Model-based, Acoustic
Subbottom Classification
Theory and Application
Mischa Tolsma
Model-based,
Acoustic
Subbot
tom
Classification
Mischa
Tolsma
Model-based,
Acoustic
Subbot
tom
Classification
Mischa
Tolsma
Model-based, Acoustic Subbottom Classification
Precise estimation of the subbottom geometry and composition is a
consider-able problem in the cost effective maintenance of rivers, lakes and harbors.
Currently, bottom samples are the only reliable method to obtain the
sub-bottom composition. Model-based, acoustic subsub-bottom classification has
been investigated in theory and application as an economic alternative.
A novel classification algorithm has been developed that is based on a model
library. Using this algorithm, it proved possible to distinguish between
silt/sand layers and gas bubble layers.
Theory
Application
A model has been developed that provides the flexibility to model a variety of
different bottom types and measurement set-ups. The model can be used for
both an accurate investigation of the identifiability and for fast model-based
measurement.
Uitnodiging
voor het bijwonen van de verdediging van mijn
proefschrift, getiteld:
Model-based, Acoustic
Subbottom Classification
De plechtigheid vindt plaats op dinsdag 25 januari 2005
om 15:30 uur in de Senaatszaal van de Aula van de Technische Universiteit Delft,
Mekelweg 5.
Voorafgaand aan de promotie zal ik om 15:00 uur
een korte uiteenzetting geven van mijn onderzoek.
Aansluitend op de promotie is er een receptie in de Aula.
Mischa Tolsma
+27-82-7765022
mischa.tolsma@sasol.com
Modelgebaseerde, Akoestische WaterbodemKlassificatie
Theorie en Toepassing
Model-based, Acoustic Subbottom Classification
Theory and Application
PROEFSCHRIFT
ter verkrijging van de graad van doctor aan de Technische Universiteit Delft,
op gezag van de Rector Magnificus prof. dr. ir. J.T. Fokkema, voorzitter van het College voor Promoties,
in het openbaar te verdedigen op 25 januarie 2004 om 15.30 uur
door
Mischa TOLSMA
natuurkundig ingenieur geboren te Winterswijk.
Dit proefschrift is goedgekeurd door de promotoren: Prof. dr. ir. A. van den Bos
Prof. dr. ir. G. Blacquière Samenstelling promotiecommissie:
Rector Magnificus voorzitter
Prof. dr. ir. A. van den Bos Technische Universiteit Delft, promotor
Prof. dr. ir. G. Blacquière Technische Universiteit Delft, promotor
Prof. dr. ir. A. Gisolf Technische Universiteit Delft
Prof. dr. ir. C.P.A. Wapenaar Technische Universiteit Delft
Prof. dr. ir. A.F.W. van der Steen Erasmus Universiteit Rotterdam
Prof. dr. ir. F.C.A. Groen Universiteit van Amsterdam
Dr. ir. N.A. Kinneging Rijkswaterstaat
Dr. ir. N.A. Kinneging heeft als begeleider in belangrijke mate aan de totstand-koming van het proefschrift bijgedragen.
ISBN 90-6464-955-3
Copyright c 2004 by M. Tolsma
All rights reserved. No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner.
Voorwoord xi
Short Summary xiii
Summary xv
Samenvatting xvii
1 Introduction 1
2 Measurement of the Subbottom 7
2.1 Introduction . . . 7 2.2 The "What-question" . . . 9 2.2.1 Geometry . . . 10 2.2.2 Composition . . . 11 2.3 The "How-question" . . . 12 2.3.1 Bottom samples . . . 12 2.3.2 Acoustic techniques . . . 13 2.3.3 Geo-statistical interpolation . . . 14 2.3.4 Conclusion . . . 20
2.4 Precision and accuracy . . . 20
2.5 Strategy . . . 26
2.6 Conclusions . . . 28
I Acoustic Classification: Theory
29
3 Introduction 31 4 Model for Acoustic Reflections 33 4.1 Introduction . . . 334.2 Overview . . . 34
4.3 Requirements . . . 36
4.4 Framework . . . 39
4.4.1 Choice of Model . . . 41
4.4.2 The Wave Equation, Frequency and Wavenumber Integration 49 4.4.3 Invariant Embedding . . . 53
4.4.4 Requirements on Geo-acoustic Models . . . 59 v
vi CONTENTS 4.4.5 Conclusion . . . 60 4.5 Measurement equipment . . . 60 4.5.1 Signal . . . 61 4.5.2 Source . . . 64 4.5.3 Receiver . . . 66 4.5.4 Normalization . . . 67 4.6 Geo-acoustic Models . . . 67
4.6.1 Layers with homogeneous density, sound speed and attenu-ation . . . 68
4.6.2 Layers with a gradual density profile . . . 70
4.6.3 Gas bubbles . . . 75
4.6.4 Grain size . . . 83
4.7 Observation Noise . . . 86
4.7.1 Stochastic model for the observations . . . 86
4.7.2 Probability density function . . . 90
4.7.3 Signal to Noise Ratio . . . 91
4.8 Conclusion . . . 92
5 Experimental Design 95 5.1 Introduction . . . 95
5.2 The Cramér Rao Lower Bound . . . 96
5.2.1 Derivation of the Fisher information matrix for observations with additive, Gaussian noise . . . 99
5.3 Tests for Acoustic Identifiability . . . 100
5.3.1 Preliminaries . . . 102
5.3.2 Basic geo-acoustic properties . . . 108
5.3.3 Gradual density profile . . . 118
5.3.4 Gas bubbles . . . 124
5.3.5 Grain size . . . 129
5.4 Optimal Design . . . 131
5.4.1 Signal settings . . . 132
5.4.2 Number and spacing of receivers . . . 136
5.5 Conclusion . . . 140
6 Model-based, Acoustic Classification 143 6.1 Introduction . . . 143
6.2 Classification approaches . . . 146
6.2.1 The model-based approach . . . 148
6.2.2 The processing approach . . . 148
