A Conceptual Approach to Dynamic Sedimentary Basin Modelling

using the Point Moment Method: the London Clay Formation Case

Study.

Sarah Elizabeth Pearce

Remote Sensing MSc. Dissertation

Department of Geomatic Engineering, University College London

September 2008

Supervisory Committee:

Dr. Tao Cheng, UCL

Dr. Matthew Free, ARUP

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ABSTRACT

The subsurface modelling of urbanized dynamic sedimentary basins is

important to inform structural planning. A generalized approach called the Point

Moment Method is presented to more effectively characterize floodplain clay soils.

Progress on the problem of modelling 4D geoscientific datasets is achieved by the

integration of borehole data into a GIS. An iterative method that incorporates historic

geomorphologic data, microfossil data, hydrology and expert scientific input drawn

across disciplines is developed. The inclusion of temporal elements allows for the

modelling of dynamic erosional subsurface environments to be better understood.

X,Y,Z elevation data are modelled as vector points to which numerous attributes are

attached; natural neighbour interpolation is used to generate subsurface digital

elevation models. The Point Moment Method is applied to a case study of the London

Clay Formation (LCF) with initial results revealing regional geospatial variation in

the formation thickness and; at one study site, the spatial distribution of existing

hollows which are the remnants of open-system pingos.

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TABLE OF CONTENTS

Supervisory

Committee…………………………………………………………………………….1

Abstract……………………………………………………………..………………...2

Table of Contents…………………………………………………………………….3

List of Tables………………………………………………………………………….5

List of Figures…………………………………………………………...……………6

Acknowledgments…………………………………………………………………….7

Dedication…………………………………………………………….………………8

Chapter 1- Introduction……………………………………………………….……..9

1.1 Background and Motivation……………………………………………….9

1.2 Case Study Area………………………………………………………….10

1.3 Problem Definition……………………………………………………….11

1.4 Objective of the Research………………………………………………...11

1.4.1 General Aim of the Research………………………………...12

1.4.2 Specific Aim of the Research………..……………………….12

1.5 Methodology Research Questions………………………………………..12

1.6 Structure of the Thesis……………………………………………………12

Chapter 2- Literature Review………………………….…………………..………13

2.1 Three Dimensional Geological Modelling…………………………….…13

2.1.1 Interaction of GIS and 3D sub-surface Geoscientific Modelling13

2.1.2 GSIS Techniques and Models………………………………….15

2.1.3 “Layer-cake” models- modelling sedimentary systems………..16

2.1.3 Modelling faults………………………………………………..18

2.2 Interpolation For Geoscientific Datasets…………………………………19

2.2.1 Comparison of Interpolation Algorithms………………………20

2.2.2 2.5D versus 3D subsurface modelling………………………….23

2.2.3 Uncertainty in Error DEM surfaces…………………………….23

2.5 Conclusions from the Review……………………………………………24

Chapter 3- Methodology……………………………………………………………25

3.1 The Point Moment Method………………………………………………25

3.2 Case Study: The London Clay Formation………………………………..29

3.2.1 Palaeogeography of the London Clay………………………….29

3.2.2 Methods of Stratigraphic Analysis……………………………..32

3.2.3 Stratigraphy of the London Clay…………….…………………33

3.2.4 Regional Variation across the London Basin…………………..34

3.2.5 Engineering Geology of the London Clay………………….….36

3.3 Available Datasets………………………………………………………..36

3.3.1 Existing Geotechnical Data ……………………………………37

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3.3.2 Existing gINT Borehole Database……………………………..37

3.3.3 Existing Spreadsheets ………………………………………….37

3.3.4 Hard Copy Historic Geological Maps………………………….38

3.3.5 Existing Raster Data……………................................................38

3.3.6 Existing Vector Data...................................................................39

3.4 Data Compilation………………………………………………………...40

3.4.1 Description of the Geographical Information System………….40

3.4.2 Geotechnical Data from the gINT……………………………...40

3.4.3 Geotechnical Data from Excel Spreadsheets…………………...41

3.4.4 Importing the .csv files into the ArcGIS Environment………...41

3.5 Data Processing…………………………………………………………..41

3.5.1 Derived Surface Data Creation…………………………………41

3.5.2 DTM Creation for Larger Study Area………………………….42

3.5.3 Surface Hydrology Modelling………………………………….42

3.5.4 Digitizing Historic Tributaries from Historic Maps……………43

3.5.5 Interpolating the Top and Bottom Strata of the LCF…………..44

3.5.6 Determining Cell Size for the Interpolation Function………….44

3.5.7 Deriving Contours for the LCF Top and Bottom Strata……….45

3.5.8 LCF Total Thickness Calculations for Eight Study Sites……...46

3.6 Cartographic Outputs…………………………………………………….46

3.7 2.5 D Layer Cake Method Visualization…………………………………46

3.8 Creating the Geodatabase………………………………………………...47

Chapter 4- Results………………………………………………………......………47

4.1 DTM Creation for the Larger Study Area………………………………..47

4.2 Surface Hydrology Modelling…………………………………………....48

4.3 Historic Tributaries………………………………………………………49

4.4 Interpolating the Top and Bottom Strata of the LCF…………………….50

4.4.1 Determining Cell Size………………………………………….51

4.4.2 LCF Study Sites 1-8 Results…………………………………...52

4.5 Geodatabase Stratigraphy Structure……………………………………...60

Chapter 5- Discussion and Conclusions…………………………………………...60

5.1 Techniques for DEM Error Modelling…………………………………..60

5.1.1 The Root Mean Square Error Statistic………………………....60

5.1.2 Spatially Distributed Error Surfaces…………………………....61

5.2 Conclusions and Future Work……………………………………………62

Literature Reviewed………………………………..……………………………….62

Appendix A – Glossary of Terms…………………………………………………..66

Appendix B – Cartographic Outputs………………………………..…………….71

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List of Tables

Table 1: Stratigraphy Codes for London Clay Formation Layers……………………60

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List of Figures

Figure 1: Case study area: Central London, England………………………………..10

Figure 2: Distribution of the London Clay Formation, solid geology 1:250 000……11

Figure 3: the fundamental difficulty in building subsurface geological models……..15

Figure 4: Example of model construction of a sedimentary sequence accounting for

erosion and non-deposition…………………………………………………………..18

Figure 5: 2D natural neighbour interpolation for the point x……………………….. 22

Figure 6: Pliocene palaeogeography showing the North Sea basin…………………30

Figure 7: Early Eocene palaeogeography of the British Isles and surrounding areas..30

Figure 8: Early Eocene London Clay palaeogeography of the British Isles and

surrounding areas…………………………………………………………………….30

Figure 9: Spatial distribution of Paleocene and Eocene sediments in SE England and

surrounding areas…………………………………………………………………….31

Figure 10: Sequence Stratigraphy- the Effect of sea level fluctuations on the lithology

of the London Clay…………………………………………………………………..32

Figure 11: BGS lithostratigraphic units scheme and King’s 1981 sequence

stratigraphy divisions scheme………………………………………………………..34

Figure 12: Cross-section through the Paleocene and Eocene of the London Basin….35

Figure 13: Stratigraphic profile summary of the London Clay Formation based on key

area samples………………………………………………………………………….35

Figures 13.01-13.13: Surface Hydrological Modelling…………………………..48-49

Figure 14: Source data: geological survey of England and Wales, edition 1920……50

Figure 15: Digitizing historic map tributaries data…………………………………..50

Figures 16-18: Determining Cell Size………………………………………………..51

Figures 19-23: Study Site 1: Kings Cross……………………………………………52

Figures 24-28: Study Site 2: Cross Rail……………………………………………...53

Figures 29-33: Study Site 3: London Millennium Tower……………………………54

Figures 34-37: Study Site 4: Millennium Bridge…………………………………….55

Figures 38-41: Study Site 5: Tottenham Court Road………………………………...56

Figures 42-45: Study Site 6: Moorhouse……………..………………………………57

Figures 46-50: Study Site 7: Milton Court……………..…………………………….58

Figures 51-54: Study Site 8: Harris City Academy…………………………………..59

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Acknowledgments

Thank you to Dr. Tao Cheng of the University College London Geomatic Engineering

Department and Dr. Matthew Free of the ARUP Geotechnics division for their help in

supervising me; thank you to the London ARUP staff for their help and guidance in

my time as a summer student; and thank you to Val Hughes, Eric Druyts and Valerie

Blakely for their proof reading and encouragement along the way.

