Deltas and Sea-Level Change

Journal of Sedimentary Research, 2006, v. 76, 0–0 Research Article DOI: 10.2110/jsr.2006.034

DELTAS AND SEA-LEVEL CHANGE SZCZEPAN J. PORE˛BSKI1

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RONALD J. STEEL2

1

Polish Academy of Sciences, Institute of Geological Sciences, Krako´w Research Centre, Senacka 1, 31-002 Krako´w, Poland 2 The University of Texas at Austin, Geological Sciences Department, 1 University Station C1100, Austin, Texas 78712-0254, U.S.A. e-mail: [email protected]

ABSTRACT: Sea-level shift from the innermost shelf out to the shelf edge produces bayhead, inner-shelf, mid-shelf, and shelfmargin deltas. We suggest that these delta types are distinguishable in the ancient record and that such distinction has advantages as compared to the conventional, entirely process-based classification. Bayhead and inner-shelf deltas tend to form thin clinoforms (a few meters to tens of meters amplitude, respectively), and as they aggrade with rising relative sea level they generate a ‘‘tail’’ of thick paralic deposits. Mid-shelf deltas produce clinoforms as high as the mid-shelf water depth, tend to follow a subhorizontal trajectory, generate little or no paralic tail, and are commonly thinned by transgressive ravinement. Shelf-edge deltas in a stable-to-falling relative sea level usually have no paralic tail, create by far the highest clinoforms, and can have a thick succession of sandy turbidites on the delta fronts. If sea level falls below the shelf margin, the shelf-edge delta becomes incised by its own channels and large volumes of sand can be delivered onto the slope and the basin floor. Many deltas require a strong fluvial drive to attain a shelf transit, though as they approach the outer shelf they commonly become wave dominated. Tidal influence can increase on the outermost shelf if relative sea level is falling, if the shelf-break is poorly developed, and if basinal water depth is shallow. During transgression, the system tends to be tidally and/or wave influenced. Deltas that transit back and forth on the shelf on short time scales (tens of kiloyears to 100 ky) and that are driven largely by sea-level fluctuations are referred to here as accommodation-driven deltas. Deltas that can reach the shelf edge without sealevel fall are termed supply-driven deltas. These highstand deltas deposit thick, sandy, stacked parasequences during their shelf transit, and they tend to have an extensive muddy delta front on reaching the shelf-edge area. Such deltas would not normally be incised at the shelf edge, and they would produce a progradational, shelf-edge attached, sandy slope apron (Exxonian shelfmargin systems tract) rather than basin-floor fans. Sequence boundaries are best developed on accommodation-driven deltas, and are likely to be represented on a variety of time scales (third, fourth, and fifth order). Sequence boundaries in supply-dominated deltas may be identifiable only at lowerorder time scales, or they may be non-existent.

STEADY-STATE VERSUS EVOLUTIONARY DELTA CLASSIFICATION

Deltas have traditionally been classified in terms of process–product reaction, where delta type is defined by the relative contribution of fluvial-, wave-, or tidal-energy flux that was dominant during deposition at the seaward edge of the delta (Galloway 1975). In this actualistic (based on present highstand of sea level) and uniformitarian (steady-state) approach, the delta system is seen as the outcome of intrabasinal processes, whereas external controls are held constant. However, studies of Quaternary shelves have shown that deltas also vary greatly in their external geometry and internal characteristics in response to falling and rising of sea level (e.g., McMaster et al. 1970; Suter and Berryhill 1985; Kolla et al. 2000; Tesson et al. 2000). End members in this sea-leveldriven family are bayhead deltas, inner-shelf (or shoal-water platform) deltas, mid-shelf (or shelf-phase) deltas, and shelf-margin (shelf-edge, or deep-water) deltas. There is also an analogous family of deltas in a ramp (non-shelf–slope break) setting (Fig. 1). The regressive–transgressive transits of deltas during repeated sea-level cycles produce the shelf platforms and shelf margins known to occur around the edges of deepwater basins. If a delta reaches a platform-margin position, it also

Copyright E 2006, SEPM (Society for Sedimentary Geology)

has the potential to deliver, directly or indirectly, significant volumes of sand into the deep-water areas (but see Steel et al. 2003). Although it has long been known that inner-shelf and middle-shelf deltas are different from shelf-edge deltas (Edwards 1981; Winker 1982; Suter and Berryhill 1985; Suter et al. 1987; Elliot 1989), there is surprisingly little mention of these delta types from pre-Pleistocene successions. We suggest that this type of delta classification and the recognition of this family of deltas in the ancient record is important; because: (1) it emphasizes mixed energy systems rather than the conventional end-member energy categories, and places deltas within a more dynamic sequence stratigraphic context, (2) it is a powerful tool for prediction of sand partitioning across the shelf, onto slope and basinal settings, and (3) it can help in choosing the best location for the sequence boundary. We are not suggesting the above delta types as alternatives to the process-based, conventional classification (Galloway 1975 and its modifications) (Orton and Reading 1993; Postma 1990), but we believe that both of these approaches should be integrated to achieve better understanding of deltas. We are following the concept outlined by Boyd

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FIG. 1.— Classification of shelf deltas in terms of relative sea-level change in shelf–slope (A–D) setting. A similar suite of deltas also exists in ramp setting (based on Pore˛bski and Steel 2003).

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et al. (1992), based on the seminal paper of Curray (1964), where direction of base-level (sea-level) change was used to distinguish regressive coastlines from transgressive ones (see also Swift et al. 1991). We also build here on previous suggestions about how deltas tend to change during falling relative sea level by Edwards (1981), Suter and Berryhill (1985), Postma (1995), Posamentier and Allen (1999), Suter (1999), Kolla et al. (2000), Pore˛bski and Steel (2001, 2003), and Anderson et al. (2004). Although we are emphasizing deltas in settings with a shelf–slope break, an analogous suite of deltas exists in shallow-water, ramp settings. SHELF TRANSITS BY DELTAS: CONTROLS AND DURATION

