# Journal of Sedimentary Research

- Copyright © 2014, SEPM (Society for Sedimentary Geology)

## Abstract:

Active and relic channels with extensive levees are common on the seafloor adjacent to the continental margin. Exponential, power-law, and logarithmic functions have been proposed by others to describe the lateral thickness decay of submarine levees. In the present study, experiments have been conducted to study submarine levee growth by flow stripping at a channel bend. Various functions have been fitted to the data. The results show that a third-order polynomial function best describes the levee thickness in the cross-stream direction near a submarine channel bend. Generalized model coefficients are derived as functions of deposit thickness adjacent to the channel bank. The model is applied to experimental data obtained by others as well as levee shapes derived from seismic data. In both cases, satisfactory agreements are found. The proposed model can be a useful tool for stratigraphic modeling of submarine channel–levee systems and fill gaps in field data.

## Introduction

The continental margin and submarine fans abound with channel–levee systems of various size, shape, and complexity (e.g., Garrison et al. 1982; Damuth et al. 1983; Pirmez and Flood 1995; Kolla et al. 2001; Kolla et al. 2007; Skene et al. 2002; Skene and Piper 2006). These channels are recognized as an important element of submarine morphology for being major conduits of turbidity currents transporting terrigenous sediment to the deep ocean (Imran et al. 1998; Kane et al. 2010). There are many similarities between submarine and subaerial channels such as intricately meandering patterns, cutoffs, scroll bars, and planform characteristics including width-depth ratio, wave length-width ratio, and amplitude-width ratio (e.g., Damuth et al. 1988; Pirmez 1994; Clark and Pickering 1996; Pirmez and Imran 2003; Kolla et al. 2007). These similarities notwithstanding, there are a number of notable differences between submarine and subaerial channels. Owing to a small density difference between turbidity currents and the ambient ocean water, submarine levees can undergo significant vertical aggradation without experiencing frequent avulsion (Imran et al. 1998; Straub and Mohrig 2008). Overbank flow is also more common in the submarine environment than in rivers (Peakall et al. 2000; Kolla et al. 2007; Islam et al. 2008). Three different processes, namely flow spilling, stripping, and inertial overspill, are considered to be responsible for transporting sediment out of the channel in the submarine environment. Flow spilling or continuous overspill describes a process in which a suprachannel fraction of a current spreads laterally out across the overbank surface (Clark and Pickering 1996; Straub et al. 2008). Piper and Normark (1983) described flow stripping as the process by which part of a turbidity current that rises above the levee crest at sharp bend does not follow the channelized portion of the flow but continues in the pre-bend direction (Kane 2007). Hay (1987) defined inertial overspill as the process by which the fluid columns are carried up the bank and over the levee by the forward momentum whenever the curvature of the outer bank in a channel bend is greater than that of the channel axis.

Recent advances in 3-D seismic technology have enabled scientists to study submarine strata, including channel–levee complexes in great detail (e.g., Deptuck et al. 2007; Kolla et al. 2007). A number of studies have shown that levee building depends on four properties of the overbanking flow: relative current height to channel relief, current velocity, suspended particles size distribution, and concentration profile (e.g., Pirmez and Imran 2003; Skene et al. 2002; Straub et al. 2008; Straub and Mohrig 2008). Skene et al. (2002) performed a comprehensive analysis of data on levee thickness for a number of large submarine channels and concluded that levee thickness typically follows an exponential function both in the cross-channel and down-channel directions. Kane et al. (2007) observed a power-law thickness decay along a channel-normal transect of a levee in the Rosario Formation, Baja California. Dykstra et al. (2012) also observed a power-law thickness decay away from the levee crest for a small-scale proglacial channel–levee system. Straub and Mohrig (2008) combined measurements of submarine levees from seismic data of a continental slope in the South China Sea with laboratory data and developed a model of levee growth based on an advection–settling scheme coupled to the Rouse equation of sediment concentration profile. Kane et al. (2010) conducted experiments with a 1-bend constant-curvature-rectangular channel, and levees were constructed from successive fixed-volume release of silt-laden flows. Their study showed that in proximal areas, i.e., close to the source, the levee thickness decays according to a power-law function, followed by a transition area which follows a logarithmic function, and finally the thickness decay follows an exponential function. Khan and Arnott (2011) observed that the lateral thinning of individual medium- and thick-bedded strata in the proximal outer-bend levee of a channel–levee complex within the Isaac Formation, western Canada can be described by both linear and power-law functions.