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Dedication

This thesis is dedicated to my father, Peter Thomas Edward Pearce, who will always

be a ‘top maps guy’ in my eyes.

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Chapter 1- Introduction

1.1 Background and Motivation

A clay database is useful to ARUP due to the ways in which the spatial

variations of subsurface conditions inform structural planning. The interaction of

subsurface clay, silt, sand and water can influence the demands of building piles and

foundations in cities located in floodplain areas. A vast amount of soil characteristic

data or SI information has been collected for the London Clay Formation (LCF) in the

form of borehole logs and continues to accumulate when new site investigations are

undertaken for engineering projects. This research is concerned with consolidating

borehole datasets and geotechnical reports with information on the material properties

for London Clay and translating the information into a GIS database allowing for

subsequent subsurface modelling. The modelling theory behind the methodology

developed is the key contribution to the existing literature. The motivation of this

database is to populate it with basic material and index properties which will facilitate

the modelling of the London Clay strata and the establishment of strong correlations

between the profile of the stratum and its geotechnical variation across the London

basin. Modelling the dynamic floodplain clay soils is important to inform structural

planning in any urbanized area within it. The case study model outputs focused on

the generation of a number of interpolated subsurface digital elevation model surfaces

from point elevation data representing the strata of the London Clay and the most

suitable algorithms to generate these.

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1.2 Case Study Area

The London Clay is located within the London and Hampshire basins, situated

in south-east England. The study area for this research focused on central London

(Figure 1), incorporating geotechnical data from engineering projects at eight study

sites. Seven sites in central London, north of the Thames River, were chosen and one

site, south of the Thames River, was investigated.

Fi

gure 1: Case study area: Central London, England.

Source: Google Earth Image, 2008.

The London Clay is a stiff, marine clay deposited across both the London

basin (Figure 2) and Hampshire basin during the Lower Eocene Epoch which

occurred between 56-49 mya (King, 1981). Variations in the London Clay strength,

stiffness and consolidation characteristics are linked to the variable depositional

history of the area (Pantelidou and Simpson, 2007). The depth of the London clay

strata varies with the sequence’s depositional history.

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Figure 2: Distribution of the London Clay Formation, solid geology 1:250 000 Source: British Geological Survey, 2008.

1.3 Problem Definition

The London Clay formation is often treated as having a uniform distribution

and depth but this is not valid as its stratigraphy, thickness and amount of erosion

varies greatly across the study area. These geoscientific variations, such as variation

in liquid limit, are of great interest to geotechnical engineers as they inform structural

planning. Presently much data exists in the form of borehole logs but has not been

integrated into a geographic information system that would enable the modelling and

geostatistical analysis of the datasets.

1.4 Objectives of the Research

1.4.1 General Aim of the Research

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The general objective of this research is to investigate the literature for the

most appropriate algorithm for borehole data stratigraphic surface interpolation and to

identify the best methods to create a geodatabase related to the stratigraphy and

geotechnical properties of the London basin, in particular the base of the London Clay

Formation (LCF), which will facilitate the useful modelling of its behaviours as they

relate to engineering projects.

1.4.2 Specific Aims of the Research

The specific objectives of this research are to firstly collect available data on

the geotechnical properties of the Formation, mainly from borehole logs from the

Arup gINT database and integrate these data into a geodatabase within a geographic

information system. A second objective is to investigate the most suitable algorithm

to be applied to interpolate digital elevation models delineating the stratigraphic

horizons within the London clay from geoscientific point data sets.

1.5 Methodology research questions

A) What is the most suitable 3D subsurface modelling technique for the London

Clay Formation within a Geographic Information System?

B) What is the most suitable algorithm within existing literature for the horizontal

interpolation of geoscientific datasets from vertical borehole data sets?

C) How can error be represented for the interpolated functional surfaces?

1.6 Structure of the Thesis

This thesis is structured into five chapters which include the introduction, a

through literature review, the methodology developed, the assessment of the case

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study model outputs and conclusions. The introduction familiarizes the reader with

the study area and research questions addressed in this research. The literature review

summarizes previous research on the topic of sub surface GIS models, interpolation

algorithms for geoscientific datasets and error surfaces while pointing out the gap

within the literature for the useful subsurface modelling of dynamic systems. The

methodology chapter details the method developed, the point moment method, for

modelling dynamic systems, the characterization of London Clay Formation, data

compilation and processing procedures applied in this research, the development of

the digital elevation model layers and ways in which to model error within these

outputs. Chapter four presents the outputs from the model. Chapter five presents

conclusions from this research, including the limitations of this research and

suggestions for future investigation.

Chapter 2- Literature Review

2.1 Three Dimensional Geological Modelling

2.1.1 Interaction of GIS and 3D sub-surface Geoscientific Modelling

Geographic information system (GIS) technology for subsurface geologic

modelling has a number of core applications which include: data organization, data

visualization, spatial data query, diverse data type integration, data analysis and

prediction studies. Data organization includes activities such as data modelling,

compilation and database construction that is relevant in geoscience projects using

diverse data sources such as geology, geochemistry, subsurface hydrology and

geotechnical data. Visualization includes the creation of digital and hard copy maps

which are useful for expert review. Spatial query capability is possible because the

GIS maintains the connection between the spatial features and their associated non-

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spatial attributes allowing for complex Boolean, arithmetic, or relational expressions

to be constructed and queried (Setijadji, 2003). A key characteristic of GIS operation

is spatial analysis, which is when the commonality between multiple layers is used to

reveal relationships between datasets that are otherwise undiscovered and unexplored.

These spatial associations between data layers are used in prediction modelling by

applying different statistical and mathematical models of variable accuracy and

validity (Setijadji, 2003). 3D modelling technologies, often termed geoscientific

information systems, or GSIS- have been evolving over the past two decades to

facilitate the characterization of the subsurface. These require the extension of

traditional GIS methods to incorporate volumetric representations referenced to three

orthogonal axes which must then be analysed by various mathematical data

manipulations. Each new data stream defining the subsurface conditions incorporated

into the GSIS adds to the complexity of its overall modelling capabilities (Turner,

2006). Therefore, it is desirable to incorporate as many data streams as are available

to increase the robustness of any subsurface model. Raper (1989,1991) introduced the

concept of “geo-objects” which are considered to be subsurface geological features,

units or sequences. There are two different types of geo-objects – “sampling-limited

geo-objects” such as sediment layers or fault planes where definition is limited by the

number of samples and “definition-limited geo-objects” such as conductivity or

pollution plumes which must be visualized by selecting an appropriate threshold level

parameter for inspection. Another key limiting factor to successful 3D subsurface

modelling is the lack of definitive data. Data derived from field observations such as

boreholes are often widely spaced, of variable temporal resolution and are costly to

acquire, posing further challenges to the robustness of the model. The model creator

must interpolate between these widely spaced data points (Figure 3), which requires

15

expert geological knowledge, suitable interpolation algorithms and iterative methods

of assessment and progressive refinements to the model (Turner, 2006). Therefore a

long term commitment to iterative model building, validation, and expert input drawn

across numerous geoscientific disciplines should be incorporated.

Figure 3: the fundamental difficulty in building subsurface geological models Source: Turner, 2006.

2.1.2 GSIS techniques and Models

The characterization of the LCF involves the determination of the spatial

variation of selected geological or geotechnical parameters within the subsurface.

Integrating a broad range of data types (such as borehole, seismic, hydrology and

human-made features data) in this characterization is routine in engineering, mining

and hydrogeology fields. Incorporating a time series component within the model is

also desirable when modelling dynamic, erosional environments. This can be

accomplished by incorporating values, features, attributes and rasters indexed by a

time stamp (Maidment et al., 2004). Defining surfaces as static or transient is one

example of how a time component can be incorporated, moving towards a 4D model.