Deltas are river-attached (point-sourced) shorelines that can prograde during either rise or fall in relative sea level. They tend to prograde across the preexisting ‘‘ramp’’ of shallow-water basins, or the shelf platform of deeper-water basins that have a shelf–slope break. Although these shallow-water platforms vary greatly in their width and tectonic setting (Swift and Thorne 1991, their fig. 1), we refer loosely here to the ‘‘inner,’’ ‘‘middle,’’ and ‘‘outer’’ segments of such morphological shelves. Repeated regressive and transgressive transits of the ramp or shelf platform cause an aggradation of the shelf, accretion of the shelf margin, and eventually the infilling of the basin. Shelf and Delta Regimes In more dynamic terms, deltas are coastal bulges formed where sediment input (Q) of a given grain size (M) exceeds the combined effect of relative sea-level rise (R, where R $ 0) and reworking capacity (D) of marine processes (Swift and Thorne 1991, p. 13). These geohistorical variables were used to define the shelf regime ratio, ¥ 5 RD/Q M, which can be used to differentiate between accommodation-dominated and supply-dominated shelf regimes (Thorne and Swift 1991, p. 195–197). Accommodation-dominated regime (¥ . 1) characterizes transgressive shelves with the concomitant development of estuaries and retreating shorefaces, whereas supply-dominated regime (¥ , 1) describes regressive shelf conditions with the prevalence of deltas and prograding strandplains (see also Galloway 1989; Boyd et al. 1992; Meckel and Galloway 1996). The trajectory of the delta’s offlap break reflects stratigraphic adjustment to a changing sediment accommodation to sediment supply, and can vary between progradation with downstep (¥ R 0), horizontal progradation (¥ , 1), aggradation (¥ 5 1), and landward stepping rather than retrogradation (¥ . 1). At two extremes, this adjustment may however take place in response to changes in only one of the critical regime terms. Thorne and Swift (1991, p. 197) introduced the concept of sedimentation modes, where the R-dominated mode is dynamically governed by relative sea-level change (¥ is proportional to R), whereas the Q-dominated mode is one where variations in sediment input exerts the primary control upon sedimentation (¥ is inversely proportional to Q). Such a concept appears also applicable for deltaic-shelf conditions (¥ , 1) prevailing on a fourth-order time scale (e.g. Meckel and Galloway 1996), where two general scenarios emerge. (1) In R mode, a forced-regressive delta is driven across the shelf only by relative sea-level fall, and the subsequent rapid rise shifts the deltaic depocenter back onto the inner shelf (e.g., Posamentier et al. 1992; Kolla et al. 2000). (2) In Q mode, high or increasing sediment supply drives the delta in a setting of only modestly varying accommodation. These two scenarios correspond to two contrasting delta regimes (see also Reading and Collinson 1996, p. 171). Accommodation-driven deltas (or R-dependent deltas) will transit back and forth across the shelf on time scales of surprisingly short duration (see below). Supply-driven deltas (Q-dependent deltas) not only can prograde to the shelf break and beyond but also can remain on the outer shelf for longer periods, even during times of minor accommodation increase.

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Accommodation-Driven versus Supply-Driven Deltas During regression with sea-level rise, great sediment flux is required to maintain delta progradation, because of the need to fill an ever-increasing accommodation space behind the rising delta front. Lack of sufficient sediment flux and rising relative sea level usually results in an inevitable shoreline retreat (auto-retreat) after a brief interval of deltaic progradation and aggradation, even without any change in the rates of sediment supply or relative sea-level rise (Muto and Steel 1992, 1997). For river feeders of small to moderate size, it seems likely that deltas can prograde only some tens of kilometers, if sea level is rising even modestly (Muto and Steel 2002). In the case of regression with stable or falling sea level, however, the delta transits the entire width of the shelf without any auto-retreat tendency. This creates a flat-to-falling shoreline trajectory (purely progradational stratigraphic pattern), and generally enables the delta to cross a wide shelf relatively quickly, without having to access an unusually high sediment supply. Calculations of time necessary for modern deltas to cross their respective shelf widths under such conditions are given by Burgess and Hovius (1998) and Muto and Steel (2002). Results show that the transit time varies with sediment and water discharge, subaerial delta gradient, shelf width, shelf gradient, and deltafront slope as well as with sea-level behavior, but indicate that only rarely is more than 100 ky required for shelf transit, for even the widest shelves, provided that the delta is able to reach the shelf edge at all. Shelf transit times calculated for a relative sea-level rise of 2.1 m/ky (a value typical for Holocene highstand systems tracts) are plotted against sediment supply (Fig. 2A; for calculation details, see Muto and Steel 2002). The plot suggests that many of the modern deltas that are presently on the inner shelf (e.g., Colorado, Mackenzie, Orinoco, Po) would never be able to reach the shelf edge with such a rate of base-level rise (Fig. 2A). However, the late Pleistocene eustatic fall brought these deltas to the shelf margin, and the Holocene rise shifted them 100–200 km back updip on the shelf. This illustrates that high-amplitude, high-frequency variations in accommodation are one of the main controls on deltaic transit across the shelf. However, these calculated transit times (Fig. 2A) appear conservative, because they ignore changes in the delta-mouth hydraulic regime during progradation with relative sea-level rise. The increasing wave impact upon the delta entering deeper and more open waters can expend much, or all, of the sediment budget on building shoals and spits (Galloway 2001), before the delta ever nears the shelf edge. Hence, many more modern deltas may actually belong to the R-dependent category than implied by the graph in Figure 2A. In terms of shelf width and inclination, accommodation-driven deltas, together with large-yield (. 100 km3/ky) deltas tend to be associated with wide and low-gradient shelves (Fig. 2B). This suggests that for deltas of intermediate sediment load (ca. 10–80 km3/ky) entering shelves wider than 100 km, a lowering in relative sea level becomes critical in bringing the delta to the shelf edge. The diagrams in Figure 2 suggest that, for great shelf widths and supply ranges, deltas are likely to form shelf-wide sandbodies within the forced regressive, lowstand, and highstand systems tracts of fourth-order sequences, generated by only small-amplitude fluctuations in accommodation. Such supply-driven deltas would be commonplace on relatively narrow and high-gradient shelves, but extremely high-discharge rivers, particularly those that tap glaciated terrains or rising mountain belts, can also drive deltas that defy auto-retreat on the widest shelves. An obvious example of this is the Balize lobe of the present-day Mississippi River. This delta lobe, now in moderately deep water (Fisk 1955; Gould 1970), not only reached nearly to the shelf edge during the last 1000 years of the Holocene highstand but was able to retain its birdfoot geometry across the entire open shelf. Goodbred et al. (2003), in their study of the late Quaternary Ganges–Brahmaputra delta, concluded that this delta system

