emphasize different aspects of fluvial deposits to interpret changes in accommodation through time (Table 1; Wright and Marriott, 1993; Currie, 1997; Atchley et al., 2004; McCarthy and Plint, 2013; Weissmann et al., 2013). Variations in terminology, methodology, and scale of the analyses can lead to differing interpretations of how nonmarine facies respond to changes in accommodation (Hajek and Wolinsky, 2011). Comparisons among basins may even result in the absence of an expected trend in large-scale stacking patterns (Colombera et al., 2015). Given the numerous influences on stratal stacking in nonmarine systems and the many ways that these patterns have been characterized, it is not surprising that studies report broad variations or counterintuitive trends in facies stacking. A model that attempts to incorporate many of the important drivers of nonmarine deposition with expected stratigraphic outcomes would help explain the variability in observed nonmarine facies trends.

TABLE 1.

SELECTED NONMARINE SEQUENCE-STRATIGRAPHIC MODELS RELATING ACCOMMODATION (A), SEDIMENTATION (S), WATER (W), AND PEAT PRODUCTION (PP)

Fundamentally, the principal conceptual frameworks of nonmarine sequence stratigraphy incorporate different drivers (Table 1). Existing frameworks have been based on the relationship between accommodation and sedimentation (often expressed as the A:S ratio); the relationship between accommodation and a measure of water availability; and sometimes the combination of accommodation, sediment supply, and water availability, but always within in a two-dimensional model space (Posamentier and Vail, 1988; Posamentier et al., 1988; Catuneanu, 2006; Wadsworth et al., 2002). We present a conceptual framework for nonmarine sequence stratigraphy that considers accommodation, sedimentation, and water availability as distinct axes in a three-dimensional space (Fig. 1). We present this model as a way to analyze changes in facies architecture as a function of the shifting relationships among accommodation rate, sediment flux, and water balance that occur over the history of nonmarine basins. Our intention is to offer a way to visualize the combined influences on facies and facies stacking at a given point in basin history and how they change through time. The model allows changes in each driver to be assessed over the history of deposition within a basin and offers a way to account for changes in stacking patterns through time.

Figure 1.

The model space, formed by the combination of accommodation (A), sediment flux (S), and water balance (W).

Figure 1.

The model space, formed by the combination of accommodation (A), sediment flux (S), and water balance (W).

Marine Sequence Stratigraphy

In marine settings, accommodation space is generated by tectonic subsidence and eustatic sea-level rise, and it is reduced by tectonic uplift and eustatic sea-level fall (Posamentier et al., 1988; Catuneanu, 2006). These drivers combine to produce changes in relative sea level, which increases or decreases the space in which sediment may accumulate. Differing rates of generating accommodation relative to the rate of sediment supply govern the stacking patterns of marine and coastal facies. The resulting facies architecture is characterized by well-known marine systems tracts in depositional sequences (Van Wagoner et al., 1988; Hunt and Tucker, 1992; Neal and Abreu, 2009).

The lowstand systems tract (LST) develops as accommodation slowly increases, and it is characterized by progradational to aggradational stacking. The transgressive systems tract (TST) is deposited during rapid rates of relative sea-level rise, when accommodation outpaces the rate of sediment input, fostering retrogradational stacking. The highstand systems tract (HST) develops as the rate of accommodation slows, and it is characterized by aggradational to progradational facies stacking. The falling-stage systems tract (FSST) is deposited during a relative fall of sea-level—that is, negative accommodation—and it is characterized by degradational stacking (Hunt and Tucker, 1992). A sequence boundary characterized by a subaerial unconformity depositionally updip defines the end of the depositional sequence (Van Wagoner et al., 1988).

The rate of accommodation and the rate of sedimentation are the two components required to understand the generation of marine facies architecture and the systems tracts that describe it. These components are evaluated within two-dimensional sequence-stratigraphic models (Catuneanu, 2006) and can be applied to any marine stratal succession. Several models of marine sequence stratigraphy have been developed (e.g., Posamentier et al., 1988; Posamentier and Vail, 1988; Van Wagoner et al., 1988; Galloway, 1989; Hunt and Tucker, 1992). Although these models differ in the number of systems tracts and which surface bounds sequences, the overall framework and processes depicted in these models are similar (Catuneanu, 2006). These models allow specific stacking patterns to be associated with specific processes, which facilitates translation among models and the studies that use them.

Nonmarine Sequence Stratigraphy

In nonmarine settings away from the influence of eustasy, accommodation is controlled solely by tectonic subsidence and uplift (Shanley and McCabe, 1994). Climate is important in nonmarine settings not only because it controls sediment supply (Galloway, 1989; Bull, 1991; Shanley and McCabe, 1994), but also because it controls the types of environments that form (e.g., lakes, rivers, eolian dunes). Even so, the effects of climate on facies architecture are not well understood. The most tangible aspect of climate that is often incorporated into sequence-stratigraphic frameworks is water availability, which is most pertinent to lacustrine systems (Garcia-Castellanos, 2006). While climate is not the sole driver behind the development of lacustrine facies (Carroll and Bohacs, 1999), it exerts a first-order control on the amount of water in the system and determines whether lakes are able to form and persist (Lambiase, 1990).

Most sequence-stratigraphic analyses of nonmarine strata focus on changes in fluvial architecture in relation to accommodation (Wright and Marriott, 1993; Shanley and McCabe, 1994). The depositional systems model of Wright and Marriott (1993) forms the framework for most nonmarine sequence-stratigraphic analyses (Table 1). This model preserves the terminology of marine systems tracts and is largely presented in terms of coastal fluvial systems. Currie (1997) adapted this model for fully inland systems and proposed new systems-tract nomenclature to emphasize the separation from marine settings (Table 1). These models are largely similar and relate changes in accommodation to the processes of channel incision, channel migration, and floodplain aggradation to the generation of stratal stacking patterns.

A sequence boundary in nonmarine settings is typically characterized by a widespread surface of erosion, which may have low or relatively high relief. Well-developed paleosols typically form at this hiatal surface, particularly on interfluves and terraces (Wright and Marriott, 1993). As accommodation slowly increases, fluvial systems are characterized by laterally migrating channels. The architecture that forms under such low-accommodation conditions is characterized by stacked channel sandstones and minor floodplain deposits typically containing well-developed paleosols (Catuneanu, 2006). As the rate of accommodation increases, aggradation rate increases, and fluvial systems are characterized by vertically accreting floodplains, producing isolated channel sandstones encased in thick floodplain mudstone. The transition between stacked sandstone bodies and isolated sandstone bodies marks the increase in accommodation and is called the expansion surface, if the transition is abrupt, or the expansion zone, if the transition is gradual (Martinsen et al., 1999). Near the top of the sequence, channel sandstones become more amalgamated as accommodation decreases, and the sequence is bounded above by an unconformity (Wright and Marriott, 1993; Shanley and McCabe, 1994; Currie, 1997).

Other nonmarine sequence-stratigraphic models typically incorporate accommodation and varying aspects of sediment and water inputs. Carroll and Bohacs (1999) presented a model showing the development of lacustrine facies in response to the rate of accommodation relative to the rates of fill by water and sediment. In this model, hypothetical basins and their predicted facies associations develop under different combinations of accommodation and the water and sediment available to fill the basins (Table 1). Basins are underfilled when accommodation rate is much greater than the supply of water and sediment (A >> W + S), keeping lake level well below the bounding sills, and shallow or evaporative lakes form under these conditions. Basins are overfilled when the rate of water and sediment supply is much greater than the rate of accommodation (A < W + S). If sill levels are exceeded by water and sediment, fluvial-lacustrine systems occur. When the rates of accommodation and water and sediment supply are roughly equal, balanced-fill conditions exist, in which lake level remains at or near the maximum level determined by the elevation of the bounding sills (Carroll and Bohacs, 1999).

Bohacs and Suter (1997) considered the sequence-stratigraphic constraints on coal formation by modeling peat-production rate against accommodation rate (see also Wadsworth et al., 2002). Although this model does not explicitly include water and sediment supply, they are implied to increase with increasing accommodation rate. When peat-production rate exceeds accommodation rate (A < PP), organic material oxidizes and decomposes before it can be buried below the water table (cf. Gastaldo and Demko, 2011). When accommodation rate exceeds the peat-production rate (A > PP), mires are flooded or buried by clastic material, preventing coal from forming (Bohacs and Suter, 1997). Based on empirical studies of peat formation, coal forms when accommodation is slightly greater than peat production (A:PP = 1.18). Where accommodation rate and peat-production rate are balanced, coal and coaly shale can form, and the coal window widens as the rates of accommodation and peat production increase, although coal is unlikely to form at very high rates of accommodation and peat production (Bohacs and Suter, 1997). Bohacs and Suter (1997) further detail how their model of coal formation relates to the marine systems tracts in coastal settings.

