Abstract: 

Submarine sediment density flows are one of the volumetrically most important processes for sediment transport across Earth. The sediment concentration of flows that reach the deep ocean has never been measured directly, and understanding these long-runout flows remains a major challenge. The Miocene Marnoso-Arenacea Formation in the Italian Apennines is the only ancient sequence where individual submarine sediment-density-flow deposits (single beds) have been mapped out for more than 100 km down-flow. Here we document the external shape and internal architecture of thirty-two individual beds that record flow evolution and can be compared to deposit shapes in mathematical or experimental models. The large number of beds allows modes of flow behavior to be identified. Larger-volume turbidites are typically dominated by massive (TA) or planar-laminated (TB) sandstone intervals that have a broad thickness maximum. This shape is important because it suggests that massive and planar laminated sandstones record hindered settling from dense near-bed layers, which have high (> 10% by volume) sediment concentrations. Previously, some authors have inferred that planar-laminated sandstones (TB) are deposited mainly by dilute flows. The position of the broad thickness maximum moves basinward as the volume of sand in the flow increases. This is consistent with mathematical modeling that suggests the position of the thickness maximum depends on flow thickness, flow speed, and sediment settling velocity, as well as sediment concentration, variations in seawater entrainment rate, and local changes in seafloor gradient. Smaller-volume turbidite sandstone intervals are finer grained and dominated by ripple cross-lamination (TC) and have a near exponential decay in thickness that is consistent with deposition from a dilute sediment suspension. The rate of near exponential thinning is controlled by sandstone volume. In contrast, turbidite mudstone intervals show an approximately linear increase in thickness with distance. Flows that entered the basin in opposite directions produced turbidite mudstone intervals that thicken towards the same location, indicating that muddy turbidity currents can drain back over long distances to basinal lows.

Introduction

There are remarkably few direct measurements from active submarine sediment-laden density flows (Xu 2011; Puig et al. 2014; Talling et al. 2014; Talling 2014), even though they dominate sediment fluxes across large areas of the planet. For instance, the sediment concentration of flows that reach the deep ocean (beyond the base of the continental slope) has never been measured directly, and it is uncertain whether they contain dense near-bed layers. This means that much of our understanding of such flows must be pieced together from studies of their deposits.

Here we analyze the shape of individual ancient flow deposits (single beds) in order to understand how submarine flows evolve. In particular, we wish to understand whether deposit shape provides evidence for (or against) deposition from dense near-bed layers characterized by hindered settling. Very few studies have documented the shape of turbidite beds by correlating individual flow deposits for long (> 100 km) distances (Amy and Talling 2006; their table 1). This is because turbidite deposits are commonly eroded by subsequent flows, causing local bed truncation and amalgamation (Enos 1969), and because suitable marker beds that allow correlation are rare. The Miocene Marnoso-Arenacea Formation, in the northern Italian Apennines, provides the most extensive correlation of individual flow deposits (single beds) yet documented for any ancient turbidite sequence (Ricci Lucchi and Valmori 1980; Amy and Talling 2006; Talling et al. 2007a, 2012, 2013a, 2013b; Muzzi Magalhaes and Tinterri 2011), although longer-distance (up to 2,000 km) correlations have been made using relatively short (< 10 m) cores from the modern sea floor (Frenz et al. 2008; Talling et al. 2007c; Wynn et al. 2010). The Marnoso-Arenacea Formation has an advantage over modern sea-floor cores in that many tens of beds can be studied, allowing modes of down-flow evolution be better constrained. However, changes in sea-floor gradient are more poorly constrained for ancient rock sequences. We therefore discuss the extent to which it is possible to determine how variable seafloor gradients affected these ancient bed geometries.

This study is novel because of the large number of beds described, which aids recognition of underlying first-order trends in bed shape (cf. Tinterri et al. 2003; Falcini et al. 2009, and others). Previous analyses of bed shape by Talling et al. (2007a) and Sumner et al. (2012) were qualitative, rather than the quantitative analysis that is presented here. This contribution then presents novel results from mathematical models of the flows that provide key insights into how deposit shape is related to sediment concentration at the base of the flow. In particular, it assesses whether bed shape provides a record of hindered settling, and hence relatively dense near-bed concentrations. This comparison helps to understand the origin of different types of sandstone, especially planar-laminated sandstone comprising the TB division of Bouma (1962). Debate surrounds whether planar laminated TB intervals are formed by flows with high or low near-bed concentrations, inasmuch as both dilute and dense flows can form planar lamination in laboratory experiments (Kuenen 1966; Best and Bridge 1992; Leclair and Arnott 2005; Sumner et al. 2008). More generally, it is hoped that future studies will compare the field dataset presented here to the deposits of laboratory and mathematical models in order to better understand flow processes, issues of scaling in laboratory flows, and the validity of assumptions used to formulate numerical models.

Aims

Initial analysis of field observations aims to determine (i) whether beds or depositional intervals (e.g., Bouma-sequence intervals TA-to-E) within beds display consistent shapes, and what these shapes are, (ii) how bed or interval shape changes with increasing flow volume or grain size, and (iii) how bed architecture most likely records flow processes. The aim of subsequent numerical modeling is to investigate how sandstone interval shape depends on the sediment concentration within the flow. Numerical modeling tests the specific hypothesis that massive (TA) and planar-laminated (TB) sandstone intervals are deposited by flows with dense near-bed layers from which hindered settling occurs, whilst thinner sandstones dominated by cross-laminated (TC) intervals are deposited by dilute flows.