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FIG. 2.— A) Graph showing relationships between constant sediment supply and travel time necessary for a delta to reach the shelf edge for the rate of relative sea-level rise 2.1 m/ky, which is typical for the Holocene highstand (travel times after Muto and Steel 2002, based on database of Burgess and Hovius 1998). Open squares mark deltas that would require relative sea-level drop in order to cross the entire shelf (accommodation-driven deltas). Solid circles mark deltas that are able reach the shelf edge during highstands up to 50 ky in duration (supply-driven deltas). Note, however, that calculated transit times ignore increased impact of wave energy, which tends to slow down or even arrest delta progradation during highstand conditions. Therefore, more modern deltas are likely to fall into the accommodation-driven class than implied by the graph. B) Delta stratigraphic regime versus shelf geometry. Wide and low-gradient shelves tend to support predominantly accommodation-driven deltas. Irrespective of its absolute value, supply factor can become the sufficient driver for highstand deltas prograding onto relatively narrow and steep shelves.

came into existence much earlier than other Holocene deltas, due to an extremely high sediment yield (combined result of tectonically active catchment and monsoonal climate). The high and sustained sediment supply apparently hindered transgression and maintained conditions of vigorous delta progradation despite significant sea-level rise (see also Goodbred and Kuehl 2000). Galloway (1989, 1990) drew attention to several distinct periods of shelf-edge delta development in the Cenozoic evolution of the northern Gulf of Mexico Coast. Whereas the Pliocene and Pleistocene stratigraphic sequences of the Gulf reflect predominantly ‘‘icehouse’’ cyclicity (Galloway 1989) and, accordingly, probably contain mostly accommodation-controlled deltas, the Paleogene record, in contrast, contains a strong supply signature in the delta stratigraphy (Edwards 1981; Galloway 1989, 1990, 2001). For instance, Xue and Galloway (1995) divided the Paleocene middle Wilcox strata of Texas coastal plain into two genetic stratigraphic sequences, 0.75–1.1 My in duration, both typified by strongly aggradational stacking patterns without any marked relative base-level falls. Each sequence in the Rio Grande embayment contains shelf-edge deltas that belong both to highstand (lower sequence) and lowstand (upper sequence) deposits (Xue and Galloway 1995, p. 224). Even so, middle Wilcox deltas were typified by rather low accumulation rates (Galloway and Williams 1991) and presumed low

sediment-input rates (Galloway 2001, his fig. 2); they were obviously able to attain the shelf edge even in conditions of progradation with base-level rise, which suggest a strong supply control. Similarly, the Eocene Yegua Formation (except in its uppermost part) records a supply-dominated shelf regime alternating with periods of quasi-equilibrium conditions. This interval contains deltas that, during sea-level oscillations of ca. 0.8 My periodicity, appear to have moved only short distances back and forth on the outer shelf, in close proximity to the shelf-edge (Meckel and Galloway 1996). The above discussion strongly suggests that although supply rate can be a critical factor controlling the distribution of deltas on narrow shelves, it becomes subordinate in importance to high-amplitude sea-level oscillations on wide shelves. It is therefore likely that accommodationdriven deltas were particularly common on passive margins during icehouse times. It is worth noting that the concept of accommodation-driven and supplydriven delta complexes advocated above bears some resemblance to the former Exxonian Type 1 and Type 2 sequences (Vail et al. 1984) respectively, particularly supply-driven deltas and the sand-rich, progradational ‘‘shelfmargin systems tracts.’’ However, the delta concept, in contrast to the abandoned sequence types (Posamentier and Allen 1999), will tolerate considerable along-strike variability in architecture and morphology.

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DELTAS AND SEA-LEVEL CHANGE SEA-LEVEL CHANGE AND DELTA TYPES

Sea-level shift from the innermost shelf out to the shelf edge produces a family of delta types consisting of bayhead, inner-shelf, mid-shelf, and shelf-margin deltas. Evolution of a delta system transiting the shelf along such a path reflects (1) the increasing degree of wave reworking when deltas leave river- or tide-dominated intracoastal settings, and (2) increased accommodation, which determines the primary height of the delta clinoform, while (3) subsequent transgressive ravinement controls the degree of preservation of delta topsets and foresets. We believe that these processes generate a range of characteristic features allowing the main members of this sea level-driven delta family to be distinguished in the ancient record. However, establishing a comprehensive set of diagnostic criteria is hindered at present by several factors. As Bhattacharya and Giosan (2003) have pointed out, interpretation of a fossil delta in terms of a tripartite process model can be controversial because many delta systems are a product of a mixed-energy system, and fluvial, tidal, vs. wave domination can vary even between individual lobes on the same delta (see also Lambiase et al. 2003). Another serious problem is that, although delta facies descriptions from the ancient record are legion, usually little is known about the location of the delta on the shelf. Conversely, even where this location is well established, as in many seismically aided, subsurface studies, insufficient facies information from cores is available (e.g., Xue and Galloway 1995; Pore˛bski et al. 2003). These deficiencies in our database may result in overemphasizing criteria that may have a local significance only, or lead to unjustified generalizations. Keeping in mind these potential pitfalls, we hope, however, that the description below can serve at least as an initial conceptual framework for classifying deltas in terms of their position on the shelf. The classification below is underpinned by the notion that constructional shelves are shallow platforms built gradually by sediment-delivery systems, especially deltas, as sediment is partitioned from land and into the basin (Swift and Thorne 1991). The term ‘‘shelf’’ further implies the presence of a break in slope between the shallow platform and a marine slope beyond. Shelves gradually extend out from land by the basinward migration of the shelf–slope break, i.e., by accretion of the shelf margin because of the addition of sediment, mainly from shelf-transiting deltas. The terms ‘‘inner’’ and ‘‘outer’’ shelf are frequently used, but only in a purely qualitative manner, to describe the landward and seaward reaches of the platform. Where the shelf becomes wider, e.g., . 30 km, a middle zone or mid-shelf reach is also designated. Because the shelf accretes by the repeated regressive–transgressive transits of a shoreline (not all of which necessarily even reach the shelf edge), the sedimentdelivery system is referred to as being on the inner, middle, or outer shelf at any point in time. Inner-Shelf Deltas Significant development of paralic delta-plain deposits is probably the most distinctive feature of inner-shelf deltas (Fig. 1A). The delta-plain deposits reflect deposition during rising relative sea level, and consequent accommodation creation behind the delta front. This, together with the shallow water depths into which this type of delta grows, generates lowamplitude (a few tens of meters), long sigmoidal clinoforms. Proximity to source area results in a high sediment yield and high rates of aggradation and, in turn, an extensive areal development of mouth bars and rapidly filling interdistributary bays (Gould 1970; Coleman 1988). Depending on the dominant regime type, mouth-bar to delta-front deposits range from heterolithic hyperpycnites in river-dominated deltas (e.g., Rodriguez et al. 2000), hummocky cross-bedded facies in wavedominated systems (e.g., Bhattacharya and Walker 1992), to complex, heterolithic bars in tide-dominated ones (Willis and Gabel 2001), or a combination of these in mixed-energy systems (Bhattacharya and Giosan 2003). It is worth emphasizing that for strong wave or tidal

