Quantification of the bed‐scale architecture of submarine depositional environments

Submarine channel and fan deposits form the largest sediment accumulations on Earth and host significant reservoirs for hydrocarbons. While many studies of ancient fan deposits describe architectural variability along 2D transects (e.g. axis‐to‐fringe, proximal‐to‐distal), these relationships are often qualitative and are rarely quantified at the event‐bed scale. In order to enable quantitative comparison of the fine‐scale architecture of submarine depositional environments, 56 bed‐scale outcrop correlation panels from five broadly categorized environments (channel, levee, lobe, channel‐lobe transition zone, CLTZ and basin plain) were digitized. Measured architectural parameters (bed thickness, bed thinning rates, lateral correlation distance, net‐to‐gross) provide a large (n = 28,525) and statistically robust framework to compare event‐bed architectures within and between environments. “Thinning rate” data (i.e. the lateral rate of change of bed thickness) clearly differentiate deposits from different submarine depositional environments, helping to quantify generally accepted models for proximal‐to‐distal evolution of stratigraphic architecture. The thinning rates of sandstone beds and mudstone‐dominated intervals vary predictably between environments. For example, the highest sandstone thinning rates occur in channel deposits (0.2–6 cm/m; P10 and P90 values here and below) and decrease to lobe (0.1–1.6 cm/m), CLTZ (0.2–0.9 cm/m), levee (0.0024–0.078 cm/m) and basin‐plain deposits (0.000017–0.0054 cm/m). These quantitative relationships provide valuable insights for downslope flow evolution and the construction of stratigraphic architecture in submarine settings. Due to intra‐environment variability, net‐to‐gross is highly variable and thus (when considered alone) is not a diagnostic indicator of depositional environment. Submarine lobe deposits show the most variability in event bed thickness, thinning rate and net‐to‐gross, likely due to the inherent facies variability and differing boundary conditions. To explore this variability, lobe deposits were sub‐classified based on position (proximal, distal) and effective confinement (unconfined, semiconfined, confined) to provide a more detailed sub‐environment analysis. Unconfined lobe deposits show a proximal‐to‐distal increase in sandstone thickness and decrease in mudstone thickness, supporting conceptual models. Confined lobe deposits have thicker sandstone and mudstone beds and lower net‐to‐gross values as compared to unconfined and semiconfined lobes, supporting a sediment trapping mechanism by confinement. These quantified bed‐scale parameter comparisons enable the recognition of architectural similarities and differences within and between environments, demonstrating the need for more quantitative studies of bed‐scale heterogeneity. The results from this study are immediately applicable to parameterizing forward stratigraphic models, constraining property distribution in reservoir models, and probabilistic determination of depositional environment from outcrop and core descriptions of submarine depositional environments.

In this study, a newly compiled database was created (from published bed-scale correlation panels) of event-bed parameters (e.g. bed thickness, bed and facies thinning rates, net-togross) from different submarine depositional environments (channel, levee, CLTZ, lobe and basin plain). This database enables the recognition of (a) architectural similarities and differences between environments and (b) sub-environments within lobe environments (e.g. medial vs. distal, confined vs. unconfined). The database was analysed to develop quantitative and statistical insights into bed thickness and lateral heterogeneity relationships within and among submarine depositional environments. This data provide quantitative data for constructing realistic geological and reservoir models, particularly in datapoor settings where lateral variability in bed-scale architecture is not observable and thus a major uncertainty (Hofstra et al., 2017).

| Compilation database
In order to enable comparison of multiple depositional environments, event-bed geometries were collected (e.g. bed thickness and lateral extent of a single bed) from publications containing detailed bed-scale correlations from various ancient submarine depositional environments ( Figure 1; Table  1). This database consists of 2,251 event beds from 56 correlation panels that represent 17 different formations from outcrops around the world (Figure 1; Table 1). Geometry data was not collected for larger hierarchical scales (e.g. channel or lobe elements), due to variable author interpretations of stratigraphic hierarchy. For each panel, each event bed was digitized with an assigned lithology (e.g. turbidite sandstone, turbidite mudstone, hybrid event bed, debrite) and computed net-to-gross values as compared to unconfined and semiconfined lobes, supporting a sediment trapping mechanism by confinement. These quantified bed-scale parameter comparisons enable the recognition of architectural similarities and differences within and between environments, demonstrating the need for more quantitative studies of bed-scale heterogeneity. The results from this study are immediately applicable to parameterizing forward stratigraphic models, constraining property distribution in reservoir models, and probabilistic determination of depositional environment from outcrop and core descriptions of submarine depositional environments.