Martinsen et al. (1999) proposed additional terminology for nonmarine systems tracts and did not attempt to equate them to the traditional marine systems tracts (Table 1). These systems tracts are defined by the ratio of accommodation to sediment supply (A:S), with low-accommodation systems tracts (LAST) forming when A:S is low and high-accommodation systems tracts (HAST) forming when A:S is high. The LAST is characterized by stacked channel sandstones, few floodplain deposits, and mature paleosols, whereas the HAST is characterized by isolated channel sandstones surrounded by thick floodplain deposits with little to no pedogenic development (Catuneanu, 2006). How well the features of these systems tracts are developed varies with the A:S ratio, and a full spectrum of systems tracts are possible, from ultra-LAST–like to ultra-HAST–like (Fig. 2; Holland and Loughney, 2021).

Figure 2.

Hypothetical spectrum of nonmarine architectural stacking in relation to the aggradation rate, with schematic examples of stacking patterns. Low-aggradation systems tract (LAST) architectures form at lower aggradation rates, and high-aggradation systems tract (HAST) architectures form at higher rates of aggradation. Adapted from Holland and Loughney (2021).

Figure 2.

Hypothetical spectrum of nonmarine architectural stacking in relation to the aggradation rate, with schematic examples of stacking patterns. Low-aggradation systems tract (LAST) architectures form at lower aggradation rates, and high-aggradation systems tract (HAST) architectures form at higher rates of aggradation. Adapted from Holland and Loughney (2021).

In a different approach, the fluvial-aggradation cycle (FAC) framework of Atchley et al. (2004) adapts the methods of carbonate cyclostratigraphy to identify cyclic trends in alluvial successions dominated by paleosols. This hierarchical framework permits the drivers of fluvial architecture to be interpreted from differing scales of stacking patterns. Meter-scale FACs represent autogenic depositional processes; decameter-scale FAC cycles represent allogenic processes.

These frameworks each model some aspect of facies stacking from governing concepts or from observations. The two-dimensional models (e.g., A:S or A:W), however, can evaluate facies architecture only in relation to two variables at a time. While the factors that govern the development and filling of a basin over long timescales are numerous and complex, it is possible to assess the relationships between all three major drivers (A, S, W) of nonmarine facies architecture in a unified model.

Model Axes

The three-dimensional model space encompasses the major allogenic controls on nonmarine deposition, important boundaries created by the combination of these controls, and existing architectural frameworks. Because negative rates of accommodation prevent stratigraphic accumulation, and because negative sediment flux or water flux to a basin are hard to conceptualize, we focus only on positive values of accommodation, sediment flux, and water balance.

The model space is defined by accommodation rate (A), sediment flux (S), and water balance (W; Fig. 1). The accommodation axis is the rate of accommodation, corresponding to subsidence rate in nonmarine basins (Catuneanu, 2006). As A increases, more space is available to be filled by sediment or water. When A < 0, as during tectonic uplift, long-term accumulation of sediment and water is prevented. The sedimentation axis is sediment flux: the volume or supply of sediment to the system per unit area. As S increases, more sediment is supplied to the system, favoring thicker deposits if accommodation is sufficient. The water balance axis reflects the combination of total inflows to the basin (e.g., precipitation, infiltration, stream input) and total outflows (e.g., evaporation, stream export, groundwater export) from the basin (Bengtsson, 2012). As W increases, inflows increase relative to outflows. When W < 0, arid conditions exist in the system.

The Seven Model Planes

Seven planes define principal boundaries of the model space. Three of these boundaries correspond to planes where A = 0, S = 0, or W = 0, which are the limits of the model space (Fig. 1). Three planes correspond to simple balances between two of the variables, where A:S = 1, A:W = 1, and S:W = 1 (Figs. 3AC). The seventh plane corresponds to a more complex balance, where A:(S+W) = 1 (Fig. 3D). Examination of each of these planes in isolation reveals several fundamental divisions in the model space.

Figure 3.

Divisions of the model space created by the relationships between accommodation (A), sediment flux (S), and water balance (W). The limits of each division are the 1:1 lines created by each pair of axes. (A) A:S = 1 separates the sediment-limited and accommodation-limited portions. (B) A:W = 1 separates the water-limited and accommodation-limited portions. (C) S:W = 1 separates lacustrine-prone and fluvial-prone portions. (D) A:S:W = 1 separates the underfilled and overfilled portions of the model space.

Figure 3.

Divisions of the model space created by the relationships between accommodation (A), sediment flux (S), and water balance (W). The limits of each division are the 1:1 lines created by each pair of axes. (A) A:S = 1 separates the sediment-limited and accommodation-limited portions. (B) A:W = 1 separates the water-limited and accommodation-limited portions. (C) S:W = 1 separates lacustrine-prone and fluvial-prone portions. (D) A:S:W = 1 separates the underfilled and overfilled portions of the model space.

A:S = 1

Maximum aggradation rates are achieved where the rates of accommodation and sedimentation are equal (i.e., A:S = 1; Fig. 4A). Above this plane, accommodation exceeds sediment flux, and the system is therefore sediment-limited (Fig. 4B) and cannot aggrade any faster than sediment supply allows. In such cases, the basin would be underfilled (Fig. 4C). Below this plane, sediment flux exceeds accommodation, and aggradation rates are limited by accommodation (Fig. 4B). In these cases, the basin is overfilled (Fig. 4C). The plane corresponding to A:S = 1 therefore corresponds to the maximum aggradation rates for any given value of accommodation or sediment flux (Fig. 4A). Near the plane where A = 0, the insufficient accommodation means that the basin will largely experience bypass of the sediment supplied to it.

Figure 4.

The model conditions along the intersection of the accommodation (A) and sediment flux (S) axes. (A) Fluvial-prone region. (B) Accommodation-limited (A:S < 1) and sediment-limited (A:S > 1) regions. (C) Underfilled and overfilled regions. (D) Facies architecture in relation to A:S, showing hypothetical divisions of low-aggradation (LAST) and high-aggradation (HAST) systems tracts in accommodation-limited (A:S < 1) and sediment-limited (A:S > 1) portions of the model. (E) Three-dimensional representation of hypothetical architecture in relation to A, S, and water balance (W).

Figure 4.

The model conditions along the intersection of the accommodation (A) and sediment flux (S) axes. (A) Fluvial-prone region. (B) Accommodation-limited (A:S < 1) and sediment-limited (A:S > 1) regions. (C) Underfilled and overfilled regions. (D) Facies architecture in relation to A:S, showing hypothetical divisions of low-aggradation (LAST) and high-aggradation (HAST) systems tracts in accommodation-limited (A:S < 1) and sediment-limited (A:S > 1) portions of the model. (E) Three-dimensional representation of hypothetical architecture in relation to A, S, and water balance (W).

Moreover, the A:S = 1 plane governs the widely used nonmarine high-accommodation (HAST) and low-accommodation systems tracts (LAST) of Martinsen et al. (1999). HAST deposits are generally described as being mostly floodplain deposits with isolated single-story channel deposits. Paleosols tend to be immature, and if climate permits, coals are well-developed (Catuneanu, 2006). In contrast, LAST deposits consist mainly of multi-story and multi-lateral fluvial channels with isolated lenses of floodplain deposits (Fig. 2). Within those floodplain deposits, paleosols tend to be mature, and coals are thin or poorly developed, climate permitting (Catuneanu, 2006). A similar reasoning was used to establish high-accommodation and low-accommodation settings within sedimentary basins, which are areas that tend to favor high-accommodation and low-accommodation systems tracts, respectively (Catuneanu, 2006). Because aggradation rates control these architectures (Bridge and Leeder, 1979) rather than accommodation per se, we recommend that these terms be replaced with high- and low-aggradation systems tracts, and high- and low-aggradation settings. This change would still permit the continued use of the established abbreviations HAST and LAST.

As currently recognized, HAST and LAST represent a simple division of what must be a spectrum of conditions (Fig. 2; Holland and Loughney, 2021), and this spectrum is arrayed along an axis of aggradation rate (A:S = 1; Figs. 4D and 4E). Near the origin would be conditions that could be described as ultra-LAST, having an extreme form of a LAST-style architecture. At progressively higher values of aggradation rate would be LAST and HAST architectures. At the highest combinations of accommodation and sedimentation would be architectures best described as ultra-HAST, having an extreme form of a HAST-style architecture.

The boundaries between all these subdivisions of the spectrum of architectures run parallel to the A and S axes. For example, at any given point along the A:S = 1 plane, increasing sediment flux will not increase the aggradation rate, as the system is accommodation-limited, and the architecture will remain the same. Similarly, increasing only the rate of accommodation will not change the architecture because the system is sediment-limited (Figs. 4D and 4E). This counterintuitive relationship therefore indicates that LAST-like architectures can form under high rates of accommodation, provided that sediment flux is less than the available accommodation. HAST-like architectures, however, cannot form under low rates of accommodation, as they require high rates of both accommodation and sedimentation. The preservation potential of systems tracts will vary in relation to the balance of accommodation and sedimentation. We expect preservation potential to be high along and close to the A:S = 1 plane where accommodation and sediment flux are balanced. Accordingly, preservation decreases with proximity to the A = 0 plane where sediment bypass occurs owing to low accommodation, and preservation decreases with proximity to the S = 0 plane where sediment is not supplied. These relationships indicate that LAST-like architectures have lower preservation potential than HAST-like architectures.