6.2.3 Example: Five different approaches to attenuation estima-tion . . . 150
6.3 Existing Techniques . . . 152
CONTENTS vii
6.3.2 Processing approach, classification based on geo-acoustic
prop-erties . . . 157
6.3.3 Model-based approach . . . 159
6.3.4 Conclusion . . . 160
6.4 Arrival Time Estimation . . . 161
6.4.1 The criterium value of the maximum likelihood estimator . 162 6.4.2 The Hilbert transform . . . 164
6.4.3 Discretization . . . 166
6.4.4 Conclusion . . . 173
6.5 Reflection Detection . . . 173
6.5.1 Generalized likelihood ratio test . . . 174
6.5.2 Probability density function for the likelihood ratio . . . 177
6.5.3 Conclusion . . . 181
6.6 Layer Classification . . . 182
6.6.1 Maximum likelihood estimation . . . 182
6.6.2 Starting values and parameter transformations . . . 185
6.6.3 Layer detection . . . 190
6.6.4 Model selection . . . 192
6.6.5 Use of 1-D and 2-D modelling for 3-D observations . . . 193
6.6.6 Conclusion . . . 198
6.7 Conclusion . . . 199
7 Conclusion 201
II Acoustic Classification: Application
205
8 Introduction 207 9 Techniques and Instrumentation 209 9.1 Introduction . . . 2099.2 Available Techniques and Instruments . . . 210
9.2.1 Bottom samples and cores . . . 213
9.2.2 In-situ probes . . . 215
9.2.3 Contact based, continuous techniques . . . 218
9.2.4 Remote sensing . . . 223
9.2.5 Conclusion . . . 225
9.3 X-STAR: subbottom classification system . . . 226
9.3.1 Specifications . . . 226
9.3.2 Transmitted signal . . . 229
9.3.3 Gain settings . . . 233
9.3.4 Theoretical behavior of the SB-0512 Tow-Fish . . . 234
9.3.5 Pitch and roll dependent behavior of alternative configura-tions . . . 247
viii CONTENTS
9.3.6 Experimental Set-up of the Haringvliet Measurements . . . 254
9.3.7 Experimental Set-up of the Calibration Measurements . . . 255
9.3.8 Calibration Results . . . 257
9.3.9 Conclusion . . . 260
9.4 50 kHz TNO TPD transducer . . . 260
9.5 Conclusions . . . 263
10 Measurements at the Haringvliet 265 10.1 Introduction . . . 265
10.2 Involved Projects . . . 266
10.3 Survey area . . . 269
10.3.1 Morphology . . . 270
10.3.2 Grain diameter and Silt fraction . . . 272
10.4 Selections of the available observations . . . 273
10.4.1 Selection A: Rak van Scheelhoek, South . . . 277
10.4.2 Selection B: Between Rak van Scheelhoek and Hindergat . . 279
10.4.3 Selection C: Rak van Scheelhoek, North . . . 280
10.4.4 Selection D: Middengeul . . . 281
10.4.5 Selection E: Beyond Hindergat . . . 282
10.4.6 Conclusion . . . 283
10.5 Conclusion . . . 284
11 Classification Algorithm Design 287 11.1 Introduction . . . 287
11.2 Requirements . . . 287
11.3 Description . . . 289
11.3.1 Overview . . . 290
11.3.2 Signals and Models . . . 293
11.3.3 Noise . . . 297
11.3.4 Classification . . . 298
11.3.5 Detection . . . 308
11.3.6 Optimization . . . 310
11.4 Compliance with requirements . . . 311
11.5 Application . . . 313
11.5.1 Survey preparation . . . 313
11.5.2 Survey execution . . . 315
11.5.3 Classification with human supervision . . . 316
11.6 Conclusions . . . 317 12 Classification Results 319 12.1 Introduction . . . 319 12.2 Preliminary investigation . . . 321 12.2.1 Time domain . . . 321 12.2.2 Frequency domain . . . 327
CONTENTS ix
12.2.3 Average time domain . . . 329
12.2.4 Conclusions . . . 331
12.3 Model Library . . . 332
12.4 Investigation with the Model Library . . . 336
12.4.1 Layer detection . . . 337 12.4.2 Layer classification . . . 342 12.4.3 Conclusions . . . 351 12.5 Conclusions . . . 353 13 Conclusions 357 Bibliography 361
List of Symbols and Abbreviations 373
De onderwaterbodem vormt een uitdagend raakvlak tussen de oceaan-akoestiek en de seismiek. De uitdaging wordt gevormd door de veelheid aan processen die zich voordoen in dit gebied: sedimentologisch, fysisch, chemisch en organisch. De combinatie van deze uitdaging met de uitdaging van model-gebaseerd meten heeft geleid tot een zeer gevarieerd promotieonderzoek.
Allereerst wil ik graag mijn dank richten aan mijn begeleiders: prof. van
den Bos, Gerrit Blacquière en Niels Kinneging. Jullie adviezen en gevarieerde achtergronden hebben in belangrijke mate bijgedragen aan de totstandkoming van dit proefschrift. Prof. van den Hof wil ik bedanken voor de mogelijkheid mijn promotie onderzoek te kunnen uitvoeren in de groep Modelgebaseerd Meten en Regelen. Daarnaast wil ik prof. Gisolf bedanken voor het onderdak gedurende de laatste maanden van het onderzoek. Remco Romijn, Peter Frantsen en Chris Mesdag wil ik bedanken voor hun hulp bij het uitvoeren en interpreteren van de praktijkmetingen. TNO TPD en de Adviesdienst Geo-informatie en ICT van Rijkswaterstaat wil ik bedanken voor de financiële ondersteuning van mijn pro-motieonderzoek.
Op het persoonlijke vlak wil ik mijn collega’s van Modelgebaseerd Meten en Regelen bedanken voor de zeer aangename tijd, zowel tijdens als na werkuren. Mijn ouders wil ik bedanken voor hun ondersteuning door de jaren heen. En natuurlijk Elsa, bedankt voor jouw geduld en aangename afleiding tijdens de afronding van het proefschrift.