Nakazima and Kneller (2013) studied a number of channel–levee complexes from 3D seismic data and concluded that the variation in levee thickness perpendicular to the channel shows a power-law decay on steeper slopes (> 0.6°) and either exponential or logarithmic decay on gentle slopes.

We have carried out laboratory experiments by releasing successive long-duration turbidity currents in a relatively large sinuous channel. The experiments allowed quantification of levee growth from overbank flow that was dominated by continuous stripping aided by run-up (e.g., Straub et al. 2008; Islam et al. 2008). Despite a lack of consensus on its definition (e.g., Peakall et al. 2000; Straub et al. 2008), we classify the overbank flow process in the present experiment as stripping. The deposit thickness was mapped after every few runs using a high-precision laser profiler. A generalized polynomial model describing the levee thickness in the lateral direction as a function of the near-bank deposit thickness and distance away from the bank is developed. The model is then applied to the laboratory data of Straub et al. (2008), Kane et al. (2010), and a seismically derived levee-thickness data set from the Gulf of Mexico.

## Experimental Setup and Procedure

The experimental setup consisted of a 3-bend channel with a sine-generated planform (Johannesson and Parker 1989; Imran et al. 1999; Islam et al. 2008) having an angular amplitude of 45°. The total channel length was 11.62 m in the longitudinal direction. The channel had a trapezoidal cross section with 0.3 m bottom width, 0.8 m top width, and 0.15 m depth, and a slope of 0.75% along the thalweg. The channel sinuosity was 1.15. The sinuous channel was constructed in a basin 12.2 m long, 6.1 m wide, and 1.5 m deep (Fig. 1). The basin had a false floor 0.3 m high surrounded by a sump 0.3 m wide to prevent current reflections from the side walls. At one of the downstream corners of the basin, a small pump was placed in the sump to remove dense fluid exiting the channel and thereby maintain the density contrast between the current and the ambient fluid during the experiment.

The turbidity current mixture consisted of 1.0% medium silt (25 µm), 0.1% coarse silt (45 µm), and 0.5% salt by mass with an inflow rate of 2.5 L/s for the majority of the runs. The percentage of silt and salt differed in a few selected runs.

The basin was filled with fresh water, and a turbidity current was introduced at a constant rate through an inlet box at the channel entrance for one hour. Salt and silt were mixed with water for several hours using mechanical stirrers in three tanks with a total volume of 3800 L. The mixture was then pumped to an elevated head tank from which it was discharged to the inlet box under a constant head. After each run was finished, the basin water was drained to a minimum level with the channel and levees remaining submerged, and fresh water was added to refill the basin again. After every three or four runs, the deposit was scanned using an automated Keyance laser profiler. Additional detail of the experiment can be found in Ezz et al. (2013).

## Results and Analysis

The flow remained mostly within the channel except at the bends, where flow stripping led to overbank flow. Once the front left the downstream end of the channel and a quasi-steady flow was established, sustained stripping occurred only at the entrance and the first bend. A difference map between bed elevation after the 25th run and the base elevation shows the cumulative deposit thickness from the entire experiment (Fig. 2). The map is constructed with data points 12.5 cm and 1.75 mm apart, respectively, in the downvalley and lateral direction. From successive runs, a wedge developed inside the channel that increased the thalweg slope in the affected area. The overbank deposits formed mainly from stripping at channel bends. During the later runs, some spilling occurred concurrently with stripping at the entrance bend due to reduction in channel relief. The lobate shapes of these deposits represent the dominant overbank flow direction. Two transects on each of these lobes are considered: one normal to the channel axis and one along the overbank flow direction. Solid lines in Figure 3 show the measured levee profiles at different times along these transects. The left panel shows levee profiles normal to the channel axis, and the right panel shows those along the direction of overbank flow. The plots show that the levee thickness decreased with distance from the source of the current. The levee became steeper throughout the runs, but the rate of levee growth decreased with time due to increased transport efficiency caused by an increase in channel slope from deposition. This is consistent with observations made by others that individual intervals in a levee may often show a different regression to the overall levee (e.g., Dykstra et al. 2012; Nakajima and Kneller 2013).