Editing the nodes of a meandering watercourse over time to represent the erosional

history is another example of incorporating a time element into a model (Clevis et al.,

2006).

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Raw data collected are considered as two broad categories which are spatial

data and attribute data. Spatial data are used to create a 3D geometry model in which

two main steps are involved. The first step is the development of an adequate

geometric representation of the core geological framework. The second step is the

subdivision of this framework to act as a control to the analysis within the numerical

models applied in the subsequent predictive modelling (Turner, 2006). The initial

results from the numerical models may lead to the revision of the geometry model by

the modeller in an iterative process. The goal of geometry modelling is to establish

geometric controls and attribute spatial distribution for a chosen type of numerical

modelling. The objective of numerical modelling is prediction, leading to decision

making, which is extrapolative as it involves risk and uncertainty (Turner, 2006). The

overall confidence in the model increases as more data streams and expert knowledge

are incorporated into it. Model validation for the subsurface can be accomplished by

comparison with another similar model, such as one created by the British Geological

Survey for the LCF (which has a coarser resolution) or by subsequent ground truthing

of model outputs.

2.1.3 “Layer-cake” models- Modelling Sedimentary Systems

Sedimentary environments such as the LCF are characterized by stacks of

sedimentary strata. Thus modellers often define the most important stratigraphic

layers and their interfaces by creating continuous surfaces defining the strata, stacking

them in stratigraphic sequence and then defining geological units as the zones

between the surfaces. Interpolation of borehole data has been proven to be complex

and involves extensive validation procedures to ensure the resulting model is reliable.

In evaluating previous 3D geological models created from extensive borehole and

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well datasets, it became evident that the stratigraphy was complex with few

continuous strata layers and with erosional channels significantly impacting the

layered sequence (Turner, 2006). A further consideration is that deeper horizons are

generally more problematic to model because there are less data available. Numerous

subsurface models exist, however most do not incorporate historic data, microfossil

data or extensively evaluate the contribution of surface and subsurface hydrology on

the temporal behaviour of the sediments. Characterizing and incorporating both the

surface and subterranean hydrology is paramount to successful model creation in soft

sediment erosional environments such as the LCF.

Construction of individual surfaces is usually achieved using borehole point

data by either: a) creating a triangulated irregular network (TIN), b) applying any of

several surface contouring and generation procedures or c) developing interpretive

cross-sections between boreholes for higher accuracy surface geometry. All of these

surface generation methods result in several problems persisting.

As surfaces are created independently, some surfaces may intersect each other

in geologically invalid situations which usually require subsequent editing (Turner,

2006). Surfaces must be checked to allow for erosional areas and non-deposition

areas, by assigning “zero-thickness” units but most software systems require surfaces

to be continuous or do not possess adequate capability for “zero-thickness” area

display (Figure 4), posing further challenges to modelling complex strata of many

interlacing units by the creation of the large data volumes associated with the

generation of numerous discrete surfaces. To avoid this problem, thicker zones are

modelled into elemental volumes which are then subdivided, and then facies

definitions are made by interpolation of borehole obversations (Turner, 2006).

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Incorporating indicator microfossil data as x,y,z data points in a GSIS would facilitate

the overall interpretation of complex interlacing strata.

Figure 4: Example of model construction of a sedimentary sequence accounting for

erosion and non-deposition. Source: Turner, 2006.

2.1.3 Modelling Faults

The process of fault modelling is important in geological model creation

because strata on either side of a fault may possess different or similar characteristics

and thicknesses depending on the fault type and its temporal relationship to the

depositional sequences. Faults and fractures may also have a strong influence on the

structural properties of the sediments and the porosity or ability of fluids to move

through the subsurface. Modelling vertical or near-vertical faults is relatively

straightforward in existing GSIS software systems. In this case, fault planes are added

to a model by adding additional surfaces to the existing stratigraphic layers. Inclined

fault modelling involves insuring that the geometric intersections are correctly defined

without gaps, overlaps and that sediment thickness on either side of the fault reflects

its origins (Turner, 2006). Known faults can be digitized from existing geological

maps and oriented with expert input for incorporation into a model.

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2.2 Interpolation for Geoscientific Datasets

Methods of interpolation have been used as a tool for modelling elevation in

GIS for many years. Interpolation is often used as a tool to convert data from one

format to another, for example from scattered point data to continuous raster surfaces.

The results of interpolation, often a surface representing real world terrain, aim to be

as accurate possible as these interpolated surfaces are often used as the basis of

subsequent spatial analysis. Interpolation is based on the principle of spatial

autocorrelation, whereby sample points that are closer together are more similar than

points that are further apart.

Considering a set of samples to which a known attribute (e.g. elevation, liquid

limit, conductivity) k is attached, spatial interpolation is used to estimate the value of

the attribute at an unsampled and unknown location u. Different functions try to

mathematically fit the known values to the unknown values as well as possible.

Therefore the interpolant i, is the function best suited to both the data set and the

parameter being interpolated. While interpolation is used in creating 3D surfaces, it is

intrinsically a 2D (x,y) operation, with elevation considered as an attribute. Typical

geoscience datasets are 3D (x,y,z) to which numerous attributes (e.g. sediment grain

size, pH, phosphate level, percentage of platinum in a rock) are attached; when a

given attribute is interpolated, it is defined as a continuous function called a field (e.g.

liquid limit = f(x,y,z )) (Goodchild, 1992).

Borehole datasets are vertically abundant yet sparse horizontally, therefore

possessing a highly anisotropic (exhibiting properties that differ according to the

direction of measurement) distribution. In modelling borehole datasets, 3D

interpolation methods must consider the specific qualities of the data. When extending

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to 3D, it is appropriate to use an interpolation method that is the most suitable,

preserving the data properties. Essential properties of the ideal interpolation algorithm

for geoscientific datasets are (from Ledoux and Gold, 2005):

a) exact: the interpolation function must pass through the data points.

b) continuous: at each location a single and unique value must be returned; a Co

interpolant.

c) smooth: an interpolation function for which both the 1st and 2

nd derivatives are

possible to differentiate at every location; C1 and C

2 interpolants.

d) efficient: a function that computes in the least demanding way possible,

expedient.

e) adaptable: the interpolation function should return realistic results for

anisotropic distributions and datasets of variable data sampling density spatial

distribution.

f) local: an interpolation function that only uses a few surrounding samples to

estimate the value at an unknown location, thereby ensuring that samples with

gross errors will not propagate these through the entire interpolation function.

g) scalable: the interpolation function should be appropriate for application in

two and higher dimensions.

2.2.1Comparison of Interpolation Algorithms for Geoscientific Datasets

Various interpolation techniques have been applied to geoscience datasets.

These include kriging, splines and weighted average methods such as IDW and

natural neighbour interpolation methods. To satisfy as many requirements as possible

of the ‘ideal’ interpolation algorithm for borehole data, as outlined above,

interpolation methods are discussed in terms of their applicability.

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Kriging produces an interpolation function that minimises error variance at

each location and outputs an error surface. Kriging function estimates are created by

characterizing the dependence between any two sample attributes at a given distance

from each other (Ledoux and Gold, 2005). Applied to regional geotechnical models,

ordinary kriging techniques produce geological model results which are strongly

smoothed, leading to inaccurate regional geological characterization (Marinoni,

2003). Kriging is not an exact interpolant nor can it be realistically used in a dynamic

environment, where defining the function parameters would have to be repeated each

time the dataset was modified. However, using Kriging in conjunction with another

interpolation methods can provide two surfaces for comparison.

Weighted average interpolation techniques such as distance based methods

(i.e. IDW) can be used to model geoscientific datasets when the dataset is uniformly

distributed but return unacceptable results when the data has an anisotropic or variable

density in spatial distribution, such as is typical of borehole datasets.

Spline interpolation is an exact interpolant useful for surfaces with gradual

change where one desires to output results that are above or below the minima or

maxima of sample values. There are two types of splines, regular and tension splines.

Tension splines constrain the estimates closer to the input data. However, in instances

of sudden terrain change such as faults or erosional channels, spline interpolants are

not suitable.