Mischa Tolsma, Kudu Wildsplaats, April 2004
Model-based, Acoustic Subbottom Classification, Theory and Applica-tion - Precise estimaApplica-tion of the subbottom geometry and composiApplica-tion is a con-siderable problem in the cost effective maintenance of rivers, lakes and harbors. Currently, bottom samples are the only reliable method to obtain the subbottom composition. Model-based, acoustic subbottom classification has been investigated in theory and application as an economic alternative. A model has been devel-oped that provides the flexibility to model a variety of different bottom types and measurement set-ups. The model can be used for both an accurate investigation of the identifiability and for fast model-based measurement. A novel classification algorithm has been developed that is based on a model library. Using this algo-rithm, it proved possible to distinguish between silt/sand layers and gas bubble
layers. Mischa Tolsma
Model-based, Acoustic Subbottom Classification Theory and Application
Precise estimation of the subbottom geometry and composition is a consider-able problem in the cost effective maintenance of rivers, lakes and harbors. Cur-rently, the only reliable method to obtain the subbottom composition is the collec-tion of bottom samples, an expensive method due to the large number of bottom samples required. A more economic approach would be the use of acoustic tech-niques. However, up to now, acoustic techniques have only been reliably used for estimation of the subbottom geometry and not for classification of the subbottom composition. Model-based, acoustic subbottom classification has, therefore, been investigated in theory and application to determine the possibilities of acoustic classification and to provide a practical classification technique.
Theory A recurrent problem during the development of new measurement
tech-niques is the question: can the desired parameters be determined with the proposed measurement technique, i.e., is the problem identifiable? This question can be an-swered when a stochastic model for the observations is available. A modelling approach has been developed that provides the flexibility to model a variety of dif-ferent bottom types and measurement set-ups. This approach makes an explicit distinction between a framework model and geo-acoustic (sub)models, i.e., the framework integrates the propagation and reflection coefficients provided by the individual geo-acoustic models. These geo-acoustic models describe different bot-tom types, e.g. silt/sand or gas bubbles, and each have their own parametrization, e.g. grain diameter or gas fraction.
The framework model can be used for both an accurate investigation of the
identifiability and for fast model-based measurement. The importance of this
model is that it allows the development of a quantitative approach to subbottom classification, in contrast with the existing qualitative techniques. With respect to identifiability, one of the findings has been that gas bubble layers can be identified. Also, it was found that, in general, it pays to have a larger bandwidth at the expense of transmitted power.
A new arrival time estimator has been developed that has been shown to be more robust, accurate and precise than existing methods based on discretized cross-correlation. A reflection detection method has been developed to test if a reflection found by the arrival time estimator is significant.
Application A novel classification algorithm has been developed that is based
on a model library. This library contains a collection of pre-calculated reflections xv
xvi
of the subbottom. The entries of the model library are compared with the obser-vations and the best fit is used to determine the subbottom parameters. This best fit can either be used as the classification result, or, used as a starting value for non-linear, model-based parameter estimation, i.e., model inversion.
The model library leads to an algorithm that is robust and usable for real-life observations. The model library is both flexible and expandable, i.e., it can hold the responses obtained from a variety of different models and can be easily improved when new models become available.
The new algorithm has been applied to practical, acoustic observations taken during a survey of the Haringvliet estuary. Using the model library, it proved possible to distinguish between silt/sand layers and gas bubble layers. Also, grain size estimates have been obtained that correlate well with bottom samples.
Modelgebaseerde, Akoestische WaterbodemKlassificatie Theorie en Toepassing
Efficient onderhoud aan rivieren, meren en havens vereist kennis van de bo-dem geometrie en samenstelling. Het verzamelen van bobo-demmonsters is, op dit moment, de enige betrouwbare methode om kennis over de bodemsamenstelling te krijgen, een dure methode vanwege het grote aantal bodemmonsters dat is vereist. Een meer economische aanpak zou het gebruik van akoestische methodes zijn. Echter, akoestische technieken zijn, tot nu toe, alleen nog maar betrouwbaar ge-bruikt voor het bepalen van de bodemgeometrie en nog niet voor de bodemsamen-stelling. Modelgebaseerde, akoestiche bodemclassificatie is daarom onderzocht in theorie en toepassing om de mogelijkheden van akoestische classificatie te bepalen en een praktische classificatie methode te verschaffen.
Theorie Een herhalend probleem gedurende de ontwikkeling van nieuwe
meet-technieken is de vraag: kunnen de gewenste grootheden bepaald worden met de voorgestelde meettechniek, ofwel, is het probleem identificeerbaar? Deze vraag kan worden beantwoord wanneer een stochastisch model voor de waarnemingen beschikbaar is. Een modellerings aanpak is ontwikkeld die de flexibiliteit biedt voor een varieteit aan bodemtypes en meet-opzetten. Deze aanpak maakt een expliciet onderscheid tussen een raamwerk model en geo-akoestische modellen. Het raamwerk integreert de propagatie en reflectie coefficienten gegeven door de individuele geo-akoestische modellen. Deze geo-akoestische modellen beschrijven verschillende bodemtypes, bijvoorbeeld slib/zand en gasbellen, en hebben elk hun eigen parametrisatie, bijvoorbeeld korrelgrootte en gasfractie.
Het model kan worden gebruikt voor nauwkeurig identificeerbaarheidsonder-zoek en voor snelle classificatie. Het belang van dit model is dat het de ontwikkel-ing toestaat van quantitatieve bodemclassificatie, in contrast met bestaande qual-itatieve methodes. Eén van de vindingen, met betrekking tot identificeerbaarheid, is dat gasbellagen identificeerbaar zijn. Een andere vinding is dat, in het algemeen, het gunstig is de frequentie bandbreedte te vergroten ten koste van signaalvermo-gen.
Een nieuwe aankomsttijd-schatter is ontwikkeld die robuuster, nauwkeuriger en precieser is dan bestaande methodes die gebaseerd zijn op gediscretiseerde kruis-correlatie. Een reflectie-detectie-methode is ontwikkeld die test of een reflectie significant is die gevonden is met de nieuwe aankomsttijd-schatter.