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signatures, deltas may not always be easily distinguishable from prograding shorefaces (Bhattacharya and Walker 1992), or estuarine complexes (Pore˛bski 1995, 2000), respectively. The combination of high sedimentation rates, abundance of undercompacted mud in the system, and low slope promotes the generation of a variety of bed-scale soft-sediment deformations. Even though these may occasionally become voluminous (Bhattacharya and Davies 2001), they are subordinate (in their scale) to the effects of growth faulting, rotational sliding, and slumping, which affect shelf-edge deltas (e.g., Winker 1982) and reflect a persistent tendency for slope gravity spreading in this highaccommodation setting. Thick sandy turbidites are usually conspicuously absent from deltas whose ‘‘fronts’’ are sited on the inner shelf, mainly because of limited water depth, short runout slopes, and fast subsidence of mouth-bar sands into rapidly compacted interdistributary fine-grained sediments (Nummedal 1983). In contrast to deltas farther out on the shelf, high aggradation rates cause a significant degree of delta lobe switching on the inner shelf areas (Gould 1970), leading to the development of wide and thick lobate delta fronts composed of vertically stacked mouth bar and distributary bay units (Coleman and Gagliano 1964; Posamentier and Allen 1999). Mid-Shelf Deltas Deltas Formed during Falling Relative Sea Level.—Although deltas that have prograded out onto mid-shelf areas should be as thick as the mid-shelf water depth, they are commonly thin, patchily developed, and composed of low-angle-dipping clinoforms (Suter and Berryhill 1985). This apparent contradiction is due to incision generated by both distributary-channel feeders and major valley systems (Suter et al. 1987). Otherwise, midshelf-delta clinoforms are commonly truncated in a landward direction by a transgressive ravinement surface and overlain by open-shelf mudstones. This thin, patchy distribution, capping erosional truncation, together with little to no occurrence of coastalplain deposits, are commonly interpreted to reflect delta progradation under conditions of falling relative sea level (Suter and Berryhill 1985) (Fig. 1B). Decreasing accommodation tends to stabilize distributary channels through enhanced incision (Suter 1999; Posamentier and Morris 2000) and create distinct, widely separated delta lobes (Ritchie et al. 2004). It also results in laterally (frontally) stacked mouth bars separated by minor downlap unconformities that mostly reflect minor discrete pulses in base-level fall rather than an autocyclic switch (Tesson et al. 2000). Larger-amplitude falls, though not exposing the shelf edge, are likely to be recorded in a series of basinward-detached delta bodies overlain by a ravinement surface and then by transgressive muds (Posamentier et al. 1992; Ainsworth and Pattison 1994). Reworking of an increasingly emergent shelf substratum causes sediment bypassing on the shelf and enhances sand content and sorting of sand in distal (seaward) progradational increments (Sydow and Roberts 1994; Anderson et al. 2004). This, in turn, can lead to a significant steepening of the delta front as it reaches deeper mid-shelf waters and to the deposition of sand in the deltaic toes from turbidity currents, grain flows, and other high-concentration gravity flows. Sandy turbidites have been reported from some Cretaceous shallow-water, ramp deltas of the U.S. Western Interior Basin, such as the Panther Tongue of the Star Point Formation (Van Wagoner et al. 1990; Posamentier and Morris 2000) and the Ferron Sandstone Member of the Mancos Shale (Bhattacharya and Davies 2001, 2004). These deltas are interpreted as forced-regressive features deposited far basinwards from their initial highstand shorelines. Therefore, the mechanisms of sediment bypass, of progressive sand sorting at such distant shelf locations, or simply of strong river flooding could possibly be responsible for the turbidite fronts or toes in these deltas, although slope steepening due to local fault-induced accommodation provides an alternative (cf. Bhattacharya and Davies 2001).

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Because of the erosional truncation associated both with the downward-directed, regressive transit of a delta across the shelf and with the subsequent transgressive ravinement (can be 15–40 m deep on wavedominated systems; Rodriguez et al. 2001; Bhattacharya and Willis 2001, p. 287–288; Cattaneo and Steel 2002), the preservation potential of midshelf deltas associated with falling sea level is likely to be limited. Deltas Formed during Transgression.—During transgression, deltas tend to change into estuaries as the older distributary system becomes backfilled (Dalrymple et al. 1992; Reinson 1992), although high-discharge rivers can create mid-shelf deltaic lobes as punctuated regressions during a longer-term relative sea-level rise (Bartek et al. 1990; Anderson et al. 2004). Little is known of such deltas and their preservation potential in mid-shelf settings, and anomalous or dual terminologies, such as transgressive estuarine–deltaic complexes, are sometimes adopted for Quaternary deltas (Yoo and Park 2000). Bartek et al. (1990) found that during the late Pleistocene–Holocene sea-level rise, the Brazos River produced backstepping, deltaic clinoforms, 9–10 m thick, interpreted from their geometry as formed within wave-dominated deltas. Such mid-shelf clinoforms are likely to be more muddy and devoid of sandy turbidites as compared to their forcedregressive counterparts, because they are directly fed by the primary fluvial source from an increasingly distant location through time. Although already reduced by ravinement erosion, even such remnant clinoforms have a low chance to be preserved intact, because they are likely to be partly or entirely reworked by geostrophic circulation on an increasingly open shelf as the water deepens during further transgression and early highstand (cf. Rine et al. 1991). It is therefore probable that mid-shelf deltas on transgressive shelves are transient phenomena. If preserved, they may form cores to composite sand bodies, such as shoalretreat massifs attached to incised-valley estuaries (Swift et al. 1991, their fig. 24), or shelf sand ridges (e.g., Nummedal and Suter 2002). Fast (glacioeustatic) rises also hamper the formation of transgressive deltas in mid-shelf settings. However, for supply-dominated systems and relatively low rates of relative sea-level rise mid-shelf deltas are likely to form a significant component of transgressive systems tracts. Regressive mid- to outer-shelf deltas in ramp settings can begin to aggrade significantly when sea level turns around from fall to rise. Such deltas, commonly referred to as lowstand deltas (Mellere and Steel 2000), are broadly analogous to turbidite-bearing, lowstand systems tracts in settings with a shelf–slope break. The aggradational behavior of such lowstand deltas both increases the preservation potential and allows the delta to develop a paralic ‘‘tail.’’ The ‘‘basinal’’ position of such deltas, together with topographic enhancement and narrowing of the seaway as sea level falls, appear to generate strong tidal influence on the delta fronts. Examples from the Campanian Western Interior Seaway, U.S.A., are discussed by Mellere and Steel (1995, 2000) and by Steel et al. (2004). Shelf-Margin Deltas Deltas Formed during Falling Relative Sea Level.—When sea-level fall brings the delta and its fluvial feeder to a position near the shelf break, deltaic clinoforms of great height and length (commonly hundreds of meters in amplitude and up to 10 km in length) can be developed, as the delta drapes across the preexisting shelf margin, into deep water (Suter and Berryhill 1985; Steel et al. 2000, 2003) (Fig. 1C). If sea level falls below the shelf edge, the clinoforms suffer erosional truncation at their landward side, but there need be no deep truncation between delta-front and fluvial distributary if the sea level falls only briefly below the shelf edge, or begins to rise after falling no lower than the shelf edge. No deltaplain deposits develop behind such shelf-edge deltas while sea level is falling, but paralic deposits do accumulate after sea level begins to rise (late lowstand), when the delta becomes aggradational.