Geological Background

The beds studied in the Marnoso-Arenacea Formation were deposited within a nonchannelized basin plain, and are separated by intervening hemipelagic mud (Ricci-Lucchi and Valmori 1980; Amy and Talling 2006; Talling et al. 2007a, 2007b, 2012; Sumner et al. 2012; Dall'Olio et al. 2013). Megaturbidites act as marker beds, allowing intervening beds to be correlated between more than one hundred sections across the whole basin. This topographically simple basin plain setting has produced a “layer cake” stratigraphy with virtually no bed amalgamation and little or no evidence for erosion or flow reflection (except in the megaturbidites; Talling et al. 2007b). It was thought initially by the authors that this topographically simple basin-plain setting would produce simple bed geometries (i.e., those lacking the confounding effects of flow reflection, deflection, or erosion due to steeper slopes) that could be easily compared to the results of numerical models. However, despite the simple topographic setting, the beds are complex. They often record multiple flow types within a single overall event, with lateral or down-flow transitions between flow types (Amy and Talling 2006; Talling et al. 2007a, 2007b, 2012, 2013a, 2013b; Sumner et al. 2012). Some of these flow transitions have now been recognized in hybrid beds from many other locations worldwide (Haughton et al. 2003, 2009; Talling et al. 2004, 2010, 2012, 2013a), whilst other types of flow transformation (e.g., those involving clean-sand debris flows; Talling et al. 2013b) are more contentious.

Methodology

Bed Correlations

Detailed bed correlation figures are presented in previous papers. Amy and Talling (2006), Talling et al. (2007a, 2007b, 2013a, 2013b) and Sumner et al. (2012) documented the geometry of 56 beds between the Contessa megabed and the first overlying Colombine marker (“above-Contessa interval” in this article). Further work (Talling et al. 2013a) mapped an additional 13 beds located immediately below the Contessa megabed (termed the “below-Contessa interval”). This contribution analyzes the shape of 32 beds in a 60-km-long cross section along the Ridracoli structural element, whose trend is subparallel to the dominant paleo-flow direction (Figs. 1, 2; Amy and Talling 2006; Talling et al. 2007a, 2007b, 2013b).

Thick (> 40 cm) beds in the above Contessa interval were named bed 0 to bed 8. Beds located between key beds are numbered according to their position above each key bed. Beds in the below Contessa interval are numbered sequentially from -1 to -20, with our Bed -20 also being bed A-20 in the scheme of Ricci Lucchi and Valmori (1980).

Differential Compaction

It is assumed herein that uniform compaction affected sandstone intervals, and their shape is not otherwise distorted significantly. The maximum burial depth of Marnoso-Arenacea Formation outcrops varies from ∼ 5 to ∼ 2.5 km across the foredeep basin (Zattin et al. 2002). This is likely to cause variations in the original sandstone thickness of approximately 16% (Amy and Talling 2006). However, burial depths show less variation along transects used to define bed shape that are orientated parallel to the basin axis (Zattin et al. 2002, their fig. 16). Mudstone intervals will have been compacted to a greater degree than sandstone intervals (Amy and Talling 2006).

Field Constraints on Seafloor Topography

We now outline available field constraints on basin topography, because changes in seafloor gradient can strongly effect deposition and erosion from submarine flows (e.g., Talling et al. 2007a; Wynn et al. 2010; Stevenson et al. 2013). We later discuss how changes in gradient can be identified in these bed geometries, and have affected bed geometry.

The beds studied here were deposited in a relatively flat basin plain, as shown by the ability of the flows to transverse the area in opposing directions, the complete absence of channelization, and the continuous “layer-cake” bed geometry (Ricci Lucchi and Valmori 1980; Amy and Talling 2006; Talling et al. 2007a, 2013a, 2013b). Modern basin plains with this type of “layer-cake” stratigraphy tend to have sea floor gradients of < 0.05° (Talling et al. 2007c), suggesting similarly low gradients for the Marnoso-Arenacea basin plain. However, the Marnoso-Arenacea basin plain was not entirely flat when these beds were deposited. Three subtle intrabasinal highs (Verghereto, Cavalmagra, and Lamoli highs, Fig. 2) were previously inferred from isopachs of the above-Contessa and below-Contessa intervals, from consistent fluctuations in mud or sand thickness within multiple consecutive beds, and from the local termination of some thin beds (Talling et al. 2007a). The Verghereto high had a greater bathymetric relief than the Cavalmagra and Lamoli highs (Talling et al. 2007a). The flows were able to overtop the highs without significant deflection (Figs. 1, 2), and their relief is inferred to be substantially less than the thickness of the flows (Talling et al. 2007a). It is also significant that beds are continuous across two of these highs, because small changes in gradient can cause changes from depositional to nondepositional flows in modern basin-plain systems (Talling et al. 2007c; Wynn et al. 2010; Stevenson et al. 2013). Changes in gradient associated with the Cavalmagra and Lamoli Highs were insufficient to cause flows to become nondepositional, although a hiatus in deposition may characterize the Verghereto High (Talling et al. 2007a). The available paleocurrent data suggest little or no reflection of the sandy component of these flows (Figs. 1, 2; Talling et al. 2007a, 2012, 2013a, 2013b), although mud reflected and ponded in the southern part of the basin, suggesting that this area was the lowest point in the basin. The correlated beds thin towards the flexural basin margin, as expected for a foreland basin (Figs. 1, 2; Amy and Talling 2006), suggesting that there was a lateral gradient within the basin.

Bed Volumes and Cross-Sectional Areas

The cross-sectional area of sandstone and mudstone intervals was estimated for each bed for the cross section along the Ridracoli structural element (Fig. 1), instead of the bed volume. This avoids uncertainties in volume estimates due to the poorly constrained basin width. The area of each bed, and lithofacies within each bed, is presented in Table 1. It is reasonable to assume that beds with larger cross-sectional area in the Ridracoli Element correspond generally to larger-volume beds in the wider basin (Fig. 2), as confirmed by a comparison between the cross-sectional area calculated in this study and the total sandstone volume obtained by Talling et al. (2007b; Fig. 3).

Depositional Processes from Observations at a Single Outcrop

The most likely origin of individual lithofacies has been described previously (see Table 1 of Talling et al. 2013b), and therefore it is only summarized briefly here.