K E Y W O R D S
Lateral heterogeneity, submarine channel, submarine fan, turbidite bed thickness bed thicknesses, thinning rates, net-to-gross and pinch-outs between measured section locations. A major uncertainty in this study is that many panels do not correlate every event bed, resulting in classified "mudstone" intervals that contain thin sandstone beds (e.g. Figure 1). This lumping of lithologies into one mudstone interval only provides a coarse resolution of mudstone-interval architectures and may obscure the details of mudstone event-bed thickness and variability.
However, this lumping occurs across all depositional environments, so corrections to individual environments/panels were not made. Also, the calculated bed thickness data are skewed towards thicker (>10 cm) beds due to ease of correlation as compared to thinner beds, causing an underestimate in netto-gross values and higher characteristic bed thickness per environment. Bed/interval thicknesses and net-to-gross values were collected at measured section locations (Figure 1).  Amy & Talling, 2006) with sandstone beds coloured in yellow, mudstone intervals coloured in light grey and debrite beds coloured in dark grey. Each bed was digitized, and thinning rates were calculated in a pairwise fashion (bottom). The number of beds (N = 12 for this example) and the number of thinning-rate values (n = 336) are provided in Table 1 for each panel. Net-to-gross values are calculated for each digitized measured section, and pinch-out locations are counted for each facies and panel  Grain-size data was not collected because some panels have no grain-size information and many authors/panels depict grain size differently, making a comprehensive comparison difficult. Hybrid event-bed and debrite lithologies were excluded from this analysis due to low sample numbers. Each panel was broadly characterized into a depositional environment (channel, levee, CLTZ, lobe or basin plain; Table  1). This scheme was chosen for simplicity of comparison, and generally, this interpretation is in agreement with the original author's interpretation (Table 1). However, the depositional environment interpreted by the original authors contains moderate uncertainty of the precise sub-environment, particularly within lobe deposits (  (Table 1).
Each panel was also associated with a broad palaeocurrent panel orientation (strike vs. dip) but a correction was not attempted, because without additional data not present in outcrop settings, corrections only introduce more uncertainty. For example, projecting a panel to be parallel or perpendicular to the palaeocurrent may correctly change the lateral correlation distance, but no information is available (due to the lack of outcrop or measured data) to constrain how bed thickness changes to the new position because there often is no outcrop available in that position.
Finally, bed thickness and geometry in channelized deposits are commonly poorly constrained due to amalgamation that makes lateral correlation difficult (Hubbard et al., 2014). In this dataset, this likely causes an overestimate in bed thickness and thus a lower associated thinning rate. To minimize this error for channelized deposits, the total package thickness was divided by the number of amalgamation surfaces documented within an amalgamated body, giving a representative (i.e. mean) bed thickness.

Quantitative parameters
For statistical comparison, bed thickness and lateral distance are the two most important types of data collected from digitized panels (Figure 1). Equation 1 was used to compute the thinning rate, a dimensionless number that enables comparison of bed thickness changes over a lateral distance (Deptuck et al., 2008;Liu et al., 2018;Marini et al., 2015;Tőkés & Patacci, 2018). The sign convention (e.g. + or −) for thinning rate is arbitrary and depends on the direction of thinning/thickening for a given change in bed thickness; thus, absolute values of thinning rate are used. With the method employed here, the computed thinning rate and lateral distance are associated with the leftmost measured section's bed thickness for all future comparisons. Thinning rates were acquired in pairwise fashion ( Figure 1B; e.g. section 1 to 2, 1 to 3, 1 to 4, etc.) to provide a distribution of thinning rates and to decrease the sampling bias created from the lateral spacing of measured sections. Thinning rates were calculated for both sandstone and mudstone lithologies. A 2D kernel density estimation was used to calculate "percent volume contours" of two cross-plotted variables, providing polygons (i.e. contours) that encompass a percentage of the data. For example, 90% of the cross-plotted data falls within the 90% volume contour map; these per cent volume contour maps, generated using python's seaborn library, are used to show the distribution of the data rather than plotting all of the data (n = 28,525) as individual points (e.g. Figure 2).
Net-to-gross ratios were calculated at each measured section location by dividing the total sandstone thickness by the total section thickness. The "probability of pinch-out" parameter is the chance that a bed pinches out in a given lateral distance, normalized by the number of beds within that panel (Equation 2). The probability of pinch-out parameter is associated with an individual panel and groups multiple panels by depositional environment. For example, if a panel has (1) F I G U R E 2 Thinning rate and thickness data for submarine depositional environments. (A) Combined (i.e. sandstone and mudstone) plots of bed thickness versus thinning rate, with a median (coloured dot) and a 90% volume contour (i.e. a polygon that encompasses 90% of the data) for each environment. Black arrows show proximal-to-distal trends. Note that while bed thickness is not a robust indicator of environment, the combination of bed thickness and thinning rate distinguishes between environments. (B) The distributions of bed thickness and thinning-rate plots for sandstone beds (yellow) and mudstone intervals (grey). Different relationships between trends in sandstone and mudstone thickness and thinning rate reflect varying transport and deposition mechanisms in different environments. Yellow and grey lines are median values five total sandstone bed pinch-outs over 20 beds with a lateral distance of 1 km, the frequency of pinch-outs for this panel would be 0.00025 per metre. For a given sandstone bed, this statistic would imply that there is a 2.5% probability a sandstone bed would pinch out over 100 m. This gives a pinch-out count per metre to enable comparable ratios between environments. Although this method is used here to calculate pinchout frequency, there are several other methods to calculate "tabularity" (Liu et al., 2018;Tőkés & Patacci, 2018).

