Analytical Model to Predict the Sediment Flux of Each Grain-Size Class in Turbidity Current Flow; Application to Gold Channel, Tres Pasos Formation, Chile

Home , Rouse number

An Analytical Model to Predict the Sediment Flux of Each Grain-Size Class in Turbidity Current Flow; Application to Gold Channel, Tres Pasos Formation, Chile

Master Thesis Report

Department of Earth Science

Utrecht University

Winda Novianti 6128955

Supervisors:

Dr. Mike Tilston

Dr. Joris Eggenhuisen An Analytical Model to predict the Sediment Flux of Each Grain-Size Class in Turbidity Current Flow; Application to Gold Channel, Tres Pasos Formation, Chile

Abstract A turbidity current is the most prominent agent for transporting sediment from the continental shelf to the basin floor. However, direct monitoring of modern turbidity currents is difficult to carry out. Meanwhile, sediment flux estimation which is particularly based on different particle size is important for many applications such as the indicating whether a turbidite sandstone is suitable to be a hydrocarbon reservoir. A study by Eggenhuisen (unpublished) has led to the development of the Sediment Budget Estimator (SBE). This tool can reconstruct sediment flux from ancient turbidity current deposits. The SBE models the flow structure, consisting of velocity and suspended-sediment concentration profile, and later uses this information to reconstruct the sediment flux. However, the equation used to model the concentration profile is only an adhoc exponential equation which neglects how each grain-size class is distributed differently throughout the water column. The main achievement of this study is to replace the decay exponential equation and incorporate the Rouse Equation into a new SBE. The Rouse equation should only be applied to open channel flow but can also to be applied to submarine turbidity currents, regardless of the difference of their flow structure. The benefit of incorporating the Rouse equation is that it can model the sediment concentration for each grain-size class, and thereby, the sediment flux. This study aims to apply the new version of SBE to reconstruct the sediment flux of turbidity currents of each grain-size class throughout the Gold Channel, Tres Pasos Formation, Chile. To achieve our goal, we conduct a grain-size distribution analysis of the Gold Channel deposit. Subsequently, to reconstruct the sediment flux using the new SBE, the boundary condition for this model needs to be defined. For this, the new SBE requires (1) the grain- size distribution at 10th, 50th, and 90th percentile from a single sample at the reference level (the base of channel axis) and (2) basin configuration and characteristic of feeder channel data obtained from the literature studies of the chosen turbidity current system. The grain-size distribution of the Gold Channel indicates that it is dominated by fine-sand particles and has a coarsening trend towards medium sand in the channel margin. Contrastingly, the total sediment budget produced by the new SBE shows that the Gold Channel is 99% dominated by very-fine-sand particles, 4.99 x 107 m3. Meanwhile, fine-sand (2.42 x 106 m3) and medium-sand particles (961.3 m3) are only concentrated at the base and cannot be suspended higher in the flow.

Keywords: Turbidity Current, Sediment Flux, The Rouse Equation, Tres Pasos Formation

An Analytical Model to predict the Sediment Flux of Each Grain-Size Class in Turbidity Current Flow; Application to Gold Channel, Tres Pasos Formation, Chile

Contents Abstract ...... 1 List of Figures ...... 3 List of Tables ...... 6 1. Introduction ...... 7 1.1. Background ...... 7 1.2. The aim and objectives ...... 8 2. Geological Setting ...... 9 2.1. Tres Pasos Formation ...... 10 2.2. Sedimentary facies ...... 11 2.2.1. Amalgamated turbidite sandstone facies (ASF) ...... 11 2.2.2. Thick-to-thin sandstone interbedded with mudstone facies (TSF) ...... 11 2.2.3. Mudstone facies (MF) ...... 12 2.3. The architecture of Gold Channel ...... 15 3. Method ...... 17 3.1. Grain Size Distribution ...... 17 3.1.1. Sample collection and preparation ...... 17 3.1.2. Image Processing ...... 17 3.1.3. Statistical Analysis ...... 18 3.2. The Sediment Budget Estimator ...... 20 3.2.1. The Rouse Equation ...... 22 4. Results...... 25 4.1. Grain Size Distribution ...... 25 4.2. Sediment budget reconstruction of Gold Channel ...... 32 4.2.1. Boundary Condition ...... 32 4.2.2. Sediment Budget of Gold Channel ...... 34 5. Discussion ...... 37 5.1. Characteristics of turbidity current formed the Gold Channel ...... 37 5.2. Matching natural deposit vs model ...... 38 5.3. Model validation ...... 39 6. Conclusion ...... 43 References ...... 44 APPENDIX I ...... 48 APPENDIX II ...... 49

An Analytical Model to predict the Sediment Flux of Each Grain-Size Class in Turbidity Current Flow; Application to Gold Channel, Tres Pasos Formation, Chile

List of Figures Figure 1. . Location of the study area in Chile (inserted map, black star); The outcrop of the sandstone- package of the Tres Pasos Formation is above Laguna Figueroa (white rectangle) (modified after Macauley and Hubbard, 2013) ...... 9 Figure 2. (A) Regional stratigraphy of the deep-water sedimentary fill of the Cretaceous Magallanes Basin; (B) Depositional environment of the Tres Pasos Formation in a base-of-slope system of submarine channel; (C) The location of the Gold Channel which is the lower sand-prone package of the Tres Pasos Formation (red rectangle); Figure adapted from Hubbard et al. (2010) and de Leeuw (2017)...... 10 Figure 3. (A) A stratigraphic panel of Tres Pasos Formation based on the outcrop above Laguna Figueroa. The lower sandstone package was studied by Macauley and Hubbard (2013) (white rectangle). The upper sandstone package was studied by Hubbard (2014) and de Leeuw (2017) (black rectangle); Note that the white line shows the measured section location of Macauley and Hubbard (2013) study; (B) Cross section of the lower sandstone package (white rectangle in part A) shows 18 channel elements. The gold channel is the third channel element in the cross-section. This study focuses on the channel margin from the third channel element (red rectangle). Figure adapted from Macauley and Hubbard (2013) ...... 13 Figure 4. Bed-scale outcrop of Tres Pasos Formation. (A) The amalgamated sandstone facies normally has a thickness of about 25 m; (B) Thick-to-thin sandstone facies is characterized by normal grading from massive-course grain sandstone to planar-medium grain sandstone; (C) Mudstone clast characterise the base of high density turbidite for ASF; (D) Changing from thin to thick sandstone is typical for TSF. Sometimes mudstone clasts are also found but not as prominent as in amalgamated sandstone facies; (E) Planar and ripple mark are commonly found in the upper part of sandstone of TSF; (F) Mudstone facies characterized by interbedded fine sandstone to siltstone and mudstone. (figures are adapted from Macauley & Hubbard (2013) and Hubbard et al (2014)...... 14 Figure 5. (A) Photograph of the Gold Channel (indicated in red rectangle in Fig. 3B) with a human for scale on the bottom left. The red dots mark the sample locations in this study; (B) A sketch of the Gold Channel based on the photograph (Fig. 5A) and the sedimentary logs from Macauley & Hubbard (2013). It shows how the facies changing in the Gold Channel and marks the location of primary and secondary channelform surface. (C) A photograph of the off-axis section of the Gold Channel, below the white line is the mudstone facies and on the top is thick-to-thin sandstone interbedded with the mudstone facies (the white rectangle in Fig. 5A). Figure 5C is adapted from Macauley & Hubbard (2013) ...... 16

An Analytical Model to predict the Sediment Flux of Each Grain-Size Class in Turbidity Current Flow; Application to Gold Channel, Tres Pasos Formation, Chile

Figure 6. 300 grids are required for the point-counting measurement. Best-fit ellipsoid is used to outline the grain (green ellipsoid) and point is used to outline matrix (yellow point) ...... 18 Figure 7. Skewness ...... 20 Figure 8. Kurtosis ...... 20 Figure 9. The shape of the concentration profile is slightly concave (left). Both the concentration profile and channel deposit show the same fining-upward trend (figure adapted from de Leeuw, 2017) ...... 21 Figure 10. The graph shows how each particle size of sediment suspends thought the water column (figure adapted from Chang, 1992) ...... 22 Figure 11. Histogram probability showing the grain-size distribution of vertical variability with height above the bed (see Fig. 5B for sample’s location)...... 26 Figure 12. Histogram probability showing the grain-size distribution of lateral variability with distance away from channel axis (see Fig. 5B for sample’s location) ...... 28 Figure 13. Grain size distribution of all sediment samples vertically in channel axis (A) and 4 samples from bed B1 of channel margin and channel axis (B). Abbreviation: Very Coarse Sand (V.C Sand) and Medium Pebbles (MP) ...... 29 Figure 14. Statistical parameters of the channel axis deposit ...... 30 Figure 15. Statistical parameters of samples from channel axis to channel margin, showing lateral variability...... 31 Figure 16. Sketch of the channel used for model application ...... 32 Figure 17. Graphs produced by SBE: (A) Velocity profile, arrow shows the inflection point where shear velocity reaches maximum; (B) Normalize concentration profile (Rouse Equation profile); (C) Concentration profile of each particle size, note that the line indicates the height above the bed where the velocity reaches maximum; (D-F) Sediment Flux of D10, D50 and D90 respectively; (G-I) Sediment Budget of D10, D50, D90 ...... 36 Figure 18. The schematic diagram illustrates how sediment transport into the channel bend is higher than sediment transported out of the channel bend which leads to deposition over the inner bend due to failure in the outer bend (A). Figure B illustrates a cross section of the lateral accretion deposit of the inner bend (point bar). Note that the wavy line is the top of a turbidity current, the jagged line is the break in the in the vertical thickness of the turbidity current, on the right side is the sediment concentration profile [Sed] (figure modified from Arnott (2007))...... 39 Figure 19. Monitoring of modern turbidity current system along the Monterey Canyon, California.. 40 Figure 20. The basis of validation study by Eggenhuisen (2019) indicates that the Rouse equation is applicable to turbidity currents of the deep-marine system because it predicts accurately for fine-sand

