EROSION IN SURFACE-BASED MODELING USING TANK

EXPERIMENT AS ANALOG Siyao Xu

Earth Energy and Environmental Sciences

Tapan Mukerji and Jef Caers

Energy Resource Engineering

Abstract

Characterizing deepwater reservoirs, their stratigraphy and structure can be highly uncertain

due to the extremely limited data. The existence of subseismic scale fine-grained layers can

significantly affect oil production of a reservoir, which requires explicitly modelling the

uncertainty of these fine-grained fluid barriers. Conventional modeling techniques, such as two-

points statistics, multipoint statistics, object-based modeling, and process-based model, are

incapable of providing a satisfying solution due to their inherent shortages and the lack of data.

This work focuses on surface-based modeling of the deepwater system. The contribution of this

work is the use of a tank experiment of delta basin to extract relevant statistics of erosion that

can be used as analogs for modeling deepwater fans.

The advantage of tank experiment data is the availability of the intermediate dynamic

topographies of a depositional process, which is a rich source of understanding not only the

deposition geometries but also the processes. Proper statistics can be inferred from these

dynamic data, and will be applied in the surface-based framework to construct geologically

realistic models.

The benefits from this research will be a workflow of applying tank experiment data as a data

source of modeling deepwater system. A highly geologically realistic model is constructed with

information inferred from the data and geological knowledge.

1. Introduction

1.1 Erosion in Deepwater System

Shale drapes, in terms of the depositional process in a deepwater lobate reservoir environment,

occur between lobes or lobe elements (Figure 1.1). The impermeability and great lateral

continuity of subseismic interbed shale layers determines that the shale drape coverage is one

of the most important model parameters in the perspective of reservoir characterization. The

shale drape coverage in a deepwater lobate reservoir environment is determined by erosion of

following depositional events (channel-lobes) (Figure 1.2). Therefore modeling erosion is a key

problem for correct modeling of a deepwater reservoir.

Challenges of modeling erosion in deepwater reservoirs are the extremely limited data and

complex processes of deepwater environment. In the early appraisal stage of a deepwater

reservoir, only a handful of wells and low quality seismic data are obtained. Thus, further

understanding of the complex stratigraphy and structure of the depositional basin are impeded.

Furthermore, erosion process, which is a function of particle sizes and turbidity flow condition,

is extremely complex. The documented workflow honors the novel surface-based modeling

technique to model the lower part of the submarine fan. For gathering more information about

the processes, we use laboratory experiments and numerical simulation results as the analogue.

The objective is to infer meaningful statistical information about channel-lobe geometry and

deposition-erosion processes of a distributary delta and build a surface-based model with the

inferred statistics.

Figure 1.1: Outcrop photograph and sedimentary log corresponding to a lobe. A lobe is bounded above and below by fine-grained units. A lobe comprises several lobe elements. After Prelat et. al. 2009

Figure 1.2: Outcrop example of eroded shale drapes. After Alpak et. al. 2010.

1.2 Geological Background

Deepwater turbidite systems transport sediments from the edge of shelf down to the ocean

basin (Figure 1.3). A turbidite system is commonly divided into three parts: the upper, middle

and lower fans. The upper fan features with submarine canyons, where canyons send

sediments down from the shelf edge. Deposits are accelerated due to the work of gravity and

erosion is the dominant process in this part. The middle fan part starts from the toe of slope,

where topography starts flattening, the acceleration weakens and sediments start to deposit.

The middle fan includes well developed channels filled with coarse-grained sediments. In the

lower fan part, the turbidity flow gets more weakened till its death. Primary feature of the

lower fan part are lobes and distributary channels. Lobes and channels form deepwater

reservoirs (Mutti and Tinterri, 1991; Chapin et al., 1994). Generally, lobate deposits are

characterized by large extent and lateral continuity (McLean, 1981). Porosity in lobes ranges

from 20 to 35%, and permeability from 100 to 2000 md. The average net-to-gross varies from

40% to 60% (Fugitt et al., 2000; Saller et al., 2008). Lobe systems are therefore important

hydrocarbon reserves.