Nonmarine systems tracts were developed to describe primarily fluvial deposits (Martinsen et al., 1999). Although the occurrence of lacustrine facies is included in nonmarine systems tract models (Currie, 1997; Holland and Loughney, 2021), well-developed lacustrine deposits do not readily fit within the LAST–HAST framework. Some have applied marine systems-tract terminology to lacustrine strata, analogizing changes in lake level and sea level, but the presence of sills greatly complicates the expected behavior of lake-level changes and therefore stratigraphic architecture (Keighley et al., 2003). Application of the classic marine systems tracts (lowstand [LST], transgressive [TST], highstand [HST], falling stage [FSST]) is therefore not advisable.

A:W = 1

The plane defined by accommodation equaling water balance corresponds to the balanced-fill conditions of Carroll and Bohacs (1999; Figs. 3B and 5A). Above this plane, accommodation exceeds water balance, and nonmarine systems are therefore water limited (Fig. 5B). Because lake levels remain below the sill level, the region where A:W > 1 corresponds to the underfilled conditions of Carroll and Bohacs (1999). Below the plane of A:W = 1, water balance exceeds the rate of accommodation, making the system accommodation limited (Fig. 5B). Likewise, because lake levels may exceed the sill level, and excess water is exported from the basin, lower A:W ratios correspond to the overfilled conditions of Carroll and Bohacs (1999).

Figure 5.

The model conditions along the intersection of the accommodation (A) and water balance (W) axes. (A) Lacustrine-prone region. (B) Accommodation-limited (A:W < 1) and water-limited (A:W > 1) regions. (C) Underfilled and overfilled regions. (D) Hypothetical gradation of lake depth in relation to A, W, and sediment flux (S).

Figure 5.

The model conditions along the intersection of the accommodation (A) and water balance (W) axes. (A) Lacustrine-prone region. (B) Accommodation-limited (A:W < 1) and water-limited (A:W > 1) regions. (C) Underfilled and overfilled regions. (D) Hypothetical gradation of lake depth in relation to A, W, and sediment flux (S).

Increasing lake depths are promoted along the plane of A:W = 1, as increasing amounts of accommodation can be filled by available water (Figs. 5D and 5E). The presence of topographic features, such as sills, also plays a role in lake depth, as a high sill can permit the formation of a deep lake even where accommodation is minimal.

Water balance can be negative where outflows (e.g., evaporation, stream export, groundwater export) exceed inflows (e.g., precipitation, infiltration, stream input). Although not explicitly shown in the three-dimensional space of this model, such conditions would lie behind the back left edge of the cube shown in Figures 1 and 3. Ephemerally wet to perennially arid conditions would be present in the region where W < 0, favoring the formation of eolian and other dryland facies (Fig. 5).

S:W = 1

The S:W = 1 plane separates two broad regimes that reflect the dominant types of sedimentary environments that are generally able to develop (Fig. 3C). Where S:W = 1, sediment flux and water balance are equal, and both fluvial and lacustrine environments may develop (Fig. 6). Where S:W > 1, more sediment is available in the system than water, and fluvial environments are more prone to develop than lacustrine environments. Where S:W < 1, the amount of water in the system is greater than the supply of sediment, and lacustrine environments are favored over fluvial environments (Fig. 6A). The S:W ratio reflects the general tendencies of basin environments, although basins can contain a variety of fluvial and lacustrine environments owing to their potentially large extent and heterogeneity of conditions. Close to the origin, deposits tend to be thinner and lakes tend to be shallower, and deposits thicken and lakes tend to deepen away from the origin as sediment or water availability increases (Fig. 6).

Figure 6.

The model conditions along the intersection of the sediment flux (S) and water balance (W) axes. (A) The division of the fluvial-prone and lacustrine-prone regions by the S:W = 1 line corresponding to (B) water-limited (accommodation [A]:W > 1) and sediment-limited (A:S > 1) regions of the model.

Figure 6.

The model conditions along the intersection of the sediment flux (S) and water balance (W) axes. (A) The division of the fluvial-prone and lacustrine-prone regions by the S:W = 1 line corresponding to (B) water-limited (accommodation [A]:W > 1) and sediment-limited (A:S > 1) regions of the model.

A:(S+W) = 1

This plane occurs where accommodation is balanced by the sum of sediment flux and water balance (Fig. 3D). Above this plane, accommodation is greater than sediment and water balance combined, and systems are underfilled. Below this plane, sediment and water balance collectively exceed accommodation, and systems are overfilled (Jordan, 1995). Underfilled systems fall entirely within the sediment- and water-limited space created by the A:S and A:W planes (Figs. 3A and 3B). These systems are characterized by overall thinner deposits and shallower lakes because accommodation increases faster than either sediment flux or water balance (Figs. 4D and 5D). Overfilled systems fall predominantly within the accommodation-limited space (Fig. 3). These systems may have overall thinner deposits and shallower lakes because accommodation is low, preventing the accumulation or preservation of thick deposits.

The Eight Architectural Zones

The constraints imposed by the seven model planes define eight zones that reflect the relative amounts of accommodation, sediment flux, and water balance (Fig. 7). Although within-basin heterogeneity can add complications, each zone tends toward a specific architectural style and type of basin fill (Table 2).

Figure 7.

Architectural zones created by the relationship between accommodation (A), sediment flux (S), water balance (W), and the planes delimiting the accommodation-, sediment-, and water-limited portions of the model. (A) Underfilled lacustrine-prone zone (A:S > 1); (B) underfilled fluvial-prone zone (A:S > 1); (C) overfilled lacustrine-prone W-limited zone (A:S > 1); (D) overfilled fluvial-prone S-limited zone (A:S > 1); (E) overfilled lacustrine-prone S-limited (A:S > 1) and S-dominated (A:S < 1) zones; (F) overfilled fluvial-prone W-limited (A:S < 1) and W-dominated (A:S < 1) zones. Characteristics of each zone are described in Table 2.

Figure 7.

Architectural zones created by the relationship between accommodation (A), sediment flux (S), water balance (W), and the planes delimiting the accommodation-, sediment-, and water-limited portions of the model. (A) Underfilled lacustrine-prone zone (A:S > 1); (B) underfilled fluvial-prone zone (A:S > 1); (C) overfilled lacustrine-prone W-limited zone (A:S > 1); (D) overfilled fluvial-prone S-limited zone (A:S > 1); (E) overfilled lacustrine-prone S-limited (A:S > 1) and S-dominated (A:S < 1) zones; (F) overfilled fluvial-prone W-limited (A:S < 1) and W-dominated (A:S < 1) zones. Characteristics of each zone are described in Table 2.

TABLE 2.

DESCRIPTIONS OF ARCHITECTURAL ZONES DERIVED FROM THE COMBINATION OF ACCOMMODATION (A), SEDIMENT FLUX (S), AND WATER BALANCE (W) IN THE MODEL

Underfilled Lacustrine-Prone

This zone encompasses lacustrine-prone environments forming in underfilled basins (Fig. 7A). This zone occupies the underfilled space where accommodation increases faster than either sediment flux or water balance. This zone is sediment-limited, and deposits are predicted to be thin or absent, resulting in widespread hiatuses and pedogenic modification. This zone is also water-limited because of its position along the lower end of the W axis (Table 2). Environments are lacustrine-prone, although ephemeral lakes may dominate in arid settings. This zone includes the narrowest range of predicted systems tracts, which tend toward highly LAST-like architectures, despite occupying the high-accommodation space in the model. These systems tracts have a low preservation potential, given the minor sediment flux and tendency toward nondeposition.

Underfilled Fluvial-Prone

This zone occupies the underfilled model space where accommodation increases faster than sediment flux and water balance (Fig. 7B). This zone is sediment-limited owing to its position along the lower end of the S axis. Deposits are expected to be thin, and hiatuses may be widespread. This zone is mostly water-limited, and although environments are fluvial-prone, the low water balance favors the development of arid environments and potentially eolian deposits (Table 2). This zone is dominated by ultra-LAST and LAST architectures, although HAST architectures may form as sediment flux increases. Systems tracts in this zone have low preservation potential, in particular ultra-LASTs forming in the most sediment-limited portion may tend toward nondeposition; LASTs and HASTs in this zone have higher potential for long-term preservation.

Overfilled Lacustrine-Prone (W-Limited)

This zone occupies the overfilled space where accommodation increases faster than water balance, and water balance increases faster than sediment flux, but at a slower pace than in the underfilled zone (Fig. 7C). The overfilled lacustrine zone is sediment- and water-limited. As a result, most deposits will be relatively thin, and most lakes will be relatively shallow, although deposits will thicken and lakes will deepen with distance from the origin. This zone exhibits a very broad range of possible systems tracts, from ultra-LAST to ultra-HAST (Table 2). Pedogenesis will be most pronounced in the most sediment-limited portion of this zone, and ultra-LASTs and LASTs may have well-developed paleosols. HASTs and ultra-HASTs forming in this zone have the highest preservation potential, and ultra-LASTs have the lowest preservation potential.