An Analytical Model to predict the Sediment Flux of Each Grain-Size Class in Turbidity Current Flow; Application to Gold Channel, Tres Pasos Formation, Chile in the lower part of the flow. (A) Comparison of the concentration profile generated from the experimental deposit (dashed line) and model produced by the Rouse equation for different grain size; (B) total sediment concentration produced by the model (solid line) and experimental-flume-lab deposit (dashed line)...... 41

An Analytical Model to predict the Sediment Flux of Each Grain-Size Class in Turbidity Current Flow; Application to Gold Channel, Tres Pasos Formation, Chile

List of Tables

Table 1. Method of Moments (Boggs, 2009) ...... 19 Table 2. Classification of sortation (Folk, 1957) ...... 19 Table 3. Classification of skewness (Folk, 1957) ...... 19 Table 4. Classification of Kurtosis ...... 20 Table 5. Simulation condition parameters ...... 33

An Analytical Model to predict the Sediment Flux of Each Grain-Size Class in Turbidity Current Flow; Application to Gold Channel, Tres Pasos Formation, Chile

1. Introduction 1.1. Background A turbidity current is a dense, sediment-laden flow moving down the slope whose motion is driven by gravity. The forward motion of a turbidity current generates a turbulence inducing a particle suspension in the flow (Tailing et al, 2012). This current can occur in deep lakes as well as in the deep sea (Nelson et al, 1995). Little is known about submarine turbidity currents. Advanced technology is required to monitor the submarine turbidity currents because of their inaccessible location, unpredictable occurrence, and destructive nature (Azpiroz-Zabala et al, 2017). Understanding the mechanism of submarine turbidity currents is important since turbidity currents are responsible for forming the topography of the seafloor through erosional and depositional processes which lead to, for instance, scouring of submarine canyons (Garcia, 1994). Also, they can form potential geohazards due to their fast-moving downslope movement, turbidite sandstones host for hydrocarbon reservoirs (Slatt et al, 2000), and they act as agents for transporting the flux of organic matter to the basin floor (Galy et al, 2007).

In 1929, the Grand Bank earthquake triggered a slump that caused a submarine turbidity current. As a consequence, a sequence of cables broke within an increasing lag time down slope. This event, for the first time, gave insight on the velocity of turbidity currents which could then be used to estimate the size of the currents and the amount of sediment they transport (Kuenen, 1952). Turbidity currents have since been known as an important agent for transporting a large volume of sediment from the continental slope to the sea floor (Tailing et al, 2012). In the Bengal Fan, Arabian Sea for instance, the volume of sediment transported by the turbidity currents is predicted to be up to 12.5 x 106 km3 (Curray et al, 2003).

Aside from acknowledging the importance of submarine turbidity current, it is necessary to understand the nature of submarine turbidity currents and their deposits. A tool has been developed by Eggenhuisen (unpublished) named the Sediment Budget Estimator (SBE). SBE is a tool to estimate the sediment flux (m3/s) and the sediment budget (m3) induced by turbidity currents that are responsible for transporting the sediment through the submarine channel over the geological timescale. The SBE was developed based on the source-to-sink perspective (Walsh et al, 2016) which simplifies the complexity of the sediment transport process yet still reflects the natural turbidity current process. The model approach used in SBE is to link the flow structure of a turbidity current to its deposit. This requires several input parameters that are determined based on the users’ understanding of the basin configuration and the characteristics of the feeder channel of the chosen system (Eggenhuisen, unpublished).

The flow structure consists of the velocity profile and the suspended sediment concentration of a turbidity current. These two aspects are a function used for estimating the sediment flux. The sediment flux of submarine turbidity current is important, particularly the sediment flux based on each particle size. For instance: (1) many reservoir hydrocarbons are derived from turbidite sanstone and a good reservoir is characterized by high porosity and low permeability which depend on the ratio of finer and coarser sediment. Hence, estimating the flux of each grain size leads to a better prediction of good quality reservoir (Meiburg & Kneller, 2010); (2) The fraction of finer sediment (clay and silt) can be used to indicate how far sediment can be transported downstream in submarine fan systems (Salahedin et al, 2000); (3) The flux of organic matter transported further down to the basin floor is

An Analytical Model to predict the Sediment Flux of Each Grain-Size Class in Turbidity Current Flow; Application to Gold Channel, Tres Pasos Formation, Chile commonly associated with finer sediment (Galy et al, 2007). Unfortunately, the previous version of SBE incorporated only a simple decay equation to model the suspended sediment concentration. This equation models an exponential distribution of sediment vertically in a channel without considering that, in a natural system, each grain-size class is distributed differently through the water column.

The Rouse equation is based on a simple diffusion model used to predict how different particle sizes are distributed through the water column in an open channel flow. Aside from the difference in terms of the flow structure in an open channel flow and turbidity current, however, the Rouse Equation has been widely used to model the concentration profile of turbidity current (Bolla Pittaluga et al, 2014; Hiscott et al, 1997; Straub et al, 2008; de Leeuw, 2017). In 2019, however, Eggenhuisen validated the Rouse equation and indicated that the Rouse equation can be applied to turbidity currents, although with caution.

1.2. The aim and objectives To address the need for modelling the suspended-sediment concentration profile in the previous version of SBE, this study incorporates the Rouse Equation to replace the simple decay equation in the new version of SBE. This novel numerical model is applied to the Gold Channel, located in the lower sandstone package of turbidite exposed of the Tres Pasos Formation, Magallanes Basin in Chile. This study area is chosen because the detailed reconstruction of the channel evolution has been studied very well by Hubbard et al, (2010), Macauley and Hubbard (2013), and Hubbard et al, 2014.

This study aims to obtain grain-size dependent predictions to estimate the sediment flux of each particle size using the improved SBE applied to the Gold Channel. The objectives are (1) To determine the grain size distribution in the channel axis and channel margin sections using thin-section analysis, (2) To develop a workflow for providing the sediment volume of each particle size based on grain-size stratification, and (3) To quantify the sediment-volume of each particle size transported through the Gold Channel.

An Analytical Model to predict the Sediment Flux of Each Grain-Size Class in Turbidity Current Flow; Application to Gold Channel, Tres Pasos Formation, Chile

2. Geological Setting The Magallanes basin (also known as the Austral basin in Argentina) developed into a back-arc basin during an extension which occurred during the Upper Jurassic in response to the breakup of the Gondwanan supercontinent. Subsequently, during the Early Cretaceous, the forming of the Andean fold-thrust belt caused the Magallanes basin to experience compression. This process induced subsidence and led to the evolution of the basin into the present-day retroact foreland basin (Romans et al., 2011; Wilson, 1991). The Magallanes basin is located in Southern Chile, South America (Fig. 1).

According to Romans et al., (2011), the Cretaceous deep-water sedimentary fill of the Magallanes basin is approximately 4 km thick and consists of three different phases (Fig. 2A). The first phase is the Punta Barrosa Formation, which is the oldest deep-water formation in this basin and interpreted to be a lobe deposit. Second is the Cerro Toro Formation, a 2.5 km shale-dominated deposit of foredeep- axial channel-levee system. The third phase consists of the deposit of a sand-rich succession and mudstone-rich mass transport deposit of the Tres Pasos Formation. The sand package of the Tres Pasos Formation is interpreted as a deposit of the base-of-slope system (Fig. 2B & 2C). The Tres Pasos Formation is capped by the Dorotea Formation, a Paleogene deltaic deposit (Fig. 2A). The interest of this study is the Tres Pasos Formation, the youngest deep-water formation of Magallanes Basin.

Figure 1. . Location of the study area in Chile (inserted map, black star); The outcrop of the sandstone-package of the Tres Pasos Formation is above Laguna Figueroa (white rectangle) (modified after Macauley and Hubbard, 2013)

An Analytical Model to predict the Sediment Flux of Each Grain-Size Class in Turbidity Current Flow; Application to Gold Channel, Tres Pasos Formation, Chile

Figure 2. (A) Regional stratigraphy of the deep-water sedimentary fill of the Cretaceous Magallanes Basin; (B) Depositional environment of the Tres Pasos Formation in a base-of-slope system of submarine channel; (C) The location of the Gold Channel which is the lower sand-prone package of the Tres Pasos Formation (red rectangle); Figure adapted from Hubbard et al. (2010) and de Leeuw (2017).

2.1. Tres Pasos Formation The slope channel strata of the Tres Pasos Formation are well exposed in the Laguna Figueroa, Ultima Esperanza District. The Tres Pasos Formation is the youngest succession of sediment gravity flow of the Magallanes Basin. It was deposited in the base-of-slope system along a high relief (±900m) clinoform during the upper Cretaceous with an average slope of 1.7˚ (Fig. 2C) (Hubbard et al., 2014; Hubbard et al., 2010). The Tres Pasos Formation records upwards shallowing from basinal deposits of the underlying Cerro Toro Formation to shallow-marine and marginal-marine deposits of the overlying Dorotea Formation. According to Romans et al., (2011), the thickness of this formation is approximately 1.2 – 1.5 km. The basin was filled axially from north to south-southeast. The sediment source was predominantly from the Andean orogenic belt (Macauley et al., 2013).

An Analytical Model to predict the Sediment Flux of Each Grain-Size Class in Turbidity Current Flow; Application to Gold Channel, Tres Pasos Formation, Chile

The Tres Pasos Formation is divided into a lower and an upper part based on the description of the outcrop belt in the Ultima Esperanza District of Chile. The lower part is characterised by lenticular to tabular sandstone intercalated with mudstone-rich mass transport deposit. Turbiditic mudstone and siltstone, hemipelagic mudstone and sparse scours filled by coarser-grained sandstone and pebble characterise the upper part of the Tres Pasos Formation in the Ultima Esperanza District (Romans et al., 2011). However, the facies and architecture of the lower part of the Tres Pasos Formation vary significantly along the trend of the 100-km long outcrop belt (Schultz et al., 2005).