| Lateral event-bed continuity by depositional environment: Results
Using data collected from the compiled correlation panels (Table 1), event bed geometries were investigated among different submarine depositional environments. Figure 2A shows the relationship between thinning rate and bed thickness (sandstone beds and mudstone-dominated intervals plotted together as one group) for each environment. Channel deposits show the highest bed thickness and thinning-rate ranges with 10 cm to 3 m, with a median at 45 cm and 0.03 to 10 cm/m, with a median at 1.0 cm/m, respectively ( Figure 2A). Basin-plain deposits show thick beds (10 cm to 3 m, with a median at 50 cm) and the lowest thinning rates (0.0001 to 0.01 cm/m, with a median at 0.0015 cm/m). Levee deposits display moderate bed thicknesses of 10 cm to 1 m, with a median at 21 cm with moderate to low thinning rates of 0.001 to 0.1 cm/m, with a median at 0.02 cm/m ( Figure 2A). Channel-lobe transition zone (CLTZ) deposits show moderate to high bed thicknesses of 5 cm to 1 m, with a median at 27 cm and moderate to high thinning rates of 0.005 to 2.5 cm/m, with a median at 0.13 cm/m. Lobe deposits overall are quite similar to channel-lobe transition zone deposits, but display the largest range of bed thicknesses (1 cm to 1 m, with a median at 15 cm) and a wide range of thinning rates (0.002-5 cm/m, with a median at 0.14 cm/m; Figure 2A). When the event-bed data are separated by lithology (i.e. sandstone beds vs. mudstone-dominated intervals), each environment displays different characteristic sandstone/mudstone thicknesses and thinning rates ( Figure 2B). Sandstone deposits in channel environments are thicker (P 50 62 cm) and have larger thinning rates (P 50 1.610 cm/m) compared to mudstone-dominated intervals (P 50 26 cm and 0.5609 cm/m; Figure 2B). Levee deposits show the opposite trend, with the mudstone-dominated intervals being thicker (P 50 69 cm) than sandstone beds (P 50 18 cm) and thinning more rapidly than sandstone beds (P 50 0.0923 and 0.0192 cm/m, respectively). This is likely caused by the lumping of multiple mudstone beds and thin sandstone beds (see Figure 1B) and thus may not reflect individual mudstone bed geometries. The CLTZ deposits appear very similar to channels, but with slightly thinner beds (P 50 31 cm and 12 cm) and slightly lower thinning rates (P 50 0.1653 and 0.1411 cm/m; Figure 2B). Lobe deposits show the widest distribution of thickness and thinning rates for both sandstone and mudstone lithologies ( Figure 2B). Also, sandstone and mudstone thickness (P 50 17 and 10 cm) and thinning rates (P 50 0.1805 and 0.1029 cm/m) are quite similar to each other ( Figure 2B). Basin-plain deposits display higher mudstone-dominated interval thickness (P 50 97 cm) and thinning rates (P 50 0.0017 cm/m) compared to sandstone beds (P 50 41 cm and 0.0012 cm/m; Figure 2B).
The lateral distance over which the thinning rate is measured (see Equation 1) is also useful to differentiate environments (Figure 3). The overall negative slope of the data in Figure 3 is intuitive and caused by distance being the denominator within the calculation for thinning rate (Equation 1). The vertical striping in Figure 3 is caused by sampling bias (i.e. caused by the measured section spacing). Channel deposits display the highest thinning rates and the shortest bed correlation distance (1-300 m, with a median at 30 m). The CLTZ deposits display moderate correlation distances from 20 to 800 m with a median at 95 m ( Figure 3). Lobe deposits span the largest range of bed correlation distances of 2 m to 8 km with a median at 70 m. Levee deposits characteristically show larger correlation distances of 300 m to 1.1 km with a median at 600 m ( Figure 3). Finally, basin-plain deposits show the largest characteristic correlation distances of 1.2 to 17 km with a median at 10 km.
The "frequency of pinch-out" parameter is the number of pinch-outs between each section normalized by the lateral distance and the number of beds within that panel (Equation 2). Figure 4 displays the 90th percentile frequency of pinchouts over a lateral distance of 25 m by lithology and environment. The P90 value represents the highest percentage of pinch-outs observed within that depositional environment. In contrast, the 10th percentile of pinch-outs over 25 m for all environments is zero (i.e. all beds correlate across 25 m). The lowest to highest P90 pinch-out percentage observed over 25 m by sandstone and mudstone lithologies is, respectively, as follows: basin plain (10 −7 and 10 −7 ), levee (0.01 and 0.16), CLTZ (0.29 and 0.10), lobe (0.22 and 0.28) and channel deposits (0.33 and 0.75; Figure 4). The P10 pinchout percentage seen over 25 m by sandstone and mudstone lithologies for all environments is 0%. Understanding the frequency of pinch-outs by environment is important for parameterizing stratigraphic forward models and reservoir models (Pyrcz et al., 2005). These results indicate that basin-plain deposits have the least likelihood of either lithology (sandstone or mudstone) pinching out over 25 m, whereas channel deposits display the highest likelihood of mudstone lithologies to pinch out within 25 m. Lobe deposits display similar pinch-out rates between sandstones and mudstones ( Figure  4), likely related to the similarity in thinning-rate distribution between sandstone and mudstone lithologies ( Figure 2B).
Net-to-gross is a commonly used parameter to infer depositional environments (Prather et al., 1998). The violin plots in Figure 5 show the distribution of net-to-gross values for each environment. Based on the medians, the lowest to highest characteristic net-to-gross environments are levee (0.24), basin-plain (0.32), lobe (0.72), CLTZ (0.85) and channel (0.86) deposits. However, the overlap in the distributions for channel, CLTZ and lobe deposits shows that net-to-gross alone is a very poor indicator of depositional environment. This effect is compounded by the often-arbitrary measurement of "gross" intervals. The CLTZ and basin-plain deposits display the smallest variances ( Figure 5), while channel deposits display the largest spread of data with the highest variance ( Figure 5). Channel, CLTZ and lobe deposits are skewed towards higher net-to-gross values than their means ( Figure 5). Figure 6 summarizes the distinctive thinning rate and bed thickness relationships in different environments. Because the distributions of net-to-gross and bed thickness overlap significantly between environments (Figures 2 and 5), these parameters alone are not sufficient in interpreting depositional environment. Instead, a combination of lithology-independent bed thickness and thinning rate ( Figure  6) is effective for differentiating between channel, levee and basin-plain environments. The CLTZ and lobe deposits have very similar bed thickness and thinning-rate distributions, indicating that these deposits may only be distinguishable when comparing sandstone to mudstone lithologies ( Figure 2B). Wynn, Kenyon, Masson, Stow, F I G U R E 3 Thinning rate plotted against the lateral distance of correlation, with a median (coloured dot) and a 90% volume contour (i.e. a polygon that encompasses 90% of the data) for each environment. Black arrows show proximal-to-distal trends. Environments are distinguished by their lateral correlation distances, with channels showing the shortest correlation distance and highest thinning rates, matching their scale and evolution. On the other hand, basin plains intuitively have the longest distance and lowest thinning rate. Lobes span across all length scales, perhaps due to the varying degree of basin confinement. The vertical striping (e.g. in levees) is associated with sampling bias (i.e. measured section spacing) and Weaver (2002) document numerous erosional features in CLTZ environments, and a parameter that quantifies erosion (e.g. amalgamation ratio) may better differentiate CLTZ and lobe deposits. Sandstone beds and mudstone-dominated intervals display distinctive thinning-rate and bed thickness relationships in different environments ( Figures 2B and 6) that are likely caused by their respective transport and deposition mechanisms. For example, sandstone and mudstone deposition in levee deposits is strongly influenced by flow stripping of the active channel (Fildani, Normark, Kostic, & Parker, 2006;Peakall, McCaffrey, & Kneller, 2000;Piper & Normark, 1983). However, the sands are only deposited by flows that are suspending sand grains higher than the active levee crest, whereas muds are suspended above the levee crest during nearly every flow (Jobe, Sylvester, Howes, et al., 2017;Straub & Mohrig, 2008). Therefore, sandstone bed thickness is indicative of a single flow event, whereas the mud event bed boundaries are likely indistinguishable (Dennielou et al., 2006), producing higher characteristic mudstone-interval thickness. The higher thinning rates within mudstone-dominated intervals are due to the high variation of thin bedded sandstone beds lumped into a single mud interval, an inability to accurately correlate thin sandstone beds between measured sections, and indistinguishable and extremely poorly correlated mudstone bed boundaries within the original panel creating a rapid mudstone bed thickness change and increased thinning rate. While this study only has one panel available for levee deposits (Table 1), the broad theoretical understanding of levee dynamics is displayed within the quantified parameters of this study (Fildani et al., 2006;Peakall et al., 2000;Piper & Normark, 1983;Straub & Mohrig, 2008). However, additional data are needed to create a more robust dataset of levee deposits, including differentiating interval and external levee environments (Hansen et al., 2015).