Massive Sandstone (TA)

Clean (mud-poor) massive sandstone can form in a number of ways from flows with high near-bed sediment concentrations, by direct sedimentation or collapse of discrete near-bed layers, as summarized by Talling et al. (2012; their fig. 15). Massive turbidite sandstone records evidence of progressive layer-by-layer deposition in the form of vertical grading, discrete horizons of mud clasts, or a gradually tapering deposit shape (see Talling et al. 2012).

Mud-Rich Cohesive Debrite Sandstone (DM)

Cohesive debris flows deposit mud-rich and predominantly ungraded sandstone that records evidence of en-masse deposition. A continuum of increasing cohesive-debris-flow-strength produces variations in debrite character (as summarized by Talling et al. 2012, 2013a). Low-strength debris flows produce clast-poor debrite sandstones, which tend to grade laterally into silt along the flow path. They may resemble fluid-mud layers, and can form through local flow transformation and turbulence collapse (Sumner et al. 2009; Baas et al. 2011). Higher-strength debrites contain larger clasts and tend to pinch out abruptly. These debris flows can run out for tens of kilometers across the basin plain from an external source (Talling et al. 2013b).

Clean Debrite Sandstone (DCS)

The fraction of mud in the matrix of these clean sandstone (DCS) debrites is similar to that in turbidite sandstone intervals (Talling et al. 2013b), and significantly lower than the mud-matrix fraction in mud-rich cohesive debrites (Talling et al. 2013). The ability of clean-sand debris flows to transport sediment into the deep ocean has previously been contentious, and the transport processes are as yet poorly understood. However, work in the Marnoso-Arenacea Formation suggests that massive clean sandstone can sometimes be deposited in an en-masse fashion by debris flow. Such clean sandy debrites often have a subtle but distinctive swirly fabric, comprising contorted areas of coarser or better-sorted grains that record pervasive liquefaction (Talling et al. 2012, 2013a). Deposition by debris flow is consistent with the observed relatively abrupt lateral pinch-out of such deposits (see Talling et al. 2012, 2013a). As with mud-rich cohesive debrites several different facies tracts are observed for clean sand debrites. The clean sand debrites could also result from late-stage turbulence collapse, as for mud-rich debrites, and variations in DCS facies tract could also be linked to changes in debris-flow yield strength (Talling et al. 2013b).

Planar-Laminated Sandstone (TB)

Laboratory experiments show that laminated sandstone intervals (TB) can potentially be formed by both low-density and high-density turbidity currents (Talling et al. 2012). Two distinct types of planar-laminated sandstone occur in the Marnoso-Arenacea Formation with finer-scale (TB-2 or TB-3) or thicker “stepped” planar (TB-1) lamination (Table 1; Sumner et al. 2012; Talling et al. 2012). Fine scale planar lamination can form incrementally by migration of low-amplitude bed waves beneath dilute flows (TB-3; Best and Bridge 1992), or by repeated collapse of traction carpets beneath high-density turbidity currents (TB-2; Kuenen 1966; Leclair and Arnott 2005; Sumner et al. 2008). Fine-scale planar laminations produced by dilute flows (TB-3) and high-density flows (TB-2) may be very difficult to distinguish in the field or laboratory deposits (Fig. 4; Talling et al. 2012). Stepped planar laminations (TB-1) characteristically occur below massive (TA) sandstone intervals, and are most likely deposited incrementally by high-density turbidity currents (Hiscott and Middleton 1979, 1980; Lowe 1982), although in the Marnoso-Arenacea Formation they lack inverse grading (Sumner et al. 2012).

Cross-Laminated (TC) Sandstone

Ripple-scale and dune-scale cross-laminated (TC) sandstones provide unambiguous evidence for deposition by low-density turbidity current (Simons et al. 1965; Harms and Fahnestock 1965; Allen 1982; Baas 1994; Southard 1991; Talling et al. 2012). Overlying planar-laminated siltstones (TD) are most likely also deposited by dilute near-bed flow (Amy and Talling 2006; Talling et al. 2012). TD divisions are rarely seen in these Marnoso-Arenacea Formation beds.

Turbidite Mudstone (TE)

Turbidite mudstone (TE) can be clearly differentiated from hemipelagic mudstone in the Marnoso-Arenacea Formation based on the texture, color, and fossil content of the deposits (Talling et al. 2012a). Turbidite mudstone can be divided into laminated and graded (TE-1), massive and graded (TE-2), and massive and ungraded (TE-3) intervals (Piper 1978; Talling et al. 2012). Laminated mudstone (TE-1) is differentiated from very fine sandstone and coarse siltstone laminated intervals of the Bouma's TD division on the basis of the modal grain size. TE intervals have been deposited from a mud density flow which can be initially fully turbulent and dilute, but may also form a denser fluid mud layer that consolidates en masse (Talling et al. 2012).

Grouping of Lithofacies and Down-Flow Facies Tracts

Lithofacies (Table 1) were grouped initially into the following four classes: (i) turbidite mudstone (TE), (ii) turbidite sandstone (TA and B), (ii) turbidite sandstone clearly deposited by dilute flow (TC and D), (iii) cohesive (mud-rich) debrite sandstone (DM), and (iv) clean sandstone debrite (DCS). Bed thickness is distinctly bimodal in the Marnoso-Arenacea Formation (Talling 2001), and thinner beds (< 40 cm) tend to comprise only TCD, together with turbidite mudstone (TE). Thicker beds (> 40 cm) typically comprise TAB, and sometimes DM or DCS, together with overlying TCD intervals and turbidite mudstone (TE). Previous work grouped bed geometries into a series of facies tracts (see Mutti 1992) that capture the presence and arrangement of different lithofacies in the bed along a down-flow transect (Fig. 5; Amy and Talling 2006; Talling et al. 2012, 2013a, 2013b).