Toepassing Een nieuw classificatie algoritme is ontwikkeld dat gebaseerd is
op een modelbibliotheek. Deze bibliotheek bevat een collectie van
voorgecal-culeerde reflecties van de waterbodem. De reflecties in de modelbibliotheek worden xvii
xviii
vergeleken met de observaties en de best passende wordt gebruikt om de bodempa-rameters te bepalen. De gevonden bodempabodempa-rameters kan worden gebruikt als het classificatie-resultaat, of, als een startwaarde voor niet-lineare, modelgebaseerde parameterschatting.
Deze aanpak resulteert in een robuust algoritme dat bruikbaar is voor prak-tijk waarnemingen. De model bibliotheek is flexibel en uitbreidbaard. Hetgeen betekent dat het reflecties van een varieteit aan modellen kan bevatten en gemakke-lijk kan worden uitgebreid zodra nieuwe modellen beschikbaar worden.
Het nieuwe algoritme is toegepast op praktische, akoestische waarnemingen genomen tijdens een survey van de Haringvliet monding. Het bleek mogelijk een onderscheid te maken tussen slib/zand lagen en gasbel lagen met behulp van de model bibliotheek. Ook zijn korrelgrootte schattingen verkregen die goed correl-eren met bodem monsters.
The Netherlands have, as the delta of the Rhine, the Meuse and the Scheldt, a strong relationship with water. A result of this relationship is that there are many civil engineering projects being performed on the Dutch rivers, canals and lakes at any one moment. Examples of current projects are ’Ruimte voor de Rivieren’, ’de Maaswerken’, and ’Project Kier’.
Ruimte voor de Rivieren The Dutch rivers need to cope with increasing vol-umes of water. This is caused in part by increased urbanization which leads to a greater effluence rate from land to river. Another cause is the current trend of more extreme weather [115]. As a result, improvements are required of the current flood protection measures and strategies. These improvements not only involve increased dike height and river depth but also the reservation of areas for temporary water storage [22][23][78].
Maaswerken The Maaswerken is a combination of three projects that are being performed on the Meuse: Zandmaas, Grensmaas and Maasroute [29]. The scope of these projects are flood protection, mineral production, environ-mental improvements and improvement of the water ways for commercial shipping [20].
Project Kier The Delta-werken are a combination of dams, dikes and sluices that protect the Netherlands from the North Sea. The primary concern of the Delta-werken has been safety. Environmental aspects gradually increased in importance during the course of the Delta-werken with the Oosterschelde
dam as crown result. This dam is normally open and only closes when
dangerous storms are predicted. Thereby, it allows normal water movement in the Oosterschelde. Another part of the Delta-werken are the Haringvliet sluices. In contrast with the Oosterschelde dam, the Haringvliet sluices are only used to sluice river water to the North Sea. Reverse movement of salt water from the North Sea to the Haringvliet is not allowed under the current sluice regime. As a result, the Haringvliet has become a fresh water lake. Project Kier investigates if it is possible to change the sluice regime and allow salt North Sea water back into the Haringvliet [21].
2 CHAPTER 1. INTRODUCTION The management of these projects requires an integral approach that combines knowledge of:
• water movement, e.g., flow speeds and tidal motion;
• a 3-D model of the subbottom, e.g., the location and amount of pollution; • processes, e.g., siltation, sediment transport and movement of pollution. One of the white spots that has been identified by the Dutch water management board is the 3-D model of the subbottom, i.e., presently, adequate knowledge is lacking of the subbottom geometry and composition [9].
Precise estimation of the subbottom geometry and composition is a consider-able problem in the cost effective maintenance of rivers, lakes and harbors. The principal problem is the high cost of precise methods versus the low precision of economic methods. Currently, the only reliable method to obtain the subbottom composition is the collection of bottom samples or cores. These are, however, very expensive due to the labor intensive measurement set-up, and the high number of samples or cores needed to obtain sufficient coverage of the area under investiga-tion. Also, it is difficult to determine the absolute position of samples and cores, which leads to inaccurate and imprecise estimates of the subbottom geometry.
A more economic approach would be the use of acoustic techniques. These can be deployed while the survey vessel is in motion and allow quick coverage of a survey area. However, at present, acoustic techniques have only been reliably used for the estimation of the subbottom geometry and not for the classification of the subbottom composition. Several methods have been developed for acoustic classification of the subbottom [67][75][158][47][150] but the problem is that the precision and accuracy of these methods is largely unknown. In fact, little is known about the identifiability of the subbottom given an acoustic signal.
Eventually, the goal is to arrive at a measurement strategy that delivers an ac-curate 3-D model of the subbottom with a specified precision for the least amount of costs. This measurement strategy will, most likely, use a combination of mea-surement techniques. In the next chapter, an initial assessment is given of the problems regarding the 3-D model and the combination of measurement equip-ment. From this assessment it has followed that reliable acoustic classification is highly beneficial for cost effective measurement of the subbottom.
So, acoustic classification of the subbottom would be highly beneficial but, at the same time, relatively little is known about its possibilities. A practical inves-tigation can deliver some information on the possibilities of acoustic classification but is marred by the complexity of the subbottom. As a result, it can be difficult to determine the cause of success or failure of a certain classification technique. A theoretical investigation is required to determine the possibilities of acoustic clas-sification. Importantly, a theoretical study can determine the attainable precision of acoustic classification. This investigation is described in the first part of this dissertation.
3
Information need Problem statement
Data collection Feedback
Data processing Information strategy
Figure 1.1: The information cycle [34].
The disadvantage of a purely theoretical investigation is that it cannot guar-antee a practical classification technique as end result. The application of acoustic classification is, for this reason, investigated in the second part of this dissertation.
Information cycle The research described in this dissertation forms part of
the innovation drive of the information cycle of AGI-RWS1, as shown in Fig.1.1
[34]. The start of the information cycle is the problem statement. An example is the environmental impact assessment for Project Kier. The second step is the determination of the information need : what information is needed to solve the problem? The third step is the information strategy: how is the required infor-mation obtained? The inforinfor-mation strategy guides data collection and processing. After data processing, feedback is given to the problem owner and, when required, the cycle starts anew.