Overfilled Fluvial-Prone (S-Limited)

This zone occupies the overfilled space where accommodation increases faster than sediment flux, and sediment flux increases faster than water balance but at a slower rate than in the underfilled space (Fig. 7D). This zone is sediment- and water-limited, relative to the available accommodation. Sediment deposits are relatively thick, and lakes are shallow or absent. Systems tracts in this zone range from LASTs to ultra-HASTs, and much of the zone is occupied by HAST-like architectures. Pedogenesis is expected to be most pronounced in LASTs, with some potential for weakly developed and immature paleosols in HASTs (Table 2). Preservation of all systems tracts in this zone is high, as the zone borders the aggradation plane, indicating that accommodation and sediment flux are well balanced throughout this zone.

Overfilled Lacustrine-Prone (A-Limited)

This zone occurs in the overfilled space where accommodation increases at a slower rate than either sediment flux or water balance, and water balance exceeds sediment flux (Fig. 7E; Table 2). This zone is bisected by the aggradation plane, splitting it into sediment-limited (A:S > 1) and sediment-dominated (A:S < 1) portions. Sediment deposits are relatively thin, and lake depths increase with increasing water balance and accommodation. Predicted systems tracts range from ultra-LASTs to HASTs. Half of this zone occurs in the sediment-limited region of the model space (Fig. 3A), and ultra-LASTs and LASTs are most likely to develop. Pedogenesis is likely to occur in the LAST-like systems tracts, with paleosols becoming less likely to form with increasing sediment. Preservation potential also increases as sediment flux increases, and ultra-LASTs forming in this zone are unlikely to be preserved.

Overfilled Fluvial-Prone (A-Limited)

This zone occurs in the overfilled space where accommodation increases at a slower rate than either sediment flux or water balance, and sediment flux exceeds water balance (Fig. 7F; Table 2). This zone is accommodation limited (A:S < 1), and it is bisected by the A:W = 1 plane, splitting it into water-limited and water-dominated portions. Deposits may display a wide range of thicknesses as sediment flux increases, and lakes will be relatively shallow. This zone may encompass the full range of potential systems tracts, from ultra-LAST to ultra-HAST. Most of the zone is occupied by LAST to ultra-HAST architectures. Because variation in characteristics is dominated by changes along the S axis, pedogenesis may occur where sediment flux is low, although well-developed paleosols may be rare or absent. The preservation potential for most systems tracts in this zone is high, as it occupies space where accommodation and sediment flux increase proportionally.

Because the relationships between accommodation rate, sediment flux, and water balance are expected to change over the history of a basin, this model allows trends in nonmarine facies architecture to be evaluated in relation to changes in each of these controls. Changes in facies architecture may occur within each zone, but the most pronounced changes in architecture are expected to occur between zones.

This model is intended to allow basin histories to be characterized in terms of the large-scale controls on basin filling. Given the scale of these controls and their variability among basins, we are interested in whether this theoretical approach can be used to evaluate the role of accommodation, sedimentation, and water balance in controlling facies architecture or to predict patterns of facies architecture through time.

Foreland, extensional, and intracratonic basins would be expected to have substantially different trajectories, but should occupy similar parts of the model space under uniformly dry and wet conditions. Hypothetical trajectories for these basins types are different and overlap in model space (Fig. 8; Table S1 in the Supplemental Material1). Accommodation decreases through time in each trajectory and is the most important variable in the foreland and extensional trajectories. The foreland trajectories initially experience large decreases in accommodation, followed by stages of increasing and decreasing accommodation and sediment flux. The extensional trajectories are also characterized by large decreases in accommodation and sedimentation but show decreasing changes with each step. All trajectories occur along the A:S = 1 plane, with the dry trajectories moving between the accommodation- and sediment-limited overfilled and underfilled zones; wet trajectories remain within the accommodation-limited overfilled zones. The foreland and extensional trajectories show more substantial changes in sedimentation than the intracratonic examples, indicating that these basin types should show higher variability in facies architecture and an overall trend toward progressively LAST-like architectures. As expected for long-lived basins characterized by low accommodation (Allen and Allen, 2013), the intracratonic trajectories show minor changes in accommodation compared with the foreland and extensional basins, and they remain entirely within zones where ultra-LAST architectures are expected (Fig. 4). These predictions indicate that the differing combinations of accommodation, sedimentation, and water balance associated with different types of basins produce distinct and characteristic trajectories. We evaluated the model and its ability to represent changes in facies stacking in modern and ancient basins. The particular histories of real basins are expected to differ slightly from these hypothetical examples, particularly in regard to water balance, which should vary through time. Visualizing these drivers over the entirety of a basin’s history can illustrate broad trends among basin types and highlight intervals of pronounced change in architecture among stratigraphic units.

Figure 8.

Hypothetical foreland (green), extensional (orange), and intracratonic (blue) basins in the model space under dry (light colors) and wet (dark colors) conditions. Arrows show trajectories of each basin through time beginning with the oldest unit. Hypothetical basin data is provided in Table S1 (see text footnote 1) after Quinlan and Beaumont (1984) and Allen and Allen (2013). The animated version of this figure is provided in the Supplemental Material. Please visit https://doi.org/10.1130/GEOS.S.23972235 to access it, and contact editing@geosociety.org with any questions.

Figure 8.

Hypothetical foreland (green), extensional (orange), and intracratonic (blue) basins in the model space under dry (light colors) and wet (dark colors) conditions. Arrows show trajectories of each basin through time beginning with the oldest unit. Hypothetical basin data is provided in Table S1 (see text footnote 1) after Quinlan and Beaumont (1984) and Allen and Allen (2013). The animated version of this figure is provided in the Supplemental Material. Please visit https://doi.org/10.1130/GEOS.S.23972235 to access it, and contact editing@geosociety.org with any questions.

We compared the histories of 16 basins in the model space. The basins span a variety of ages ranging from Paleozoic to modern, and they include a variety of basin types: pull-apart (transtensional), extensional, foreland, and intracratonic basins (Table 3). For each basin, representative stratigraphic thickness, ages, lithologies, and estimates of water balance for significant geologic units or temporal divisions were compiled from literature sources (see the Supplemental Material, Tables S2–S4). We used sediment-accumulation rates (m/k.y.) as a proxy for sediment flux. A variety of metrics can be used to derive water balance, which typically requires estimates of the volumes of water inputs and outputs to lake basins (Bengtsson, 2012). Volume estimates are generally unavailable for ancient lake basins, and other approximations of lake-basin water balance, such as the ratio of precipitation to evaporation rates, are inconsistently available among ancient basins or among temporal subdivisions within a single basin. For basins containing lake facies, we used the estimated surface area of the lake or lacustrine deposits (Al) relative to the surface area of the drainage basin or total outcrop area (Ab) in square kilometers as a proxy for water balance. We used backstripped subsidence rates (m/k.y.) as a proxy for accommodation. Thicknesses, ages, and lithologies of geologic units were used to calculate subsidence rates using the Backstrip program for macOS (Holland, 2021). Basin trajectories in the three-dimensional model space were plotted in R v. 4.2.1 (R Core Team, 2020) using the rgl package v. 1.1.3 (Murdoch and Adler, 2021) and magick package v. 2.7.4 (Ooms, 2023).

TABLE 3.

AGES, DEPOSITIONAL ENVIRONMENTS, AND TECTONIC SETTINGS OF BASINS DEPICTED IN FIGURES 912 AND ANIMATIONS S1–S16

Results

The trajectory of each basin through time shows the relative influence of accommodation, sediment flux, and water balance at different stages in basin history. As with the hypothetical trajectories, most basins show large changes in subsidence through time, but their trajectories are much more variable and typically show more than one episode of increasing and decreasing subsidence. Some basins are predominantly controlled by changes in sediment flux, while others are most influenced by changes in water balance (i.e., lake size), which defines the separation of fluvial- and lacustrine-prone systems. Similar basin types show broadly similar trends in sedimentation, water balance, and accommodation (Fig. 9), conforming to expected trends (Allen and Allen, 2013).

Figure 9.

Sixteen example basins (see basins and corresponding colors in Fig. 12) in the model space grouped by basin type. Arrows show trajectories of each basin through time beginning with the oldest unit. Foreland = green; extensional = orange; pull-apart = magenta; pluvial = purple; intracratonic = blue. The animated version of this figure is provided in the Supplemental Material. Please visit https://doi.org/10.1130/GEOS.S.23972235 to access it, and contact editing@geosociety.org with any questions.

Figure 9.

Sixteen example basins (see basins and corresponding colors in Fig. 12) in the model space grouped by basin type. Arrows show trajectories of each basin through time beginning with the oldest unit. Foreland = green; extensional = orange; pull-apart = magenta; pluvial = purple; intracratonic = blue. The animated version of this figure is provided in the Supplemental Material. Please visit https://doi.org/10.1130/GEOS.S.23972235 to access it, and contact editing@geosociety.org with any questions.