Numerical Modeling

We present a mathematical model to illustrate how the deposit shape is influenced by particle concentration and hindered settling. This modeling is not intended (nor is it possible) to simulate all aspects of the flows that were responsible for the Marnoso-Arenacea beds, but rather to demonstrate some of the generic controls on flows that may have emplaced these deposits. The important general point is how the shape of the deposit is influenced by hindered settling as near-bed sediment concentrations increase. The model is applied to the depositional part of these flow events (i.e., that formed the beds that extend continuously across our study area). The starting point for modeling is taken at the beginning of our basin-plain outcrops, and it does not simulate earlier (possibly erosive) phases of flow.

We employ a depth-averaged formulation to study the steady, two-dimensional, spatial development of a turbidity current associated with a sustained source delivering a volume flux of fluid per unit width, q, with depth-averaged concentration of sediment, φ0. Models of this type have been used extensively for these flows (see, for example, Parker et al. 1986 and Falcini et al. 2009), although often the flow is assumed to be sufficiently dilute so that hindered settling plays only a negligible role. The basic assumption is that the flow is relatively shallow, so that its streamwise extent far exceeds its depth. This implies that the vertical accelerations are negligible and the pressure adopts a locally hydrostatic distribution. Thereafter the governing equations for fluid and sediment mass conservation and for momentum balance are depth-averaged to yield equations that govern the development of the layer-averaged quantities. A critical discussion of all of the modeling assumptions is given below.

The suspension comprises sedimentary particles with settling velocity vs∞, which is related to their excess density and size. This settling velocity is the terminal velocity through an otherwise quiescent, dilute suspension. As will be argued below, “hindered settling” effects reduce this settling velocity due to the nearby presence of other suspended particles. The density of the interstitial fluid is denoted by ρ, the excess density of the solids by Δρ, and the volume fraction of solids by φ, so that the density of the current is given by ρc  =  ρ + Δρφ. Because part of our results concern hindered settling in which the concentrations of particles are relatively high, we do not assume that the presence of the suspended particles contribute negligibly to the overall density. This regime would correspond to the often studied Boussinesq case for which Δρφ/ρ << 1. Instead, as will be shown below, we explicitly account for conservation of mass in each phase and derive an expression for momentum balance in which the bulk density of the current may vary. We further denote the steady, depth-averaged flow velocity, thickness of the flowing layer, and volume fraction of suspended particles by u(x), h(x), and φ(x), where x is the downstream distance, while the deposit grows at rate /dt. In this analysis do not treat the temporal development of these flows, focusing instead on their steady form after the initial transient associated with the passage of the flow front.

Mass conservation of both phases accounts for transport in the flowing current and accumulating deposit; the latter is assumed to consist of particles with a constant volume fraction φm that corresponds to the maximum packing fraction. Additionally water may be entrained into the current at its upper interface with the surrounding fluid. Thus fluid conservation for both the current and the deposit is expressed as

 
formula

where the right-hand side of (1) represents the rate of entrainment of surrounding fluid. On the assumption that the total sediment load of the current is not supplemented by additional erosion of pre-existing sediment layers, conservation of particles within the current and the deposit is given by

 
formula

Finally, balance of momentum for the flowing layer features fluid inertia, the depth-integrated streamwise pressure gradient, downslope acceleration, and basal drag, here represented through a quadratic drag law,

 
formula

In this expression we have assumed that the normal stresses in the suspension are isotropic and that the streamwise gradients of the deposit are much smaller than the underlying gradient of the seafloor. Furthermore, and importantly for flows with relatively high volume fractions of particles, we allow the bulk density of the current, ρc, to vary. To close this model, we must specify conditions at the interface between the deposit and the current. Here we adopt a simple representation of the depositional processes and assume that the current is only depositional and that the volume fraction jumps from maximum packing in the bed to the basal concentration in the current, denoted by φb. Conservation of mass across the moving depositional interface then demands (see, for example, Kynch 1952, Dorrell et al. 2011)

 
formula

and this expression permits the rate of growth of the deposit to be evaluated.

We require parameterizations for rate of entrainment, the basal drag, the relationship between the basal and depth-averaged concentrations, and the hindered settling velocity. The entrainment coefficient, which represents the rate at which ambient water is mixed into the flowing layer, is denoted by E and treated as a function of the local Richardson number (Ri  = gcosθΔρφh/(ρcu2)). Parker et al. (1986) suggest that for dilute currents

 
formula

with constants given by E0 ≅ 0.0015 and A ≅ 0.02 (see also Johnson and Hogg 2013), and we adopt this parameterization for non-Boussinesq currents. The basal drag is expressed as a quadratic drag law with drag coefficient CD. Potentially CD could depend on the flow variables, such as the Reynolds number, the volume fraction of particles, or some rheological parameters. Here for simplicity we assume that CD is constant (CD  =  10−3), noting that other formulations could be included, as discussed below; they would affect the details of the dynamical balance, but not the essence of the model under investigation. Finally, we follow Parker et al. (1986) and relate the depth-averaged volume fraction is related to the basal volume fraction by φb  =  r φ, with r  =  1.6. This linear relationship is a further idealization as potentially one might determine the ratio of the two volume fractions in terms of the Rouse number. Finally, the hindered settling velocity at the bed is given by

 
formula

Richardson and Zaki (1954) suggest that the exponent n is approximately equal to 5. At this stage having fully specified the governing equations 14, it should be noted that they reduce to those of Parker et al. (1986) when the concentration of particles in the current is sufficiently dilute.

We apply boundary conditions at the source (x  =  0) to this system of equations 24. These specify the volume flux per unit width, u(0)h(0)  =  q, the initial concentration φ(0)  =  φ0, and the source Froude number, F0, such that ρcu(0)2/(Δρgcosθφ(0)h(0))  =  F0.