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The most proximal reaches of shelf-edge delta clinoforms can be very steep (6–8u), and the clinoforms consist of thick mouth-bar sandstones that commonly show evidence of slumping and sliding. The upper-to-mid slope reaches of clinoforms tend to be less steep (max. 3–4u) and more heterolithic. A characteristic feature is that they contain upwardthickening lobes (5–15 m thick) of turbidite sand sheets (, 60 cm thick), deep (several meters) but narrow feeder chutes also filled by massive turbidite beds, as well as steep-fronted lobes at the terminations of chutes (Plink-Bjo¨rklund et al. 2001; Mellere et al. 2002). Shelf-margin delta fronts are also a preferred site for river-flood-generated hyperpycnal flows, because of the steeper slopes and longer runout distances (PlinkBjo¨rklund and Steel 2004). The entire delta slope can be affected by largescale slope failure and growth faulting (Winker 1982; Winker and Edwards 1983; Coleman and Prior 1988; Nemec et al. 1988; Wignall and Best 2004). Shelf-edge delta clinoforms display a descending-to-ascending pattern in their offlap-break trajectory (e.g., Sydow and Roberts 1994), documenting delta growth during the change of relative sea level from fall to rise. When sea level falls below the shelf break, deltas tend to be cannibalized, leading to the linkage of shelf valleys to slope canyons, and the delivery of turbidite sands to the basin floor (Mellere et al. 2003) Deltas Formed during Rising Relative Sea Level.—There are two main types of shelf-edge delta that develop during rising relative sea level, namely highstand shelf-margin deltas and late-lowstand shelf-margin deltas. Highstand shelf-margin deltas occur particularly in basins with narrow shelves and/or strong river input. Although auto-retreat makes it difficult for deltas to reach the edges of wide shelves during rising relative sea level (Muto and Steel 1997), a Q-dominated regime does allow this to happen at times (Burgess and Hovius 1998), thus producing highstand deltas at the shelf edge. Examples of such shelf-edge deltas, probably occurring during rising relative sea level, occur in the Paleogene shelf margin of the Gulf of Mexico (Xue and Galloway 1995; Meckel and Galloway 1996). Despite the strong fluvial input necessary to bring these deltas to the shelf edge, their open-coast morphology and shelf-edge location cause a very strong, and even, dominant storm-wave imprint. Note that we are not referring to the ‘‘late’’ highstand condition of some authors (e.g., Van Wagoner et al. 1990; Anderson et al. 2004), where relative sea-level is actually falling! Late-lowstand shelf-margin deltas, forming immediately after a significant fall of sea level, become reestablished at the shelf margin as sea level rises back above the shelf edge. They often tend to show fluvial dominance, with some tide influence. Storm-wave imprint is less significant, probably because of irregular, lowstand coastal morphology. They are part of the lowstand systems tract because they occur basinwards and slightly below the early lowstand shelf edge. They are variously known as lowstand wedges or progradational complexes (Vail 1987), late lowstand wedges (Posamentier and Vail 1988; Posamentier et al. 1991), or simply late-lowstand deltas (Steel et al. 2003). These two types of shelf-edge delta are responsible for much of the accretion that occurs on shelf margins, and the following features allow them to be distinguished: Highstand deltas typically show an aggradational tendency (signaling the rising relative sea level) on the outer shelf, and this causes them to be relatively thick (up to some 100 m) and to display an internal architecture of stacked upward-coarsening and -thickening, wave-influenced parasequences. This aggradation with repetition of parasequences can be seen in the highstand deltas overlying MFS 16 and 17 in Figure 3. The highstand deltas in Figure 3 become rapidly muddier at the shelf edge. Thin-bedded, sandy tempestites (ungraded or flat-laminated units with wave-ripple cappings) occur on the delta front, signaling storm-wave influence at the shelf edge. Highstand deltas are underlain by a maximum flooding surface in muddy strata, and are overlain by transgressive deposits (Fig. 3).

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FIG. 3.—There are three delta types illustrated in the succession here, two generated during relative sea-level rise and one during stable to falling relative sea level. Each of the three types occurs in the shelf-edge reaches of a different fourth-order stratigraphic sequence. The highstand shelf-edge deltas, above mfs 16 and 17, are thick, are visibly ‘‘layered’’ with parasequences, and are documented as being wave dominated (C. Uroza, personal communication 2005).The thickness, marked development of parasequences, and apparent absence of a time-equivalent deep-water fan are consistent with the notion of rising relative sea level. The dark-colored late-lowstand delta, below mfs 15, is situated just below the shelf edge, laps down onto the deep-water slope, and is river dominated, as shown by frequent thin hyperpycnal flows on the delta front (A. Petter, personal communication 2005). The slope location of this delta and its timing as slightly younger than a basin-floor fan (off photo to right) is consistent with a late-lowstand designation and relative rise of sea level. The falling-stage or early lowstand shelf-edge delta, below mfs 16, is thinner, lighter colored (coarser grained), and has a more ‘‘compact’’ character (few parasequences) compared to the others. It is of mixed-energy (wave, fluvial, and tide) origin (A. Ponten, personal communication 2005) and is interpreted as forced regressive.