The purpose of deepwater reservoir characterization is to reproduce the complex

heterogeneity of reservoir permeability. Therefore, channel-lobe geometry must be modeled as

realistically as possible. The other important element of deepwater reservoir is the interbed

subseismic scale shale layers, which behave as flow barriers in dynamic simulation. These shale

layers and erosion on them by following channel-lobes need to be modeled explicitly.

Figure 1.3: a) Demonstration of a deepwater depositional system. After Funk et. al. 2012. b)

Geological settings of the model. After Prelat et. al. 2010.

1.3 Surface-based Modeling for Deepwater System

Surface-based modeling is a novel technique based on statistics of geometry but attempts to

place geobodies with rules mimicking deposition-erosion processes to obtain highly realistic

models (Pyrcz et al., 2004; Pyrcz and Strebelle, 2006; Miller et al., 2008; Biver et al., 2008;

Zhang et al., 2009; Michael et al., 2010). The existing models are based on a surface stacking

workflow. First the model starts by specifying the geometry of the geobody being deposited.

Then, its location of sedimentation is selected according to certain geological rules. The rules

aim at mimicking the sedimentary processes that occur in the environment of deposition. The

new geobody is stacked on top of the current depositional surface, which can be locally eroded

in the process. The geobody top surface is merged with this topography. This new surface then

becomes the current depositional surface. The stacking is repeated until a stopping criterion is

reached. Such models are stochastic because the parameters values used to perform a forward

simulation (size of the geobodies, location of the source, etc.) are uncertain and therefore

randomly drawn from probability distributions.

With surface-based technique, complex geometries can be accurately generated at low

computational costs. The disadvantage of surface-based technique is the complexity, which

comes from making proper rules for different depositional environments and model

conditioning. As a forward modeling technique, surface-based model is conditioned by

optimization-based method (Bertoncello et. al. 2011).

2. Methodology

2.1 Motivation

As stated in above, the first challenge of this research is that reasonable modeling of erosion

requires explicitly model the deposition-erosion processes, even if in an approximate manner.

The reason is that erosion on shale drapes are correlated to subsequent channel-lobes, and the

subsequent lobe geometry and placement are correlated to topography after previous events

(channel-lobe). To explicit model the complex deposition-erosion processes leads to a forward

model and will significantly increase the complexity of model conditioning.

Obviously, two-point statistics and multiple-point statistics are improper for this purpose. The

scarcity of data limits the use of two-point geostatistics, because the algorithm cannot obtain

statistical significant spatial correlations from the sparse data. Multiple-point statistics are not

ideal either. First, multiple-point statistics requires a training image to represent enough

pattern variability in order to generate realistic realizations. However, a depositional basin is

usually few in number of lobes. In other word, a training image for a lobate reservoir usually

does not provide enough information of lobe geometry. Second, multiple-point statistics places

constraints of spatial correlations of patterns implicitly through the training image, however, it

still does not consider the process information. Object-based methods exceed two-point

geostatistics and multiple-point statistics, in better representing nonlinear complex geometries

of channel and lobes. However, since object-based methods randomly place objects into the

model domain, the intermediate surface information are not used, therefore, the deposition-

erosion processes are still not explicitly modeled. Process-based methods are very limited in

reservoir modeling for their computational costs and the methods are very difficult to be

conditioned due to the inherent rigorousness of fluid dynamic equations. In summary, two-

point geostatistics, multiple-point statistics, object-based and process-based methods all face

challenges to build models representing realistic deepwater reservoirs in the perspective of

stratigraphy.

Surface-based method is proper for modeling deepwater reservoirs because it generates

complex geometries, explicitly mimicking the deposition-erosion processes with geological rules.

The method can place geobodies into reasonable places with reasonable geometries. Because

no equation is solved, the computational costs of surface-based method are just a fraction of

process-based method, but the realizations represent highly realistic stratigraphic information.