It is advantageous to analyze these equations using the following dimensionless variables. The natural scale for the downstream distances over which sedimentation occurs is q/vs∞, while the initial density-induced velocity scale is ub  =  (qgcosθΔρφ0/ρ)1/3 and the scale of the volume fraction is φ0. Thus the following set of dimensionless variables are introduced

 
formula

Eliminating the rate of deposit growth, we find that the dimensionless system is now given by

 
formula
 
formula
 
formula

where Ri  =  ψH/((1 + βψ)U2). The dimensionless source conditions are given by U(0)H(0)  =  1, ψ(0)  =  1, and (1 + β)U(0)2/H(0)  =  F0. In these expressions, there are now three additional dimensionless parameters, β, Λ, and Ω, given by

 
formula

Respectively, these measure the relative contribution of the initially suspended particles to the density of the fluid, the relative magnitude of fluid entrainment and the ratio of the buoyancy-induced velocity to the initial settling velocity. The flows under consideration are not necessarily initially dilute, and so this implies that the parameter β is of order unity (β ∼ 1). Typical sea-floor gradients are 0.05 degrees, and so we set S  =  10−3. Flows are hypothesized to have a typical initial volume flux per unit width q  =  102 m2 s−1, with an initial concentration φ0  =  0.1 (although the latter will be varied in the calculations that follow) and a settling velocity vs∞  =  10−2 ms−1, (corresponding to sediment of approximate grain size 100 µm.). This means that Λ ∼ 1 and Ω ∼ 103. Importantly, because Λ ∼ 1, this implies that entrainment of fluid may be non-negligible along the path of the turbidity current.

Particles sediment out of the flow to form the deposit, η(x, t). The dimensionless growth rate, D(X) is then given by

 
formula

The bed shape is then given by profiles for D(X), and these are calculated below.

Key Assumptions Underpinning the Numerical Model

This layer-averaged model entails a number of assumptions that need to be stated clearly. The model does not include sediment re-entrainment or erosion from the bed. This means that the modeled flows are always depositional for all grain sizes. The model cannot therefore reproduce the initial stages of powerful flows that erode or bypass sediment, as is sometimes observed in the field (Talling et al. 2007a; MacDonald et al. 2011; Stevenson et al. 2013). This could be amended to include an erosive flux of particles in equation 4, but this would add to the complexity of the analysis and is not pursued here.

The model represents drag through a constant drag coefficient, which is an appropriate representation for dilute flows at high Reynolds number; the explicit effects of molecular viscosity are therefore neglected. For higher concentrations, the flow resistance might be provided by particle interactions, and this would necessitate an alternative parameterization of the drag. This formulation also neglects the effects of yield strength that may cause non-Newtonian flows to come to an abrupt halt at their margins. Furthermore the transition between a fluid phase and a solid phase has been straightforwardly handled via a mobile depositional interface; flows with cohesive properties might arrest in different ways. Together these mean that the model is poorly suited to simulating the behavior of flows in which cohesive forces play a strong role, and it is not applied to turbidite mud or debris-flow deposits.

The seafloor is assumed to have a constant gradient of approximately 0.05° (S  =  10−3), which is typical for modern basin plains (Talling et al. 2007, 2012). Quantitative changes in gradient across the Marnoso-Arenacea basin floor are poorly constrained (see later discussion), and variations in sea-floor gradient are not included here. Model results are based on flows with one grain size (100 µm), although the Marnoso-Arenacea flows contained a wide range of grain sizes, and in some situations it is known that polydispersivity can strongly affect the properties of sediment suspensions (see, for example, Harris et al. 2002, Dorrell et al. 2011). The model is for a steady state; it is likely that oceanic flows will show some unsteadiness, especially during their initiation and cessation. However, the investigation of steady flows helps to draw out the other controls on deposit.

Results

Bed geometries are organized initially by volume (Fig. 6), and then according to down-flow facies tract (Fig. 7). These two figures illustrate both changes in deposit geometry with increasing flow volume, and modes of flow behavior that may not coincide with increasing bed volume. Scaling of the thickness axis on these plots varies to aid comparison of shape, such that maximum bed thickness corresponds to a similar length along this axis (Figs. 6, 7). The extreme vertical exaggeration of deposit shape (typically 30,000 times) should be noted, as the real shape is much flatter and more tabular. The base of each bed is shown as a horizontal datum.

Small-Volume Beds

Small-volume beds have a cross-sectional sandstone area of < 10,000 m2. Seven of these small-volume beds originated from the northwest, and they show a consistent shape (Figs. 6, 7). Their sandstone thickness declines rapidly over ∼ 20–30 km in an approximately exponential fashion, and sandstone thickness is then relatively constant across the distal part of the Ridracoli Element (Fig. 8A). Sandstone in these beds tends to be fine grained (< 187 µm), and there is little visible fining in a down-basin direction (Fig. 9A). Two small-volume beds originated from the southeast and flowed across the basin plain in the opposite direction (beds 7.1 and 1.2.3), most likely uphill. Their sandstone interval has a relatively tabular shape across the entire Ridracoli thrust sheet. In general, the average shape of small-volume beds thins in a near exponential fashion (Fig. 8A), with their volume related to their thickness at the most proximal section (Fig. 8B). The rate at which their thickness declines appear to be related to their volume (Fig. 8C).

Intermediate-Volume and Large-Volume Beds

Intermediate-volume beds have a sandstone cross-sectional area of 10,000 to 40,000 m2, whilst large-volume beds have a sandstone cross-sectional area > 40,000 m2. All of these beds originated from the northeast, with the exception of Colombine-1 bed, which was sourced from the southeast. The sandstone interval of the Colombine-1 bed has a tabular shape, similar to that of small volume beds (beds 7.1 and 1.2.3) with a similar southeastern provenance. It is the only intermediate-volume bed whose sandstone comprises only TCD intervals. All of the other intermediate-volume and large-volume beds contain intervals of massive (TA) or planar laminated (TB) turbidite sandstone, or debrite sandstone that can be mud-rich (DM) or clean (DCS). This contrasts with the dominance of TCD sandstone intervals in small-volume beds (Fig. 6).