| Lateral event bed continuity by depositional environment: Interpretation
Channelized environments are typically the highest energy portions of the submarine depositional system and thus display the highest amounts of erosion and bypass (Hubbard et al., 2014;Mutti & Normark, 1987;Stevenson et al., 2015). Thick sandstone beds and thin mudstone intervals, high net-to-gross and high frequency of pinch-outs characterize channel deposits (Figures 2, 4, 5 and 6). Confined flow in channelized environments leads to erosion, bypass of muddy sediment and deposition of coarse-grained sediment (Hiscott, Hall, & Pirmez, 1997;Jobe, Sylvester, Pittaluga, et al., 2017;Mutti & Normark, 1987;Normark, 1989;Peakall et al., 2000), creating thick sandstone beds (Figure 2), high pinch-out frequency of both sandstone and mudstone ( Figure 4) and high net-to-gross values ( Figure 5). The wide-ranging distribution of channel net-to-gross ( Figure 5) is likely caused by inclusion of axis, off-axis and margin facies into channel-deposit correlation panels (Hubbard et al., 2014). As with levee deposits, differentiating axis, off-axis and margin deposits may lead to better constraints on channel-deposit architecture. The event bed correlation distance in channel deposits is less than 300 m (Figure 3), limited by channel dimensions (Konsoer, Zinger, & Parker, 2013;Shumaker et al., 2018).
Although CLTZs are characterized by the initial loss of confinement from a channel, they still contain a high degree of erosion and bypass that is commonly displayed as smaller distributive channels and mega flutes (Brooks et al., 2018;Carvajal et al., 2017;Covault et al., 2017;Mutti & Normark, 1987;Wynn et al., 2002). The CLTZ deposits have thinner beds and lower thinning rates in both sandstone and mudstone lithologies, longer correlation distances and lower net-to-gross when compared to channel deposits (Figures 2 and 3). This is likely caused by the loss of confinement in the CLTZ environment that allows the flow to distribute sediment across a wider surface, reducing bed thickness and thinning rates. The narrow distribution of high net-to-gross found within the CLTZs supports the erosion documented in these deposits (Carvajal et al., 2017;Covault et al., 2017;Wynn et al., 2002) and suggests that mud is being bypassed and/or eroded ( Figure 5).
Lobe environments are described by the total loss of channel confinement (Piper & Normark, 1983), and thus, lobe deposits typically contain less erosion than other environments as well as a downstream and axis to off-axis decrease in thickness, grain size, sand content and sand bed amalgamation (Deptuck et al., 2008;Mutti & Normark, 1987;Prelat et al., 2009). However, basin confinement can alter this facies model (discussed below; also see Jobe, Sylvester, Howes, et al., 2017). Interestingly, sandstone and mudstone lithologies in lobe deposits have very similar thickness and thinning-rate distributions, suggesting that bed and lobe compensation F I G U R E 5 Net-to-gross "violin plot" distributions for submarine depositional environments. Due to intra-environment variability, net-to-gross is not a diagnostic indicator of environment. Net-to-gross values were calculated from the digitized panels at each measured section location ( Figure 1; Table 1 creates statistically similar bedding geometries between sandstone and mudstone facies. The broad distribution of observed bed thickness, thinning rate (Figure 2), pinch-out frequencies ( Figure 4) and net-to-gross values ( Figure 5) is supported by a traditional lobe facies model that predict spatial facies variability; the wide variability also suggests that the compiled data sample a range of lobe sub-environments that have different associated parameter values (e.g. proximal vs. medial vs. distal sub-environments). Other factors for the wide range of bed thickness, thinning rates and net-to-gross (Figures 2 and   5) may include differing sediment supply, basin configuration and tectonic setting of the compiled data (Table 1).
Basin plains are located distal to lobe environments and are locations characterized by very low gradients, tabular bedding geometry and little to no erosion (Amy & Talling, 2006;Clare et al., 2014;Malgesini et al., 2015;Weaver, Rothwell, Ebbing, Gunn, & Hunter, 1992). A key difference between basin plain and all other deposits is their long correlation distances (1,000s of m) and low thinning rates (~10 −3 ) for both sandy and muddy lithologies (Figures 2 and 3), which is likely Ranges are 10 th , 50 th and 90 th quantiles (P 10 -P 50 -P 90 ). SS = Sandstone MS = Mudstone caused by complete lack of confinement and low sea floor gradients, allowing the flow to cover large areas (Amy & Talling, 2006;Stevenson et al., 2014;Sumner et al., 2012;Weaver et al., 1992). While this study does not specifically compute bed geometry shape, Malgesini et al. (2015) document different thinning-rate relationships for sandstones with different internal structure as well as mudstone lithologies from basin-plain deposits of the Marnoso-Arenacea. Sandstone bed thicknesses in basin plains are similar or thicker than channels, CLTZs and lobes, indicating that only very large flows are depositing sand on the basin plain (Jobe, Howes, Romans, & Covault, 2018). The thick nature of mudstone-dominated intervals and low netto-gross of basin-plain deposits indicates infrequent sand-rich events (Clare et al., 2014;Jobe et al., 2018), leading to thick mud accumulations between sand beds (Figures 2 and 6).