Late-lowstand deltas also tend to be aggradationally stacked with parasequences. They can be thick (50–70 m) and sandy at the shelf edge but rapidly become heterolithic and muddy as they downlap onto the early-lowstand slope deposits. Diagnostic features of such deltas (compared to highstand deltas) are (1) stronger fluvial influence shown by turbidite lobes and turbidite-filled chute channels (see Plink-Bjo¨rklund et al. 2001; Mellere et al. 2002), (2) a dominantly outer-shelf and slope location, downlapping onto early lowstand turbidite channels and muddy slope deposits, and (3) they underlie the maximum flooding surface in their stratigraphic sequence. Some of these features can be seen in Figure 3, where slope-downlapping, late-lowstand deltas of clinoform 14 can be seen. Bayhead Deltas Bayhead deltas form at the landward end of submerged incised valleys (estuaries) and embayments after the deltaic shoreline has turned around from regression to transgression during relative sea-level rise (Dalrymple et al. 1992; Reinson 1992) (Fig. 1D). Bayhead deltas are relatively small, funnel-shaped features that are entirely confined within either the erosional base of the estuary or coastal reentrants; thus, they are unlikely to be wave dominated (Dalrymple et al. 1992.) The confinement increases tidal flow, but macrotidal estuaries lack deltaic phases at their head (Allen and Posamentier 1993). Fluvial domination can create a birdfoot geometry if the receiving central estuarine basin is sufficiently large (Donaldson et al. 1970). Low-angle ripple-dominated heterolithic delta foresets (3–8 m high commonly) are cut at the proximal end of the system by shallow distributary channel sandstones, whereas they merge distally into fine-grained, brackish, and tide-influenced sediments of the central basin.

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EVOLUTIONARY PATTERNS

During a given fall-to-rise in relative sea-level cycle, the abovedescribed delta types are likely to form a predictable evolutionary pattern in which they either form intergradational transitions or occur as distinct entities separated in space and time by major discontinuities (Fig. 4). Parallel Terminologies Sequence stratigraphic terms are also used for the individual stages in the evolutionary pattern of shelf deltas described above. Inner-shelf deltas are sometimes referred to as highstand deltas, emphasizing that deltas situated on the inner shelf are usually subject to ‘‘high’’ sea-level conditions. Mid- to outer-shelf deltas are sometimes referred to as latehighstand (Anderson et al. 2004), or more commonly as forced-regressive (Posamentier et al. 1992) or falling-stage (Plint and Nummedal 2000) deltas, because sea level usually needs to fall to cause shallow water in a shelf-edge position. Lowstand deltas typically occur in both shelf-edge settings, where they may represent the main growth increments of the shelf margin (Chiocci 1994), and ramp settings, where they refer to deltas in a distal, basinal position that are prograding-to-aggrading immediately after a fall of relative sea level (Helland-Hansen and Gjelberg 1994; Mellere and Steel 1995; Bhattacharya and Willis 2001). Again, these are not competing terminologies but complementary ones. For example, in most preQuaternary cases it is easier to document that an ancient delta was located near the basin margin, on the inner-shelf area, than to show that sea level was near its relative highstand position. Morton and Suter (1996) and Edwards (2002) suggested from their work in the Quaternary of the Gulf of Mexico that highstand and lowstand deltas cannot easily be distinguished on the basis of their facies

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FIG. 4.— Conceptual dip section showing the family of accommodation-driven shelf deltas produced on shelf-break margin A) by high-amplitude, stepped fall in relative sea level, followed by B) rapid rise, and C) the inferred parallel change in delta-front hydraulic regime. Sea-level pattern in part B is based on Kolla et al. (2000).

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spectra. However, we have shown above that this distinction can be made in settings that were more sensitive to accommodation changes. This, together with the fact that highstand deltas at the shelf edge differ from those on the inner shelf illustrates a need for classification based on the location of a delta on the shelf, although, admittedly, more facies information from cores and outcrops is needed to better evaluate the set of diagnostic criteria. Process–Regime Change during Sea-Level Cycle There are some tendencies to change the dominant process regime at the delta front during the evolutionary cycles that were outlined above (Fig. 4C) (see also Bhattacharya and Walker 1992; Miall 1997), although there are clearly many other important controls on delta-front process, such as grain size (Orton and Reading 1993), basin-margin configuration, and shelf width (Galloway and Hobday 1996). We believe that there will eventually be an integration of the process and base-level aspects of delta classification. We emphasize that relationships between relative sea-level position and basinal processes, suggested below, are merely tendencies and not correlations. These tendencies can easily be upset as morphology, or absolute values of sediment flux or basinal energy change through time. Regime Change during Falling Relative Sea Level.—Most low-latitude, present-day shoreline systems are at or near sea-level highstand and tend to assume an inner-shelf position, unless they have an unusually high sediment supply. Modern deltas on the inner shelf can be dominated by rivers, waves, or tides (Galloway 1975), with the tide domination being particularly common in deltas present in the tropical belts (Sidi et al. 2003). During initial sea-level fall, when the shelf is still wide, there is some evidence that forced regressive, inner- to mid-shelf deltas tend to be strongly river influenced. Although mid- to outer-shelf deltas typically require strong fluvial drive to bring them to such sites, they may also become increasingly wave-influenced basinwards, because decreasing shelf width during sea-level fall lessens frictional attenuation of wave energy (Suter 1999). However, the irregularity of lowstand coastal morphology dampens the wave energy; hence, it seems that forcedregressive mid-shelf deltas are unlikely to be as wave-dominated as their transgressive counterparts. Shelf-margin deltas should generally be subject to the full impact of waves and oceanic swell (Galloway and Hobday 1996), though there is increasing evidence that when these deltas arrive at the shelf edge during significant sea level fall (and coastlines are irregular) tidal influence can increase and fluvial processes (hyperpycnal flow) can locally dominate the distributary-mouth and delta-front zones. In these latter situations large volumes of sand can be delivered to deepwater areas (Mulder and Syvitski 1995; Mellere et al. 2002, 2003; Plink-Bjo¨rklund and Steel 2004). Regime Change during Rising Relative Sea Level. —Deltas that become reestablished at the shelf edge during late lowstand (early rise, after sea-level fall) also have fronts that are dominated by fluvial and, to a lesser extent, wave processes. Sediment gravity flows and slumps tend to occupy a major proportion of the delta front. Transgressive deltas have virtually no facies documentation, but it is not unlikely that they experience wave domination (Anderson et al. 2004). The fluvial driver dominates bayhead deltas (Dalrymple et al. 1992), though they can be strongly influenced by tidal flows in the embayment setting during sealevel rise. As the rise begins to slow down, deltas build to the open coast into deepened water and experience an increased wave influence upon their fronts, as documented for the Mekong River (Ta et al. 2002; Tanabe et al. 2003). On wide shelves, such influence is likely to increase during advanced highstand progradation and can produce more strike-aligned, extensive depocenters and increased preservation of strandplains (Galloway 2001). However, for supply-controlled systems, more narrowly developed, river-dominated lobes may extend across the entire shelf, as