Sandstone shape in intermediate-volume and large-volume beds differ significantly from that in small volume beds. A broad thickness maximum characterizes larger-volume sandstones (Fig. 10), and this thickness maximum moves basinward as sandstone volume increases. Intermediate-volume and large-volume beds contain massive (TA) and planar-laminated (TB) sandstone intervals that are lacking in the small-volume beds. It is the massive and planar-laminated sandstone intervals (TAB) that mainly determine the overall sandstone shape, in that they are often much thicker than overlying TCD intervals. The shape of the basal TAB (plus clean debrite) division can be approximated by a third-order polynomial function y  =  a + bx + cx3 (Fig. 10A, Table 2). The overall shape of intermediate and large beds is described by the function Ln(y)  =  a + bx2 + cx(2.5) (Fig. 11A, 12, Table 2). Unlike exponential functions for small-volume beds, these formulations cannot be interpreted in terms of physical flow processes. However, they proved the necessary flexibility to capture the shape of sandstone beds for varying volume and facies tract.

The maximum thickness and volume of the sandstone intervals are broadly related (Fig. 10B), and the thickness maximum tends to migrate farther down the basin as the volume increases (Fig. 10C). There is little correlation between sandstone volume in intermediate and large volume beds and their initial thickness at the most proximal section (Fig. 6). Intermediate-volume and large-volume beds have significantly larger maximum grain sizes than small-volume beds (Fig. 9). Rates of down-basin fining of maximum grain size can be rather slow, especially for large volume beds (Fig. 9). However, more rapid fining is observed near the down-flow termination of TAB or clean debrite sandstone (DCS) interval (Fig. 9).

Sandstone Shape Subdivided According to Facies Tract

The geometry of intermediate-volume and large-volume sandstone beds display a series of facies tracts, which capture different modes of flow behavior and evolution (Fig. 5; Amy and Talling 2006; Talling et al. 2007a, 2007b; Talling et al. 2012, 2013a, 2013b). Facies tract 1, 2a, 3a, 3b, and 3c can be described by the same characteristic function Ln(y)  =  a + bx2 + cx(2.5) (Fig. 11). However, the rate of proximal thickening and position of the thickness maximum differs for each facies tract (Fig. 12).

Small-volume beds typically comprise only TCD intervals overlain by turbidite mudstone, comprising facies tract 1a (TE; Fig. 6). The only exceptions are beds −9 and −12, in which a proximal clean sandstone debrite (DCS) pinches out abruptly, and they are assigned to facies tract 3a (Fig. 5). Intermediate-volume and large-volume beds lacking debrites (facies tract 1b) maintain an approximately constant thickness for 20 km, followed by gradual thinning that is driven by changes in the TAB interval thickness (Fig. 10). Only low-strength clast-poor cohesive debrites (facies tract 2a) are seen in this study area, with higher-strength cohesive debris flows found elsewhere in the basin plain (Talling et al. 2013b). The addition of the cohesive debrite above underlying turbidite sandstone produces a more pronounced thickness maximum in mid basin (Fig. 11D). More rapid thinning of sandstone intervals can occur due to the pinch-out of clean debrite intervals (DCS) in facies tract 3a and 3b.

Turbidite Mudstone Intervals

The shape of turbidite mudstone (TE) intervals for progressively larger-mudstone-volume beds is presented in Figure 13. In many cases mudstone constitute most of the bed. Mudstone intervals have a consistent shape, with an increase in thickness from northeast to southwest for beds derived from both the northeast and the southwest (Fig. 14). Local thickness variations are not due to erosion by successive flows, because each mudstone interval measured in this study is capped by an interval of hemipelagic marl. The two largest-volume mudstone beds (bed 6 and Colombine) have a broad thickness maximum in the central and distal part of the Ridracoli element.

Numerical Modeling

Modeling results are presented that explore how turbidite sandstone shape (expressed as a dimensionless rate of deposit growth) varies as sediment concentration increases from volume fractions of 0.05 to 0.3. Hindered settling occurs at higher sediment concentrations, reducing particle settling velocity and affecting the flux of settling particles. Model results are based on a constant sea-floor gradient of 0.05°, a steady input flux, and a single grain size.

Discussion

To What Extent Did Seafloor Topography Control Deposit Shape, and Can We Tell?

It is reasonable to ask whether changes in seafloor gradient were a dominant control on the bed geometries analyzed here. This is because studies of recent deposits below the modern seafloor show that changes in gradient can strongly influence bed shape, or indeed whether a flow is depositional or erosional (e.g., Talling et al. 2007a; Wynn et al. 2010; Stevenson et al. 2013). Field observations from ancient outcrops can only place qualitative constraints on seafloor gradients. The continuous (“layer-cake”) stratigraphy suggests that gradients did not change substantially, and were most likely less than approximately 0.05° by comparison to studies of modern basin plains. Changes in seafloor gradient are likely to affect a number of adjacent beds in a consistent fashion, providing a way of identifying their effects. Consistent but small fractional changes in bed thickness suggest that a subtle interbasinal high near the Cavalmagra section (Fig. 2) was present within the Ridracoli Element. The consistent location at which clean-sand debrites terminate (Talling et al. 2013a), or the consistent location of cohesive debrites (Talling et al. 2013b), is most likely partly due to changes in gradient. Consistent thickening of the entire correlated sequence within the central part of the Ridracoli element (Fig. 2; Amy and Talling 2006; Talling et al. 2013a, 2013b) may indicate a subtle topographic low, or area of lower gradient. Comparison of deposit geometries for flows with opposing directions provides a second test for the effects of changing seafloor gradient, as one direction must be up hill. This suggests that the shape of mudstone intervals is much more strongly affected by basin topography than the shape of sandstones, as a consistent mudstone shape is found for flows initially travelling in both directions. Sandstone deposition is more weakly affected by basin topography, although flows from the southeast tend to produce more tabular deposits.