| Lobe sub-environments and effective confinement: Results
Submarine lobe deposits show the most variability in event bed thickness, lateral continuity and net-to-gross (Figures 2 through 5). To explore this variability, lobe deposits were classified into the following sub-environments: unconfined proximal, unconfined distal, semiconfined proximal, semiconfined distal, confined proximal and confined distal. In unconfined settings, proximal lobe deposits have thicker sandstone beds (P 50 28 cm) and thinner mudstone intervals (P 50 19 cm) compared to their distal counterparts (P 50 10 cm sand and 29 cm mud; Figure 8). Unconfined proximal lobe deposits display higher thinning rates for both sandstone and mudstone lithologies (combined P 50 2.5 10 −3 cm/m) than unconfined distal lobe deposits (combined P 50 5.1 10 −4 cm/m; Figure 8); both the thickness and thinning-rate trends are intuitive and support conceptual lobe facies models. In semiconfined lobe settings, proximal deposits have thinner sandstone beds and thinner mudstone intervals than distal deposits ( Figure 8B), and proximal deposits thin more rapidly than distal deposits (P 50-proximal 2.2 10 −3 cm/m vs. P 50-distal 8.6 10 −4 cm/m; Figure  8A). In confined lobe settings, both proximal and distal deposits thin at a similar rate (P 50-proximal 3.5 10 −4 and P 50-distal 1.9 10 −4 cm/m; Figure 8), but opposite to semiconfined settings, confined proximal deposits are thicker compared to confined distal deposits, both in sandstone (P 50-proximal 63 cm, P 50-distal 39 cm) and in mudstone (P 50-proximal 79 cm, P 50-distal 32 cm; Figure 8). Out of all lobe sub-environments, confined proximal lobe deposits display the thickest sandstone and mudstone beds and the lowest thinning rates (Figure 8).
The net-to-gross values for the lobe sub-environments are broadly similar, but important differences exist (Figure 7). Median net-to-gross decreases from proximal to distal for unconfined (0.72-0.46) and semiconfined (0.77-0.69) lobe settings (Figure 7), validating classic facies models for submarine lobe deposits (Deptuck et al., 2008;Normark, 1978;Prélat et al., 2009). However, confined lobe deposits show the opposite trend, with proximal settings showing a range of net-to-gross values with a median of 0.32, but distal confined lobe deposits showing higher (P 50 0.60) net-to-gross values (Figure 7). While these trends in net-to-gross are intuitive and validate conceptual models, caution is urged when relying solely on these distributions, as they are likely incomplete due to small sample sizes (Figure 7).