The strata of interest in this study are interpreted to have been deposited at an intraslope position along a high-relief clinoform of the Magallanes foreland basin (Hubbard et al., 2014). It has 25 slope channels and their total thickness is 300 m (Fig. 3A) (Macauley and Hubbard, 2013). The 170 m thick lower part of this sandstone-dominated strata was studied by Macauley and Hubbard (2013). The 110 m thick upper part was studied by Hubbard et al., (2014) with a particular focus on the single channel element called the Gabriella Channel (Fig. 2C and 3A). De Leeuw (2017) reconstructed grain-size distribution and turbidity currents of the Gabriela Channel using the sea-floor morphology of Hubbard et al., (2014) (Fig. 3A). This study reconstructs the turbidity current of the Gold Channel, another channel element from the 170 m lower part of the sandstone package exposed at Laguna Figueroa (Fig. 3A).

2.2. Sedimentary facies This section summarizes the sedimentary facies that make up the outcrop belt at Laguna Figueroa according to the study by Hubbard et al. (2010), Macauley & Hubbard (2013), and Hubbard (2014).

2.2.1. Amalgamated turbidite sandstone facies (ASF) Amalgamated turbidite sandstone facies formed an interval of a thickness of up to 24 m with the sandstone sedimentation unit 25 cm – 4 m. This facies contains a high sandstone percentage (>70%) and high degree of amalgamation (Fig. 4A). The sedimentation unit commonly shows normal grading from medium-grained sandstone to fine-grained sandstone. The sedimentary

structure at the lower part is structureless (Ta or S3) (sensu Bouma and Lowe) and the upper part

preserved a planar structure either with or without ripple lamination (Tb-Tc) (Bouma, 1962) (Fig. 4B). The base of the bed is undulating and is locally overlain by mudstone clasts (Fig. 4C). Between one and another amalgamated sandstone, there is a lack of grain-size contrast.

Amalgamated-and-thick sandstone indicates deposition by a high-density turbidity current (Lowe, 1982). The planar and ripple laminations at the top of the sedimentation unit were deposited by the low-density tails of a turbidity current. In addition, the mudstone clasts which are overlain by the base indicate the high-density turbidity current that is able to rework the sediment beneath the turbidity current.

2.2.2. Thick-to-thin sandstone interbedded with mudstone facies (TSF) This facies is dominated by thick-bedded sandstone which is interbedded with mudstone on the lower part and graded to thin-bedded sandstone interbedded with mudstone on the upper part. It is characterised by normal grading from medium-grained sandstone to siltstone and mudstone. Locally, the mudstone clasts are also found in this facies (Fig. 4D). The top of the medium-grained

sandstone is commonly characterised by planar and ripple lamination (Tb-Tc) and capped by

siltstone & mudstone (Td-Te) (Fig. 4E). The structureless sandstone (Ta) is also preserved locally at the bottom part of the sedimentation unit. The sedimentation unit is dominated by a moderate

An Analytical Model to predict the Sediment Flux of Each Grain-Size Class in Turbidity Current Flow; Application to Gold Channel, Tres Pasos Formation, Chile

percentage of sandstone with a thickness that varies from 4-15 cm. The basal contact is commonly undulating. This facies is interpreted as the deposit from low-density turbidity current (Bouma, 1962). Mudstone and siltstone are deposited from turbidity current tails.

2.2.3. Mudstone facies (MF) The mudstone facies is dominated by thin-bedded sandstone interbedded with mudstone with an individual sedimentation unit thickness of <20 cm (Fig. 4F). The sedimentation unit shows normal grading from fine-to very-fine sandstone to siltstone and mudstone. It has a flat basal contact and a very low sandstone percentage and high siltstone and mudstone percentage (>70%). The

dominant sedimentary structures are ripple lamination (Tc) along with planar lamination on

siltstone and mudstone (Td-Te). The mudstone facies is interpreted as a deposit from the tail of a low-density turbidity current.

An Analytical Model to predict the Sediment Flux of Each Grain-Size Class in Turbidity Current Flow; Application to Gold Channel, Tres Pasos Formation, Chile

Figure 3. (A) A stratigraphic panel of Tres Pasos Formation based on the outcrop above Laguna Figueroa. The lower sandstone package was studied by Macauley and Hubbard (2013) (white rectangle). The upper sandstone package was studied by Hubbard (2014) and de Leeuw (2017) (black rectangle); Note that the white line shows the measured section location of Macauley and Hubbard (2013) study; (B) Cross section of the lower sandstone package (white rectangle in part A) shows 18 channel elements. The gold channel is the third channel element in the cross-section. This study focuses on the channel margin from the third channel element (red rectangle). Figure adapted from Macauley and Hubbard (2013)

An Analytical Model to predict the Sediment Flux of Each Grain-Size Class in Turbidity Current Flow; Application to Gold Channel, Tres Pasos Formation, Chile

Figure 4. Bed-scale outcrop of Tres Pasos Formation. (A) The amalgamated sandstone facies normally has a thickness of about 25 m; (B) Thick-to-thin sandstone facies is characterized by normal grading from massive- course grain sandstone to planar-medium grain sandstone; (C) Mudstone clast characterise the base of high density turbidite for ASF; (D) Changing from thin to thick sandstone is typical for TSF. Sometimes mudstone clasts are also found but not as prominent as in amalgamated sandstone facies; (E) Planar and ripple mark are commonly found in the upper part of sandstone of TSF; (F) Mudstone facies characterized by interbedded fine sandstone to siltstone and mudstone. (figures are adapted from Macauley & Hubbard (2013) and Hubbard et al (2014). 14

An Analytical Model to predict the Sediment Flux of Each Grain-Size Class in Turbidity Current Flow; Application to Gold Channel, Tres Pasos Formation, Chile

2.3. The architecture of Gold Channel The Gold channel is well exposed on the 1.5 km outcrop belt of the Tres Pasos Formation above Laguna Figueroa, Chile (Fig. 5A). The Gold channel is one of the channel elements from the lower sandstone package of the outcrop (the white rectangle in Fig. 3A). The lower part of the Laguna Figueroa outcrop was studied in detail by Macauley and Hubbard (2013). According to those authors, the lower sandstone package consists of 18 channel elements that are grouped into three channel complexes. The Gold channel is the third channel element of the first channel complex (Fig. 3B).

The channel elements of the first channel complex are characterised by an average width of 300 m and thickness of 12 - 15 m. Macauley and Hubbard (2013) published a sedimentary log of the left side of the Gold channel, which is the same location as the sample location in this study. According to Macauley and Hubbard (2013), the channel axis consists of the amalgamated sandstone facies that alters to thick-to- thin-sandstone interbedded with mudstone facies. The sand percentage decreases from channel axis to the channel margin section (see sedimentary log ii in Fig. 5C). The mudstone facies additionally occurs on the channel margin section (Fig. 5B and Fig. 5C).

Part C

An Analytical Model to predict the Sediment Flux of Each Grain-Size Class in Turbidity Current Flow; Application to Gold Channel, Tres Pasos Formation, Chile

7 m

Figure 5. (A) Photograph of the Gold Channel (indicated in red rectangle in Fig. 3B) with a human for scale on the bottom left. The red dots mark the sample locations in this study; (B) A sketch of the Gold Channel based on the photograph (Fig. 5A) and the sedimentary logs from Macauley & Hubbard (2013). It shows how the facies changing in the Gold Channel and marks the location of primary and secondary channelform surface. (C) A photograph of the off-axis section of the Gold Channel, below the white line is the mudstone facies and on the top is thick-to-thin sandstone interbedded with the mudstone facies (the white rectangle in Fig. 5A). Figure 5C is adapted from Macauley & Hubbard (2013)

An Analytical Model to predict the Sediment Flux of Each Grain-Size Class in Turbidity Current Flow; Application to Gold Channel, Tres Pasos Formation, Chile

3. Method 3.1. Grain Size Distribution 3.1.1. Sample collection and preparation The samples used in this study were collected by de Leeuw (2017) from a turbidity-current deposit of the Gold Channel, Magallanes Basin, Southern Chile. The samples are hand specimens of the turbidite sandstone sampled with a geological hammer. In total, there are 63 samples from the channel axis and channel margin section of the Gold Channel.

The channel-axis samples were collected from the amalgamated sandstone facies (ASF) to obtain the vertical variability of the grain-size distribution in the channel axis. On the other hand, the channel-margin samples were collected from alternating thin-bedded sandstone with mudstone facies (TSF) derived from three sandstone beds located in the base, middle and top of margin deposit. To obtain lateral variability of the grain-size distribution, several samples were taken from each bed from the channel axis to the channel margin and vertically within the channel margin (see Fig. 5A for sample location). Subsequently, the samples were cut to obtain the thin sections.

11 out of 63 samples were selected for grain-size distribution analysis to represent the channel axis and channel margin samples. Five samples from the channel axis and six samples from the channel margin were selected to analyse the vertical variability of grainsize in the channel axis and lateral variability of grainsize from the base of the channel axis to the channel margin. It is advisable for the samples to be cut perpendicular to the bedding and parallel to the paleo flow in order to get the grain orientation. However, in this study, the bedding orientation and the paleo flow of the samples are unknown. Thus, we acknowledge that there is an uncertainty related to the grain orientation.

3.1.2. Image Processing Once the thin sections were ready, the petrographic image of the turbidite deposit was captured using microscope Leica 125 together with a software package, LV46. Images were captured with a 20x objective lens using the mosaic technique with a grid of 20x20. The mosaic technique compiled several images into one image which covered almost the entire area on the thin section with a high-resolution image quality.