Another great challenge inherent to deepwater reservoir modeling is limited data. Usually, the

only available data are a handful of sparse wells and a seismic survey. Detailed reservoir

stratigraphic information cannot be inferred from the sparse well data. The seismic data can

definitely be used to infer the overall geometry information of the whole depositional basin.

However, the reservoir, in most conditions, is a small part of the depositional basin. The

reservoir top and bottom information can be inferred from the data, but the stratigraphy is

subseismic and remains uncertain. Second, as a forward method, surface-based modeling

requires the information of intermediate surface elevation evolution, which is lost in all

stratigraphy data because of erosion. Because we lack enough dynamic data from any natural

system, we propose to use tank experiment data as a new source of the deposition-erosion

processes, from which the dynamic information of the process can be inferred. However, other

sources of information, such as numeric simulation results, outcrop data, and satellite images,

may also be used in case the tank experiment data are insufficient.

The objective of documented method is to build a surface-based forward model for the lower

fan part of deepwater depositional system using statistics extracted from the dynamic tank

experiment data.

2.2 Concept of Surface-based Modeling

The workflow used in this study follows works of Michael et. al. 2010 and Bertoncello et. al.

2011 (Figure 2.1). Starting from an initial topography, a new geobody is generated with key

geometric parameters such as length, width, height drawn from probability distributions based

on a geometry template. The geobody placement is selected according to depositional rules

that partially affected by the topography. A new geobody is stacked on top of and merged with

the current topography to generate a new topography. This procedure is repeated until a

volume obtained from a seismic surface is filled. In the terminology of surface-based modeling,

the geobody in a surface is called an event, which should be distinguished from the concept of

event in sedimentology. An event in sedimentology is a single gravity flow from the top of a

shelf, while an event in surface-based modeling is a geometry that includes multiple gravity

flows.

Figure 2.1: Workflow of surface-based modeling. After Bertoncello et. al. 2011.

2.3 Surface Generation

2.3.1 Geobody Template Generation

Centerline Controlled Geometry Boundary

Observing channel-lobe geometry from laboratory experiment data (Figure 2.2) that will be

introduced in Chapter 2.4, several features of the channel-lobe morphology can be

characterized:

1) The channel parts are smooth constant-width belts with mild sinuosity corresponding

to topography;

2) The lobe geometry shows projecting oval shape with slight variance in response to

the topography;

Figure 2.2: Geometry examples obtained from tank experiment photos

For the purpose of realistically representing the geometric features, we propose to use a

centerline controlled boundary. The overall geometry are controlled by key parameters such as

lobe width/length ratio, however, the shape variance corresponding to topography can be

represented by rule-based shifting control points on the centerline (Figure 2.3). The sample in

Figure 2.3 marked out five types of centerline control points, all of which are with geological

interpretation.

1) Channel mouth: the starting point of a channel-lobe object;

2) Channel toe (lobe source): marking the end of channel and the start of a lobe;

3) Channel intermediate points: control points between 1) and 2), controlling the shape

variance of distributary channel;

4) Depocenter: the thickest point of a lobe;

5) Lobe End: the end of a lobe;

6) Boundary Control: a boundary control point is calculated from a centerline point by

Equation 2.1.

Given a set of centerline control points, the centerline can be interpolated by a spline function.

The Channel width is set to be constant relative to the lobe width, which is interpreted from

tank experiment geomorphology (Figure 2.2). The advantage of using centerline control points

is that statistics of key points with geological meaning are easier to be interpreted in case that

the analog data are imperfect. The lobe geometry (Figure 2.4) is defined by an oval shape

equation. Given a point P on the lobe part centerline, the half distance from P to its

corresponding boundary control point, 2

PW, is calculated by Equation (1).

(1)

where L is the given lobe length, maxw

Wf

L= is the lobe width/length ratio;

is the normalized distance from point P to the channel toe;

1 2,c c are built-in constants correlated to oval geometry.