| Lobe sub-environments and effective confinement: Interpretation
Confined and unconfined lobe deposits have very different planform shapes (Prélat, Covault, Hodgson, Fildani, & Flint, 2010) and sandstone/mudstone thickness distributions (Marini et al., 2015). An unconfined lobe has no lateral or distal topographic barriers, which allow the flow to fully expand and for the mud fraction to be transported to the most distal reaches of the lobe (Damuth & Flood, 1983;Picot et al., 2016). In contrast, semiconfined and confined lobe deposits have differing spatial distributions of sandstone and mudstone due to the presence of lateral or terminal topographic barriers (Prather et al., 1998;Tőkés & Patacci, 2018). A semiconfined system may force deposition of sand but allow bypass of mud (Jobe, Sylvester, Howes, et al., 2017;Lamb et al., 2006;Prather et al., 1998). On the other hand, a fully confined system has flows that cannot fully expand within the basin and would prevent the F I G U R E 7 Net-to-gross "violin plot" distributions for lobe sub-environments identified by the amount of basin confinement. Unconfined and semiconfined settings display decreasing net-to-gross from proximal to distal, while confined settings seem to show an increase in net-to-gross from proximal to distal sand and mud fractions from exiting the basin (Pirmez et al., 2012;Prather et al., 1998, Prather et al., 2012Sylvester et al., 2015), and the lower net-to-gross values support this idea (Figure 8). Sandstone thinning rates in all lobe sub-environments decrease from proximal to distal (Figure 6; cf. Tőkés & Patacci, 2018); these data confirm conceptual lobe facies models and is likely caused by decreasing transport capacity (Hiscott, 1994) in the more distal reaches of lobe environments. This loss-of-capacity relationship is also observed in sandstone bed thickness data from unconfined settings, where sandstone beds are thicker in the proximal reach (P 50 28 cm) than in the distal reach (P 50 10 cm; Figure  6B). However, this relationship is obscured in topographically complex confined and semiconfined settings. Both sandstone bed thickness and mudstone-interval thickness decrease from confined to unconfined to semiconfined lobe deposits ( Figure 6). This relationship is expected for confined to unconfined and confined to semiconfined as the flow within a confined system is unable to laterally expand, creating a thicker bed for a given flow volume Marini et al., 2015Marini et al., , 2016Prélat et al., 2010). However, the lower bed thickness results for proximal semiconfined compared to proximal-unconfined lobe deposits are counterintuitive and may represent the higher degree of erosion and/or bypass for proximal portions of semiconfined lobe deposits, creating a lower characteristic bed thickness ( Figure 6; Jobe, Sylvester, Howes, et al., 2017;Prather et al., 1998).
Depositional models and outcrop studies for submarine lobe deposition generally display decreasing sand content, amalgamation and bed thickness from axis to fringe (Deptuck et al., 2008;Etienne et al., 2012;Fonnesu, Felletti, Haughton, Patacci, & McCaffrey, 2018;Groenenberg, Hodgson, Prelat, Luthi, & Flint, 2010;Jegou et al., 2008;Prelat et al., 2009;Ricci-Lucchi, 1975;Shanmugam & Moiola, 1988;Spychala, Hodgson, Flint, & Mountney, 2015;Sullivan et al., 2000;Walker & Mutti, 1973). These results confirm that sandstone bed thickness decreases and mudstone content increases from proximal to distal for unconfined and confined lobes ( Figure 6). However, semiconfined lobes display thicker sandstones and mudstones with an increasing mud proportion within their distal reaches possibly indicating a higher degree of bypass in the proximal location ( Figure 6; Jobe, Sylvester, Howes, et al., 2017). While these relationships could differ due to a number of basin specific parameters (e.g. basin geometry, grain-size distribution, degree of confinement/bypass) or a sampling bias in the data collection/interpretation, the data presented here broadly confirm existing depositional models and provide important quantitative constraints on event-bed geometries and parameters. However, the results for semiconfined lobes indicate that the degree of lobe confinement and sub-environment is not easily interpretable at the outcrop scale unless there is direct spatial evidence (Marini et al., 2015;.