The image was then processed using ImageJ software to carry out the point-counting method (Sylvester and Lowe, 2004). First, the image scale was required to be set in mm. Secondly, grids were applied at the same distance from one point to another. According to Johnson (1994), at least 270 points are required for grain-size analysis of poorly sorted sandstone in order to get the accurate result. In this study, a minimum of 300 points was applied which covered the entire thin section area because we count the grain as well as the matrix. Thirdly, we outlined the individual grain and matrix. The outline method that would be used depended on where the grid was located. If the grid was located on the grain, then best- fit ellipsoid was used. On the other hand, if the grid was located on the matrix, we outlined the matrix as a point instead of best-fit ellipsoid due to its very small size, then the point set-up is used (Fig. 6). The matrix was also counted to obtain the percentage of the matrix contained in the sample. Upon outlining the grain, the ImageJ automatically measured four aspects; long axis, short axis, angle, and area of the grain. The result was then transferred to Microsoft Excel for further analysis. 17

An Analytical Model to predict the Sediment Flux of Each Grain-Size Class in Turbidity Current Flow; Application to Gold Channel, Tres Pasos Formation, Chile

Figure 6. 300 grids are required for the point-counting measurement. Best-fit ellipsoid is used to outline the grain (green ellipsoid) and point is used to outline matrix (yellow point)

3.1.3. Statistical Analysis The statistical analysis was performed by using a modified programming code of MatLab provided by Pohl (2019). The details of the statistical analysis described in this section follow the workflow as described in Berends (2018). The long and short axis data was used to measure the true nominal diameter (D). According to Johnson (1994), it is impossible to cut the grain through its centre and thus underestimates the diameter. The equation below by Johnson was used to get the true nominal diameter.

2 Dmm = d’mm + 0.4(a’mm – d’mm) (Eq. 1) where: d = ab1/2, a and b are long and short axis respectively.

The true nominal diameter is converted into 휑

휑 = -log2 D/D0 (Eq. 2)

The individual grain measurements were grouped in each grain-size class and displayed in a histogram- frequency curve (Fig. 10 and Fig. 11) which indicates the volume percentage of the grain-size in the sample volume (Johnson, 1994). In addition, the result was also presented in a cumulative curve (Appendix II). Calculations of the mean (in 휑 and µm unit), sorting, skewness, and kurtosis can be done either graphically (Folk, 1957) or mathematically (Boggs, 2009).

In this study, to determine those statistical parameters, the mathematical approach was applied using the method of moments for a more rigorous result.

An Analytical Model to predict the Sediment Flux of Each Grain-Size Class in Turbidity Current Flow; Application to Gold Channel, Tres Pasos Formation, Chile

Table 1. Method of Moments (Boggs, 2009)

Mean Sortation ∑(푓푚) ∑ 푓(푚− 푥̅ )2 푥̅휑 = 휑 ∑(푓) σ휑 = √ 100 Skewness Kurtosis 3 ∑ 푓(푚− 푥̅ )4 ∑ 푓(푚− 푥̅휑) 휑 K휑 = Sk휑 = √ 3 100 훼3 100 휎휑 휑

Where f is the frequency of each grain-size class based on a 0.25 휑 bin width m is the midpoint of each grain-size class, the n total number in the sample (100 when f is percent)

The sortation of the sample population corresponds to the standard deviation value of the statistical parameter which can be calculated by the equation above (Table 1). The standard deviation is expressed in the phi unit which defines the sortation (Table 2).

Table 2. Classification of sortation (Folk, 1957)

Standard Deviation (휑) Sortation <0.35 휑 Very well sorted 0.35 – 0.5 휑 Well sorted 0.5 – 0.7 휑 Moderately well sorted 0.7 – 1 휑 Moderately sorted 1 – 2 휑 Poorly sorted 2 – 4 휑 Very poorly sorted >4 휑 Extremely poorly sorted

Skewness corresponds to the degree of asymmetry of the frequency curve. The shape of the curve is commonly skewed or asymmetrical. If the sample population consists of an excess of coarse particles, the grain distribution is classified as coarse skewed or negative skewed. On the contrary, a fine-grain dominated sample is classified as fine skewed or positive skewed (see Fig. 7 and Table 3).

Table 3. Classification of skewness (Folk, 1957)

Calculated skewness Skewness >0.3 Strongly fine skewed 0.3 to 0.1 Fine skewed 0.1 to -0.11 Near symmetrical -0.1 to -0.3 Coarse skewed < -0.3 Strongly coarse skewed

An Analytical Model to predict the Sediment Flux of Each Grain-Size Class in Turbidity Current Flow; Application to Gold Channel, Tres Pasos Formation, Chile

Figure 7. Skewness

Kurtosis is the sharpness of the frequency curve and it can be calculated using the formula shown in Table 1. Kurtosis is also another aspect used to indicate the sortation (Table 4). A well-sorted grain population is indicated by the sharp curve and vice versa (Fig. 8).

Table 4. Classification of Kurtosis

Kurtosis Value Kurtosis 0.41 – 0.67 Very platykurtic 0.67 – 0.9 Platykurtic 0.9 – 1.11 Mesokurtic 1.11 – 1.5 Leptokurtic 1.5 - 3 Very leptokurtic >3 Extremely leptokurtic

Figure 8. Kurtosis 3.2. The Sediment Budget Estimator A Sediment Budget Estimator (SBE) is a tool to estimate the sediment flux (m3/s) to the sediment budget (m3) of a turbidity current which is responsible for transporting the sediment through the submarine channel over a geological timescale (Eggenhuisen, unpublished). SBE is developed based on the source- to-sink perspective (Walsh et al., 2016) to simplify the complexity of the sediment transport process, yet still reflects the natural turbidity current process. The model approach used in SBE is to link the flow

An Analytical Model to predict the Sediment Flux of Each Grain-Size Class in Turbidity Current Flow; Application to Gold Channel, Tres Pasos Formation, Chile structure of a turbidity current and the deposit of the submarine channel formed by this current (Eggenhuisen, unpublished).

SBE can be used to reconstruct the turbidity current from its deposit, the submarine fans. It requires several input parameters that are determined based on the user’s understanding of the basin configuration and the characteristics of the feeder channel of the chosen system. In general, the input parameters are divided into the flow dynamic properties and the flow duration (Table 5). The flow dynamic properties together with other fixed input values (Appendix 1) are subsequently used to determine the characteristics of the turbidity current. The characteristics of the turbidity current consist of the velocity of turbidity current and the suspended-sediment concentration. By multiplying the velocity with the concentration profile, SBE quantifies the sediment flux. Ultimately, the sediment flux is multiplied by the flow duration to obtain the sediment budget transported into the submarine channel over the geological timescale (Eggenhuisen, (Unpublished)). The more detailed equations used in SBE are discussed in Eggenhuisen (Unpublished).

Figure 9. The shape of the concentration profile is slightly concave (left). Both the concentration profile and channel deposit show the same fining-upward trend (figure adapted from de Leeuw, 2017)

This study focuses on improving the concentration profile in the SBE by integrating the Rouse Equation for the D10, D50, and D90, for the 10th, 50th, and 90th percentile of grain-size distribution as the typical grain-size classes used in sedimentology. The concentration profile shows how the sediment is suspended vertically in the flow and decaying as a function of height. The shapes of the concentration profiles from previous studies were slightly concave (Altinakar et al., 1996; de Leeuw, 2017; Garcia, 1994) (Fig. 9). Therefore, the previous version of SBE incorporated only an adhoc exponential decay function (Eggenhuisen et al., (Unpublished)) for the concentration profile (Eq. 3).

C(z) = Cb e(-kz) (Eq. 3)

Where C(z) is the sediment concentration at the height z; Cb is the sediment concentration at the base of the flow; e is exponential constant, z is the height above the bed; k is a decay constant.

An Analytical Model to predict the Sediment Flux of Each Grain-Size Class in Turbidity Current Flow; Application to Gold Channel, Tres Pasos Formation, Chile

This equation is replaced in the new SBE because it is a simple form of exponential decay function that does not include the physics-based modelling of sediment diffusivity in fluid and does not incorporate how the different particle sizes are distributed through the water column. Therefore, the new version of SBE incorporates the Rouse equation to model the concentration profile.

Figure 10. The graph shows how each particle size of sediment suspends thought the water column (figure adapted from Chang, 1992)

3.2.1. The Rouse Equation Modeling the sediment concentration profile using Rouse (1937) requires several input parameters. The input parameters are (i) grain-size distribution of a sample at the reference level, (ii) flow thickness, (iii) total sediment concentration at the reference level, and (iv) shear velocity. The steps to obtain the sediment concentration using the Rouse equation are discussed below.

- Calculating the fraction of sediment of each particle size i at the reference level 퐶 (푧) 퐹 (푧) = 푖 (Eq. 4) 푟푒푓푖 퐶(푧)

Where Frefi(z) is the fraction of each particle-size over the total particle at the reference level, Ci(z) is the frequency of each particle size, and C(z) is the total percentage of whole particle size. All three parameters can be obtained from the grain-size distribution.

An Analytical Model to predict the Sediment Flux of Each Grain-Size Class in Turbidity Current Flow; Application to Gold Channel, Tres Pasos Formation, Chile

- Calculating the concentration of sediment in grain-size class i at the reference level

Crefi = Frefi x Cref (Eq. 5)

Where Crefi is the volumetric concentration of suspended sediment of particle size i at the reference

level (zref); Frefi is the fraction of each particle size at the reference level; Cref is the saturated-near-bed sediment concentration which can be calculated as follows. 푢∗3 퐶 = (Eq. 6) 푟푒푓 140푣푔푅 Where: u* = shear velocity (m/s) v = kinematic viscosity of water at 20˚ C (m2/s) R = relative specific density of sediment in the water (kg/m3) g = gravity (m/s2)

- Calculating the settling velocity The settling velocity affects the sortation of the sediment and depends on the shear velocity of the flow and varies with particle size (Ferguson & Church, 2004). The settling velocity equation by Ferguson & Church was incorporated in SBE as this equation is applicable for all grain-size classes (Eq. 7). 푅푔퐷2 푣 = (eq. 7) 푠푖 퐶1 푣+(0.75 퐶2 푅푔퐷3)0.5

Where: C1 = the constant in Stokes’ equation for laminar settling (-) C2 = the constant drag coefficient of particle Reynolds number exceeding 103. R = relative specific density of sediment in the water (kg/m3) g = gravity (m/s2) D = grain-size particle of each grain-size class at the reference level v = kinematic viscosity of water at 200 C (m2/s) In the case of smooth spheres, the coefficient suggested by Ferguson & Church (2004) is C1 = 18 and C2 = 1.