The information strategy also analyses the mismatch between information need and availability. Based on the mismatch, the information strategy step investigates and initiates innovative solutions for data collection and processing. The investi-gation described in this dissertation originates from the information need of a 3-D model of the subbottom and the absence of an economically efficient method for determining this model.
Set-up of this Dissertation The set-up of this dissertation is shown in Fig.1.2.
The dissertation consists of a theory and application part that can be read indepen-dently. The theory and application part are preceded by chapter 2: Measurement
4 CHAPTER 1. INTRODUCTION
Introduction
Measurement of the Subbottom
Introduction
Model for Acoustic Reflections
Experimental Design
1 2
Model Based, Acoustic Classification
Conclusion
Introduction
Techniques and Instrumentation
Measurements at the Haringvliet
Classification Algorithm Design
Classification Results Conclusion 3 4 5 6 7 8 9 10 11 12 13 Theory I II Application
Figure 1.2: This figure shows the set-up of the chapters. The theory and application part can be read independently.
of the Subbottom. This chapter provides more background on the initial measure-ment question: how to obtain an accurate 3-D model of the subbottom with a specified precision for the least amount of costs? Also, a description is given of the concepts precision and accuracy.
The theory part consists of five chapters. First, an introduction is given in chapter 3 of the theory part. Second, a description is given in chapter 4 of the model for acoustic reflections. This model has been designed to provide the flex-ibility to model a variety of different bottom types. Third, chapter 5 investigates the possibilities of acoustic classification, i.e., is it possible to classify a certain property of the subbottom composition using acoustic techniques? Fourth, model based, acoustic classification will be described in chapter 6. This chapter will also review other available classification techniques. Fifth, conclusions are given in chapter 7.
The application part consists of six chapters. The application part is shaped around a survey that has been performed at the Haringvliet, a Dutch estuary. First, an introduction is given in chapter 8 of the application part. Second, chapter 9 gives an overview of the equipment that is available for measurement of the subbottom and a detailed description of the acoustic equipment that has been used during the Haringvliet survey. Third, a description is given in chapter 10 of the survey area, the Haringvliet estuary, and the observations obtained during the survey. Fourth, chapter 11 describes the developed model-based, classification algorithm. Fifth, the classification results for the Haringvliet survey are described
5 in chapter 12. Sixth, conclusions are given in chapter 13.
Advice to the reader As stated, the theory and application part can be read
independently. Nevertheless, the advice is given to the reader of the theory part to also read chapter 10 on the Haringvliet survey for more insight into the practical measurement problem. Furthermore, to the reader of the application part, the advice is given to read subsections 4.6.3 and 4.6.4 on gas bubbles and grain size for a better understanding of the classification results in chapter 12.
The most important connection between the two parts is formed by chapter 6 and 11. Chapter 11 continues with the application of the theoretical results obtained in chapter 6. Thus, for further development of the acoustic classification techniques described in this dissertation, it is necessary to read chapters 6 and 11. Finally, for readers with a special interest in the X-STAR subbottom profiler, this acoustic measurement device will be described in section 9.3.
2.1
Introduction
Efficient maintenance of rivers, canals and lakes requires an accurate 3-D model of the subbottom with a known precision. Bottom samples are the most common approach to obtain the required knowledge of the subbottom. The drawback of this approach is the high cost of the many samples that are required to obtain sufficient coverage of an area. The cost can be reduced when the bottom samples are used in conjunction with acoustic techniques. Indeed, the impression at the Dutch water management board is that the available measurement techniques are sufficient, especially when used in combination [9]. This chapter will show that this impression is principally correct, but that there are several questions regarding acoustic subbottom classification that need to be addressed.
There are many different aspects to the construction of a 3-D model of the subbottom. A selection of aspects at different scales is shown in Fig.2.1. For example, an aspect at the largest scale, 100 km, is the incorporation of information of separate surveys into a coherent whole, i.e., into a database or geographical information system. At the other end of the scale, 1 cm, is the effect of micro-properties on the bulk micro-properties of a sediment layer. The theory and application part of this dissertation will focus on the questions related to the scale of 10 m and smaller, i.e., on questions related to model-based, acoustic classification of the subbottom. The goal of the present chapter is to provide a connection between the 3-D model of the subbottom and acoustic subbottom classification.
The connection between the 3-D model and classification is provided in sections 2.2 and 2.3. These sections will describe the "What-question" and "How-question": what information is required of the subbottom, and how can this information be obtained? The former describes the requirements on the 3-D model, the latter describes bottom samples, acoustic techniques and geo-statistical interpolation: equipment and techniques used to determine the 3-D model.
On a different note, section 2.4 describes the concepts precision and accuracy. These concepts will be used frequently in this dissertation. Therefore, examples will be given of their importance and application. In section 2.5, a description will be given of the strategy that should be followed when acoustic classification is used in conjunction with bottom samples. Lastly, conclusions will be drawn in
8 CHAPTER 2. MEASUREMENT OF THE SUBBOTTOM
10 m (vertical)
the subbottom structure
The required depth range determines the usable acoustic equipment. In general, a larger depth requires a lower center frequency. The depth range is also limited by the size of the water column due to multiple reflections of the water surface. This limits the depth range to the order of 10 m for most water ways and lakes. 10 km
the Haringvliet
At the level of a survey area, relevant aspects are the "What-question" and "How-question": what information is required and how can this information be obtained? 100 km and more
The Netherlands
At the national level, a relevant aspect is the incorporation of the information of separate surveys into a coherent whole, i.e., into a database or geographical information system.
1 km
the Haringvliet mouth
The graph to the left shows the location of sailed cross-lines during a survey. The cross-lines look rather erratic. This is the result of trying to cover the largest area while being limited by the water depth. Indeed, at this level, a relevant aspect is the planning of the survey such as to cover the largest area possible.
100 m a cross-line
At the level of 100 m, a relevant aspect is the spatial variation of the subbottom. This variation determines the distance between bottom samples or cross-lines that is required to achieve a certain precision in the 3-D model obtained by interpolation of samples and cross-lines.