| Depositional relief versus erosional relief on thinning rates
This study focuses on event-bed thinning rates as a proxy for larger-scale architecture. It is important to note that thinning rates in all but the most distal environments are likely to be influenced by both depositional thinning and erosional truncation. Erosion, particularly in proximal environments, will strongly influence thinning rates due to partial thinning of a lithologic unit or complete truncation of an event bed. For example, in the axial positions of channel and lobe deposits, erosion can amalgamate beds and obscure bed boundaries, creating uncharacteristically thick "beds" in correlation panels (Stammer, 2014). For simplicity, the absolute value of thinning rate is used in the characterizations due to uncertainty in panel datums and orientation with respect to palaeocurrent; a future study with better constraints on data (or using results from a numerical model) could investigate the proportion of depositional thinning versus erosional truncation. For example, the wide distribution of thinning rates in lobe deposits (Figures 2and 8) may be caused by both depositional thinning and erosional truncation, but differentiating these two possible parameters is very difficult for much of the compiled data (Table 1). However, the generated results ( Figure 8) help to quantify the qualitatively known/assumed degree of erosion found in each environment.

| Limitations of the dataset used for this study
While the results of this study quantify and confirm our conceptual knowledge of submarine stratigraphic architecture (Figure 8), the parameters are derived from interpretations of natural outcrop exposures that are sometimes ambiguous. To avoid this ambiguity, this classification focused on the gross architecture of each system, only utilizing five broad depositional environments (Figure 8). However, this introduces error when lumping different facies (e.g. channel axis and channel margin) into the same environment. Also, it is acknowledged that there may be errors in the original interpretation of depositional environment (Table 1) and that these errors may be larger in lobe sub-environments, where differences may be minimal and subjectively defined (cf. . Another limitation is that this dataset is dependent on the detail of correlation, and most authors lump thin sandstones and multiple mudstone beds into one "bed" (Figure 1). This lumping obscures the true details of mudstone bed thickness and lateral variability, but it would be extremely difficult to correlate each individual mudstone event bed. Lastly, levee environments are underrepresented in this study; as more data is acquired, the eventbed parameter space (e.g. Figure 2) may be modified.

| Further constraining event-bed geometries with additional parameters
To overcome the limitations stated above, bed thickness and thinning-rate data could be combined with additional parameters to differentiate environments as well as the potential evolution of stratigraphic architecture that may occur within one outcrop or correlation panel. For example, distinctive sedimentary structures and ichnofacies often correlate with submarine depositional environments; perhaps the most data-rich example is from basin-plain deposits, where Sumner et al. (2012) identified several downstream trends in the distribution of sedimentary structures. Other sedimentary structures that are interpreted as being environmentspecific are supercritical flow structures (e.g. cyclic steps, antidunes) that often occur in channel or channel-lobe transition zone environments (Ono & Plink-Bjorklund, 2017;Postma, Kleverlaan, & Cartigny, 2014;Talling et al., 2015) and starved ripples that most commonly occur in distal lobe settings (Prelat et al., 2009;Spychala, et al., 2017). Different ichnofabrics and ichnofacies have also been observed to correlate with sub-environments of submarine channels (Callow, Kneller, Dykstra, & McIlroy, 2014), slope environments (Hubbard, MacEachern, & Bann, 2012), and basinfloor environments (Uchman & Wetzel, 2012).