Figure 2.3 A sample centerline controlled channel-lobe boundary

Figure 2.4: Lobe Geometry Calculation, refer to Equation 2.1.

Distance Maps

Given the centerline and the boundary of object, the channel and lobe distance map is

generated to represent the general trend of channel and lobe geometry. The channel geometry

shows a trend from centerline to boundary, therefore the trend map is generated by calculating

the normalized distance map from centerline to channel boundary (Figure 2.5 a, b).

Figure 2.5: a) Normalized distance from channel boundary to channel centerline; b) Channel

Trend Map;

The lobe geometry shows a trend from lobe boundary to channel toe, thus the lobe trend map

is generated by calculating the normalized distance map from lobe boundary to channel toe

(Figure 2.6).

Figure 2.6: a) Normalized Boundary-Channel Toe Distance; b) Lobe Trend Map

The Concept of Positive and Negative Surface for Erosion

For modeling erosion, here we introduce the concept of positive and negative surface (Figure

2.7). In surface-based modeling, deposition is represented by geometry with thickness

information. However, the increased elevation of the topography is not equal to lobe thickness

because of the erosion process. In other words, a portion of the new geobody will be below the

previous topography. In this study, we call this portion of the lobe ‘the Negative Surface’ and

the remained portion ‘the Positive Surface’. Therefore, the sum of absolute value of negative

surface and the positive surface is the lobe thickness. Our problem of modeling erosion is

converted into determining the negative surface given a new geobody, honoring statistics from

the tank experiment data.

Normalized Boundary-Channel

Toe Distance

1111

0000

a) b)

Figure 2.7: A new lobe is generated and placed onto previous surface a); Because of the erosion process, a portion of the new lobe is placed below the previous topography b); In this study, the portion below previous topography is called negative surface, representing erosion caused by the new lobe; the portion above previous topography is called positive surface, representing deposition caused by the new lobe c). Therefore, the erosion problem in surface-based modeling is converted into generating a negative surface given a positive surface, honoring statistics from tank experiment data.

Currently, we assume that the negative surface is geometrically analogous and translated to the

positive surface. Figure 2.8 demonstrates some examples of the positive/negative surface

geometries.

Figure 2.8: Examples of positive surfaces and negative surfaces.

Thickness of the positive surface and depth of the negative surface is calculated by two sets of

geometrical functions. Figure 2.9 demonstrates the calculations.

For the channel positive surface, the thickness is calculated with Equation (2).

�� � �����a? ? �� ���� (2)

where Ph is the thickness at point P ; Pd is the normalized distance generated in the channel

trend map (Figure 2.5); 1maxh is the maximum thickness of the channel positive surfaces; c is a

0.30.30.30.3

built-in geometric constant.

Equation (2) can be directly applied for obtaining depth of the negative surface by replacing

1maxh with����� � ������? ? ��� where pnf is a given parameter of the ratio of channel

positive thickness vs. channel negative depth.

Figure 2.9: Computation of Surface Thickness, refer to Equation (2) – (4).

The lobe surfaces are calculated with Equation (3) and (4).

��� � �����a? ? ���� ���������

������ (3)

�!"#$ � %& '�������(�)??*+,�-�-.//�0-�1.2 � (4)

where Ph is the thickness at point P ; Pd is the normalized distance generated in the lobe trend

map (Figure 2.5); 1maxh is the maximum thickness of the lobe positive surfaces; c is a built-in

geometric constant; channelh is the channel thickness; 1Depod is the distance from channel toe to

the thickest point of the lobe positive surface.

Equation (3) and (4) can also be directly applied to obtain the depth of the negative lobe

surface.