1 m
a layer transition
With acoustic equipment, the question is whether or not the bulk properties of the layers can be estimated from the observations. The reason for this question is that the observations only show reflections, i.e., they show the difference between properties of successive layers.
10 cm
the acoustic wavelength
The graph to the left shows a signal with a frequency of 30 kHz superimposed on a system of thin layers. At the level of the acoustic wavelength, a relevant aspect is that of resolution: can the acoustic equipment distinguish between different layers?
1 cm and less
sand grains and gas bubbles
Below the level of the acoustic wavelength, a relevant aspect is the effect of micro-properties on the bulk properties of a layer. For example, the graph to the left shows a layer of sand (dark) with gas (white) above a layer of gravel. The question is what the effect will be of the gas bubbles on the observations?
0 10 20 2 0 4 6 200 0 400 10 0 1 0 10 0 1 0 0 100200
2.2. THE "WHAT-QUESTION" 9
object type object
- object border in x,y,z geometry
- grain size - amount of polution - etc.
composition
Figure 2.2: The types of information required for a 3-D model and their relation.
section 2.6.
2.2
The "What-question"
The first question at the start of a survey for a civil engineering project is: what information is required? This is the information need step in Fig.1.1. The answer to this question depends on the specific goals of the engineering project, i.e., on the problem statement step in Fig.1.1. For example, the following information was found to be required for "de Maaswerken" [29]:
Geometry Location of the bottom layers in x,y and z to a depth of 20 meters; Layer thicknesses; Distribution of mineral deposits; Character of lateral vari-ation: continuous layers or small pockets of a certain mineral deposit; Volume estimates of sand, gravel, polluted and clean material.
Manmade Objects Location of stone and gravel dumps that have been used to prevent caving in of the river bank; Location and depth below surface of cables and pipes.
Physical properties Type of material (gravel, sand, clay, silt or otherwise); Grain size distribution; Erosion resistance.
Chemical properties Amount of pollution and pollution class; Amount of zinc, cadmium, PCB’s, PAK’s and DDT.
Ecological properties are not included in this list, but could, for example, be the amount of organic material and the distribution of flora and fauna. The 3-D model for the subbottom should contain or provide all these different types of information. The example can, however, be generalized to three groups: objects, geometry and composition.
The relation between objects, geometry and composition is shown in Fig.2.2. An object is a database entry and determines the type of information. There can be several types of objects, examples are:
10 CHAPTER 2. MEASUREMENT OF THE SUBBOTTOM
Figure 2.3: Two types of lateral variation in 2-D and 3-D. The top two graphs show a continuous layer. The bottom two graphs show small pockets of material.
• man-made objects: gravel dumps, pipes.
• ecological objects: occurrence of a certain species of fauna or flora.
The geometry describes the structure and location of the object. The composi-tion describes the other various object properties, i.e., the physical, chemical and ecological properties.
This dissertation will focus on the most important object of the 3-D model: the subbottom layers. A more detailed description of the required information on the geometry and composition of subbottom layers will be given in, respectively, subsection 2.2.1 and 2.2.2.
2.2.1 Geometry
The information requirements on the geometry, given in the list at the start of this section, can be divided into principal information and derived information. The position of the layer boundaries is the principal information. The other geometric information requirements, such as lateral variation, layer thickness and volume estimates, can be derived from the principal information.
An example of the use of the information on the subbottom geometry is the choice of a specific dredging strategy. This choice depends on the typical layer
2.2. THE "WHAT-QUESTION" 11 x position (m) y po si ti on ( m ) 20 40 60 80 100 20 40 60 80 100 gr ai n di a m et er i n -log 2 (m m) 3 3.5 4 4.5 x position (m) y posi ti on ( m ) 20 40 60 80 100 20 40 60 80 100
II Sand, grain diameter:
mean: 3.6 (-log2(mm)) stdev: 0.3 (-log2(mm))
I Silt, grain diameter:
mean: 4.5 (-log2(mm)) stdev: 0.3 (-log2(mm))
III Silt, grain diameter:
mean: 4.5 (-log2(mm)) stdev: 0.3 (-log2(mm))
II Sand I Silt
III Silt
Figure 2.4: Two ways for describing the subbottom composition: object based on the left, position based on the right.
thickness, the distribution of sediment deposits and the lateral variation. For ex-ample, it can be beneficial to dredge using a sophisticated approach that tracks the upper and lower border of a layer when the layer is sufficiently thick and con-tinuous, as shown in the top half of Fig.2.3, but not when the layer is insufficiently thick and/or occurs in small pockets, as shown in the lower half of Fig. 2.3.
Although pockets of the same material would normally be considered to be one layer, for the 3-D model they are best described as separate objects of the same type. The advantage of a description as separate objects is that the technique that is used to determine the subbottom geometry does not necessarily need to deter-mine the layer composition. Knowledge on the layer composition is required to combine pockets of material. Also, with separate objects there exists no ambiguity about the objects that have and haven’t been classified with bottom samples. For these reasons, a description as seperate objects is preferred.
The boundaries of the objects are given by the positions where two successive layers interfaces meet, the extend of measured area and from acoustic classification if possible. Acoustic classification can also be used to group separate objects together as one type, e.g., a silt layer. The most important requirement, however, is an area covering map of the layer interfaces with known accuracy and precision.
2.2.2 Composition
The information on the composition of an object can be given in two distinct ways: object based and position based, as shown in Fig.2.4.
In the object based way, only the statistical information is given per object, e.g., the mean and standard deviation. To determine this information, it is first required that the objects and their geometry are known. The object based way allows the
12 CHAPTER 2. MEASUREMENT OF THE SUBBOTTOM combination of a global technique for the geometry, with a local technique for the composition. In the position based way, an area covering estimate is given. From this estimate, it should again be possible to determine objects and their boundaries. The object based way requires only a few samples of each object. The position based way doesn’t allow this: a large number of samples is required to obtain an area covering estimate.
