Effects of sediment transport on bathymetry and sublayers of little sand bay harbor

Introduction

Little sand bay harbor is at the Apostle Islands National Lakeshore along Lake Superior. The sediment transports, depositions, and erosions are important to the navigation of boats. In this study, we employed the combined geophysical methods such as acoustic-wave and electromagnetic-wave based technology to map the bathymetry and sublayers inside and outside the harbor. The acoustic-wave based subbottom profiler (SBP) and electromagnetic-wave based ground-penetration radar (GPR) can map the bathymetry and sublayer simultaneously. There are two objectives in this study: (1) compare the differences of bathymetry inside and outside the harbor from last September to this July to understand where sediment erodes and deposits; (2) observe the differences of sublayer inside and outside the harbor from SBP and GPR data, and try to explain these differences.

    The nearshore downcutting was evaluated using two geophysical methods:

Ground penetrating radar (GPR) and Subbottom profiler (SBP) were used in Lakes Superior and Michigan. The advantages of using geophysical methods include:

·        non-destructive nature of the techniques does not disturb the nearshore sediments.

·        the surveys can be done over large areas in a short time period.

The GPR and SBP are mounted on a zodiac boat and collect the data simultaneous in aquatic environment (see Fig.1).

Fig. 1 The combinations of GPR and SBP on a zodiac boat

(1) Ground penetrating radar (GPR)

        The GPR technique sends electromagnetic (ELM) waves to detect sediments layers with contrasting dielectric permittivities. GPR systems are typically comprised of a central console that controls a transmitter and receiver (see Figure 2). The radar system emits an electromagnetic (ELM) wave which propagates away from the transmitter antenna until it finds a reflector that sends the ELM wave to the receiver antenna.

        ELM waves travel at high speeds (0.3 m/ns in air and 0.033 m/ns in water) and the resulting travel time of the wave from the transmitter to the receiver is on the order of a few tens to several thousand nanoseconds. The electromagnetic properties of a material are related to soil composition and water content, both of which control the speed and attenuation of ELM waves. The speed of the ELM wave in a geomaterial is defined in terms of the speed of light in vacuum (c_o) and the dielectric permittivity (k) of the material:

ELM wave reflections are a result of contrasts in the dielectric permittivity between adjacent materials. Greater contrasts in dielectric permittivities produce stronger reflections. Therefore, ELM waves will reflect off of soil interfaces having different electromagnetic properties.

        The effectiveness of GPR depends on the ability of the ground to transmit ELM waves. Some materials, such as ice, allow uninhibited propagation of the ELM wave while other materials including water-saturated clay and seawater absorb or reflect ELM waves to the point where no useful information can be obtained (Table 1).

  Due to the lack of the ground-truth data, the dielectric permittivity of materials can be estimated by using mixture models, for example:

where k_s=3 to 8 is permittivity of the solid minerals, k_w=80 is the permittivity of water, k_a=1 is the permittivity of air, n=0.2 to 0.8 is the porosity, S_r is the degree of saturation, and β≈0.5 is an empirically determined constant.

        The ground penetrating radar system used in this study is the pulseEKKO 100 (Sensors & Software – Mississauga, Canada). The system was deployed using 100 and 200 MHz antennae and a 400V source. The higher antennae frequencies permit increasing the resolution at the expense of the depth of penetration. To improve signal-to-noise ratios, GPR signals were collected using between 32 and 128 staked signals. The number of stacked signals was limited to reduce the acquisition time and prevent spatial aliasing and smearing the data when continuous profiling was conducted from a moving boat.

Fig. 2 A simple schematic showing the transmission and reflection of an ELM

wave from the transmitter antenna (T) to the receiver antenna (R).