2.3.2 Geobody Placement

In the documented model, the channel-lobe placement is determined by the combined

depositional model. In the framework of surface-based modeling, a depositional model is a

probability map conceptualized from geological understanding about the depositional

processes. A depositional model has several components, based on geological rules. In the

documented model, the depositional model has three components: 1) the distance to sources;

2) the distance to previous lobe; 3) the deposition thickness. The depositional model and its

components at an intermediate simulation step are demonstrated in Figure 2.10. For the

distance-to-source and distance-to-previous-channel-end components, areas closer to those

points are assigned higher probabilities; for the total-deposition-thickness component, the

thinner deposition areas are given higher probabilities. All of the probabilities are linearly

converted from distance and thickness. Finally, the intermediate deposition model is combined

from three components by Tau model, from which the next channel-end point is picked up.

Figure 2.10 a) Intermediate total deposited elevation surface (topography), the model source and previous channel end point are plotted out; b) the distance-to-source component; c) the distance-to-previous-channel-end component; e) the total-deposition-thickness map; d) the combined deposition model;

2.3 Tank Experiment Data

Tank experiment data are studied and characterized for the surface-based model. In

cooperation with Chris Paola, St. Anthony National Laboratory, an experiment for turbidite

environment is in preparation. Currently, we start with a dataset from a distributary delta

experiment. The data includes three sets of 1D intermediate dynamic topography, respectively

measured from proximal, medial, distal part of a distributary delta experiment.

2.3.1 Experiment Setting

The experiment discussed here (DB-03) was performed and originally documented by Sheets et

al. (2007). The main focus of the work of Sheets et al. was documenting the creation and

preservation of channel-form sand bodies in alluvial systems. Since this initial publication, data

from the DB-03 experiment have been used in studies on compensational stacking of

sedimentary deposits (Straub et al., 2009) and clustering of sand bodies in fluvial stratigraphy

(Hajek et al., 2010). In this section we provide a short description of the experimental setup. For

a more detailed description see Sheets et al. (2007).

The motivation for the DB-03 experiment was to obtain detailed records of fluvial processes,

topographic evolution and stratigraphy, with sufficient spatial and temporal resolution to

observe and quantify the formation of channel sand bodies. The experiment was performed in

the Delta Basin at St. Anthony Falls Laboratory at the University of Minnesota. This basin is 5 m

by 5 m and 0.61 m deep (Figure 2.11). Accommodation is created in the Delta Basin by slowly

increasing base level by way of a siphon-based ocean controller. This system allows for the

control of base level with mm-scale precision (Sheets et al., 2007).

Figure 2.11: a) Schematic of the experimental arrangement. b) A photograph of the DB-03

experiment at a run time of approximately 11h. After Genti et. al. 2011.

The experiment included an initial build-out phase in which sediment and water were mixed in

a funnel and fed into one corner of the basin while base-level remained constant. The delta was

allowed to prograde into the basin and produced an approximately radially symmetrical fluvial

system. After the system prograded 2.5 m from source to shoreline a base-level rise was

initiated. Subsidence in the Delta Basin was simulated via a gradual rise in base level, at a rate

equal to the total sediment discharge divided by the desired fluvial system area. This sediment

feed rate allowed the shoreline to be maintained at an approximately constant location

through the course of the experiment. A photograph of the experimental set-up, including the

topographic measurement line, is shown in Figure 2.11. (Sheets et al. 2007) used a sediment

mixture of 70% 120? ?m silica sand and 30% bimodal (190? ?m and 460? ?m) anthracite coal.

Topographic measurements were taken in a manner modeled on the Experimental Earthscape

Basin (XES) subaerial laser topography scanning system (Sheets et al., 2002). Unlike the XES

system, however, where the topography of the entire fluvial surface is mapped periodically,

topography was monitored at 2 minute intervals along a flow-perpendicular transect located

1.75 m from the infeed point. A time series of deposition along this transect is shown in Figure

2.12. This system provided measurements with a data-sampling interval of 0.8 mm in the

horizontal and with a measurement precision of 0.9 mm in the vertical. The experiment lasted

30 hours and produced an average of 0.2m of stratigraphy.

Upon completion of the experiment, the deposit was sectioned and imaged at the topographic

strike transect. This allows direct comparison of the preserved stratigraphy to the elevation

fluctuations that generated the stratigraphy.