The interpolation of choice for modelling borehole data in three or more

dimensions is natural neighbour interpolation (Boissonnat and Cazals 2000; Ledoux

and Gold, 2005; Ledoux and Gold, 2004; Tsai et al., 2005) Natural neighbour (NN)

interpolation finds the closest subset of observations to a query point and assigns

22

weights to them based on proportionate areas to interpolate a value (Sibson, 1981).

The NN interpolation function is

Where:

f(x) is the interpolated function value at the location x.

In the literature NN interpolation is also referred to as “area-stealing” or

Sibson interpolation. Numerous researchers (Gold, 1989; Sambridge et al.,1995;

Watson, 1992) have shown that NN interpolation avoids most of the issues other

methods have anisotropic datasets (Ledoux and Gold, 2005).

Figure 5: 2D natural neighbour interpolation for the point x. The shaded area

represents Vx. Source: Ledoux and Gold, 2005.

The NN coordinate of x with respect to a point pi in 2D is

The NN coordinate of x with respect to a point pi in 3D is

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Source: Ledoux and Gold, 2004.

2.2.2 2.5D versus 3D subsurface modelling

The difference between 2.5D and true 3D should be made clear. Three

dimensional (3D) is a commonly misused term to describe software applications that

display and store data in two and a half dimensions (2.5D). ESRI’s ArcGIS 3D

Analyst application is one example of this, which can display and store raster, terrain

data and TINs as functional surfaces which are in fact 2.5D. Functional surfaces have

only one z value, or elevation value per x,y coordinate or pixel.

True 3D data is represented by either voxels - which are 3D volumetric pixels,

or tetrahedral objects - which are essentially 3D TINs, both of which can store

multiple z, or elevation values for each x,y coordinate or pixel and are commonly

referred to as solid surface models. ArcGIS software does not currently have voxel

capability but can represent true 3D data as tetrahedral objects using an application

called multipatch features.

However, individual geologic strata are usually modelled as 2.5 D functional

surfaces, which are continuous, as is the case in ‘layer-cake’ sedimentary basin

models. This method poses a problem to the stratigraphic modelling of the LCF which

has numerous discrete surfaces or strata that interfinger or interlace due to areas of

sediment deposition, non-deposition, fissuring, possible faulting and erosion and are

further complicated by the temporally dynamic subsurface environment common to

floodplain clay soils.

2.2.3 Uncertainty in DEM surfaces

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Digital elevation models (DEMs) are representations of topographical surfaces

or real world terrain. They can be derived from point elevation data, map contours,

radar data or lidar data. All DEMs contain varying amounts of random and systematic

errors. Errors can be defined as the divergence of an elevation measurement from its

true value. Uncertainty can be defined as the insufficiency of knowledge regarding the

reliability of an elevation measurement.

Error within digital elevation models is grouped into two broad categories.

The first type of errors are called random errors which arise from mistakes in primary

data capture or data input. The second type of errors are called systematic errors

which arise from the DEM creation process, for example from the interpolation of

spot heights to a continuous surface (Holm,K., 2000). There are various methods to

reduce and estimate uncertainty in digital elevation models. These range from a single

value to represent error in input points to spatially distributed error surfaces which

consider the statistical and spatial distribution (spatial autocorrelation) of the error.

Error modelling facilitates informed judgements and must be calculated for the useful

application of derived surface models.

2.3 Conclusions from the Review

The natural neighbour interpolation method is the algorithm of choice for

modelling borehole data in three or more dimensions. Previous subsurface

sedimentary basin models have shown that models derived from borehole data should

incorporate hydrogeologic information to characterize the influence of erosional

channels for more reliable model outputs. Incorporating time elements into a

subsurface model is preferable when modelling dynamic environments because

sediment behaviour is likely to be temporally dynamic. Error modelling is a critical

25

component for reporting uncertainty in derived digital elevation surfaces and there are

various statistical methods for calculating uncertainty which range widely in their

complexity. Iterative model editing as more data streams are incorporated will

increase the overall confidence in model estimates which can be validated by ground

truthing in the case when no higher resolution data is available.

Chapter 3 Methodology

3.1 The Point Moment Method

When evaluating a dynamic urbanized sedimentary basin from a modeller’s

perspective, such as the LCF, a number of challenges present. There exist numerous

models to characterize the 3D subsurface, each with its own advantages and

disadvantages. Within this research, a new model framework is developed to move

towards the dynamic modelling of urbanized floodplain clay soil systems within a

GIS. The aim of this research is to model at the watershed level an urbanized

floodplain system in order to better understand the natural processes which impact

engineering projects within it.

1) Determine the extent of the study area by delineating the surrounding watershed.

2) Characterize the palaeogeography of the study area. In order to gain a better

understanding of the subsurface strata which is to be modelled, investigate the historic

geological and geomorphologic processes which lead to the probable current

subsurface conditions. Identify key geological processes such as the depositional

history, past glacial events and the effects of sea level fluctuations on the present

lithology.

26

3) Investigate the historic hydrology and any hydraulic alterations to the study area. If

possible, map the historic drainage patterns from remotely sensed imagery. The goal

of historic hydrological investigation is to establish a baseline fixed in time from

which to compare current hydrological analysis in order to understand the dynamic

nature of a floodplain environment. Obtain any data sources that may be useful in the

characterization of the subsurface hydrology. These can include well data, storm

sewer data, weather data and any data related to hydrological or sediment transport

and fate experiments.

4) Summarize any past stratigraphical research of the study area. In order to most

effectively characterize the stratigraphy of the area, incorporate the lithostratigraphy,

chronostratigraphy, magnetostratigraphy and, perhaps most importantly, the

biostratigraphy of the study area. Identify and spatially reference key indicator

microfossils or marker fossils within the strata. Delineate the horizon boundaries of

the formation under investigation and assign unique horizon codes to each of these

strata.

5) Choose an appropriate geological model schema, such as the one available from

ESRI or a more sophisticated database architecture for geological modelling and

apply the schema to a scaleable geodatabase within the GIS. Begin populating the

geodatabase with pre-existing datasets; being meticulous about including a time

reference and geospatial metadata standards. Include georeferenced photo links to

core samples.

27

6) Obtain data from which to derive a digital terrain model, preferably Lidar. In the

case when Lidar data is not available, Radar data can be used and calibrated. In the

case where neither Radar nor Lidar data is available, a coarse resolution DTM derived

from map contours can be used.

7) Watershed modelling: once you have a bare ground DTM, conduct a hydrological

analysis, using either the D8 method or a more sophisticated approach to watershed

modelling. Derive flow accumulation and stream grid analysis and vectorize these as

polylines.

8) Create a surface TIN incorporating derived hydrological breaklines as soft and hard

surface breaklines respectively. Eventually this surface TIN can be extruded

downwards incorporating the subsurface data points into a 3D finite element mesh

which can cope with modelling areas of sediment deposition, non-deposition, faults

and water bodies for visualization purposes.

9) Consolidate borehole data: create point vectors for each regional study site which

have an X,Y,Z format and add all available geotechnical, geochemical, stratigraphical

data as attribute fields connected to the point in three dimensional space. Incorporate a

time stamp for each field, representing the sampling or observation date and time. Be

certain to include microfossil data as an attribute of each georeferenced point.

10) A very important component to this model is the incorporation of expert

knowledge and interpretation of subsurface conditions. Incorporating expert

knowledge into the modelling procedure has often been over looked or not possible.

28

Once you have this large volume of data accumulated, organized, and integrated into

the GIS geodatabase begin generating model outputs and place these within the

geodatabase

11) Investigate the most suitable algorithms for the attribute under investigation based

on the data distribution and parameter being interpolated. In the case of subsurface

digital elevation modelling, use an area stealing approach known as natural

neighbours interpolation. The NN function is deterministic but a modeller may also

want to compare geostatistical functions such as Kriging which generate a statistical

error surface. Investigate the most suitable methods for error modelling of the derived

surface model outputs, in order to avoid lending too much confidence to the outputs.

12) Interpolate points into continuous raster fields, being certain to understand the

limitations of interpolating from small sample sets. Cell size should be determined

based on the parameter being interpolated and the output resolution of the functional

surfaces.