Most of the basin trajectories show substantial changes in accommodation through time (Figs. 1012; Animations S1–S16). Pull-apart and extensional basins record greater changes in accommodation than the foreland or intracratonic basins. Large-magnitude changes in subsidence rates are pronounced in the pull-apart (Animations S1–S3) and extensional (Animations S4–S10) basins, many of which show similar trajectories, with late-stage increases in subsidence followed by rapid decreases. Rapid subsidence during early rifting phases followed by rapid decrease in subsidence is common in extensional basins, although subsidence in transtensional basins tends to increase with time (Allen and Allen, 2013). The hypothetical extensional trajectory shows steadily decreasing accommodation (Fig. 8), but accommodation in many of the modeled pull-apart and extensional basins increases over time, typically coupled with increased sedimentation rate (Fig. 10).

Figure 10.

Sixteen example basins (see basins and corresponding colors in Fig. 12) in the model space. Arrows show trajectories of each basin through time beginning with the oldest unit. See the Supplemental Material (see text footnote 1) for a list of references for each basin. The animated version of this figure is provided in the Supplemental Material. Please visit https://doi.org/10.1130/GEOS.S.23972235 to access it, and contact editing@geosociety.org with any questions.

Figure 10.

Sixteen example basins (see basins and corresponding colors in Fig. 12) in the model space. Arrows show trajectories of each basin through time beginning with the oldest unit. See the Supplemental Material (see text footnote 1) for a list of references for each basin. The animated version of this figure is provided in the Supplemental Material. Please visit https://doi.org/10.1130/GEOS.S.23972235 to access it, and contact editing@geosociety.org with any questions.

Figure 11.

Selected screenshots from Figure 10 (see basins and corresponding colors in Fig. 12). See the Supplemental Material (see text footnote 1) for animations of individual basins.

Figure 11.

Selected screenshots from Figure 10 (see basins and corresponding colors in Fig. 12). See the Supplemental Material (see text footnote 1) for animations of individual basins.

Figure 12.

Two-dimensional views of the model results along the primary axes. (A) Subsidence rate and sediment-accumulation rate. (B) Subsidence rate and water balance. (C) Sediment-accumulation rate and water balance. See Table 3 for basin details and locations.

Figure 12.

Two-dimensional views of the model results along the primary axes. (A) Subsidence rate and sediment-accumulation rate. (B) Subsidence rate and water balance. (C) Sediment-accumulation rate and water balance. See Table 3 for basin details and locations.

Subsidence rates in the foreland (Animations S11–S15) and intracratonic (Animation S16) basins vary less over time than in the extensional basins. These basins each have different trajectories, but all show one or two phases of increasing and decreasing subsidence (Fig. 11; Animations S11–S15), similar to the hypothetical trajectories (Fig. 8). Subsidence rates in foreland basins tend to increase as the thrust load propagates and decline as thrusting slows or stops (Allen and Allen, 2013). Coupled with the often-complex deformation of thrust wedges and evolving isostatic compensation, this trend produces episodes of waxing and waning subsidence in foredeeps (Heller et al., 1988; Jordan, 1995). Stratigraphic columns from across the Jurassic–Cretaceous Wyoming (USA) foreland show the influence of subsidence across the basin (Fig. 13; Table S5). The column measured proximal to the load has a similar trajectory to the hypothetical foreland trajectories (Fig. 8) and other foreland basins in Figure 10, in that overall subsidence rate decreases over time but shows a large pulse of subsidence midway through its history. Columns from progressively distal areas have substantially lower rates of subsidence and sedimentation than the foredeep column (Fig. 13). More proximal columns show diminishing magnitude of subsidence and sediment flux through time, but distal columns have slightly increasing subsidence rates over time. It is unclear if this is related to propagation of the load or an effect of poor age constraints on stratigraphic units. The histories of other foreland basins in Figure 10 represent composite stratigraphic columns and are likely heavily influenced by columns obtained from proximal areas near the foredeep. Other basin types are predicted to show similar variation in subsidence with position relative to the locus of maximum accommodation if columns can be compiled along a dip line.

Figure 13.

Eight stratigraphic columns across the Jurassic–Cretaceous Wyoming foreland basin from Heller et al. (1988), showing the variation in subsidence rate with distance from the tectonic load. (A) All eight columns from proximal (black) to distal (light gray) areas. (B) Detail plot of the seven distal columns. Data are from Love et al. (1945), Mirsky (1962), Eyer (1969), Furer (1970), and Winslow (1986); see Table S5 (see text footnote 1).

Figure 13.

Eight stratigraphic columns across the Jurassic–Cretaceous Wyoming foreland basin from Heller et al. (1988), showing the variation in subsidence rate with distance from the tectonic load. (A) All eight columns from proximal (black) to distal (light gray) areas. (B) Detail plot of the seven distal columns. Data are from Love et al. (1945), Mirsky (1962), Eyer (1969), Furer (1970), and Winslow (1986); see Table S5 (see text footnote 1).

The basins characterized by large changes in sedimentation are those that are dominantly filled by fluvial deposits or those that occur in arid environments (e.g., Dead Sea [Israel and Jordan], Death Valley [USA]; Table 3). Although all types of basins show changes in sediment accumulation over time, these shifts are most pronounced in pull-apart (transtensional) and extensional basins, which show similar trends of coupled changes in sedimentation and subsidence (Figs. 11 and 12; Animations S1–S10). The hypothetical extensional trajectories also show large declines in sedimentation rates coupled with declining subsidence, but without the same variation in rates as the modeled basins (Fig. 8). Sedimentation rates in the foreland basins variably increase and decrease but have smaller changes between time steps than either pull-apart or extensional basins (Animations S11–S15); these trends are generally similar to the hypothetical foreland trajectories (Fig. 8). The pluvial intervals of lake basins also show large variations in sedimentation over their short durations (Animations S7 and S8). The intracratonic basin has the lowest rates of sedimentation over its history. For most modeled basins, large increases in sediment flux accompany increasing subsidence rates, and decreases in sedimentation occur with declining subsidence.

Basin histories dominated by water-balance changes occur in basins with well-developed lacustrine deposits or those that have experienced large changes in lake levels over time (Table 3). These tend to be the foreland basins and the Late Pleistocene pluvial lake basins (e.g., Lake Bonneville [Utah, USA]; Fig. 12; Table 3). Unlike changes in sedimentation, changes in water balance are pronounced under lower rates of subsidence in foreland and extensional basins (Figs. 10 and 11). However, the Bonneville and Lahontan (Nevada, USA) lake basins are unusual in showing increasing water balance with increasing accommodation. The magnitudes of the shifts in water balance shown by these basins are otherwise similar to the overall magnitude of water-balance changes of the other modern lake basins, which all occur in transtensional or extensional settings (Table 3).

The ages of the basins may affect the irregular trends in Figures 1012 and explain some of the differences from the hypothetical trajectories (Fig. 8). The intracratonic and most of the foreland examples are Paleozoic to early Cenozoic basins with typically coarse age control on constituent stratigraphic divisions. In contrast, the extensional and pull-apart examples are Neogene basins, most of which are currently active, have robust age estimates, and are divided more finely into intervals of shorter duration. The pluvial intervals of extensional basins show large increases in accommodation despite their recent history (Table 3). Large-magnitude changes in accommodation are evident in younger basins or in the recent records of Cenozoic basins, with most older basin records showing little or negligible changes in accommodation. This trend is expected for narrow timescales of assessment.

The Influence of Subsidence

The modeled basin trajectories predominantly occur in overfilled space, with few points plotting in the underfilled space. Only the highest-accommodation points of the pull-apart, extensional, and pluvial basins occur within the underfilled zones. High subsidence rates characterize pull-apart and extensional basins, as well as early phases of foreland basins (Allen and Allen, 2013), so it is surprising that so little of their histories occur in underfilled space. This result suggests that sedimentation and water balance keep pace with changes in accommodation in many of these example basins. Most of the basins in this data set occupy the overfilled (A-limited) zones (Fig. 7); the fluvial-prone basins are water-limited over much or all of their histories, and lacustrine-prone basins are sediment limited or water limited at certain times in their histories (Figs. 6 and 12). When any component of the A:S:W balance changes faster than others, basins shift between fluvial or lacustrine phases or stacking patterns change.

Accommodation is an important control on most of the basin histories, and may in part affect when basins become lacustrine-prone. At high rates of subsidence, changes in sedimentation and water balance appear secondary, and their effects are more evident at low subsidence rates. When subsidence rates are low, changes in sedimentation and water balance are more pronounced (Figs. 11 and 12). Many basins with well-developed lacustrine phases have relatively low subsidence rates throughout their histories. For basins that alternate between fluvial and lacustrine phases, the increases in water balance typically occur during the coupled declines in accommodation and sedimentation rates. These trends are seen in the Lake Malawi (East Africa) and Greater Green River (Wyoming) basins, where well-developed lacustrine facies form under low relative accommodation and sedimentation rates.

Architectural zones.

There is clear distinction in the model between fluvial- and lacustrine-prone basins (Fig. 10). The basin histories dominated by sediment flux occur in the underfilled and overfilled W-limited fluvial (A:S < 1) zones (Figs. 7B and 7F). Few basins cross into the underfilled space when accommodation increases faster than sediment flux. Coupled increases in accommodation and sedimentation bring trajectories closer to the A:S = 1 plane. No basins occur in the overfilled W-limited (A:S > 1) fluvial zone (Fig. 7D).