No attempt was made to formally scale the results from this experiment to field scale, nor were

the experimental parameters set to produce an analog to any particular field case. Rather, the

goal of the experiment was to create a self-organized, distributary depositional system in which

many of the processes characteristic of larger depositional channel systems could be monitored

in detail over spatial and temporal scales which are impossible to obtain in the field. The

rationale for such experiments is discussed in detail in (Paola et al 2009). The point here is that

our focus is on identifying the general class of distributions (i.e. heavy vs. thin tail) that

characterize the kinematics of topography in the DB-03 experiment and their relationship to the

architecture of the preserved stratigraphy.

2.3.2 Data Exploration

For each section, we have 1180 dynamic intermediate surfaces. The finalized surfaces of the

distal cross line are demonstrated in Figure 2.12. Figure 2.13 demonstrates the surface

evolution with a subset of the distal section. The first problem for data exploration is to

determine regions in the tank sediments that are equivalent to reservoirs in a real deepwater

system and visualize geometry information of positive surfaces and negative surfaces.

Depending on visualized geometry patterns, statistics will be characterized, however, since the

tank experiment is not scaled to any real environment, only dimensionless geometric ratios will

be extracted but not the absolute length, width etc.

Terminology

For the ease of quantifying geology and formulating the problem, several geological

concepts are formulated as follows and will be used through this study.

Topography

intermediate top surfaces at every t

Symbol: Zt(x,i), x is the location vector; surface index is a scalar i = 1,2,3,…,t

Stratigraphy

all previous surfaces at every t

Symbol: St(x,i), x is the location vector; surface index is a vector i = [1,2,3,…,t]

Erosion

Et+dt(x,i) Where Zt+dt(x,i) < Zt(x,i)

Deposition

Dt+dt(x,i) Where Zt+dt(x,i) > Zt(x,i)

Figure 2.12: Finalized surfaces of the distal cross section.

Figure 2.13: Surface evolution in the deposition process at the distal section. Numbers represent

the sequence of charts.

Geobody Definition in Surfaces

Because we are looking for geometry information of channel-lobe objects, the first step is to

identify these objects in the tank data. The deposition/erosion geometries (Figure 2.14) are

plotted to visualize patterns of deposition/erosion. In Figure 2.14, a), b) are the deposition and

erosion maps for the distal section.The vertical axis represents time and horizontal axis

represents section line vertical to flow direction (refer to Figure 2.11 a). All maps are

thresholded to clean up minor deposition/erosion and to emphasize the primary patterns.

The plots reveal several interesting features of the patterns:

1) Deposition and erosion processes demonstrate spatial and temporal clustering. Discontinuity

appears both spatially and temporally between clusters;

2) Depositional process is usually correlated to erosion processes. However, the erosion is not

as laterally continuous as correlated deposition.

Feature 1) can be interpreted as several deposition events that occurs in similar region, which

can be defined as one geobody. The spatial and temporal gap between one cluster and the

other is the interruption of two sets of deposition events and therefore distinguish two

geobodies formed by them.

Feature 2) provides some hints of geobody geometry. Deposition is represented by the positive

surface, which are generated by given geobody template. Erosion is represented by the

negative surface, however, erosion pattern in the data are laterally less continuous than

deposition pattern, which indicates that the negative surfaces can be discontinous patterns and

modifications should be made on our current geobody design.

Figure 2.14: a) Deposition geometry of the highlighted region in Figure 2.12; b) Erosion geometry

of the highlighted region in Figure 2.12; c) the overlapped geometries of 2.14 a) and 2.14 b); d) the zoomed in geometry of highlighted region in 2.14 c);

Further studying the geometries in Figure 2.14 d), the geometries can be grouped into three

categories, which correlate to different channel-lobe types (Table 2.1). According to the relative

width of a pair of deposition-erosion geometry, the geometries are interpreted to be 1)

channels; 2) lobes with erosion; 3) lobes without erosion. Three statistics are characterized

from Figure 2.14 d) for each of the groups: 1) ratio of lobes with erosion over lobes without

erosion; 2) the probability distribution of dimensionless ratio of maximum lobe erosion depth

dEL over maximum lobe deposition thickness dDL; 3) the probability distribution of

dimensionless ratio of maximum channel erosion dEC over the maximum channel deposition

thickness dDC.