The knowledge required of the subbottom will differ from survey to survey, but, in general, the mean and standard deviation should provide sufficient information about the subbottom composition.
2.3
The "How-question"
After establishing the required information with the "What-question", the ques-tion becomes how the required informaques-tion is obtained. In other words, what measurement equipment should be used? This is the information strategy step of Fig.1.1.
A study of all available equipment is required to answer this question properly. For brevity, however, only two measurement techniques will be discussed in this section: bottom samples in subsection 2.3.1 and acoustic techniques in subsection 2.3.2. These two techniques are examples of, respectively, local and global mea-surement techniques as mentioned in the previous section. More techniques will be discussed in chapter 9 of the application part.
Bottom samples and acoustic techniques have been chosen because they are widely used in practice. Bottom samples are commonly used to determine the subbottom composition as well as the subbottom geometry. Acoustic techniques, on the other hand, are, in general, solely used to determine the subbottom geom-etry.
Both bottom samples and acoustic techniques do not provide the area covering result required for a 3-D model. Interpolation between measurements is required to obtain an area covering result. This will be described in subsection 2.3.3. This subsection will also show the advantage of combining bottom samples and acoustic techniques.
2.3.1 Bottom samples
The collection of bottom samples is the most common approach to the measure-ment of the (sub)bottom. Several different types of samples exist: from relatively simple samples of the bottom surface to cores of the subbottom [56]. The analysis of these samples can be either performed on the survey vessel, or, at a later stage in a laboratory. A schematic example of a core analysis is shown in Fig.2.5.
The advantage of bottom samples is the wealth of information that can be extracted from them. Also, additional analysis can be performed at a later stage when required. Samples allow, in fact, the direct measurement of the required
2.3. THE "HOW-QUESTION" 13 Silt Coarse sand Fine sand Medium sand D50 (m m) silt fract ion (%) orga nic frac. (% ) polu tion clas s soun d sp eed (m/s ) dens ity (k g/m 3) ... ... ... ... . 0.05 0.18 0.71 0.43 85 30 20 25 1510 1400 6 3/4 1550 1720 3 1/2 1645 1950 4 1/2 1620 1880 1 1/2
Figure 2.5: Schematic example of a subbottom core.
subbottom properties. This contrasts with acoustic measurements that mostly only provide an indirect measurement of the required subbottom properties.
The disadvantage of bottom samples is the expense of the large number of samples required to obtain an area covering result. Also, it can be difficult to determine the correct depth of layer transitions due to compaction of unconsoli-dated sediment or due to incorrect storage. Furthermore, there are some bottom properties that can change during the extraction of the bottom sample and can, therefore, lead to inaccurate results, e.g., sound speed and gas fraction.
In conclusion, bottom samples are, in general, the best option for determin-ing the subbottom composition, but can be too expensive for determindetermin-ing the geometry.
2.3.2 Acoustic techniques
Acoustic techniques work by sending a sound pulse to the subbottom and measur-ing its reflection. The principle is shown in Fig.2.6. Acoustic techniques only work when there is a difference in impedance between objects, i.e., there should be a difference in sound speed and/or density between two layers in order to determine the layer interface. Also, acoustic techniques don’t measure the depth directly, but the time it takes for the transmitted signal to return, the two way travel time. This travel time can be translated to depth when the sound speed in the water column and subbottom layers is known. Therefore, calibration measurements are required to determine the sound speed. For example, in-situ sound speed measurements can be made, or, transitions in bottom cores can be matched with transitions in acoustic observations.
The advantage of acoustic techniques is that quick coverage is possible of a survey area, i.e., they are highly suitable for determining the subbottom geometry. A disadvantage of acoustic techniques is that they only provide an indirect method
14 CHAPTER 2. MEASUREMENT OF THE SUBBOTTOM position position tim e ( s) depth (m) transducer reflection acoustic observations
Figure 2.6: A schematic example of acoustic observations. The measurement set-up is shown at the left-hand side, the observations are shown as a gray value plot on the right-hand side. Note the difference in the vertical axis: depth on the left and time on the right.
for measuring the subbottom properties.
An open question is the usability of acoustic techniques for subbottom clas-sification. The problem is that a description of the reflection from a realistic subbottom usually requires a rather complex model [123]. This makes it hard to say if a certain property of the composition can be classified at all, and, if possible, with what precision? This question will be investigated in chapter 5 of this disser-tation. Despite the limited theoretical knowledge, there are several classification techniques that have been developed from a practical perspective. These will be discussed in chapter 6.
So, acoustic techniques are most suitable for quick estimation of the subbot-tom geometry. Their use for classification of the subbotsubbot-tom composition will be investigated in this dissertation.
2.3.3 Geo-statistical interpolation
Bottom samples and acoustic techniques only provide the layer positions at, re-spectively, points and lines. The requirement from the "what-question", however, is an area covering estimate. Interpolation between points and lines is required to obtain this estimate. Three examples of interpolation are shown in Fig.2.7: near-est neighbor, linear interpolation and universal kriging. The latter is an example of geo-statistical interpolation.
The advantage of universal kriging over the other methods is that it has the best precision [50]. Also, it is possible to give an estimate of the precision for each interpolated point [50]. Having the best precision does not necessarily mean that
2.3. THE "HOW-QUESTION" 15 true interpolation observation
1-D
100 m 100 m2-D
Figure 2.7: Examples of 1-D and 2-D interpolation with three different techniques. Note: synthetic example.
16 CHAPTER 2. MEASUREMENT OF THE SUBBOTTOM
truth
20 m grid 50 m grid
10 m grid
sample
Figure 2.8: Results of universal kriging for a range of sample grid distances. Note:
synthetic example.
it has the most visually appealing result, for example, see the results for the 50 m grid in Fig.2.8.
It is not the goal of this subsection to explain geo-statistical interpolation in detail, for that, the reader is referred to literature [50]. The goal of this section is to show the benefit of combining bottom samples and acoustic techniques. This will be done using three examples. The first two show the benefit for, respectively, geometry estimates and area covering composition estimates. The third example shows the benefit for geo-statistical interpolation itself.