The basins containing significant lacustrine deposits occur in the overfilled S-limited (A:S > 1) and A-limited (A:S < 1) lacustrine zones (Fig. 7E). Lowstand episodes of these basins occupy the overfilled A-limited (A:S < 1) fluvial-prone zone (Fig. 11). Highstand episodes in lacustrine-prone basins mostly occupy the overfilled lacustrine S-limited (A:S > 1) and A-limited (A:S < 1) zones (Figs. 7E and 9). Only part of the Lake Bonneville trajectory enters the underfilled lacustrine zone (Figs. 10 and 11; Fig. S8), supporting the prediction that this zone may have overall low preservation potential. It is, however, likely that the Bonneville and Lahontan trajectories are the result of calculating subsidence and sedimentation rates over short time spans (Sadler, 1981). The clear distinction between fluvial- and lacustrine-dominated basins may be due to our method of estimating water balance, which resulted in zero scores for nonlacustrine phases of basin histories. This approach over-accentuates changes between wet and dry phases in basin history and potentially prevents points from plotting in the underfilled lacustrine zone. Underfilled basins in Carroll and Bohac’s (1999) model are expected to experience rapid changes in water levels, with fills oscillating between shallow lakes and evaporites. This effect is similar to the large changes along the W axis seen by some basins.

Implications for Nonmarine Architecture

Our model allows the controls on facies architecture to be assessed among basins and over the history of a single basin. Figures 9 and 10 emphasize similar trends in basin trajectories through time, allowing comparison of the differing influences of accommodation, sediment flux, and water balance among extensional, pull-apart, foreland, and intracratonic basins. Accommodation typically emerges as the most important control on long-term basin evolution and facies development, regardless of the tectonic setting (Fig. 9). Because many of the basins are limited with respect to accommodation (Figs. 3, 10, and 11), LAST-like architectures appear to dominate the stratigraphic record of these basins (Fig. 6). Few basins occupy the high-subsidence, high-sedimentation space of the overfilled fluvial-prone zones where higher-aggradation/ultra HAST-like architectures are expected. Field studies in many of these basins have interpreted facies architectures as alternating between LAST-like and HAST-like patterns. For the model to be useful, it should represent changes in architectural patterns that result from changes in the relative contribution of accommodation, sediment flux, and water balance. While basin trajectories are useful for illustrating variations in A, S, and W, the question is: How well do these changes align with field observations and interpretations of facies stacking?

Martinsen et al. (1999) interpreted the Trail, Rusty, and Canyon Creek members of the Cretaceous Ericson Formation of Wyoming as exhibiting LAST, HAST, and LAST architectures, respectively. In the model space (Animation S14), these members all plot in the low-accommodation portion of the overfilled A-limited (A:S < 1) fluvial zone where LAST-like architectures are expected, but each point varies relative to others in its rate of accommodation and sediment flux. All points plot close to the A:S = 1 plane, where changes in accommodation and sedimentation should have the greatest effect on facies architecture. An increase in accommodation and sedimentation between the Trail and Rusty members changes the position of the Rusty Member along the A:S = 1 line, which may be sufficient to produce observable changes in facies stacking between these units and could be interpreted as more HAST-like than older units. The subsequent decrease in accommodation and sedimentation during deposition of the Canyon Creek Member would then result in more LAST-like architectures relative to those in the Rusty Member, consistent with the interpretations of Martinsen et al. (1999).

Wroblewski (2002) interpreted changes in facies stacking in relation to accommodation through the Cretaceous–Paleocene Ferris and Hanna formations in Wyoming. The Ferris Formation encompasses three cycles of slowly to quickly increasing accommodation, each with architectures that may be interpreted as transitioning from LAST to HAST. Wroblewski (2002) interpreted the transition from amalgamated channel sandstones to single-story sandstones in the upper Ferris Formation as resulting from a rapid increase in accommodation through its deposition. The Hanna Formation represents steadily increasing accommodation, with architectures that may be interpreted as changing from LAST to HAST to late HAST. The Hanna Basin trajectory somewhat reflects these interpreted changes in facies stacking. In the model (Animation S13), accommodation and sedimentation decrease from the lower to upper Ferris Formation, which would correspond with progressively more LAST-like architectures and seems to counter the interpreted increasing accommodation through the deposition of these units (Wroblewski, 2002). The changing rate of decline in A from the early to middle part of the Hanna trajectory, however, could influence facies architectural trends. Between the middle and upper Ferris Formation, S decreases faster than A, which could produce a trend toward HAST-like stacking. The model trajectory agrees with the architecture interpretation of the Hanna Formation, which shows increasing A and S, followed by decreased A and S from the lower to upper Hanna Formation. These transitions correspond to the observed shift from LAST-like to HAST architecture from the lower to middle Hanna Formation, and HAST to late-stage HAST from the middle to upper Hanna Formation.

The Casa Grande, Rio Grande, and Pisungo formations were deposited in the evolving Tres Cruces foreland basin (Argentina) in association with the migrating orogenic front (Villalba Ulberich et al., 2021). Depositional settings in the basin transitioned from meandering streams to sandy braided streams to increasingly coarse-grained channels of alluvial fans; in the model, the increasing sedimentation and rapid increase in accommodation is consistent with the development of the foredeep. The Tres Cruces Basin (Animation S15) occurs entirely within the low-accommodation portion of overfilled model space but close to the A:S = 1 plane where LAST-like architectures are expected. Floodplain deposits decrease in occurrence through the basin, and sandstones of the Rio Grande and Pisungo formations are characterized by internal scouring, lateral continuity, and increasing amalgamation (Villalba Ulberich et al., 2021), which indicate deposition under low-aggradation conditions. The increase in A from the Casa Grande to the Rio Grande formations should correspond to more HAST-like architectures, although an observed upward increase in sandstone amalgamation through the Rio Grande Formation indicates slowing subsidence rates. This trend toward LAST-like architectures into the Pisungo Formation is indicated in the model, as S increases much faster than A, causing the trajectory to depart from the A:S = 1 line. Facies of the Casa Grande and Mal Paso formations indicate higher-aggradation conditions, yet they plot close together near the origin where more pronounced LAST-like architectures are expected. It may be that the decreasing A balances the decrease in S from the Pisungo to the Mal Paso formations. The overall low accommodation rates of the Tres Cruces Basin make it a low-aggradation setting (Catuneanu, 2006) that may constrain facies development, although some of the A:S trends in the model seem to oppose the observed architecture.

In the Paso del Sapo Basin of Argentina, the deposits of the La Pava and Collón Cura formations represent medial to distal alluvial fans, deltaic and lacustrine environments, and medial to proximal alluvial fans (Bucher et al., 2021). Alluvial progradation in the upper part of the basin occurred with decreased mean annual precipitation and a slight increase in sediment accumulation. Amalgamated and sheet sandstones, paleosols, and conglomerates of the La Pava and upper Collón Cura formations are consistent with deposition in low-aggradation systems under low A (Animation S11). The largest change in the basin trajectory occurs with the development of lacustrine environments in the lower Collón Cura Formation and the increase in W, but the overall indication of LAST-like architecture is consistent with the position of the basin trajectory in the model, where low accommodation constrains architectural development.

The Greater Green River Basin alternated between overfilled, balanced-fill, and underfilled conditions through time (Carroll and Bohacs, 1999; Smith et al., 2008). Members of the Green River and Wasatch formations represent the transition from alluvial and fluvial-lacustrine facies (Niland Tongue, Luman Tongue), to fluctuating profundal (Tipton Member), to evaporative (Wilkins Peak Member), to fluctuating profundal and fluvial-lacustrine facies (Laney Member). This progression corresponds to the evolution of the basin from overfilled to balanced-fill to underfilled to balanced-fill to overfilled conditions (Smith et al., 2008). Although changes in W are pronounced in the model trajectory, transitions among units of the Greater Green River Basin highlight the interplay of A, S, and W in influencing facies architecture and its movement between fluvial- and lacustrine-prone zones (Animation S12). Transitions from deeper-lacustrine units to shallow-lacustrine or alluvial units (i.e., Tipton Shale to Wilkins Peak members, lower Laney Member to Bridger Formation) accompany decreases in W and increases in A and S. Increasing A and S in the model correspond with fluvial units such as the Niland Tongue of the Wasatch Formation and upper Laney Member of the Green River Formation, and transitions to units dominated by deep-lacustrine facies occur with decreased A as well as increased W. Decreasing A and W between the lower and upper Tipton Member and increasing A and S between the upper Tipton and Wilkins Peak members is consistent with a change from deep- to shallow-lacustrine facies (fluctuating profundal and evaporative facies of Carroll and Bohacs, 1999). The lower Tipton and lower Laney members have similar W values yet are characterized by deep- and shallow-lacustrine facies, respectively (Smith et al., 2008). The lower Laney Member has higher A and S than the lower Tipton Member (Animation S12), which may sustain balanced-fill conditions in this unit. The transition from the lower Laney Member to the fluvial Bridger Formation also involves a cycle of decreasing W with increasing A and S, supporting the interpretation that tectonics were an important control on lake development in the Green River Basin (Carroll and Bohacs, 1999).