Shape of Small-Volume Sandstones—Dilute and Dissipative Flow

Small-volume sandstones in thin beds in the Marnoso-Arenacea sequence are dominated by cross-laminated (TC) intervals that provide evidence of deposition from dilute flow (Talling et al. 2012). The almost exponentially thinning shape of these small-volume sandstones is also similar to the general shape of dilute flow deposits in the layer-averaged model.

Similar facies comprise the thin beds that dominate levees formed adjacent to submarine channels. Submarine levee packages also tend to thin away from levee crests in a near exponential fashion, although this shape can sometimes be described by a power-law relationship (Skene et al. 2002; Skene and Piper 2005; Kane et al. 2007, 2010; Dykstra et al. 2012; Birman et al. 2009; Nakajima and Kneller 2011). A near exponential decay in deposit thickness characterizes the deposits of dilute flows in flume experiments and numerical models that decelerate with distance (i.e., they are dissipative; Talling et al. 2007b). It was therefore proposed by Talling et al. (2007b) that a near exponential decay of deposit thickness is a characteristic feature of dilute flows that decelerate along their flow path (dissipate). However, the e-folding distance (that in which the bed thickness declines by 37%) seen in levee sequences and numerical or flume experiments is typically much shorter than that in the thin beds of the Marnoso-Arenacea Formation (Talling et al. 2007b). This more rapid decay of deposit thickness (shorter e-fold distance) most likely results from radial flow expansion or thinner flow (Talling et al. 2007b).

How Does Flow Concentration and Hindered Settling Affect Sandstone Shape?

We now explore how hindered settling from dense near-bed layers might influence deposit shape, and whether it can explain observed sandstone shapes. Hindered settling starts to occur at sediment volume concentrations of ∼ 10% as grain interactions become important (Bagnold 1954), and its effects become increasingly (nonlinearly) important as volume concentrations increase further (Fig. 15; Richardson and Zaki 1954). Talling et al. (2007a) proposed that hindered settling was the primary reason for the broad thickness maximum observed in larger-volume beds dominated by massive (TA) and planar-laminated (TB) sandstone intervals. This hypothesis was based in part on observation that planar-laminated (TB) intervals were typically laterally equivalent to massive (TA) intervals of similar thickness, and there is consensus that TA intervals are more clearly deposited by dense flows.

This hypothesis was tested using the layer-averaged flow model. A series of model runs were undertaken with a constant sea-floor gradient of 0.05°, with a steady input flux, and using a single grain size. Model results are expressed initially as the dimensionless rate of deposit growth, D(X), (see Eq. 12) for a wide range of source volume fractions, φ0 (Fig. 16). The distinctive shape of TA and TB sandstone intervals characterized by a broad thickness maximum is well reproduced in numerical models that include hindered settling (Fig. 16). Dilute sediment flows have deposits whose thickness decays almost exponentially (Fig. 16). The broad thickness maximum only appears once elevated sediment concentrations result in hindered settling (Figs. 15, 16).

The sediment accumulation rate is proportional to the product of near-bed sediment concentration and the sediment settling velocity. The broad thickness maximum results from initially strongly hindered settling, which results in low sediment accumulation rates. Intermediate sediment concentrations and settling rates produce the highest sediment accumulation rates, which form the broad thickness maximum. Reduced sediment concentrations farther from source cause a transition into non-hindered settling from dilute flow, which produced a distal deposit that thins in a near exponential fashion. We can show that the deposit thickens with downstream distance when the instantaneous bed concentration is sufficiently large (φb > 1/(n + 1)), where n is the exponent in the Richardson-Zaki settling velocity equation (Figs. 15, 16).

What Determines the Distance to the Deposit Maximum?

The distance to the deposit maximum increases for flows with a higher input flux (q), which are initially thicker or faster. An increase in grain size and hence settling rate (vs∞) tends to reduce the distance to the thickness maximum. Higher rates of fluid entrainment also increase the distance to the deposit thickness maximum.

The distance to the thickness maximum is 10 to 40 km in the field dataset, although this depends on the location of the most proximal outcrop (i.e., where x  =  0). The deposit maximum occurs at dimensionless distances of 1 to 4 in the model runs (Fig. 16A). This implies that the ratio of q/vs∞ is ∼ 104 m, if the model is to reproduce the distance to the deposit maximum seen in the field. Using a terminal sediment settling velocity (vs∞) of ∼ 10−2 ms−1 for a 100 µm grain (Fig. 16B), this implies an input flux per unit width (q) of ∼ 100 m2 s−1, which would equate to flow that is 65 m thick and travelling at ∼ 1.6 ms−1. The distance to the deposit thickness maximum seen in the field can therefore be reproduced by reasonable values of the parameters q and vs∞ (Fig. 16B). See Tallinget al. 2014 for a summary of turbidity current thicknesses and speeds measured in the field. Sediment deposition was found to occur below speeds of ∼ 1.6 m in the experiments of Sumner et al. (2009), so flows travelling at such speed might be expected to be depositional. For these parameter values the entrainment parameter is approximately 0.1.

Deposition Rates, Flow Duration, and Lithofacies

Rates of sediment accumulation can be estimated at the deposit thickness maximum. Assuming a value of ∼ 10−2 m/s for vs∞ (for a 100 µm grain), r  =  1.6 (Parker et al. 1986), and a porosity of ∼ 0.5 in the deposit, this implies that peak nondimensionalized sediment accumulation rates (D) of ∼ 0.2 to 0.45 seen in the model runs (Fig. 16) equate to sediment accumulation rates of ∼ 0.2 mm s−1. Flows that lasted ∼ 50 minutes would be needed to build up sandstone intervals that had peak thicknesses of ∼ 1 m, as seen in the field examples. Assuming a speed of ∼ 1.6 m/s, this 50 minute duration would imply that the depositional part of the flow was ∼ 3 km in length, from its head to tail.