- Setting the current thickness The current thickness is set to be 1.3 times the channel depth. This number is based on Mohrig & Buttles (2007). Mohrig & Buttles (2007) quantified the thickness of the turbidity current relative to the depth according to their experiment which resolved a systematic change of the thickness of the turbidity current that affects the sedimentation pattern. They classified the flow into channelized,

quasi channelized and unconfined defined using Ux/Uy and H/h, where Ux is longitudinal velocity and

describes the rate of current lengthening down the channel centreline, Uy describes the rate of increase in the half-width of the current, and H/h is the ratio of current thickness to channel depth. In this case, we incorporate the fully channelized flow into SBE. Therefore, we set the turbidity current thickness as 1.3*Channel depth

An Analytical Model to predict the Sediment Flux of Each Grain-Size Class in Turbidity Current Flow; Application to Gold Channel, Tres Pasos Formation, Chile

- Calculating the sediment concentration of each grain-size class (the Rouse Equation) Ultimately, all parameters explained above are used to calculate the sediment concentration of each grain-size class through. The shear velocity (U*) is calculated automatically in the SBE and later used in this equation.

푣푠푖 훽휅푢∗ 퐻−푧 푧푟푒푓 퐶푖(푧) = 퐶푟푒푓푖 ( ( )) (eq. 8) 푧 퐻−푧푟푒푓

Where:

H = the thickness of the flow (m) Z = the height above the bed (m) vsi = settling velocity of the sediment in grain-size class I (m/s) K = von karman constant (0.4) U* = the shear velocity (m/s) 훽 = the coefficient between turbulent diffusivity and sediment diffusivity (set to 1 in this study)

Crefi = concentration of sediment in grain-size class i at the reference level

An Analytical Model to predict the Sediment Flux of Each Grain-Size Class in Turbidity Current Flow; Application to Gold Channel, Tres Pasos Formation, Chile

4. Results 4.1. Grain Size Distribution Histograms of grain-size distribution of channel axis and channel margin samples are plotted in Fig. 11 and Fig. 12, respectively, along with corresponding thin-section photographs. The histogram curves of each section are compiled into two graphs, one for the channel axis and another for the channel margin, as shown in Fig. 13A and Fig 13B respectively. In general, the grain size distribution analysis of the Gold Channel indicates a vertically fining-upwards trend with height in channel axis section (Fig. 13A) and a laterally coarsening trend with distance away to the channel margin (Fig. 13B). The channel axis is dominated by the fine-sand grain size fraction while fine-to-medium-sand grain size dominates the channel margin. The modal grain size of the channel axis is approximately 3φ finer than the channel margin. This results achieve our first objective of this study.

An Analytical Model to predict the Sediment Flux of Each Grain-Size Class in Turbidity Current Flow; Application to Gold Channel, Tres Pasos Formation, Chile

Figure 11. Histogram probability showing the grain-size distribution of vertical variability with height above the bed (see Fig. 5B for sample’s location)

An Analytical Model to predict the Sediment Flux of Each Grain-Size Class in Turbidity Current Flow; Application to Gold Channel, Tres Pasos Formation, Chile

Figure 12. Histogram probability showing the grain-size distribution of lateral variability with distance away from channel axis (see Fig. 5B for sample’s location)

An Analytical Model to predict the Sediment Flux of Each Grain-Size Class in Turbidity Current Flow; Application to Gold Channel, Tres Pasos Formation, Chile

Figure 13. Grain size distribution of all sediment samples vertically in channel axis (A) and 4 samples from bed B1 of channel margin and channel axis (B). Abbreviation: Very Coarse Sand (V.C Sand) and Medium Pebbles (MP)

Eleven samples were selected for grain-size analysis consisting of 5 representative samples from the channel axis and six representative samples from bed B1, B2, and B3 of the channel margin deposit (see Fig. 5A for sample location). The grain-size distribution of the channel axis shows a shift from fine-sand to very-fine-sand with height above the thalweg, excluding sample AX 180 whose modal grain size is relatively finer (±80 µm). Additionally, statistical parameters such as sortation and kurtosis indicate that the grain population is moderately sorted while AX 180 is well sorted (Fig. 14).

An Analytical Model to predict the Sediment Flux of Each Grain-Size Class in Turbidity Current Flow; Application to Gold Channel, Tres Pasos Formation, Chile

AX 180 is indicated as an anomaly sample. As mentioned in the method section, samples from the channel axis section were taken from the amalgamated sandstone facies characterized by medium to fine sandstone. Meanwhile, sample AX 180 is characterized by very-fine-sand particles. There are two possibilities to explain this outlier sample. Firstly, it seems that the AX 180 was sampled from finer bed that might be deposited within a turbidity current tail. This finer bed was not completely eroded and is still preserved locally in the channel axis section. Secondly, AX180 might have been sampled from the channel margin section but was mislabelled as a sample from the channel axis section.

Figure 14. Statistical parameters of the channel axis deposit

Six samples from three different beds in the channel margin were selected (Fig. 5B). Samples from B1 were investigated further to obtain lateral variability of grain size (Fig. 13B), given that bed B1 is located in the lower bed of channel margin and has denser samples compared to bed B2 and B3. Fig. 13B demonstrates a shift from fine-sand to medium-sand towards the edge of the channel margin with a modal grain size that is 67 µm coarser than channel axis sample. Statistical parameters (sorting, kurtosis and skewness) do not show any trend of lateral variability (Fig. 15).

An Analytical Model to predict the Sediment Flux of Each Grain-Size Class in Turbidity Current Flow; Application to Gold Channel, Tres Pasos Formation, Chile

Figure 15. Statistical parameters of samples from channel axis to channel margin, showing lateral variability

An Analytical Model to predict the Sediment Flux of Each Grain-Size Class in Turbidity Current Flow; Application to Gold Channel, Tres Pasos Formation, Chile

4.2. Sediment budget reconstruction of Gold Channel Reconstruction of the sediment budget was carried out with a new version of SBE and used to answer the third objective in this study, which is to estimate the sediment flux of each grain-size class. Section 4.2.1 below explains the details of how we define boundary conditions for modelling the sediment budget as presented in the results section 4.2.2. 4.2.1. Boundary Condition The input parameters of SBE are divided into two parts, the simulation parameters and simulation conditions. The simulation parameters are the fixed value set by the SBE while the simulation conditions are determined by the user’s understanding of the chosen turbidity system. The user-defined boundary conditions of the model, in this case, were based on the turbidite system of the Gold Channel of the Tres Pasos Formation. This section emphasizes how the boundary conditions for the simulation-condition are determined. Details concerning the simulation parameters can be found in Appendix 1.

The significant difference of input parameters in the new version of SBE requires the grain-size distribution of the single sample, which consists of the grain size and frequency of each grain-size class (D10, D50, D90) at the reference level from the base of the channel axis. The grain-size distribution is required to calculate the near-bed sediment concentration at the reference level. By doing so, we can estimate the sediment budget of each grain size class. Other details of the input parameters for defining the boundary condition are explained below.

Flow dynamic properties - Channel geometry Channel-geometry parameters consist of channel width, channel depth, bank angles, and slope, assuming that the channel shape is trapezoidal. The values used are within a range that is based on literature studies of the Tres Pasos Formation by Hubbard et al., (2010), Hubbard et al., (2014), Macauley and Hubbard (2013). A channel width of 300-430 m is set because 300 m is the average channel elements width for channel complex one in which the Gold Channel is located. The maximum channel width of the channel element in channel complex one is 430 m. The channel depth is interpreted as the fraction of channel fill which is 7-7.01 m (Fig. 5B). In this case, it is not set as a wide range value due to a technical issue in SBE However, it does not significantly affect the results. The mean slope of the Tres Pasos Formation is 1.7˚ and was set as a range of 1.5˚-2˚ in the SBE (Fig. 2C). Bank angles are calculated according to the tangential angle of the width and height average, which is 130 (Fig. 16). Summaries of channel geometry can be found in the figure below (Fig. 16)

7 m

Figure 16. Sketch of the channel used for model application

An Analytical Model to predict the Sediment Flux of Each Grain-Size Class in Turbidity Current Flow; Application to Gold Channel, Tres Pasos Formation, Chile

- Depth average sediment concentration (퐶) In this model, the value set for this variable is 0.2% - 0.6 % based on the experiment by Konsoer et al. (2013) in which the driving force between rivers and submarine channels was compared to the analogy of the simplified hydraulic flow between river and submarine channel. That analogy is based on the similarity in the balance of forces acting on these flows. The value of 0.2 – 0.6 % can be used as the basis to study the channelized flow over different scales and environments.

- Grain-size distribution

The sample selected for the input is AX 30, which is the sample from the base of the channel axis (Fig. 5A) as the reference grain size distribution at the reference level. The grain size of the 10th, 50th & 90th percentile and the frequency of each percentile have been calculated from the grain-size distribution (Fig. 11A). The D10, D50, and D90 percentile of AX30 are 82.5, 184.3, and 348.7 µm respectively. The frequency applied is not the frequency of each percentile. However, the frequency of the bin (bin width is 0.25 휑) in which each percentile values are included in that bin.

Table 5. Simulation condition parameters

Parameters Symbol Unit Remarks Flow dynamic properties Channel width W Meter 300-430 Channel depth D Meter 7 – 7.01 Bank Angles BankAngles Degree 13 Slope S Degree 1.5 - 2 Initial average sediment Cin volume [%] 0.2 - 0.6 concentration (퐶) Grain size for 10th, 50th d10; d50; d90 meter D10: 8.25 x10-5 and 90th percentile D50: 1.84 x10-4 (Sample AX30) D90: 3.49x10-4 Frequency Fref [-] D10: 0.044 (Sample AX30) D50: 0.139 D90: 0.091 Maximum sediment Cmax [-] 0.585 concentration in a granular shear layer at the bed (fixed value set by SBE) Flow duration properties Turbidity current CurDur hours 3-6 duration Frequency of turbidity CurFreq #/year 0.1-0.2 current Geological system activity SystAct kyr 2-4

An Analytical Model to predict the Sediment Flux of Each Grain-Size Class in Turbidity Current Flow; Application to Gold Channel, Tres Pasos Formation, Chile

Flow duration properties Flow duration properties define the duration of the recurrence of a turbidity current over the geological timescale. In this model, we applied a range of values according to Eggenhuisen (Unpublished) (Table 5), which has also been applied to the Gabriele Channel from the same turbidity system of the Tres Pasos Formation. 4.2.2. Sediment Budget of Gold Channel The sediment-transfer volume of each grain-size class of the Gold Channel was modelled with the new SBE and is presented here. The model is constrained by the boundary conditions as explained in section 4.2.1. The new SBE produces nine graphs, namely the shear velocity (Fig. 17A), Rouse profile (normalize concentration profile) (Fig. 17B), concentration profile of total sediment volume (Fig. 17C), three histograms of the sediment flux for each particle size (Fig. 17D-F), and three histograms of the sediment budget of each particle size (Fig. 17G-I).