The levee-thickness data are fitted with different functions including logarithmic, exponential, power law (e.g., Skene et al. 2002; Birman et al. 2009; Kane et al. 2010; Dykstraet al. 2012; Nakajima and Kneller 2013) and a third order polynomial function expressed as

where *y* represents the levee thickness at a distance *x* from the origin and *a*, *b*, and *c* are the polynomial coefficients. The polynomial equation contains a constant term, *d*, that has a physical meaning. It represents levee thickness at *x* = 0 which is selected to be a location close to the channel bank. The regression coefficients for various models listed in Figure 3 show that the polynomial equation gives the highest correlation for data both in the cross stream and the dominant overbank flow directions. The exponential and the logarithmic functions also give high values of *R ^{2}*, but the power-law gives rather small values. The high regression coefficients notwithstanding, the plots of the logarithmic and exponential models in Figure 3 show significant deviation from the measurements, especially in the vicinity of the channel bank, while the polynomial model matches the data satisfactorily for the entire levee width.

## Generalized Model of Levee Thickness

When fitted to the levee profiles of different thickness, similar to the other functions, the polynomial equation gives different values of the coefficients. Therefore, in its present form, like other models, Equation 1 lacks generality. In order to generalize the model, at least for similar flow events, we need to obtain a single set of values for the model coefficients.

First, we obtain values of *a*, *b*, and *c* for different events (i.e., levee thickness at different time sequences) by fitting Equation 1 with the levee profiles. Then, we use these values to perform a linear regression analysis and obtain a relationship between each of the coefficients and the levee thickness at *x* = 0, i.e., *d*, such that

Finally, we substitute Equation 2 into Equation 1 to obtain the following relation

Equation 3 represents a generalized levee thickness model with all the coefficients expressed as linear functions of *d*. The model coefficients for the entrance and the first bend outer bank levee thickness are listed in Table 1.

## Model Verification and Application

In order to verify the model, first, we consider the experimental data set of Straub et al. (2008). In this experiment, a sinuous channel with trapezoidal cross section was built in a basin 5 m long, 5 m wide, and 1.2 m deep. The channel consisted of three bends and had a sinuosity of 1.32. Straub et al. (2008) released 24 depositional turbidity currents. The current deposited sediment on the overbank areas by both spilling and stripping. Out of these 24 runs, we randomly pick five (9th, 12th, 17th, 21st, 24th), and fit the polynomial model to the data. Figure 4 shows a satisfactory match between the proposed model and the measurement. Model coefficients are reported in Table 1.

The experiment of Kane et al. (2010) was done in a single bend contained inside a 1.7 m × 1.7 m tank. Deposits were built from successive surge-type currents. The medial transect of the outer bend that experienced a combination of stripping and spilling is selected (their fig. 6B). Following Kane et al. (2010), a short segment near the channel bank, about 3% of the total levee width, is excluded from the analysis, as this part was subjected to excessive sediment fallout from spilling. Using the procedure described above, we determine the model coefficients for this transect and report the values in Table 1. Figure 5 shows a comparison of the model prediction and the measured levee thickness after 15, 20, and 25 flows. The plot demonstrates that the generalized polynomial model can also satisfactorily predict deposit thickness of a levee built by surge-type currents.