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exemplified by the modern Mississippi Delta. In cases where deltas manage to prograde to the shelf margin without a significant fall of relative sea level (Q-dependent case), there is commonly strong wave influence on the front of the delta, and thick development of stacked parasequences (Deibert et al. 2003). Attached vs. Detached Geometries Accommodation-Driven Deltas.—High-amplitude, stepped fall followed by rapid rise of relative sea level promotes the development of an irregular belt of detached deltas across the shelf down to the upper slope (Kolla et al. 2000) (Fig. 4A). The length of bypass segments would be controlled mainly by rate of relative sea-level change. Individual deltas in the thin, forced-regressive segment on the outer shelf would be irregularly linked by a series of basinward-younging and basinward-inclined surfaces of bypass and downlap (Posamentier et al. 1992). The fluvial feeder would erosively truncate this series of forced regressive surfaces, and the irregularity of the deltaic belt would be further exaggerated by later transgressive erosion across the top of the tract. The maximum lowstand depocenter is formed by shelf-edge deltas. During subsequent transgression, bayhead deltas are deposited above the subaerial erosion surface and would be best developed where incision was greatest, that is, at either the former highstand shoreline (Fig. 4A) or the shelf edge when the latter became incised. Because of the rapid rise, the reestablishment of deltaic deposition is likely to begin at the former highstand shoreline, so that the newly formed inner-shelf deltas are detached from the shelf-edge deltas by a transgressive-mud blanket with shelf-wide persistence (e.g., Tesson et al. 2000). The basinward extent of these inner-shelf (highstand) deltas is unlikely to be great, because the ensuing sea-level fall forces the locus of active deltaic deposition into mid-shelf and shelf-edge settings. All this results in aggradation on the inner shelf during highstands and shelf-edge accretion during lowstands (e.g., Chiocci 1994), the latter being damped or stopped in areas where the fluvial feeder dissects the shelf edge, allowing the sand to escape into deep water. Supply-Driven Deltas.—For low-amplitude base-level oscillations when fluctuations in supply rate becomes the dominant control, an attached delta belt is likely to be generated across the wide shelf (Fig. 5A). The landward reaches of the belt consist of aggrading inner-shelf deltas with thick paralic tails, whereas mid-shelf deltas assume a flat to weakly descending delta-front trajectory with a resultant lack or poor development of paralic deposits. Upon crossing the shelf break, the deltaic section expands considerably and there is an increasingly turbiditic delta front because of the steepening and lengthening of the slope when the delta meets increasingly deeper water. The subsequent transgressive systems tract can be thick and either deltaic (Anderson et al. 2004), or estuarine (Schellpeper 2000), but in contrast to R-dominated systems not necessarily extending far inboard of the shelf edge (Meckel and Galloway 1996). The resumed delta progradation during the ensuing highstand starts from near mid-shelf locations, and this, together with high sediment supply, allows the deltas to easily work their way back to the shelf edge, particularly when relative-sea level rise begins to slow down. Little is known about facies of highstand shelf-edge deltas. We speculate that the sea-level rise, coupled with increasing wave domination, may arrest and redistribute much of the sand on the shelf so that the deltas reaching the shelf edge become more muddy. This, together with the heightened slope (enlarged by highstand offlap; Fig. 5A), may generate large slides and slumps as well as muddy hyperpycnal flows from the freshly constructed deltaic shelf edge. The preservation potential of highstand shelf-edge deltas may be small at times. This scenario predicts shelf aggradation and progradation throughout the entire relative-sea cycle. Though little or no fluvial erosion is present

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at the shelf edge, linkage to the deep sea can occasionally develop during both lowstand and highstand times, because the very high and sustained sediment supply to the slope may enhance a tendency for slope chutes and gullies to develop into submarine canyons (e.g., Pratson and Coakley 1996). SEQUENCE BOUNDARY

Although the legitimacy of the ‘‘sequence boundary’’ as a single widespread, synchronous surface is still being debated (J. Bhattacharya, personal communication), there is probably more agreement about the value of this term as an indicator of time intervals when base-level fall was accompanied by significant (albeit local) sediment bypass in the subaerial reaches of the sedimentary system. Recent numerical and physical experimental work (Muto and Swenson in press) suggests that this state or time interval corresponds with the condition of ‘‘grade’’ in the fluvial system, and is effective during particular styles of base-level fall. Despite this, steady base-level fall produces much complexity, with autogenic shifting, erosion, and deposition (Muto and Steel 2004). Nevertheless, a consideration of shelf-transiting deltas, especially the accommodationdriven types, allows some insight regarding the debate about the broad positioning of the sequence boundary (Posamentier et al. 1992; Morton and Suter 1996; Edwards 2002): whether it should broadly correspond with (1) the beginning or (2) the end of relative sea level fall (Fig. 4A). In choosing the former, the sequence boundary is placed along the first, forced-regressive downlap surface, separating the (highstand) deltas that have a flat or rising, regressive trajectory from those that have a downward-directed (falling-stage), regressive trajectory (Posamentier et al. 1992; Posamentier and Morris 2000). In choosing the latter, the sequence boundary is placed near the last and lowest, forced-regressive downlap surface, separating falling-stage deposits from the deposits generated after the initial rise of relative sea level, i.e., the lowstand prograding wedge of Hunt and Tucker (1992), Helland-Hansen and Gjelberg, (1994), and Plint and Nummedal (2000). In the latter choice, the sequence boundary extends as an erosional unconformity back across the top of the entire falling-stage systems tract, whereas in the former choice it forms the basal, downlap surface for this tract. Although there are compelling cases for both positions, we argue that, for broad shelves, sea level commonly falls for a significant period of time (tens of thousands of years) before deltas even reach the shelf margin, and therefore before significant volumes of sand are delivered across the shelf break. Choice (1) above, therefore, does not coincide with the main introduction of sands into deep-water areas. Choice (2), on the other hand, nearer to the time of incision of the shelf edge (provided that sea level falls to or below the shelf edge) is more nearly time equivalent with the first emplacement of deep-water sand (SB in Fig. 4A, B). Although shelf-edge incision and lowest sea level (change from fall to rise) do not necessarily coincide, the first major erosion surface linking the shelf edge and slope can be argued to be a good practical choice of sequence boundary, and reasonably justified conceptually. This choice assigns the deposits below the shelf edge to the lowstand systems tract. In basins without a shelf–slope break, the corresponding sequence boundary is