Fig. 3 Using GPR system on the shore

(2) Subbottom profiler (SBP)

        The Subottom profiler (see Figure 6) allows for identification of the water-sediment interface and sediment structures that may exist in the subbottom based on the propagation and reflection of acoustic waves. Information is gathered by detecting changes in mechanical impedance Z (=V*ρ – where V is the P-wave velocity and ρ is the mass density) . The reflection coefficient (R_c) between two media is defined as:

        Collected reflection traces along survey lines are used to create 2D images of the subbottom stratigaphy as well as erosion and sedimentation processes. Typical SBP systems send narrow-angle acoustic waves with two different scanning frequencies: low (10 - 30 kHz) and high (200 kHz). The low frequency waves penetrate sub-bottom formations and the high-frequency waves produce high-resolution information about bathymetry (see Figure 4). SBP effectiveness depends on the sediment type. For example, sand and other coarse sediments provide stronger bathymetric reflections and poor depth penetration, while clay and other fine sediments yield weaker bathymetric reflections and deeper penetrations into subbottom sediments. The resolution of the technique depends both on the frequency and the P-wave velocity of the water and sediment layers. The resolution of the low-frequency signal is equal to Res = wavelength/4 ≈ (1500 m/s)/(4·20 kHz) = 0.018 m. Sediment layer thicknesses depends on the estimated sediment velocities. The P-wave velocity in saturated sediments varies between 1400 to 1700 m/s. The SBP measurement system is complemented with a GPS receiver to record the coordinates of measurement locations.

Fig. 4 Tritech Seaking Subbottom Profiler

Fig. 5 A simple schematic showing the effectiveness of the high frequency

and low frequency acoustic waves emitted from the subbottom profiler.

Limitations of Geophysical Techniques

        Each geophysical technique has a range of applications that depends not only on the system performance but also on the physical properties of the water and near surface sediments (Table 1). A qualitative determination of the depth range of each technique is given by the skin depth (the inverse of the attenuation coefficient). Table 1 shows that skin depth depends on the frequency of the P-wave; however, the application of the SBP is not limited by the skin depth, but rather by the geometric spreading as the P-wave propagates deeper into the water. The application of GPR in off-shore environments is greatly limited by the skin depth in sea water but it can be easily applied in fresh water.

        Another parameter that is important in the collection of meaningful off-shore data is the reflection coefficient. In the case of the SBP, the P-wave velocity is similar both in water and sediments (Table 1). Therefore, contrasts in the mechanical impedance must be caused by the difference in density. Coarse sediments (e.g., sands and gravels) provide more distinct density contrasts than unconsolidated soft sediments (e.g., clays). The sharper density contrasts in coarse sediments yield stronger bathymetric reflections but lower depth penetration into subbottom sediments. Fine soils provide a weaker reflection at the soil-water interface, allowing a greater amount of energy to reach subbottom sediment structures. The reversed situation is seen in the case of GPR surveys and the propagation of ELM waves. Softer sediments typically have higher electrical conductivities, greater energy absorption, and low signal penetration. Coarse sediments (typically associated with low conductivities) allow the ELM waves to penetrate deeper into the subbottom to obtain clear images of subbottom sediments. These analyses are summarized in Table 2 and show the complementary information provided by SBP and ground penetrating radars. The field surveys were designed in part to verify these analyses.

Table 1  Typical geophysical properties – Several sources

Table 2:  Penetration and resolution of SBP and GPR

Survey Results

     The bathymetry surveyed on Sep. 29th, 2007 and July 15th, 2008 are provided in Fig. 6 and Fig.7. The water depth is shallower in the east side of the harbor but is deeper in the west side of the harbor, where the docks for the boat are. Due to lack of the dredge history, it is hard to explain sediment transport phenomena based upon the bathymetry data only. 

Fig.6 Bathymetry data collected on Sep, 29th, 2007 inside and outside the little sand bay harbor

Fig.7 Bathymetry data collected on July 15th, 2008 inside and outside the little sand bay harbor

    In order to compare the bathymetry variations between two different dates, the water level should be corrected firstly. The water level data can be obtained in three NOAA stations (Duluth, Ontonagon and Grand Marais) most adjacent to the little sand bay harbor (see Fig. 8). 