Now, we apply the model to predict levee thickness at the field scale. Figure 6 shows a high-resolution 2D seismic line across the Einstein channel–levee system (Shew et al. 1994; Sylvester et al. 2012) in the Northeastern Gulf of Mexico. The seismic data show an actively migrating channel. We consider six different strata from the levee near the cut bank, fit these time-sequences of levee thickness with Equation 1, and determine the model coefficients of Equation 3. Comparison of levee thickness represented by Equation 3 with interpreted levee thickness from the seismic reflectors show a good match (Fig. 7).

## Discussion

It is commonly accepted that spilling is responsible for transferring the finer fraction of the suspended sediment out of the channel confinement (e.g., Komar 1973; Piper and Normark 1983; Hiscott et al. 1997; Peakall et al. 2000). Hay (1987) envisaged that stripping would occur in surge-type flows encountering a sharp bend and the portion of the current higher than the levees will strip off. Accordingly, only fine-grained material will be transported to the overbank areas (e.g., Hiscott et al. 1997). The experiments of Straub et al. (2008), however, have demonstrated that sustained stripping aided by run-up to the outer bank can carry and deposit coarse material on the overbank areas. In the present experiment, and those of Islam et al. (2008) and Straub et al. (2008), the relatively mild slope of the channel banks allowed the flow to become significantly tilted and transfer sediment and fluid from the bottom near the inner bank to the outer overbank. We suggest that the original definition of stripping (Piper and Normark 1983) should be broadened to include transfer of coarse material to the outer overbank area due to runup. The recent experiments (Islam et al. 2008; Straub et al. 2008) have also shown that the stripping process is not limited to surge-type currents.

Compared to the proposed polynomial model, the exponential (*y = ae ^{bx}*) and the power law (

*y = ax*) functions contain fewer model parameters, i.e., one coefficient and one exponent constant. The coefficient

^{b}*a*is equivalent to

*d*in Equations 1–3, i.e., levee thickness at

*x*= 0 (Skene et al. 2002). While fitting the exponential function to the deposit thickness at different time sequences of the present data,

*b*is found to be nearly constant, which supports the conclusion of Skene et al. (2002) that this parameter is a length scale related to levee width. However, Figure 3 shows that the exponential model significantly underpredicts the thickness near the channel bank. If a constant value is used for

*b*, and

*a*is replaced by levee thickness at

*x*= 0 in a single model equation for all the deposition sequences, the predicted profiles will be shifted up and away from the data. This is demonstrated in Figure 8.

## Summary and Conclusions

We conducted laboratory experiments to study levee growth at a submarine channel bend. In-channel and overbank deposits were built by successive release of constant-discharge turbidity currents in a pre-formed submerged channel. The overbank deposit was primarily the result of flow stripping at channel bends. By fitting exponential, logarithmic, power-law, and a polynomial function to transects of the deposit in two different directions, it was observed that a third-order polynomial provides the best match with the levee-thickness profiles. A generalized polynomial model (Equation 3) is developed.

The model is applied to the experimental data of Straub et al. (2008), Kane et al. (2010), and interpreted seismic data of a channel cross section from the Northeastern Gulf of Mexico. Satisfactory agreement is found between measurements and predictions.

Along with the exponential and power-law functions proposed by others, the present model contains a physical parameter, i.e., levee thickness at a specified near-bank location, that can be obtained from core or limited seismic data. Compared with other models, the proposed polynomial model shows a better match with data, especially closer to the source of the overbank flows. A single set of model coefficients can be used for predicting levee thickness at different stages of levee growth. The model coefficients vary between experiments and are expected to vary among different field conditions. Nevertheless, by analyzing a variety of seismic, sonar, and outcrop data, it may be possible to develop a limited set of coefficients.

## Acknowledgments

The authors gratefully acknowledge funding support from Shell International Exploration and Production Company. The experimental setup was built with funding from an equipment grant from the University of South Carolina. The paper benefited from suggestions by Associate Editor Steve Hubbard, Ian Kane, Mason Dykstra and an anonymous reviewer. Kyle Straub kindly provided data from his experiment for model verification.

- Received August 13, 2012.
- Accepted July 8, 2013.