13) Update and validate the model in an iterative process as more data streams are

incorporated over time. Use ground truthing or site investigation to validate the model

outputs. Use the model for storage, query and prediction study outputs. Finally, use

the time referenced data to animate the model and conduct predictive modelling for

pulse events such as extreme weather or floods of a particular magnitude.

29

The following case study for the London Clay Formation attempts to apply only a

small portion of this method; named the Point Moment Method (PMM).

3.2 Case Study: the London Clay Formation

3.2.1 Palaeogeography of the London Clay

The London Clay Formation (LCF) is the drowned margins of the North Sea

(Figure 6) basin which was entirely deposited in marine conditions, either on a

restricted lagoon or an open shelf (Ellison, 2004). The strata were deposited between

52 and 55 mya which was the first stage of the early Eocene Epoch (Freitas and

Mannion, 2007). At the time of deposition the Hampshire and London basins were

connected to form a single depositional region (Figure 7) which was subsequently

divided into two discrete synclinal structures (Figure 9) due to tectonic events during

the mid-Cenozoic Alpine orogeny (Freitas and Mannion, 2007). The LCF is a stiff,

overconsolidated clay consisting of an assemblage of layered sediments composed of

varying amounts of clay, silt and sand. The depositional history (Figures 7 and 8)

accounts for the significant variation in sediment consolidation, stiffness and strength

across London (Pantelidou and Simpson, 2007).

London is situated in the floodplain of the Thames Valley located within the

London Basin. The Thames River, a significant feature of present day London, is a

tidal, meandering river which crosses the city from the south-west to the east.

Historically the Thames was approximately five times wider, and a much shallower

river with extensive tributaries and estuarine salt marsh riparian zones. During the last

two centuries, sections of the Thames and many of its tributaries have been

30

extensively embanked, in-filled, and diverted to flow underground. Presently London

is protected by a network of flood barriers but remains vulnerable to flooding events.

Figure 6: Pliocene palaeogeography showing the North Sea basin.

Source: http://www.searchanddiscovery.com/documents/97020/plate_21.jpg

Figure 7: Early Eocene palaeogeography of the British Isles and surrounding areas.

31

Figure 8: Early Eocene London Clay palaeogeography of the British Isles and

surrounding areas.

Source:http://www.geolsoc.org.uk/webdav/site/GSL/shared/pdfs/specialist%20and%20regional%20gro

ups/Dr_C_King.pdf

Figure 9: Spatial distribution of Paleocene and Eocene sediments in SE England and

surrounding areas.

Source:http://www.geolsoc.org.uk/webdav/site/GSL/shared/pdfs/specialist%20and%20regional%20gro

ups/Dr_C_King.pdf

32

Figure 10: Sequence Stratigraphy- the Effect of sea level fluctuations on the lithology

of the London Clay

Source:http://www.geolsoc.org.uk/webdav/site/GSL/shared/pdfs/specialist%20and%20regional%20gro

ups/Dr_C_King.pdf

3.2.2 Methods of Stratigraphic Analysis

There are various techniques used for the study of strata such as those of the

LCF. These include lithostratigraphy (the study of particle characteristics),

chronostratigraphy (the study of strata age), magnetostratigraphy (the magnetism

within the strata) and biostratigraphy (the study of strata fossil contents). When

analysing a sedimentary succession, such as the London Clay, it is recommended to

integrate many stratigraphic disciplines to improve the overall interpretation (Freitas

and Mannion, 2007). Biostratigraphy uses selected fossil species to correlate strata of

similar age, by way of distinctive marker fossils allowing for sedimentary strata to be

subdivided regardless of subsequent bedding plane shear, stretching or warping. In the

case of the London Clay, microfossils including forminifera, diatoms, radiolaria,

ostracods, palynomorphs and calcareous nannofossils are the most suitable marker

fossils (Freitas and Mannion, 2007). The study of the microfauna of the London Clay

33

Formation has identified repeated episodes of sea level rise and fall to be identified

throughout its deposition (Freitas and Mannion, 2007).

3.2.3 Stratigraphy of the London Clay

While the stratigraphy of the London Clay has been researched for

over 150 years, these investigations have been complicated by the lack of natural

exposures, the limited number of boreholes and the similarity of the silty clays that

compose the majority of the formation (Freitas and Mannion, 2007). In King’s 1981

paper ‘The Stratigraphy of the London Clay and Associated Deposits’ the author uses

biostratigraphy, lithological variation and historic flooding events to define five

divisions (A-E) within the London Clay with each division coinciding with a full

sedimentary cycle (Ellison, 2004). The British Geological Survey has defined five

lithostratigraphic units (A-D and the Claygate Member) based solely on lithology for

mapping purposes (Figure 8). Where Unit A is: a relatively sandy unit at the base of

the LCF which is 7-14 m thick. Unit B is: dominated by silty clay with several sandy

horizons and is 7-18 m thick. Unit C is: the middle part of the LCF dominated by clay

which is 40-52 m thick. Unit D is: interbedded bioturbated and glauconitic sandy

clayey silt to sandy silt in beds up to 5 m of thickness and wholly is 30-45 m thick.

Finally, the Claygate member is: alternating beds of clayey silt, very silty clay, sand

silt and glauconitic silty fine sand in beds 1-5 m thick and is defined as including all

the deposits above the base of the underlying relatively homogenous clays of Unit D

(Ellison, 2004). It is King’s 1981 scheme that most research refers to, which has been

developed into higher resolution sub-divisions. In April of 2007, King was a keynote

speaker at the ‘Engineering Geology of the London Clay’ meeting where he presented

that the London Clay can be divided using sequence stratigraphy into more than ten

depositional sequences each bounded by a transgressive phase surface.

34

Figure 11: BGS lithostratigraphic units scheme and King’s 1981 sequence

stratigraphy divisions scheme.

Source: Freitas and Mannion, 2007

3.2.4 Regional variation across the London Basin

The present and original thickness, prior to any erosion, of the London Clay

Formation varies throughout the London and Hampshire Basins (Pantelidou and

Simpson, 2007). Using sequence stratigraphy, the LCF can divided into over ten

depositional sequences which can be correlated throughout both the London and

Hampshire Basins (King, 2007). Lithological units can be resolved within each

sequence and these are generally consistent over distances ranging from 20-50 km,

however they may not be sustained over larger areas (King, 2007). At two locations

within the London Basin, Hampstead Heath and Crystal Palace, the maximum and

near maximum original thickness of the LCF sequence is present. However, in most

parts of the London Basin, including central London, significant erosion has changed

the thickness of the overburden of both the LFC and the overlying Bagshot Sand

35

resulting in the absence of sub-divisions C, D and E (Pantelidou and Simpson, 2007).

King (1981) estimates the thickness of the LCF in central London to be 130 m.

Figure 12: Cross-section through the Paleocene and Eocene of the London Basin

Source:http://www.geolsoc.org.uk/webdav/site/GSL/shared/pdfs/specialist%20and%20regional%20gro

ups/Dr_C_King.pdf

Figure 13: Stratigraphic profile summary of the London Clay Formation based on key

area samples

Source:http://www.geolsoc.org.uk/webdav/site/GSL/shared/pdfs/specialist%20and%20regional%20gro

ups/Dr_C_King.pdf

36

3.2.5 Engineering Geology of the London Clay

Large scale or complex construction projects, and environmental and natural

hazard assessments require a precise definition of the subsurface conditions.

Therefore the geotechnical properties of the LCF which underlies most of the district

are closely associated with building design and construction in London. The common

reference point for the LCF is its base, unit A which is 7 to 14 m thick. A

characteristic of the lowest beds of unit A is the abundant presence of clusters of

horizontal, flattened white silt tubes which are 1 mm in width and up to 30 mm in

length and are the fragments of compacted tabular foraminiferids (Ellison, 2004).

Interpretation of the LCF stratigraphy can significantly refine the geotechnical

interpretation of borehole data as vertical changes in lithology are correlated with

changes in geotechnical characteristics such as liquid limit and conductivity

measurements.