Laboratory experiments suggest that a sediment accumulation rate of ∼ 0.44 mm s−1 characterizes the boundary between the formation of massive (TA) and planar-laminated (TB) sand (Sumner et al. 2008). The sediment accumulation rates near the deposit thickness maximum seen in the model runs are therefore broadly consistent with deposition of massive or planar-laminated sandstone intervals, as is observed in the field (Fig. 16b).

Comparison with Previous Work

Most previous numerical studies of bed shape have assumed that flow is sufficiently dilute so that sediment settling is unhindered, and they have tended (Talling et al. 2007a) to produce deposits shapes whose thickness decreases monotonically down-flow in a quasi-exponential fashion (Zeng and Lowe 1997; Salaheldin et al. 2000; Felix 2001, 2002; Harris et al. 2002; Das et al. 2004, Gray et al. 2005; Falcini et al. 2009). A broadly similar continuously thinning shape characterizes most experimental turbidity current deposits (Talling et al. 2007a), including laboratory studies with both steady and nonsteady (lock release) inputs, and unimodal or ploydisperse grain sizes (Bonnecaze et al. 1996; Gladstone et al. 1998; Woods et al. 1998; De Rooij and Dalziel 2001; Choux and Druitt 2002; Kubo 2004; Gray et al. 2005). It appears that dilute flows that decelerate spatially tend to produce deposit shapes that thin almost exponentially, as seen discussed previously when considering channel–levee deposits.

Tinterri et al. (2003) is one of the few previous modeling studies to include effects of hindered settling, and their model results suggest that a thickness maximum is a general feature of hindered settling. Their model differed from that presented here in key regards. It comprised a dense lower layer in which sand was liquefied, and from which hindered settling occurred (Tinterri et al. 2003). This type of liquefied dense flow most closely resembles clean-sand debris flow (that form DCS or Tinterri et al.'s F5 facies; see Talling et al. 2012), rather than high-density turbidity currents (that form TA or TB1&2). This is consistent with the narrow thickness maximum in Tinterri et al.'s (2003) modeled deposits, which more closely resembles the shape of clean-sand debrites (DCS) than the broader thickness maximum of TAB intervals within Marnoso-Arenacea beds.

Alternative Hypotheses to Explain the Broad Thickness Maximum: Flow Carrying Capacity

Modeling presented here shows that hindered settling provides a plausible mechanism to reduce sediment settling fluxes and produce thinner sand deposits in the proximal part of the bed and a broad thickness maximum (Fig. 16). However, there are other plausible mechanisms that may generate this type of deposit shape, which are not addressed. For instance, the model does not include resuspension of sediment from the bed, and changes in mass of sediment that the flow could suspend (its capacity; Kuenen and Sengupta 1970; Hiscott 1994). The initial stages of a flow may be sufficiently powerful to suspend all of the sediment that is carried by the flow, resulting in sediment bypass, potentially with erosion of the bed. As the flow speed and capacity then declines, there may be a region in which the sediment load in the flow is similar to the sediment carrying capacity of the flow. This would lead to an initial area of reduced sediment deposition and an increase in deposit thickness with distance, forming a thickness maximum. More generally, modeling presented here shows that hindered settling may produce a deposit shape with a broad thickness maximum, but there may be other processes that can also cause this type of shape.

Conclusions

There are few studies that have documented the shape of individual submarine flow deposits. Here we show the shape of 32 individual submarine flow deposits in a down-flow direction in an ancient basin plain that lacks channels or even bed amalgamation. Field observations (including this “layer-cake” stratigraphy) suggest that seafloor topography was subdued in this basin plain, although quantitative constraints on changes in seafloor gradient cannot be measured. Despite the complexity of these deposits in this topographically simple basin-plain setting, there are distinct types of down-flow evolution (captured by facies tracts; Fig. 5). Sandstone intervals in thin beds with smaller volumes are typically dominated by cross lamination (TC). Their almost exponentially thinning shape is consistent with deposition from dilute and dissipative flows, which is consistent with the presence of migrating bedforms. This exponentially thinning shape resembles that seen in levee sequences adjacent to submarine channels, and deposits in dilute and dissipative laboratory and numerical models, although the rate of thinning of the Marnoso-Arenacea sandstones is rather slow. Thicker and larger-volume sandstone intervals in the Marnoso-Arenacea Formation are dominated by massive (TA) and planar-laminated (TB) sandstone, and they display a different shape with a broad thickness maximum. The results from a layer-averaged numerical model suggest that this shape records hindered settling from dense near-bed flow. This result is important because it suggests that both massive and planar-laminated sandstones were deposited from high-density turbidity currents. Many beds also contain sandstone intervals that can pinch out more rapidly, and were deposited by cohesive (muddy) or clean-sand debris flows. Their shape has been analyzed elsewhere (Amy et al. 2005; Talling et al. 2013a, 2013b). Deposition of turbidite mud is more strongly affected by basin-floor topography, in that a similar mudstone shape is generated by flows that traversed the basin plain in opposing directions. This unusual field data set suggests that planar-laminated (TB) sandstone intervals may record deposition from dense near-bed layers, which is important because they can also be formed by dilute flow in laboratory experiments.

This work was part of a UK-TAPS project, funded by NERC Ocean Margins LINK grant NER/T/S/ 2000/0106 and NER/M/S/2000/00264, and cosponsored by ConocoPhillips, BHP Billiton, and Shell. The authors wish to thank Gianni Zuffa and Franco Ricci Lucchi (Bologna University) and Luca Martelli (Emilia Romagna Geological Survey) for advice initially on fieldwork in northern Italy. Bed correlations that form the basis of this study were made possible by the outstanding mapping of marker beds by the Italian Geological Surveys. We wish to thank Zoltan Sylvester for his insightful and constructive comments, and two anonymous reviewers.