Fig. 8 Water level gauges in Lake Superior

    The mean water level on the above-mentioned dates are listed in Table 3.

Table 3 Water level in three NOAA stations

PS: The water level is based upon IGLD 1985.

    The water level variations in these three stations are 0.325 m, used to correct the bathymetry at different dates. After data corrections, the bathymetry differences are shown in Fig. 9 and Fig. 10 for detailed around harbor regions.  Red color means depth-decreasing (erosions), and blue color means depth-increasing (depositions). Inside the harbor, It seems like that sediment deposition occurs near the docks, and sediment erosions happen in other places including the harbor inlet. When the water flow comes into the harbor, the flow velocities are faster than those inside the harbor, inducing sediment resuspension easily. Therefore, the sediment erosion is severer than other areas of the harbor.   When the sediment is brought into the harbor, the slower velocities are supposed to make sediment deposits inside the harbor.  From Fig. 10, inside the harbor, the west side has sediment deposition. However, the sediment erodes in the east side, which may be due to the scarcity of data points.  On the other hand, outside the harbor areas, the sediment erosion and deposition occurs intermittently.  

Fig. 9 Bathymetry differences in whole survey regions

Fig. 10 Bathymetry differences around the harbor regions

        The GPR and SBP also provided the sublayer information. Fig. 11 shows the sublayer inside the harbor. We only see visible layers at point C, and from the particle size analysis, the surface sediment is sand. Due to lack of ground-truth data, we don't know what type of soil in the second layer.  

Fig. 11(a) Survey lines and mean particle size for surface sediment inside the harbor

SPB data

GPR data

 Fig.11 (b) SBP and GPR results

     The sublyer at the inlet of the harbor is in Fig.12. As mentioned in the previous section, the flow velocities are faster at the inlet of the harbor than inside the harbor. Therefore, the sediment at the inlet of the harbor is easily resuspended, which result in the loose top layer. From the SBP and GPR results, we can at least observe two visible layers. The material for the top layer should be sand, and the material for the lower layer is unknown. 

Fig. 12(a) Survey lines and mean particle size for surface sediment at the inlet of the harbor

SBP data

GPR data

 Fig.12 (b) SBP and GPR results

    As for the outside the harbor, the east side outside the harbor is a lower bluff. The survey lines and sublayer are in Fig. 13. We can observe a sand bar exisitng between the nearshore and offshore, and two-layer substrate in the sand bar regions.

Fig. 13(a) Survey lines in the east outside the harbor

SBP data

GPR data

Fig.13 (b) SBP and GPR results

    We also surveyed northern regions outside the harbor (see Fig.14). The water depth is shallower right outside the harbor because the sediment deposition results from the slower water flow blocked by the harbor. Without the obstruction of the harbor, the higher water flow induces the lower sediment deposition, and then deeper water depth.

  Fig. 14(a) Survey lines in the north outside the harbor

SBP data

GPR data

Fig.14 (b) SBP and GPR results

Conclusion

    From these survey, we can obtain the following conclusions:

1. Inside the harbor, the water depth is deeper in the west side of the harbor, and shallower in the east side of the

    harbor.

1. In comparison with data collected at last and this year, the bathymetry differences can be obtained after water

    level corrections. The west side inside the harbor is sediment-deposited, but due to the lack of the dredge

    record, it is hard to explain the sediment transport phenomena.

2. At the inlet of the harbor, the faster flow velocities result in the sediment erosion, and make the top sediment

    layer loose, inducing the two visible layers.

2. Thirdly, the patterns of sediment depositions and erosions occurs intermittently outside the harbor.

3. Finally, the harbor can block the water flow, i.e. slower flow velocities, therefore, we observed the sediment

   deposition in the north outside the harbor.