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simply taken along the zone of shoreline change from falling to rising (aggrading) regressive trajectory. In the case of supply-driven deltas, the delineation of a sequence boundary is fraught with even greater difficulties. In such deltas, fluctuation in supply rates rather than relative sea-level change is the dominant control on shelf transit, and sea level, if it falls at all, is less likely to fall below the shelf edge. As a result of this, aggradation of the deltas is a dominant theme, and a sequence boundary, sensu bypass and graded condition, is likely to be absent, although there may be many local erosion surfaces. In such cases there is a broad aggradational turnaround from regression to transgression rather than any significant basinward shift of facies. CONCLUSIONS

Because deltas are the key element in the building of constructional shelves and shelf margins, we advocate the use of a delta classification based on shelf location, in addition to the conventional process-based classification. Shelf-transiting deltas thus form a spectrum of types from bayhead deltas, through inner- and mid-shelf deltas to shelf-margin deltas, followed by transgressive deltas or estuaries, each with their own geometrical, architectural, and facies characteristics. Main diagnostic features include clinoform height, presence or lack of paralic tails, and sand-turbiditic versus non-turbiditic delta front. The recognition of this family of deltas is important because it provides an improved understanding of sequence stratigraphic patterns, is a powerful tool for prediction of sand partitioning across the shelf onto slope and basinal settings, it emphasizes mixed energy rather than the traditional endmember energies, and it can help in choosing the best location for the sequence boundary. In transits to and from the shelf margin, deltas are either accommodation driven (high amplitude and frequency of relative sea-level changes as the main control, e.g., icehouse times) or supply driven (fluctuating supply as main control, e.g., greenhouse times). The former tend to have repeated, shelf-wide transits on short time scales (tens to hundreds of thousands of years), change from highstand to falling-stage and to lowstand deltas with transit distance on the shelf, and are deeply incised if sea level falls significantly below the shelf edge. The latter can remain out near the shelf-edge reaches (albeit with lateral shifting) for longer periods as highstand deltas. Such highstand deltas are most common where rates of sea-level rise are modest and shelf width is narrow to moderate, and they would not normally be incised at the shelf edge (they do not experience a fall of sea level at the shelf edge) and would therefore less often have a focused or channelized shelf-edge to slope conduit. Viewed in this dynamic context, deltas can undergo significant regime change and sediment-budget partitioning across the shelf. Inner-shelf deltas can be dominated by fluvial, wave, or tidal regimes. When deltas approach the shelf edge, they can become increasingly wave reworked because of exposure to ocean swell, particularly if sea level is still rising. With forced-regressive conditions on the outer shelf they tend to develop on an irregular coastline morphology, and so maintain their river-driven character. Onset of sea-level rise (while sea level is still low and progradation continues) tends to be accompanied by an increased tidal

r FIG. 5.—Dip section showing A) the family of supply-driven shelf-deltas produced on the shelf-break margin by low-amplitude fall followed by B) prolonged rise in relative sea level, and C) the inferred parallel change in delta-front hydraulic regime. Although the fall did not expose the entire shelf, the high sediment supply drives the delta beyond the former shelf break. The offlap break escapes a major incision because it is being constantly constructed seawards off the distributary channels during delta progradation. During rise, wave-dominated deltas backstep on the outer shelf, and are followed up by a transgressive shale packet that because of the high supply is unlikely to extend far landward on the shelf. The ensuing highstand progradation may bring the deltas back to the preexisting shelf edge, but the extended slope would promote wave reworking and large-scale mass wasting rather than delta accretion. Hence, a slope-toe wedge of slumps and slides may record the arrival of highstand deltas to the shelf edge. When the deltas are already at this location, the subsequent fall, even of a very small magnitude, may however result in the shelf-edge dissection and the formation of basin-floor fans.

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influence, especially along parasequence tops. Continued rise during transgression, particularly out near the shelf margin, tends to result in stronger wave and tide influence. Although the validity of the term ‘‘sequence boundary’’ in the sense of a single synchronous surface is still legitimately debated, it is accepted as an indicator of base-level fall, sediment bypass (at least locally) and basinward facies shift. Sequence boundaries, generated during shelf transits with significant subaerial sediment bypass and relative sea-level fall, are best developed on accommodation-driven deltas, and are likely to be represented on a variety of time scales (third, fourth, and fifth order). Supply-driven deltas can reach and remain at the shelf margin for longer periods and tend to be highly aggradational. Sequence boundaries in such supply-dominated systems may be difficult to identify (and then only at lower order time scales, e.g., third order), or may be non-existent if there is little or no relative sea-level fall during delta transit. We prefer to designate the extended period of erosion associated with falling and lowest relative sea level as the sequence boundary, rather than the time line of earliest fall, because of the tendency of lowest to early rising sea level to be associated with channelization of the shelf margin. ACKNOWLEDGMENTS

This paper has grown partly out of WOLF project work at the Universities of Wyoming and Texas at Austin (thanks to BP, BHP, ConocoPhilips, ExxonMobil, Norsk Hydro, PDVSA, Shell, and Statoil for continued support and discussion), and partly out of National Research Council support of a Twinning Project (Poland–USA). The study was also supported by Landmark Graphics Corporation via the Landmark University Grant Program to Institute of Geological Sciences, Polish Academy of Sciences. We are grateful to Bill Galloway, John Suter, Janok Bhattacharya, Antonio Rodriguez, and Colin North for helpful and stimulating comments on an early draft of this paper, and to Bob Dalrymple and Shuji Yoshida for continued creative discussion on sea-level change and shoreline processes. REFERENCES

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Received 2 February 2005; accepted 8 September 2005.

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