As shown in Fig. 17A, the velocity profile has a “nose” shape and reaches a velocity maximum (Umax) at 2.1 m/s with height 2.6 m above the channel bed. The point where the velocity reaches its maximum is known as the velocity inflection point. Above the velocity inflection point, the current starts to decelerate. The concentration profile has a concave-up shape and is a typical shape for the concentration profile of turbidity currents (Altinakar et al., 1996; de Leeuw, 2017; Garcia, 1994). The concentration profile shows that the average bulk of sediments for D90, D50, and D10 particle sizes are 0.2, 0.05, and almost 0 respectively (Fig. 17C). Both the concentration profile and Rouse profile show how the grain-size is distributed differently within the flow. The very-fine-sand particle (D10 = 82.5 µm) are distributed more homogeneously in the flow. Meanwhile, fine-sand particle (D50 = 184.3 µm) are more concentrated in the lower region and decrease with the height above the bed although they can be suspended up to the upper part of the flow (see normalized concentration profile Fig. 17B). In addition, the medium-sand particle (D90 = 348.7 µm), is difficult to observe from the concentration profile. The concentration profile therefore suggests that this particle size is only concentrated on the base of the flow and cannot be suspended higher in the flow.

Subsequently, the model estimates the sediment flux and sediment budget based on grain-size stratification. It indicates that the median of sediment flux of finer sediment (D10) is the most abundant particle size transported through the channel and reaches up to 7.9 m3/s, followed by a relatively medium- grained sediment (D50 = 184 µm (fine sand)) with a flux of about 0.37 m3/s. The coarser sediment is the least abundant which is D90 (medium sand) and has a flux of 1.45x 10-4 m3/s (Fig. 17D-F). The sediment budget is the total flux estimated over a geological timescale. The median of the sediment budget of very fine sand (D10) is 4.99 x 107 m3, D50 is 2.42 x 106 m3, and D90 is 961.3 m3. The reconstruction model of the sediment budget indicates that the Gold Channel of Tres Pasos Formation is dominated by very fine sand sediment. Therefore, sediment flux and sediment budget data reveal that 99% of the sediment transported through the Gold Channel is very-fine-sand particle.

In summary, the flow structure of the Gold Channel has a maximum flow velocity that reaches up to 2.1 m/s and the concentration profile suggests that the sediment is not homogenously transported within the flow and is dominated by very fine sand (D10 = 82.5 µm).

An Analytical Model to predict the Sediment Flux of Each Grain-Size Class in Turbidity Current Flow; Application to Gold Channel, Tres Pasos Formation, Chile

Height: 2.67 m Umax 2.1 m/s A B

Median: 7.9 m3/s

Height: 2.67 m

C D

Median: 0.37 m3/s Median: 1.45x 10-4 m3/s

E F

Median: 4.99 x 107 m3 Median: 2.42 x 106 m3

G H

An Analytical Model to predict the Sediment Flux of Each Grain-Size Class in Turbidity Current Flow; Application to Gold Channel, Tres Pasos Formation, Chile

Median: 961.3 m3

Figure 17. Graphs produced by SBE: (A) Velocity profile, arrow shows the inflection point where shear velocity reaches maximum; (B) Normalize concentration profile (Rouse Equation profile); (C) Concentration profile of each particle size, note that the line indicates the height above the bed where the velocity reaches maximum; (D-F) Sediment Flux of D10, D50 and D90 respectively; (G-I) Sediment Budget of D10, D50, D90

An Analytical Model to predict the Sediment Flux of Each Grain-Size Class in Turbidity Current Flow; Application to Gold Channel, Tres Pasos Formation, Chile

5. Discussion This section discusses the (1) Model inference which focuses on the flow structure of turbidity current and sediment-transfer volume; (2) Matching natural deposit vs model; and (2) Model Validation. 5.1. Characteristics of turbidity current formed the Gold Channel The model constructed with the new SBE gives us insight into the flow structure of turbidity currents responsible for forming the Gold Channel deposit. The flow went through the Gold Channel is characterized by having relatively low shear velocity (Fig. 17A) which is associated with a more intense grain-size stratification. Fig. 17C shows a concentration profile which indicates grain-size stratification. It demonstrates that relatively medium (D50) and coarser (D90) grains are concentrated solely at the base of the flow. This observation can be explained as follows: Two parameters act on a grain in the flow, namely Reynold number and the Rouse number. Focusing on the latter one, the Rouse number is a function of shear velocity (u*) over settling velocity (Vsi), the coefficient between turbulent and sediment diffusivity (ß) and the von Karman constant (k) (Eq. 9). Since ß and k are constant and are applied equally to all particle sizes, we can neglect them. This means two main factors are left for controlling the Rouse number, which are shear velocity (u*) and settling velocity (Vsi). Shear velocity is a force that is induced by the turbulent mixing as a compensation of gravity and pulls the grain up in the flow. The settling velocity is an opposing force that pulls the grain down due to the gravity.

푣푠푖 푧 ∗ = (eq 9) ß푘푢∗ The main factor controlling the settling velocity is the grain size (see Eq. 7) as settling velocity increases with increasing grain coarseness. Therefore, if the settling velocity is higher than the shear velocity, this results in an increase of the Rouse number and vice versa. The Rouse number indicates how the different particle sizes are distributed and transported in the flow. The Rouse number (z*) of each particle size that has been generated from the model is shown in the Rouse profile (Fig. 17B). The Rouse profile shows that medium-sand particles (D90) are only concentrated on near-bed, fine- sand particles (D50) are more concentrated in the lower part of the flow, and very-fine-sand particles (D90) can be suspended higher in the flow. It implies that D90 was transported as bed load, D50 as a mixture of bed load and suspended load because it can still be found higher up in the flow, and D10 was transported as a suspended load. As described in section 4.2.2, Gold Channel is dominated by very-fine sand (99%). This information allows us to predict the volume of sediment of each grain- size class further down-dip the slope. It means that the lithology of the submarine channel fill located further down-dip of Gold Channel is dominated by very-fine sand.

The total sediment budget of sediment of three grain-size class going through the Gold Channel is 4.46 x 107 m3. This value lies within reasonable order of magnitude. According to Jobe et al., 2018, sediment volume in the intraslope setting is approximately 107, such as the Niger fan system, Nigeria that is predicted having the sediment volume ranging from 1.2 x 107 m3 to 3.6 x 107 m3. This value is relatively small compared to other different slope/basin positions, such as basin floor and ponded system that can

An Analytical Model to predict the Sediment Flux of Each Grain-Size Class in Turbidity Current Flow; Application to Gold Channel, Tres Pasos Formation, Chile reach the sediment volume up to 109 m3. This means that the lobes formed further downstream the Gold Channel is predicted small lobes. 5.2. Matching natural deposit vs model This study is subject to the limitations that arise when matching the grain-size stratification constructed by the new SBE with grain-size gradient indicated from Gold Channel deposit.

Comparing both data shows us that the grain-size stratification produced by SBE does not demonstrate an agreement with the natural deposit. Typically, a grain-size gradient in other natural deep-water systems show a fining-upward trend vertically in the channel fill such as in the Amazon Fan (Hiscott et al., 1997; Pirmez and Imran, 2003). We found that this, however, is not the case for the Gold Channel whose grain-size distribution data indicates a coarsening-trend with distance towards channel margin. This lateral coarsening trend might be a cause of lateral accretion deposit (LAD). In this case, we refer to the grain-size gradient laterally towards the channel margin instead of the grain-size gradient in channel axis. Since the deposit in channel axis is more prone to rework by the subsequent flow, while in channel margin has greater chance to preserve its deposit. Particularly, in this study we use the reference samples of channel margin section from the same bed, the B1.

Following the mechanism of LAD by Arnott (2007), a lateral accretion deposit occurs since the channel in a natural system is not straight, but sinuous. In the sinuous channel, when the sediment transport condition cannot reach an equilibrium state, there is an excess of sediment transported into the channel bend (Qin > Qout) (Fig.18A) which leads to the failure of the cut-bank margin (outer band). It causes sediment from the outer band to be transported further down-dip and deposited over the point-bar (inner band) by the subsequent flow coming through the channel bend.

Due to the constant change between an equilibrium and non-equilibrium state, the LADs is characterized by an interfingering of coarse- and thin-grained LADs where coarse LADS pinch out to fine-grained further up-dip channel position (Fig. 18B). The location where the coarse LADS terminate abruptly to fine LADS is associated with tractional sedimentary structures such as medium-scale cross stratification or planar lamination which is found locally. If LADs is responsible for forming the bed B1, then B1 might have been deposited as coarse LADs. To prove our hypothesis, we need to verify with the field data. However, the evidence is lacking from our study as we only have one sample from the bed right above the bed B1 and do not have an observation of the point where bed B1 pinches out to the above bed. Additionally, it is difficult to follow the continuity of bed B1 due to the presence of bushes in between, meaning that the samples of B1 might have been sampled from a different interfingering bed.

Matching the model with its natural deposit cannot be done since the grain-size stratification from its deposit cannot be performed due to its natural complexity. It is advisable to have more samples and do detail bed-scale sedimentary log in future research to confirm it. Despite all the complexities, it is also important to note that the SBE can only produce a one-dimensional model. The current SBE can therefore not capture the lateral variability in the flow and the temporal evolution of a turbidity current. To do so, a new tool has to be developed that can model the cross-sectional dimension.