3.3 Available Datasets

For the purpose of the case study presented in this research, a subset of all the

available data was used to demonstrate some aspects of the methodological

framework theory developed. The case study focused its attention broadly on the

surface hydrological modelling from a DTM, the incorporation of historic data

sources, subsurface interpolation of eight study sites within the larger study area and

the generation of the layer codes for the LCF stratigraphy. The results from the data

subset begin to reveal some of the merits of this method. Another issue which is

relevant to this research but is outside the scope of this thesis is the positional

accuracy of the vertical positions of the point data.

37

3.3.1 Existing Geotechnical Data

Borehole logs and interpretative reports from ARUP geotechnics division

were consolidated for the study area. These were in both soft and hard copy

formats. The positional accuracy of the borehole logs is recorded as +/- 5

meters.

3.3.2 Existing gINT Borehole Database

gINT version 8.0 is a geotechnical software package which stores borehole

data in a relational database format based on the Microsoft Access database

architecture. A portion of the study area borehole data had been previously

inputted into this database, providing strata elevation data in mOD. Contour

data for top and bottom elevations for the LCF was exported as .csv files for

import into the GIS.

3.3.3 Existing Spreadsheets

Previous studies within the ARUP geotechnics division had resulted in data

pertaining to the LCF existing as excel spreadsheets. These excel spreadsheets

provided georeferenced point data for a number of site specific study areas

pertaining to LCF top and bottom strata elevation values based on a portion of

the previous research of Dr. Helini Pantelidou in 2002. The majority of

borehole locations are geogreferenced as eastings and northing on OS the

38

national grid, with data for some sites being stated in meters above tunnel

datum (mTD).

3.3.4 Hard Copy Historic Geological Maps

Historic geological maps from the Ordnance Survey were utilized. The

historic map sheets were published from 1935-1936 and covered central

London.

London Sheet NV. S.E. Geological Survey of England and Wales. Edition of

1919. scale 1:10,560.

London Sheet NV. S.W. Geological Survey of England and Wales. Edition of

1920., scale 1:10,560.

London Sheet NV. N.W. Geological Survey of England and Wales. Edition of

1920. scale 1:10,560.

London Sheet NV. N.E. Geological Survey of England and Wales. Edition of

1920. scale 1:10,560.

3.1.5 Existing Raster Data

Two Landsat7 etm+ image tiles of the London area were used as base

imagery. The first was downloaded as a greyscale geotiff from Geogratis upon

which a coordinate transformation was preformed from WGS84 to OSGB36.

The second was provided by ARUP geotechnical division staff as an RGB

raster tile. Both satellite images had been previously orthorectified,

georeferenced and atmospherically corrected. NASA’s Landsat 7 etm+ earth

39

resource satellite has a spatial resolution of 30 x 30 meter pixels. Both images

were acquired in 2000 by the passive optical sensor aboard the satellite.

Street view OS raster map tile for central London was used as a .tiff file. This

map series is created by the OS and is available in user defined 5 x 5 km tiles.

The specific tile covers the central London area using OSGB36, with a

resolution of 254 dpi with 1 x1 m spatial resolution. It was generated from a

vector dataset created at the 1:10 000 scale in November of 2002.

3.3.6 Existing Vector Data

An Ordnance Survey Landform profile ASCII x,y,x point file was provided by

the ARUP geotechnics division, licensed for 2008. The OS Landform Profile

DTM ASCII XYZ data was created on a 10m grid which is derived from

contours at 5m intervals. The contour data is created by using photogrammetry

techniques and its accuracy is +/- 1 to 1.8m. The grid is subsequently derived

from these contours with an accuracy of +/- 2.5m.

The raw datasets used were examined for positional accuracy, attribute accuracy,

logical consistency, completeness and lineage. All spatial data are of limited

accuracy and inconsistencies that were found are discussed in the data compilation

and processing procedures that follow. Of particular interest is the assessment of

the positional accuracy of the borehole locations and methods to track the way

errors are propagated through the GIS operations as to avoid ascribing greater

accuracy than both the existing and derived datasets deserve. This is relevant to

40

the larger context of this research but is considered to be future work worth

through investigation.

3.4 Data Compilation

3.4.1 Description of the Geographic Information System (GIS)

ESRI’s ArcGIS version 9.2 software was used as the GIS in this research for

collecting, storing, displaying, manipulating and analysing both the existing and

derived data. ArcMap, ArcCatelog and ArcScene were each employed using an

ArcEditor Licence. Toolbar extensions that were used included the 3D analyst and

Spatial analyst toolbars. All derived data was spatially referenced to the OSGB

National Grid Reference System. The elevation values were created with reference to

the OS datum Newlyn vertical coordinate system. The limitations to this vertical

reference coordinate system are worthy of future research but are outside the scope of

this research.

3.4.2 Geotechnical data from the gINT

To eventually introduce both the top and bottom elevations of the LCF strata as point

shapefiles into the GIS, contour data was exported from the gINT software by the

construction of a data query to export all the top and then the bottom elevation values

for the London Clay (LC) from within the geol_geol database table. These were

exported as .csv files which were organized for subsequent import into the GIS. The

final table structure included fields for a unique identifier, the job number, which is

unique for each geotechnical project that is undertaken. The final table structure had

41

the following fields: JOB_NUMBER, JOB_NAME, BOREHOLE, EASTING,

NORTHING, ELEV_MOD and STRATA.

3.4.2 Geotechnical Data from Excel Spreadsheets

Top and bottom elevations for the LCF for various study sites had been previously

organized into excel spreadsheets, these tables included the borehole number

reference, easting, northing, and elevation values in OS grid meters above datum

(mOD) or meters above tunnel datum (mTD). These tables were organized in the

identical format to the exported gINT data (as.csv files): JOB_NUMBER,

JOB_NAME, BOREHOLE, EASTING, NORTHING, ELEV_MOD and STRATA.

3.2.4 Importing the .csv files into the ArcGIS Environment

In order to create the vector point shapefiles, the .csv files were added to ArcMap, by

displaying xy data, using the OSGB36 as the spatial reference system and then saving

these as layer files which were subsequently exported as point shapefiles. There were

two shapefiles created for each study area or data location, one for the top LCF strata

and one for the bottom of the LCF strata. A total of approximately 26 shapefiles were

created; broadly a set of two for each regional site and a set of two merged files

containing all of the borehole dataset for the LCF watershed study area.

3.5 Data Processing

3.5.1 Derived Surface Data Creation

42

The literature had highlighted the need to incorporate hydrological

information into any subsurface model or interpretation from borehole data. While

Lidar (Light Detection and Ranging) data would have provided a higher resolution

DTM for surface hydrological modelling, no Lidar data covering the study areas was

readily available and therefore the coarser resolution OS Landform Profile DTM

ASCII XYZ data was used for this purpose.

3.5.2 DTM Creation for Larger Study Area

The OS Landform Profile DTM ASCII XYZ data was imported in the GIS and

displayed as xy data points. A TIN was created using the z field for the elevation

values. This TIN was then converted to a digital terrain model (DTM) raster using the

ArcToolbox. The DTM raster was then coloured to represent the topographic

variation of the study area.

3.5.3 Surface Hydrology Modelling

Using the Spatial Analyst hydrological analysis tools, the D8 method was used

for surface hydrological analysis, in particular to derive polyline vector files for flow

accumulation paths and stream paths within the study area. Firstly the sinks were

filled by establishing the z_limit for the deepest sink within the DTM which was

found to be a value of 3.31665. Secondly a flow direction raster was derived using the

Flow Direction tool. Thirdly flow accumulation was derived using the Flow

Accumulation tool with all the DTM cells being weighted equally; this function

43

calculates the accumulated weights of the surrounding eight raster cells to derive the

cells flowing to each downslope cell in the output raster file. Finally the Con tool was

used to derive both the flow accumulation and stream grid vector polyline shapefiles.

The flow accumulation vector was derived using a threshold of 350. The

stream grid vector was derived using a threshold of 3200, after numerous iterations to

determine an appropriate threshold value. These derived vectors were used as an aid

for overlay, visualization and interpretation of derived subsurface layers. They could

also be used in the future as soft breakline constraints for subsurface strata, however it

is important to remember that they represent derived surface features and can not be

realistically extrapolated to the subsurface environment with a reasonable level of

confidence. Identifying subterranean stream networks and flow accumulation is

relevant to this research but is considered future work.