Deposition Width <= Erosion Width Interpreted as channels

Deposition Width > Erosion WidthInterpreted as Lobes

with erosion

No ErosionInterpreted as Lobes

without erosion

Table 2.1: Groups of different Geometries

The ratio of lobes with erosion over lobes with erosion is 30%. The pdfs and cdfs of statistics 2)

and 3) are demonstrated in Table 2.2. These three statistics are used to control the simulation

using the simple surface-based model documented in the above sections.

PDF CDF

Lobe

with

erosion

Channel

Table 2.2: Statistics of dimensionless ratios of maximum erosion depth and deposition thickness from Figure 2.14 d).

3. Simulation Results

The objective of this test simulation aims at verifying that the statistics from a simulated cross

section reproduces the statistics in Section 2.3.3, therefore the model is not correlated to any

real length scale but just the model unit representing relative sizes and locations of the

geometries. The geometry scales are given by lobe length L, other parameters such as lobe

width, lobe thickness etc. are set correlated to the lobe length by a ratio. Primary parameters

are listed in Table 3.1. Some intermediate steps of the simulation are demonstrated in Figure

3.1.

Grid Dimension 300 x 250

dx 1

Lobe Length [50dx, 130dx] uniformly distributed

Lobe Width [0.3L, 0.7L] uniformly distributed

Lobe Thickness [0.002L,0.008L] uniformly distributed

Number of Surfaces 1180

Initial Surface Flat

Table 3.1: Primary simulation Parameters

Figure 3.1: Intermediate depositional thickness of one simulation. a) Depositional thickness at T = 20; b) Depositional thickness at T = 40; c) Depositional thickness at T = 200; d) Depositional thickness at T = 1180, a cross section at the line is taken out for comparison of statistics;

a) b) c)

d)

Figure 3.2: a) Distal cross section of the simulated realization b) Deposition-erosion geometries of a subregion of

the simulated realization circled out in Figure 3.2 a).

The same statistics in Table 2.2 is characterized from this Figure 3.2 (Table 3.2).

Lobe

with

Erosion

Channel

Table 3.2: Statistics of dimensionless ratios of maximum erosion depth and deposition thickness from Figure 3.2.

Figure 3.3 a) QQ-plot comparing Lobe Erosion/Deposition Ratio Distribution and Simulated Lobe Erosion/Deposition Ratio Distribution; b) QQ-plot comparing Channel Erosion/Deposition Ratio Distribution and Simulated Lobe Erosion/Deposition Ratio Distribution;

One obvious observation from Figure 3.3 is that the pdfs from the simulated realization

have close to the pdfs directly interpreted from the tank experiment data. Moreover, the

ratio of lobes with erosion over lobes with erosion is from the simulated realization is

32.1%, similar to 30% that is interpreted from the tank experiment data. However, no

attempt has been made to control the geobody placement, the clustering of geobody in the

simulated realization (Figure 3.2 a and b) is different from the tank experiment data (Figure

2.14 d).

5. Conclusion and Future Works

In summary of the documented study, with the surface-based modeling techniques, our

simulation produced similar dimensionless statistics in the cross section taken at the similar

location of that taken in the tank experiment. However, no real spatial patterns and

statistics are achievable using information from a 1D cross section data. The further study

will focus on the use of 2D overhead photos taken at the same intervals of the dynamic

cross section data. More specific geometry information and spatial statistics can be

interpreted from the overhead photos when the photos are matched with the topography

cross section, such as the spatial correlation of the negative surface and the positive surface.

More specific geometric information and rules of geobody placement are expected to be

extracted from the overhead photos as well.

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