| Future data collection and digitalization
The dataset presented in this study represents all detailed event-bed correlation panels in the published literature. Figures 2 and 8 summarize the variability in event-bed statistics for submarine channel, levee, CLTZ, lobe and basinplain deposits. While the medians show clear differences between environments (dots in Figure 2A), the 90% volume contour maps (polygons in Figure 2A) show significant overlap between environments. This ambiguity underscores the need for more quantification of event-bed metrics, not only thickness and thinning rate, and correlation distance, but also metrics discussed above like sedimentary structure proportion, ichnofacies and stacking pattern variability. These metrics must also be digitized and available in standardized formats for interrogation. The creation of such a dataset would help to tighten the distributions of event-bed parameters to help distinguish environments and sub-environments, allow probabilistic assessment of classification uncertainty and minimize the impact of misclassified data. Additionally, statistical methods for estimating true bed lengths from limited exposures (Visser & Chessa, 2000;Willis & White, 2000) could be employed to explore reservoir connectivity (Stephen et al., 2001). As more data are collected and analysed, event-bed parameters will become more useful for constructing realistic geological and reservoir models, particularly in data-poor settings where lateral lithology variability at the bed-scale is not observable and a major uncertainty (Hofstra et al., 2017).

| CONCLUSIONS
To understand and quantify the thickness and lateral heterogeneity of turbidite event beds across different submarine depositional environments, previously published bed-scale data was compiled from channel, levee, channel-lobe transition zone, lobe and basin-plain deposits. A total of 28,525 individual measurements of event-bed parameters indicate that a combination of thinning rate, bed thickness, and correlation distance (i.e. the lateral distance over which thinning rate is measured) clearly differentiates deposits from different submarine depositional environments. The highest sandstone bed thinning rates were found in channel deposits (0.2-6 cm/m; P 10 and P 90 values here and below) and incrementally decreased to lobe deposits (0.1-1.6 cm/m), channellobe transition zone deposits (0.2-0.9 cm/m), levee deposits (0.0024-0.078 cm/m) and basin-plain deposits (0.000017-0.0054 cm/m). These quantitative relationships provide valuable insights for downslope flow evolution and the construction of stratigraphic architecture in submarine settings. Channel and basin-plain deposits have similar sandstone bed thicknesses (21-171 cm and 9-101 cm, respectively), but basin-plain deposits have thicker mudstone-dominated interval thickness (39-226 cm vs. 9-136 cm for channel deposits). Channel-lobe transition zone and lobe deposits are broadly similar in terms of sandstone bed thickness (10-78 cm and 3-83 cm, respectively) and mudstone-interval thickness (5-38 cm and 4-59 cm, respectively). Levee deposits contain the smallest sandstone bed thicknesses of 9-27 cm but contained the second thickest mudstone-dominated intervals (13-220 cm). Due to intra-environment variability, net-to-gross is highly variable and thus not a diagnostic indicator of depositional environment.
Submarine lobe deposits show the most variability in event bed thickness, thinning rate and net-to-gross, likely due to the inherent facies variability in lobe deposits and differing sediment supply, basin configuration, and tectonic settings of compiled data. To explore this variability, lobe deposits were sub-classified based on position (proximal, distal) and effective confinement (unconfined, semiconfined, confined) to provide a more detailed sub-environment analysis. Unconfined lobe deposits show a proximal-to-distal increase in sandstone thickness and decrease in mudstone thickness, supporting conceptual models. Confined lobe deposits have thicker sandstone and mudstone beds and lower net-to-gross values as compared to unconfined and semiconfined lobes, supporting a sediment trapping mechanism by confinement. However, the results for semiconfined lobes are non-intuitive and suggest that either these settings are not fully understood or there is uncertainty caused by subjectivity of the classification/interpretation of the environment.
These quantified bed-scale parameter comparisons enable the recognition of architectural similarities and differences between environments and lobe sub-environments, demonstrating the need for more quantitative studies of bedscale heterogeneity. This study provides quantitative and statistical insights into lateral variability within and among submarine depositional deposits and provides quantitative data for (1) a probabilistic assessment of depositional environment from outcrop and core descriptions and (2) constructing realistic geological and reservoir models. This data can also be used to constrain well log correlations, providing a more confident classification of depositional environment.

ACKNOWLEDGMENTS
We acknowledge reviewers Marco Patacci, Steve Hubbard and Chris Stevenson as well as Associate Editor Matthieu Cartigny, whose careful and thoughtful reviews greatly enhanced the quality and readability of this article. We also thank Piret Plink-Bjorklund, Jeffrey May and Fabien Laugier for providing extremely insightful comments throughout this project. RF acknowledges the funding support from the Chevron Center for Research Excellence (core.mines.edu) at Colorado School of Mines, AAPG Grants-in-Aid and GSA Student Research Grants.