The model shows the Dead Sea Basin occupying the overfilled fluvial-prone zone, and architectural predictions seem counterintuitive (Animation S1). The early history of the Dead Sea Basin records increasing subsidence through deposition of the Miocene Hazeva Formation (Bar and Zilberman, 2016), followed by the evaporite-dominated Sedom Formation. Units formed in the past 3 m.y. (Amora, Samra, Lisan, and Ze’elim formations) were deposited under fluctuating subsidence and climatic conditions that produced several episodes of lake-level fluctuation (Coianiz et al., 2019). In the model, the lower Hazeva, Rotem, and Hufeira members plot with rapidly increasing A and S that would indicate increasingly HAST-like architecture. High subsidence and sedimentation in the early Dead Sea Basin resulted in widespread fluvial environments across the region (Garfunkel and Ben-Avraham, 1996), consistent with the trajectory’s position in the overfilled (A:S < 1) W-limited zone. The most recent 3 m.y. of the Dead Sea record appear to be dominated by changes in S and A. From the model, these changes along the S axis would indicate pronounced changes in architecture, from LAST-like (Amora Formation) to very HAST-like (Ze’elim Formation). The architectures of these formations in outcrop may not conform to the predictions in the model, and stacking interpreted from gamma ray and resistivity logs by Coianiz et al. (2019) as aggradational (Amora Formation) to progradational (Samra Formation) to retrogradational (Lisan Formation) to aggradational (Ze’elim Formation) has mixed agreement with the relative changes in A:S shown in the model (Animation S1).

Facies stacking can be difficult to assess from many studies of the East African Lakes where stratigraphy is typically interpreted from seismic investigations. As a relatively low-accommodation lake basin that experienced alternating fluvial- and lacustrine-dominated episodes, the depositional history of the Turkana Basin may be interpreted as overfilled to balanced-filled (sensu Carroll and Bohacs, 1999). The basin plots entirely within overfilled fluvial-prone space, alternating between W-limited and A-limited zones (Animation S6). Fluvial deposits dominated the basin during its early history (Feibel, 2011; Gagotho, 2017). Alternating fluvial and lacustrine deposits (Feibel, 2011; Gagotho, 2017) indicate that the basin experienced overfilled to balanced-fill conditions for several million years, where changes in accommodation were balanced by changes in sedimentation. The increasing accommodation and sedimentation during the last ~1 m.y. of the Turkana Basin history may correspond with either overfilled or balanced-fill conditions that would be expected for basins with fluctuating lacustrine–fluvial intervals. Throughout basin history, changes in sedimentation and accommodation dominate basin trends, with little relative change in W. Lake Turkana is relatively shallow (mean depth ~30 m), and its basin has relatively low elevation (~365 m) and low relief (~3000 m) for the East African Rift system (Chorowicz, 2005; Gagotho, 2017), so it is not surprising that the basin occurs in overfilled space where relatively small changes in W would affect facies development under low A. Transitions among lacustrine and fluvial phases in the Turkana Basin were mediated by tectonic activity (Gagotho, 2017), consistent with trends dominated by changes in A.

Lake Malawi has a different model trajectory from the other rift basins (Figs. 10 and 11; Animation S4). This difference partly stems from Malawi being a large lake with a relatively small catchment compared to other East African Rift lakes (Hinderer and Einsele, 2001). For this reason, the Lake Malawi Basin spans a wider range along the W axis than other rift basins. Like other East African Rift lakes, Malawi has experienced multiple episodes of lake-level fluctuations (Lyons et al., 2011), although fluvial environments were likely more widespread earlier in basin history (Flannery and Rosendahl, 1990). Modeled rates of subsidence and sedimentation in the basin are similar (Lyons et al., 2011), which may explain why the basin trajectory remains in overfilled zones, although it plots closer to underfilled space than most other basins (Figs. 7 and 10). As with many basins, the development of deeper lacustrine environments accompanies declining A and S with increasing W. Bohacs et al. (2000) characterized modern Lake Malawi as a balanced-fill lake, and its history of fluctuating lake levels indicates that similar conditions have persisted since at least the mid Pleistocene (Scholz et al., 2011; Lyons et al., 2011). The Malawi trajectory shifts into the overfilled (A:S < 1) lacustrine zone from the overfilled (A:S < 1) fluvial zone around this point (Animation S4), but it is difficult to determine whether this corresponds with architectural trends interpreted from cores or seismic profiles.

Our model has variable success in representing changes in facies architecture. In the model, changes in A:S:W and expected architecture match observed facies architecture trends better for some basins (e.g., Rock Springs [Wyoming]) than for others (e.g., Dead Sea). The model applies well to lacustrine-dominated basins (e.g., Greater Green River), where A:S:W values track observed transitions between lacustrine and fluvial phases in basin history. The ability to visualize the relationships among these variables is a key benefit of the three-dimensional model. Differences between model predictions and observations may arise from the data used to reconstruct A, S, and W, matching model results to observed or inferred architecture from literature sources, or the stratal units chosen for analysis. For the most part, however, changes in basin trajectory and the relationship among A, S, and W do correspond with important changes in architecture observed in these basins. Within any basin, the changes in accommodation, sediment flux, and water balance are the most relevant to interpretations of facies architecture, and these are represented by basin trajectories. How well the A:S:W relationship depicted in the model corresponds with the LAST–HAST framework depends on the relative changes in these controls within a single basin. Relative changes in A:S:W within any basin are more informative for basin architecture than absolute position in the model. Interpretations of facies stacking are based on observed patterns through a single stratal succession, which may tend toward LAST- or HAST-like stacking. Because nonmarine systems tracts occur along a spectrum (Fig. 2; Holland and Loughney, 2021), the relative differences between the LAST and HAST may be as significant as the differences between ultra-LAST and LAST or HAST and ultra-HAST architectures. The relative changes in stacking that occur within a stratal succession are the key to interpreting changes in drivers over time.

Preservation of Nonmarine Successions

The preservation of systems tracts in the rock record depends in part on the rate of aggradation, as well as the overall tectonic setting that may govern whether the basin is subsiding (net depositional) or uplifting (net erosional). Preservation reflects A:S at the time of deposition, as well as changes in A:S through time, leading to the burial of previous deposits. Given the higher aggradation that characterizes HASTs, we may expect HAST-like deposits to have higher preservation potential—of both the systems tract as a whole and of deposits within—than LAST-like deposits. The low aggradation conditions of LASTs cause them to contain more hiatuses, and their occurrence in low-accommodation settings may limit or slow their burial over time. The long-term preservation of LAST and HAST architectures will depend on the long-term accommodation trends of the basin.

Even so, the positions of many basin trajectories in the overfilled lacustrine and fluvial zones (Figs. 7E and 7F) indicates that LAST-like architectures are well-represented in the rock record. Although much of the model space corresponding with HAST and ultra-HAST architectures is not occupied, HAST-like architectures are interpreted in many of the example basins in Figure 10. Many of the fluvial-prone basins in the overfilled W-limited zone (Fig. 7F) plot near the A:S = 1 plane. Whether or not the model positions correspond with outcrop-based architecture interpretations, the occurrence of so many points and trajectories near the aggradation plane shows that the A:S relationship is important for building architecture in fluvial-prone systems. The relative balance between A and S may also promote the preservation of these architectures. The dearth of basins in the underfilled zones could result from the model data and calculations (see Measuring Controls on Nonmarine Architecture section), or it could indicate that underfilled basins are relatively rare in the rock record. It could also be difficult to interpret whether a basin experienced underfilled conditions if estimates of accommodation are made from the relatively thin, LAST-like deposits that would be expected to form in such basins. If the balance between A and S is fundamental to the preservation of basin deposits, it may explain the absence of basins in high-accommodation regions of the model.

The Significance of Coal

Coal occurs in many of the basins in Figure 10, and several are well known for their abundant coal resources, including the Hanna (Wyoming), Cooper (Australia), and Greater Green River basins. Coal forms under a variety of environmental and climatic conditions, and the distribution and morphology of coal is related to stratigraphic architecture (Bohacs and Suter, 1997; Wadsworth et al., 2002). Much like their overall trajectories, significant coal-bearing units of the Hanna, Cooper, and Greater Green River basins in Figure 10 plot in different locations with different A:S:W values (Animations S12, S13, and S16) and do not seem to show any common pattern. The balance between accommodation, sedimentation, and water availability is key to coal preservation, and coal forms when sedimentation rates are low and peat-production rates are high (Bohacs and Suter, 1997). While coal-bearing units of the Cooper and Hanna basins plot at the low end of the S axis, coal-bearing units of the Greater Green River Basin have somewhat higher values of S and A. The Cooper basin has very low A, but experiences fluctuations in S and W that could influence coal formation. None of these basins is characterized by relatively higher rates of accommodation than sedimentation, which would be broadly consistent with sequence-stratigraphic controls on coal formation (Bohacs and Suter, 1997; Wadsworth et al., 2002). The Greater Green River coal-bearing units have slightly higher rates of sedimentation than accommodation, which should preclude coal development. Whether the particular A:S:W relationship of these units is meaningful for coal presence is poorly constrained. Peat production (PP) is not incorporated into our model as it is by Bohacs and Suter (1997) and Wadsworth et al. (2002), and so coal presence is not tracked in a systematic way.