3.5.4 Digitising Historic Tributaries from Historic Maps.

Due to the extensive hydraulic alteration within the study area, it was

appropriate to incorporate information from historic map sheets to add to the overall

interpretation of the subsurface environment. Using the historic map sheets and the

Street view OS raster map tile for central London, the extent of the Fleet River and

other significant tributaries were digitized on screen using the Editor Toolbar. It

should be noted that the derived polyline vector shapefile is of limited accuracy due to

the digitizing method and it would have been preferable to use a high resolution

scanner for the historic maps, to georeference them and then to integrate all the

historic tributaries into a single shapefile using a digitizing tablet and puck. However,

44

the derived historic tributaries vector was again used in overlay as an aid to the

overall interpretation of the subsurface contour maps.

3.5.5 Interpolating the Top and Bottom Strata of the LCF

The Natural Neighbours interpolation method was used to interpolate

continuous float raster surfaces from derived vector point shapefiles for both the top

and bottom strata of the LCF for eight smaller study sites within the study area. The

eight study sites were chosen on the basis of the number of borehole observations that

were available. Seven of the sites are in central London north of the river Thames and

the eight is approximately 10 km south of the River Thames. The number of null

value cells is variable, dependent on the number of borehole observations available

for the site under investigation. This was accomplished by the creation of TIN and

then using the ArcToolbox to interpolate these TINs to rasters using the Natural

Neighbour interpolation function and using the float parameter for output surfaces. It

is important for the cartographic interpreter to recognize the difference between

looking at the shape of the interpolant function, as is the case when there are few

observations to constrain the surface generation procedure, and a surface constructed

from a large enough sample size of borehole observations to resolve localized

subsurface features such as pingos, scour holes or erosional channels.

3.5.6 Determining Cell Size for the Interpolation Function

When choosing an appropriate cell size the density of data points was considered. In

the case of modelling the LCF subsurface, it is appropriate to use a uniform cell size

45

for output rasters so that each derived surface can be integrated into a larger overall

model. In a surface DTM, point distribution of input data should be adequate for the

output raster resolution, for example in a grid with one meter pixel resolution we

would ideally have at least one data observation per cell. However, unlike surface

point data such as Lidar or Radar, in the case of borehole data there is a limited

number of point observations. The effect of using different cell sizes was investigated

and finally cell size was chosen to be 1 x 1 m pixel resolution to represent a mean

approximation of various core sample diameters. This parameter choice was a

compromise: the smaller the cell size, the larger the data volumes and the larger the

number of cells with null values; however the higher the spatial resolution of the

output raster surfaces and the smaller the area we are suggesting we can know about

with a reasonable amount of accuracy. The assumption made was that with 1 m pixel

resolution we can know with reasonable accuracy from a given bore core about an

area that is 1 x 1x1 m3 in volume. In the future, the workflow of the data processing

can be documented and automated with the Model Builder tools within the GIS.

3.5.7 Deriving Contours for the LCF Top and Bottom Strata

The terrain analysis tools within the ArcToolbox were used to derive contour

vector polyline shapefiles for each of the derived raster surfaces. These were created

using contour intervals of 5 meters, 1 meter and 0.25 meters depending on the range

of elevation data within the derived subsurface rasters. The resulting contours were

then classified into five equal interval categories for subsequent isoline labelling and

cartographic display. The contour lines were used in overlay on the interpolated

surfaces to aid in the interpretation of the subsurface topography. A total of 16

46

contour files were created, one for each of the top and bottom strata of the LCF for

each of the eight study sites.

3.5.8 LCF Total Thickness Calculations for Eight Study Sites

The spatial analyst toolbar was used to calculate the total thickness of the LCF

from the interpolated surfaces. The raster calculator was used to subtract the top LCF

surfaces from the base LCF surfaces to output total thickness raster grids for the eight

study sites. The raster calculator expression subtracted the top of LCF elevation value

grid from the base of LCF value grid to output a floating point raster value summary

of the total thickness of the LCF at the study sites. The limitations of these outputs are

addressed in the discussion section below.

3. 6 Cartographic Outputs

Subsurface contour maps for study sites were created for top and base of the

LCF strata using ArcMap showing elevation in mOD. The derived total thickness of

LCF raster calculation grids were also made into cartographic outputs showing the

spatial variations in the total thickness of the London Clay Formation sequences. All

derived maps included a spatial reference, north arrow, scale bar in meters, absolute

scale text and most included legends.

3.7 2.5 Dimension Layer Cake Method Visualization

47

In order to visualize the variation in the LCF thickness across the study area,

eight ArcScene documents were created, one for each study site. The interpolated

surfaces for the top and base strata of the LCF were added with no vertical

exaggeration. This visualization allows us to clearly see the variation of the London

Clay Formation thickness across the study area. It should be noted that while the

surfaces derived from numerous borehole observations are resolving more subsurface

topographic features, it does not mean that the surfaces derived from less borehole

observations do not also contain the same subsurface terrain features.

3.8 Creating the Geodatabase

To create an organized storage container for all of the derived file for this case

study, a file geodatabse was created within ArcCatelog. This geodatabase included

feature classes for surface and subsurface features and model outputs. The horizon ID

structure for the LCF was established based on the stratigraphic layers of King (1981).

Chapter 4- Results

4.1 DTM creation for larger study area

48

4.2 Surface Hydrology Modelling

Initial Flow direction Depressionless DEM

Derived Flow Grid Flow accumulation (a)

Flow accumulation (b) Flow direction (a)

49

Filled flow direction (a) Filled flow direction (b)

Sink depth Sink maximum values

Sink minimum values Watershed flow

Figures 13.01-13.13: Surface Hydrological Modelling

4.3.5 Historic Tributaries

50

Figure 14: Source data: geological survey of England and Wales, edition 1920.

Modifications and additional notes by F.B.A. Welch, 1933.

Published 1935 by the Director General at the Ordnance Survey Office, Southampton.

Figure 15: Digitizing historic map tributaries data.

4.4 Interpolating the Top and Bottom Strata of the LCF

51

4.4.1 Figures 16-18: Determining Cell Size

Cell size =3 Cell size = 5.9 (default)

Cell size= 1

4.4.2 LCF Study Site Results

52

Figures 19-23: Study Site 1: Kings Cross

Figure 19: Top of LCF generated from 416 borehole observations.

Figure 20: Base of LCF generated from 95 borehole observations.

21

(22) (23)

Figures 24-28: Study Site 2: Cross Rail

53

Figure 24: Top of LCF generated from 31 borehole observations.

Figure 25: Base of LCF generated from 31 borehole observations.

26

(27)

(28)

Figures 29-33: Study Site 3: London Millennium Tower

54

Figure 29: Top of LCF generated from 11 borehole observations.

Figure 30: Base of LCF generated from 11 borehole observations.

31

32 33

Figures 34-37: Study Site 4: Millennium Bridge

55

Figure 34: Top of LCF generated from 6 borehole observations.

Figure 35: Base of LCF generated from 6 borehole observations.

36

37

56

Figures 38-41: Study Site 5: Tottenham Court Road

Figure 38: Top of LCF generated from 13 borehole observations.

Figure 39: Base of LCF generated from 8 borehole observations.

40

41

Figures 42-45: Study Area 6: Moorhouse

57

Figure 42: Top of LCF generated from 6 borehole observations.

Figure 43: Base of LCF generated from 5 borehole observations.

44

45

Figures 46-50: Study Site 7: Milton Court

58

Figure 46: Top of the LCF generated from 6 borehole observations.

Figure 47: Base of the LCF generated from 4 borehole observations.

48

49 50

Figures 51-54: Study Site 8: Harris City Academy

59

Figure 51: Top of the LCF generated from 29 borehole observations.

Figure 52: Base of the LCF generated from 3 borehole observations.