An Analytical Model to predict the Sediment Flux of Each Grain-Size Class in Turbidity Current Flow; Application to Gold Channel, Tres Pasos Formation, Chile Flow direction

A B

Figure 18. The schematic diagram illustrates how sediment transport into the channel bend is higher than sediment transported out of the channel bend which leads to deposition over the inner bend due to failure in the outer bend (A). Figure B illustrates a cross section of the lateral accretion deposit of the inner bend (point bar). Note that the wavy line is the top of a turbidity current, the jagged line is the break in the in the vertical thickness of the turbidity current, on the right side is the sediment concentration profile [Sed] (figure modified from Arnott (2007)). 5.3. Model validation The Rouse equation has been integrated into SBE. The new SBE is now able to model the concentration for each grain-size class and, ultimately, the sediment budget. Nevertheless, the accuracy of the reconstructed model is arguable. The discussion below discusses approaches and issues regarding he model validation.

As explained in the section above, we could not match grain-size stratification of each grain-size class constructed by SBE with grain-size gradient indicated from its deposit. Therefore, validation of this model cannot be performed in this study due to the natural complexity in terms of the deposition process of Gold Channel deposit. A simple validation approach within SBE tool can be done by verifying whether the sum of the average bulk sediment concentration of each grain-size class is within the range of initial average sediment concentration (푪) (Table 6) which is 0.2% - 0.6%. As mentioned in section 4.2.2, the total average concentration obtained from the model is approximately 0.205% (Fig. 17C). It means that the output value of the total sediment concentration returns to the range value given by the initial sediment concentration. Hence, this confirms that the workflow of the new SBE, after integrating the Rouse equation, yields internally consistent results. Additionally, if we consider the total average bulk sediment concentration from all grain-size class, we estimated the total values still within the range of initial sediment concentration. Since the sediment is only dominated by the very-fine-sand particle and finer grain, while the coarser grain is very low.

Furthermore, we acknowledge that, at present, there is no better approach available to validate this model. This is caused because: (1) In this study, we only integrate the concentration of three percentiles. Hence, in order to estimate total sediment budget, it is necessary to integrate the concentration of all grain-size classes obtained from the grain-size distribution histogram and to ultimately calculate the total concentration from all grain-size classes; (2) A more accurate validation approach can be done if the model is applied to a submarine channel whose deposit of axis and margin section have been confirmed to be from the same flow, which is not the case in the Gold Channel; (3) Additionally, the even better approach 39

An Analytical Model to predict the Sediment Flux of Each Grain-Size Class in Turbidity Current Flow; Application to Gold Channel, Tres Pasos Formation, Chile would be if both the outcrops of the up-dip and down-dip turbidite channel are exposed very well. In our case, the outcrop of down-dip deposit of Gold Channel is not exposed (De Leeuw (2017)). Therefore, we cannot perform model validation.

Validation of point 2 and 3 aforementioned can only be perform in the modern turbidity current system. Due to the complexities of the ancient turbidity system, such as the Gold Channel, it is unlikely to confirm whether the deposit from channel axis and margin is deposited from the same flow. An example of modern turbidity current system is Monterey Canyon, California where there is direct monitoring of turbidity current along the canyon (Fig. 19). The new SBE is then suggested to be applied to the modern system to validate the reconstructed model.

Figure 19. Monitoring of modern turbidity current system along the Monterey Canyon, California

Despite the study limitations above, however, the Rouse equation has been validated by Eggenhuisen (2019). Validation of the Rouse equation provided by Eggenhuisen (2019) was done by comparing the model with an experimental flume lab deposit. It was assumed that the grain-size gradient obtained from the flume lab experiment is similar to the trend showed in the natural deposit of the deep-water channel fill. Eggenhuisen (2019) found that finer particles, such as very-fine grain sand, silt, and clay, are

An Analytical Model to predict the Sediment Flux of Each Grain-Size Class in Turbidity Current Flow; Application to Gold Channel, Tres Pasos Formation, Chile overestimated when we apply the Rouse equation to the deep-water system (Fig. 20). Meanwhile, the model predicts accurately for the fine-grain sand, particularly in the lower region of the flow where most of the sediment is concentrated and the prediction is overestimated in the upper part of the flow. It is caused by an overestimation of finer particles that becomes more significant in the upper part of the flow, which leads to a more pronounced suppression of coarser grain in the upper part of the flow.

A B

Figure 20. The basis of validation study by Eggenhuisen (2019) indicates that the Rouse equation is applicable to turbidity currents of the deep-marine system because it predicts accurately for fine-sand in the lower part of the flow. (A) Comparison of the concentration profile generated from the experimental deposit (dashed line) and model produced by the Rouse equation for different grain size; (B) total sediment concentration produced by the model (solid line) and experimental-flume-lab deposit (dashed line).

It remains unclear what mechanism causes this mismatch, yet, Eggenhuisen (2019) proposed that the difference in turbulent diffusivity between turbidity current and open channel flow might be the cause. In turbidity currents, there is a mixing of the turbidity current and ambient water, which is different from an open channel flow.

Interestingly, in the Eggenhuisen (2019) study, the coarser grain used for the experimental flume lab is not coarser than 224 µm, while in the natural deposit we still can find coarser sediment as is the case in the Gold channel which is up to 348 µm for D90. It is not possible to observe any coarser grains in the experimental flume lab due to the scaling issue. Therefore, future studies are needed to investigate this issue since, in this study, it could not be investigated as comparison of the grain-size gradient between the model and deposit is not possible. It would be interesting to study how the concentration profile of coarser grain (>300 µm) compares with the natural deposit, whether (1) the coarser grain (>300 µm) is predicted accurately in the lower part of the flow and underestimated in the upper part of the flow as if fine-sand particle; or (2) whether the coarser grain is completely underestimated by the Rouse equation.

An Analytical Model to predict the Sediment Flux of Each Grain-Size Class in Turbidity Current Flow; Application to Gold Channel, Tres Pasos Formation, Chile

In the context of our study, a dilemma is caused as, according to the model, the Gold Channel is dominated by very-fine grained sand (99%). The finer grain fraction is the main issue with this model, and it is therefore unclear how much the percentage of finer sediment is overpredicted. It is necessary to investigate further how much this overprediction contributes to our model based on different grain-size class. Thus, in our case, since the model estimates that 99% of sediment-transfer volume of the Gold Channel is composed of very-fine sand, we predict that the overestimation does not reach that high, it might be around 70%-80% still dominated by very-fine-sand particle. Thus, it is likely the down-dip turbidite might still be dominated by finer grain but that this is not as much as what we predict in the model. The concentration of D50 (fine grained sand) is underestimated in this upper part of the flow, while D90 might not that significant since its concentration is predicted to be very low even in the lower part of the flow (Fig. 17C), almost approaching zero.

Finally, despite the limitations explained above, integrating the Rouse equation into the SBE has led to a successful reconstruction of the sediment-budget of the D10, D50 and D90 grain-size classes. However, this tool should be applied with caution.

An Analytical Model to predict the Sediment Flux of Each Grain-Size Class in Turbidity Current Flow; Application to Gold Channel, Tres Pasos Formation, Chile

6. Conclusion This study has been successfully integrating the Rouse Equation to the SBE. The new version of SBE is applied to the Gold Channel, Tres Pasos Formation, Chile. Grain-size distribution of the Gold channel shows lateral coarsening trend with the distance from channel axis, a fining-upward trend towards the surface of channel and dominated by fine-sand grain. The sediment-transfer volume of each grain-size class has been modelled with the new SBE by using the sample at the reference level of Gold Channel deposit (AX 30) to obtain the concentration profile of each grain-size class at the reference level. The model is able to estimate the velocity profile, the concentration profile using the Rouse equation for each particle size. The flow structure characterized the turbidity current went through the Gold Channel reached velocity of 2.1 m/s and associated with highly grain-size stratification. Ultimately, the new SBE produces sediment flux and sediment budget based on grain-size stratification for each grain size class. The model demonstrates the total sediment-budget going through the Gold Channel is 4.22 x 10-6 m3/s and 99% of that volume is dominated by very-fine sand. Despite all the limitations, this study has contributed in understanding the relationship of ancient turbidite, the flow structure responsible to formed them and the amount of sediment volume they transported through the numerical modelling.

An Analytical Model to predict the Sediment Flux of Each Grain-Size Class in Turbidity Current Flow; Application to Gold Channel, Tres Pasos Formation, Chile

References Altinakar, M. S., Graf, W. H., & Hopfinger, E. J. (1996). Flow structure in turbidity currents. Journal of Hydraulic Research, 34(5), 713–718. https://doi.org/10.1080/00221689609498467 Azpiroz-Zabala, M., Cartigny, M. J., Talling, P. J., Parsons, D. R., Sumner, E. J., Clare, M. A., ... & Pope, E. L. (2017). Newly recognized turbidity current structure can explain prolonged flushing of submarine canyons. Science advances, 3(10), e1700200. Berends, S. H. (2018). Grain size analysis by thin section images of Permian deep-marine sediments from the Fort Brown Formation, Karoo Basin, South Africa (Master's thesis). Universiteit Utrecht, Utrecht, The Netherlands

Boggs Jr, S., & Boggs, S. (2009). Petrology of sedimentary rocks. Cambridge University Press. Bolla Pittaluga, M., & Imran, J. (2014). Journal of Geophysical Research: Earth Surface A simple model for vertical profiles of velocity and suspended sediment concentration in straight and curved. Journal of Geophysical Research: Earth Surface, 119(3), 483–503. https://doi.org/10.1002/2013JF002812.Received Bouma, A.H., 1962. Sedimentology of Some Flysch Deposits; A Graphic Approach to Facies Interpretation: Amsterdam, Elsevier, 168 p. Chang, H. H. (1992). Fluvial processes in river engineering. Curray, J. R., Emmel, F. J., & Moore, D. G. (2003). The Bengal Fan: Morphology, geometry, stratigraphy, history and processes. Marine and Petroleum Geology, 19(10), 1191–1223. https://doi.org/10.1016/S0264-8172(03)00035-7 De Leeuw, J. (2017). The sedimentary record of submarine channel morphodynamics (Doctoral dissertation, University Utrecht). Eggenhuisen, J. (unpublished). The EuroSEDS Sediment Budget Estimator (SBE); integrating a turbidity current process model in Source-to-Sink sediment budget estimates. Eggenhuisen, J. T., Tilston, M. C., de Leeuw, J., Pohl, F., & Cartigny, M. J. B. Turbulent diffusion modelling of sediment in turbidity currents; an experimental validation of the Rouse approach. The Depositional Record. Ferguson, R.I., Church, M., 2004. A simple universal equation for grain settling velocity. Journal of Sedimentary Research, 74, 933–937. doi:10.1306/051204740933 Folk, R.L., and Ward, W.C., 1957, Brazos River Bar: A study in the significance of grain size parameters: Journal of Sedimentary Petrology, v. 27, no. 1, p. 3-26.