Measuring Controls on Nonmarine Architecture

Our model depicts the effects of three important drivers of nonmarine architecture that act over a variety of spatial and temporal scales. As a conceptual model, it is useful to consider how these drivers act in concert, rather than to assess each individually. In practice, some aspects of the model better characterize basin architecture than others. The results of the model are likely affected by integrating several types of data that may need to be compiled from multiple sources. Many aspects of subsidence, sedimentation, and water availability pertinent to basin evolution are not easily recorded or characterized by original data sources, and they may not be quantified in a way that can be incorporated into the model. This is the principal hurdle in plotting any basin within the model space.

Accommodation is estimated through backstripping, which accounts for the effects of sediment compaction and the isostatic response to the sediment load. In nonmarine settings, backstripping is generally unable to account for changes in elevation, compared with water depth in marine settings, which can be a significant reflection of accommodation. Because elevation is generally not known, it is difficult to recognize uplift in the backstripping on nonmarine strata, and uplift is likely to have a significant effect on architecture and its long-term preservation.

Estimates of sediment flux require estimates of basin area, which may not be available for all ancient basins. Sediment-accumulation rate is a readily available substitute for sediment flux, although spatial variation in rates, nondeposition, and bypass are not easily incorporated. The timescales over which sediment-accumulation rates are calculated may also affect trends through time. Short durations of accumulation can produce rates of sedimentation orders of magnitude greater than rates measured over longer durations (Sadler, 1981), resulting in wide variation in recent basin histories. This phenomenon also applies to subsidence rates and is evident in the pluvial lake basins and later phases of some extensional and pull-apart basins (Figs. 1012), where sedimentation and subsidence rates were inferred over differing timescales.

For water balance, commensurate records are not available for all basins. This may make it difficult to compare different basin histories or to accurately characterize changes in water availability over a basin’s history. Estimates of lake area based on outcrop area of lacustrine facies or lake shoreline elevations are more widely available than estimates of precipitation and evaporation, but these records are most robust for more recent lake basins. This approach over-simplifies water availability of basins and underestimates lake area, as variations in lake area with basin hypsometry are difficult to account for. Changes in basin area through time are similarly difficult to reconstruct and are therefore not attempted here. This approach also precludes estimates of water balance during fluvial deposition, forcing fluvial-prone basins to plot at 0 on the W axis (Fig. 12B). Well-constrained estimates of lake area or alternative measures of water balance will yield more nuanced basin histories.

Water Balance as an Indication of Climate

Water balance as considered here is a broad representation of climate. Climate is often cited as one of the major influences on nonmarine architecture (Shanley and McCabe, 1994). Its effects may be difficult to isolate from those of accommodation (Allen et al., 2013), and studies differ over whether climate is a relatively weak control (Gagotho, 2017) or a major control (Flannery and Rosendahl, 1990; Bohacs et al., 2000; Keighley et al., 2003) on basin architecture. Our model incorporates the influence of climate on basin history insofar as climate determines the development of lacustrine facies.

The relationship of water balance to climate is most easily detected in recent lake basin records. For example, the pluvial lakes Bonneville and Lahontan have well-characterized histories of lake-level fluctuations associated with the Pleistocene glacial–interglacial cycles (Morrison, 1991). The relationship of these basin histories to climate are among the most robust in this data set given their recent ages and the plethora of Quaternary climatic data. These areally extensive lakes also formed during the recent history of the Basin and Range characterized by low extension rates (McQuarrie and Wernicke, 2005), allowing climate to emerge as a dominant control on their formation. The specific influences of climate on older basin records may be less evident. In the Greater Green River Basin, climate cycles have been interpreted from alternating shallow- and deep-lacustrine facies, including extensive evaporite deposits (Carroll and Bohacs, 1999; Aswasereelert et al., 2013). These alternating cycles are represented in the model because of their well-developed lithological records. Keighley et al. (2003) proposed that the influence of climate on lacustrine systems would be strongest during underfilled and balanced-fill phases (sensu Carroll and Bohacs, 1999). The evaporative and fluctuating-profundal lacustrine facies associations of Carroll and Bohacs (1999) that respectively form in underfilled and balanced-fill phases preserve strong evidence of fluctuating lake levels, which may be linked to changing Paleogene climate (Dechesne et al., 2020). Sediment supply is linked to climate and lake level, but this link is weak in hydrologically open or overfilled basins (Bohacs et al., 2000). Fluvial-prone systems may therefore be less likely to record facies changes in relation to climate than lacustrine-prone systems, although climate-driven variations in fluvial architecture can be detected (Allen et al., 2013).

Basin trajectories in the model appear to confirm the relationship of fluvial-prone and lacustrine-prone systems to climate. Because water balance as used here can be difficult to reconstruct in fluvial-dominated basins, it is a weak representation of climate for these systems. Water balance estimates are more robust for lacustrine-dominated basins, and the trajectories of these basins along the W axis may more accurately track climatic changes through time. Although climate is a broad determinant of lake systems, it may be difficult to interpret climatic conditions in some settings from lithological indicators alone. Additional sources of information from paleofloral records or geochemical analyses are typically required to fully interpret climatic conditions in the past.

Facies architecture in nonmarine basins results from the combined influence of accommodation, sedimentation, and climate. Comparing the influence of each of these drivers over the history of a basin is complex but important for understanding the development of fluvial and lacustrine strata and patterns of stratal stacking over the history of a basin. We present a model that combines these three drivers, enabling the evaluation of basin-wide architectural patterns in relation to the changing relationship among each driver. The model axes of accommodation rate, sedimentation rate, and water availability represent the three drivers and allow the evolution of a basin to be evaluated in a three-dimensional space. The eight architectural zones that result from the combined bounding relationships of accommodation, sediment flux, and water balance have implications for the types of deposits and their stratal stacking patterns (Fig. 7; Table 2). As basins evolve, the relationships among accommodation, sedimentation, and water balance change. Our model allows relative changes in these controls to be visualized over a basin’s history and large-scale changes in basin architecture to be assessed through time and space.

Modeled basin trajectories show that the model can represent important changes in facies architecture through time and space, although their agreement with field studies of facies architecture is variable. The main strength of the model is its ability to depict the evolving relationships among accommodation, sediment flux, and water balance, and their implications for facies development. In particular, the model emphasizes that well-developed lacustrine systems occur under low accommodation and sedimentation and relatively higher water balance. In all cases, the relative changes in the relationships among accommodation, sediment flux, and water balance within each basin is more informative for tracking the potential drivers of architectural change than absolute position within the model space. The model may then be most useful for tracking the history of a single basin through time and space, rather than comparing the histories of multiple basins. This application reflects the methodology of field studies, where architectural interpretations are based on relative changes throughout several stratigraphic columns or well logs for a single basin (or a portion of it). This, as well as the need for commensurate data for each basin, are necessary considerations when using the model and interpreting results.

1Supplemental Material. Animations S1–S14: Trajectories of the Dead Sea Basin (S1), Death Valley (S2), Owens Valley (S3), Lake Malawi Basin (S4), Lake Tanganyika Basin (S5), Lake Turkana Basin (S6), Lake Lahontan Basin (S7), Lake Bonneville Basin (S8), Lake Baikal Basin (S9), Española Basin (S10), Paso del Sapo Basin (S11), Greater Green River Basin (S12), Hanna Basin (S13), and Rock Springs Basin (S14). Table S1: Data used for hypothetical basin trajectories in Figure 8. Table S2: Sediment-accumulation rates (SAR) for each division of the basins in Figures 912, Animations S1–S16, and Table 3. Table S3: Subsidence rates for each division of the basins in Figures 912, Animations S1–S16, and Table 3. Accommodation calculated with Backstripper (Holland, 2021). Table S4: Water balance estimates from lake level and outcrop area for each division of basins in Figures 912, Animations S1–S16, and Table 3. Table S5. Data used to calculate sediment-accumulation rates (SAR) and subsidence rates for stratigraphic columns in Figure 13. References Cited: Literature sources used to compile information in Tables S2–S4. Item S1: R code to transform data, code to plot Figures 9, 10, 12, 13, and Animations S1–S16. Item S2: Data file of basin names, sedimentation rates, subsidence rates, and water balance estimates used to make Figures 9, 10, 12, 13, and Animations S1–S16. Item S3: Data file of hypothetical basin type, sedimentation rates, subsidence rates, and water balance estimates used to make Figure 8. Item S4: Data file of columns, sedimentation rates, and subsidence rates used to make Figure 13. Please visit https://doi.org/10.1130/GEOS.S.23972235 to access the supplemental material, and contact editing@geosociety.org with any questions.
Science Editor: Andrea Hampel
Associate Editor: Cathy Busby

We thank Joaquín Bucher and an anonymous reviewer for their helpful comments. This work was funded by National Science Foundation grant EAR-PF No. 1952643.

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