53

54

60

4.2 Geodatabase Stratigraphy Structure

LCF layer code Stratigraphy from King, 1981

BS 0 top of LC; base of Bagshot sands

LC 11 E2; base

LC 10 E1; base

LC 9 D2; base

LC 8 D1; base

LC 7 C3; base

LC 6 C2; base

LC 5 C1;base

LC 4 B2; base

LC 3 B1;base

LC 2 A3.2; base

LC 1 A3.1; base

LC 0 A2;base

Table 1: Stratigraphy codes for London Clay Formation layers

Chapter 5- Discussion and Conclusions

As revealed by the Kings Cross top of London Clay dataset consisting of 416

boreholes, we can begin to resolve deep hollows within the LCF by using the NN

interpolation of densely distributed borehole datasets. At a couple of the sites under

investigation, we see a general trend emerging, which is that the base of the LCF has a

relatively smooth surface topography, while the top of the LCF has a topographic

pattern of localized, round, vertical depressions which extend downwards from the

top of the formation to the base of the London Clay; areas of zero thickness.

5.1 Techniques for DEM Error Modelling

5.1.1 The Root Mean Square Error Statistic

61

The standard way to describe error in DEMs is as a single value, the root mean

square error (RMSE) statistic, which assumes errors are random and have a Gaussian

distribution. This value is derived from the equation:

Where:

yi is an elevation value from the derived digital elevation model

yj is the measured elevation of a test point and

N is the number of sample points.

RMSE error modelling outputs a single value for a surface and this value

estimates how well the DEM may correspond to the data from which it was derived. It

is important to note that this statistic does not represent the difference between DEM

elevation estimates and true elevation values.

5.1.2 Spatially Distributed Error Surfaces

Within the literature there is general agreement on the limitations of using a

single RMSE statistic to represent DEM uncertainty. Various studies have established

that the rate of uncertainty in a DEM is dependent on the spatial autocorrelation of the

error (Fisher, P. 1998). RMSE surfaces or error surface techniques are based on the

hypothesis that the scale and spatial distribution of the errors are related to terrain

characteristics. For example, one could expect lower error in areas of low topographic

variation and higher error in areas of complex topography when interpolating from

point data. However, these techniques often involve the comparison of derived DEM

surfaces to higher accuracy measurement datasets. Another method of error

modelling worth mention is the use of error covariance matrices to assess uncertainty

62

in estimated value outputs, these methods are based on the research of Carrera and

Neuman,1986 and Tsai et al.,2005.

5.2 Conclusions and Future Work

The thickness of the London Clay Formation has been proven to be variable

within the study sites. Further, the identification of pingos and their spatial

distribution becomes possible to resolve at higher borehole data densities. Eventually

when the database’s population has reached a robust level, it will become a very

valuable tool for characterization of the regional variation of the LCF. The case study

presented here is only a small portion of the overall point moment model. Using

microscopy to identify indicator microfossils will significantly improve the models

stratigraphical interpretations. Only by applying the methodology with a firm

commitment to model editing and review as new data streams become available and

incorporated with a temporal index system will its full potential be realised. As more

analysis are conducted using the model, the overall picture of the subsurface

environment will begin to resolve at an increasing accuracy. The concept of

constraining subsurface digital elevation models could be explored in future research.

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interpolation of distance functions, Computational Geometry, France.

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Castrignano A, Buttafuoco G, Comolli R, and Ballabio C.,2004. Accuracy assessment of

digital elevation model using stochastic simulation. 7th International Symposium on Spatial

Accuracy Assessment in Natural Resources and Environmental Sciences.

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Appendix A: Glossary

4D model: a model which incorporates a time element.

Algorithm: a mathematical sequence of instructions often used in data processing.

Bare ground digital terrain model (DTM): a digital representation of the earth’s

surface with all the structures removed; often used in hydrological modelling studies.

Bedding plane shear: a soil characteristic value which is incorporated into

geotechnical engineering analytical and numerical analysis.

Biostratigraphy: a subfield of geology within stratigraphy that is concerned with the

correlation of rock strata ages by assessing the fossil species within them.

Bioturbated: soils impacted by the lifecycles of animals which live within them.

Boolean: a branch of algebra concerned with operations of conjunction, disjunction,

compliment or negation.

Borehole: a general term to describe a narrow vertical shaft drilled into the ground as

part of a geotechnical or environmental site assessment.

Cenozoic: the current era which covers approximately the last 65 million years.

Consolidation characteristics: the geomorpholgical process whereby soil decreases

in volume due to stress; when soil particles become more tightly packed together.

Datasets: a collection of data usually in a tabular format, with each column

representing a specific variable.

Diatoms: most commonly unicellular eukaryotic algae characterized by a silica cell

wall.

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Digital elevation model (DEM): a digital representation of either raster or vector data

types, representing earth’s terrain. It is an umbrella term that encompasses surface

topography both with and without buildings.

DPI: dots per inch.

Eocene Epoch: approximately the geological time span from 56 to 34 mya; the

second epoch of the Palaeogene period during the Cenozoic era.

Erosion: most commonly the displacement of soil, rock or sediments by the forces of

water, wind, gravity or ice.

Facies: a body of rock or soil with distinctive, specified characteristics formed under

sedimentary processes.

Function: a mathematical concept expressing the dependance between quantities.

Geodatabase: usually a relational database designed to store and manipulate

geospatial data and information.

Geostatistical analysis: the application of numerical analysis to spatial datasets.

Geotechnical: concerned with the engineering properties and behaviours of earth

materials.

GIS: geographic information system; a system for managing and manipulating data

which are spatially referenced.

Ground truthing: a geomatics technique for validating data by sampling or obtaining

reference data in the field.

GSIS: a geoscientific information system.

Hydrology: the study of the distribution and movement of water on Earth.

Interpolation: a type of numerical analysis which involves generating new data

points within a range of a discrete set of known data points.

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Iterative methods: the repetition of a process.

Layer-cake models: also known as horizon models; a 2.5 D modelling approach to

the digital characterization of sedimentary systems.

Liquid limit: a measure of the quantity of water in a soil before it changes its

behaviour from plastic to liquid.

Lithology: a subfield of geology concerned with the geological description of

macroscopic rock samples.

Lithostratigraphy: a subfield of geology within stratigraphy that is concerned with

the study of rock strata.

Modelling: the process of deriving estimations by the creation of spatial arrays.

MS access database: Microsoft Office Access is another type of relational database

used to store and query data.

MYA: the abbreviation for ‘millions of years ago’.

Microfossils: fossils which are below a size that can be analysed with the naked eye.

Microfauna: microscopic animals.

Open shelf: the outer extremity of a continental coastal plain extending into the

surrounding sea during interglacial periods.

Orogeny: a mountain building event, usually due to two tectonic plates colliding and

causing uplift.

Overburden: the stress placed upon a soil or rock layer by the weight of the material

overlying it.

Overconsolidated: the state of mud or clayrocks that have been subjected to

pressures far greater than they experience presently.

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Palaeogeography: the study of past physical geographies.

Pliocene: the geological epoch that occurred in the time span between approximately

5.5 to 1.8 million years before present.

Point elevation data: the x,y, z coordinates of a geographical location, with reference

to a height above or below a fixed reference point, such as mean sea level or geoid;

geometric height.

Porosity: a measure of the void space within a soil or rock; expressed as a fraction or

a percentage.

Raster: a grid data structure consisting of rows and columns of pixels.

Seismic data: a technique used in the determination of sedimentary rock strata.

SI information: a standardized way of reporting soil characteristics.

Spatial autocorrelation: a geographical concept which states that objects or

phenomena which are closer together are more similar than objects or phenomena that

are further apart.

Stratigraphy: the branch of geology concerned with rock or sediment layers and

layering which includes the subfields of lithostratigraphy and biostratigraphy.

Synclinal structures: within structural geology, a term to describe a downward

curving fold with layers that dip towards the structure’s center.

Tectonic: the forces and movements that operate on the earth’s continental and ocean

plates.

Tetrahedral objects: in modelling a polyhedron made up of four triangular faces.

Time stamp: data referenced with the sampling date and time as an attribute.

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TIN: a triangular irregular network; here to represent terrain by a mesh composed of

triangles.

Voxels: three dimensional volumetric pixels.

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Appendix B- Study Sites

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75

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

91

92

93

Appendix B Continued- Surface Outputs

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95

96

97

98

99

100

101

102

Appendix B Continued 2- Total Thickness for all Study Sites

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104

105

106

107

108

109

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