An Analytical Model to predict the Sediment Flux of Each Grain-Size Class in Turbidity Current Flow; Application to Gold Channel, Tres Pasos Formation, Chile

Galy, V., France-Lanord, C., Beyssac, O., Faure, P., Kudrass, H., & Palhol, F. (2007). Efficient organic carbon burial in the Bengal fan sustained by the Himalayan erosional system. Nature, 450(7168), 407. Garcia, M. H. (1994). Depositional turbidity currents laden with poorly sorted sediment. Journal of Hydraulic Engineering, 120(11), 1240–1263. https://doi.org/https://doi.org/10.1061/(ASCE)0733- 9429(1994)120:11(1240) Hiscott, R. N., Hall, F. R., & Pirmez, C. (1997). Turbidity-current overspill from the Amazon Channel: texture of the silt/sand load, paleoflow from anisotropy of magnetic susceptibility, and implications for flow processes. Proceedings of the Ocean Drilling Program, 155 Scientific Results, 155(January), 53–78. https://doi.org/10.2973/odp.proc.sr.155.202.1997 Hubbard, S. M., Fildani, A., Romans, B. W., Covault, J. A., & McHargue, T. R. (2010). High-Relief Slope Clinoform Development: Insights from Outcrop, Magallanes Basin, Chile. Journal of Sedimentary Research, 80(5), 357–375. https://doi.org/10.2110/jsr.2010.042 Hubbard, Stephen M., Covault, J. A., Fildani, A., & Romans, B. W. (2014). Sediment transfer and deposition in slope channels: Deciphering the record of enigmatic deep-sea processes from outcrop. Geological Society of America Bulletin, 126 (5-6) (1), 857–871. https://doi.org/10.1130/B30996.1 Jobe, Z. R., Howes, N., Romans, B. W., & Covault, J. A. (2018). Volume and recurrence of submarine‐fan‐ building turbidity currents. The Depositional Record. Johnson, M., 1994. thin-section grain size analysis revised. Sedimentology, 41, 985–999. Konsoer, K., Zinger, J., & Parker, G. (2013). Bankfull hydraulic geometry of submarine channels created by turbidity currents: Relations between bankfull channel characteristics and formative flow discharge. Journal of Geophysical Research: Earth Surface, 118(1), 216-228.

Kuenen, P. H. (1952). Estimated size of the Grand Banks [Newfoundland] turbidity current. American Journal of Science. https://doi.org/10.2475/ajs.250.12.874 Lowe, D.R., 1982, Sediment gravity flows: II. Depositional models with special reference to the deposits of high-density turbidity currents: Journal of Sedimentary Petrology, v. 52, p. 279–297. Macauley, R. V., & Hubbard, S. M. (2013). Slope channel sedimentary processes and stratigraphic stacking, Cretaceous Tres Pasos Formation slope system, Chilean Patagonia. Marine and Petroleum Geology, 41(1), 146–162. https://doi.org/10.1016/j.marpetgeo.2012.02.004 Meiburg, E., & Kneller, B. (2010). Turbidity Currents and Their Deposits. Annu. Rev. Fluid Mech, 42, 135– 156. https://doi.org/10.1146/annurev-fluid-121108-145618 Milliman, J.D. and Syvitski, J.P.M. (1992) Geomorphic tectonic controls of sediment discharge to the ocean – the importance of small mountain rivers. J. Geol., 100, 525–544. 45

An Analytical Model to predict the Sediment Flux of Each Grain-Size Class in Turbidity Current Flow; Application to Gold Channel, Tres Pasos Formation, Chile

Mohrig, D., Buttles, J., 2007. Deep turbidity currents in shallow channels. Geology, 35, 155-158. doi:10.1130/G22716A.1 Nelson, C. H., Karabanov, E. B., & Colman, S. M. (1995). Late quaternary turbidite systems in Lake Baikal, Russia. In Atlas of Deep Water Environments (pp. 29-33). Springer, Dordrecht. Peakall, J., McCaffrey, W.D., Kneller, B., Stelting, C.E., McHargue, Schweller, W.J., 2000. A process model for the evolution of submarine channels: implication for sedimentary architecture. In: Bouma, A.H., Stone, C.G. (Eds.), Fine-Grained Turbidite Systems. AAPG Memoir 72/ SEPM Special Publication 68, pp. 73–88. Piper, D.J.W., Normark, W.R., 2001. Sandy fans—from Amazon to Hueneme and beyond. Amercian Association of Petroleum Geologist Bulletin 85, 1407–1438. Pirmez, C., and Imran, J., 2003, Reconstruction of turbidity currents in Amazon Channel: Marine and Petroleum Geology, v. 20, p. 823–849, doi: 10.1016/j.marpetgeo.2003.03.005. Pohl, F. (2019). Turbidity currents and their deposits in abrupt morphological transition zones (Doctoral dissertation, UU Dept. of Earth Sciences). Romans, B. W., Fildani, A., Hubbard, S. M., Covault, J. A., Fosdick, J. C., & Graham, S. A. (2011). Evolution of deep-water stratigraphic architecture, Magallanes Basin, Chile. Marine and Petroleum Geology, 28(3), 612–628. https://doi.org/10.1016/j.marpetgeo.2010.05.002 Rouse, H., 1937. Modern Conceptions of the Mechanics of Fluid Turbulence. Transactions of the American Society of Civil Engineers, 102, 463–505. Shultz, M. R., Fildani, A., Cope, T. D., & Graham, S. A. (2005). Deposition and stratigraphic architecture of an outcropping ancient slope system: Tres Pasos Formation, Magallanes Basin, southern Chile. Geological Society, London, Special Publications, 244, 27–50. https://doi.org/10.1144/GSL.SP.2005.244.01.03 Slatt, R. M., Coleman, J., Rosen, N. C., Nelson, H., Bouma, A. H., Styzen, M. J., & Lawrence, D. T. (2000). Deep-water reservoirs of the world. Straub, K. M., & Mohrig, D. (2008). Quantifying the morphology and growth of levees in aggrading submarine channels. Journal of Geophysical Research: Earth Surface, 113(3), 1–20. https://doi.org/10.1029/2007JF000896 Sylvester, Z., & Lowe, D. R. (2004). Textural trends in turbidites and slurry beds from the Oligocene flysch of the East Carpathians, Romania. Sedimentology, 51(5), 945-972. Talling, P. J., Masson, D. G., Sumner, E. J., & Malgesini, G. (2012). Subaqueous sediment density flows: Depositional processes and deposit types. Sedimentology, 59(7), 1937-2003.

An Analytical Model to predict the Sediment Flux of Each Grain-Size Class in Turbidity Current Flow; Application to Gold Channel, Tres Pasos Formation, Chile

Walsh, J. P., Wiberg, P. L., Aalto, R., Nittrouer, C. A., & Kuehl, S. A. (2016). Source-to-sink research: Economy of the Earth’s surface and its strata. Earth-Science Reviews, 153, 1–6. https://doi.org/10.1016/j.earscirev.2015.11.010 Wilson, T. J. (1991). Transition from back-arc to foreland basin development in the southernmost Andes: stratigraphic record from the Ultima Esperanza District, Chile. Geological Society of America Bulletin, 103(1), 98–111. https://doi.org/10.1130/0016-7606(1991)103<0098:TFBATF>2.3.CO;2

An Analytical Model to predict the Sediment Flux of Each Grain-Size Class in Turbidity Current Flow; Application to Gold Channel, Tres Pasos Formation, Chile

APPENDIX I Simulation Parameters

The simulation parameters are the input parameters fixed by the tools

Parameter Value Remarks 3 Density of water (ρw) 1000 kg/m 3 Density of quartz (ρs) 2650 kg/m Dynamic viscosity of water (μ) 1.3x10-3 At T=100C Kinematic viscosity of water (v) 1.3 x10-6 m2/s; at T=200C; v = μ / v Gravity (g) 9.81 m2/s2 Von Karman’s constant (K) 0.4 [-] Proportional coefficient between 1 [-] turbulent and sediment diffusivity (ß) Constant in Stokes’ equation for laminar 18 [-] settling (C1) Constant drag coefficient (C2) 1 [-]

An Analytical Model to predict the Sediment Flux of Each Grain-Size Class in Turbidity Current Flow; Application to Gold Channel, Tres Pasos Formation, Chile

APPENDIX II AX 30

An Analytical Model to predict the Sediment Flux of Each Grain-Size Class in Turbidity Current Flow; Application to Gold Channel, Tres Pasos Formation, Chile

AX 180

AX 290

An Analytical Model to predict the Sediment Flux of Each Grain-Size Class in Turbidity Current Flow; Application to Gold Channel, Tres Pasos Formation, Chile

AX 510

AX 810

An Analytical Model to predict the Sediment Flux of Each Grain-Size Class in Turbidity Current Flow; Application to Gold Channel, Tres Pasos Formation, Chile

B1 2.2

B1 10.30

An Analytical Model to predict the Sediment Flux of Each Grain-Size Class in Turbidity Current Flow; Application to Gold Channel, Tres Pasos Formation, Chile

B1 16.07

B1 40.90

An Analytical Model to predict the Sediment Flux of Each Grain-Size Class in Turbidity Current Flow; Application to Gold Channel, Tres Pasos Formation, Chile

B2 31

B3 12