Example 1 Benefit for geometry estimation
This example investigates the estimation of the layer interface between polluted and clean sand. The measurement problem is shown in Fig.2.9. Suppose that estima-tion of this interface is only possible with bottom cores, i.e., acoustic techniques do not detect the interface. Also, suppose that the variation of this interface follows the overlying silt-sand interface. In that case, the combination of bottom samples and acoustic techniques can deliver a marked improvement over bottom samples alone, see Fig.2.9.
Example 2 Benefit for area covering composition estimation
2.3. THE "HOW-QUESTION" 17
Water Silt
100 m
True
Bottom samples & acoustic observations Only bottom samples
d1 d2 Poluted sand Clean sand Situation sketch d3 100 m
Figure 2.9: The situation sketch at the left shows the measurement problem: the top d2
and bottom d3of a layer of poluted sand need to be estimated. The top can be measured
acoustically, the bottom cannot. Both depths d2and d3vary strongly, but their difference
does not. As a result, it is highly beneficial to combine acoustic observations with bottom
samples. This can be seen by comparing the true values in the gray-value graph true
with the estimated values in graphsonly bottom samples and bottom samples & acoustic
observations. Both estimates use the same number of bottom samples. Note: synthetic example.
bottom samples are required if only these could be used to estimate the grain ameter. Now, suppose that it is possible to classify the subbottom on grain di-ameter using acoustic techniques. Then, a large reduction in bottom samples is possible because they are only needed for calibration, see Fig.2.10. Other advan-tages of acoustic classification are the possibility of combining pockets of material with a similar composition and the prevention of mix ups of subbottom layers, see Fig.2.11.
Example 3 Benefit for variogram estimation
The most difficult part of geo-statistical interpolation is the estimation of the var-iogram. The variogram describes the variance of the difference between points as
a function of their lag h:
γ (h) = 12Var[Z (x + h) − Z (x)] ,
withZ (x) some subbottom property, e.g., depth or grain diameter. An example of
a variogram is shown in Fig.2.12.
The variogram has to be estimated from the same observations as those that are used for interpolation. One problem is that a large number of observations is re-quired to obtain a precise estimate of the variogram, see Fig.2.12. Another problem is that variogram estimation and interpolation have different requirements on the position of the observations: Variogram estimation requires samples at a range of
18 CHAPTER 2. MEASUREMENT OF THE SUBBOTTOM po siti on y interpolated, biased, acoustic classification result
6 bottom samples gr ai n d iam et er φ (l o g2 (m )) gr ain di am et er φ (l o g2 (m )) calibration results after calibration 6 7 8 9 position x po si tio n y 2.5 3 3.5 4 position x po si tio n y gr ai n d iam et er φ (l o g2 (m )) 121 bottom samples interpolation
bottom samples only
bo ttom sam ples & a cou stic te chn iqu es position x po si tion y 4 6 8 10 1 2 3 4 5 φsample = 0.48 ⋅ φacoustic - 0.44 observations optimal fit φsampl e (l o g2 (m )) φacoustic (log2(m)) 2.5 3 3.5 4 position x po si tio n y position x 100 m 10 0 m
Figure 2.10: The top part of this figure shows an area covering grain diameter estimate based on 121 bottom samples. The bottom part shows an area covering, acoustic grain diameter estimate that is calibrated by 6 bottom samples. The acoustic observations are
taken every 1 m in the x-direction and every 20 m in the y-direction. Note: synthetic
example.
different positions in order to cover each lag h; Interpolation, on the other hand, requires samples at regular positions in order to decrease the variation [50]. Both these problems can be solved with acoustic techniques. Firstly, there are many more observations of the subbottom available. Secondly, the observations have a wide variety of lags between them.
The benefit of these three examples can be quantified further using Monte Carlo simulations. For further insight, it is also advisable to investigate variations of the assumptions made in the examples. This falls, however, outside the scope of this dissertation. Geo-statistical interpolation is a well developed field of research. There are several software packages available with provisions for the interpolation of observations obtained from rivers and canals [50][24][156]. For this reason, the choice has been made not to investigate problems regarding interpolation in this dissertation.
2.3. THE "HOW-QUESTION" 19 a b b c c d d e cross line 1 cross line 1 transducer reflection
truth without classification with classification
Figure 2.11: Classification of acoustic observations can prevent mix ups between layers during interpolation. The left-hand graph shows the true subbottom structure. The
subbottom is measured using a transducer, i.e., with an acoustic technique. In this
example, the two sailed cross-lines are above two different top layers. This can cause a mix up between the layers, as shown in the middle graph. Classification of the acoustic observations can prevent this, as shown in the right-hand graph.
0 20 40 0 0.5 1 1.5 100 observations lag (m) 0 20 40 0 0.5 1 1.5 lag (m) 1000 observations 1 MC simulation True 95 % MC simulations 0 20 40 0 0.5 1 1.5 lag (m) n o rm a li z e d v a ri o g ra m 50 observations
Figure 2.12: The normalized variogram based on 50, 100 and 1000 observations. The black dots in the three graphs are a single result from Monte Carlo simulation. The gray background is the 95% confidence region for the Monte Carlo simulations. The confidence region is slightly rough because it is also obtained from Monte Carlo simulations. The black line shows the true variogram.
20 CHAPTER 2. MEASUREMENT OF THE SUBBOTTOM In conclusion, this section has shown how bottom samples and acoustic tech-niques can be combined to deliver both precise and cost effective estimates of the subbottom geometry and composition. The first step in the combination is the in-terpolation of the acoustic observations. These results are then used in conjunction with bottom samples, or, calibrated with bottom samples.
2.3.4 Conclusion
The goal of this section was to show how bottom samples and acoustic techniques can be used in combination to answer the "How-question", .i.e., how to measure the layer interfaces and the subbottom composition. With examples, it has been shown in subsection 2.3.3 that results from acoustic observations can be combined with bottom samples through geo-statistical interpolation. The approach is to first obtain an area covering estimate from the acoustic observations and calibrate this result with bottom samples.
This section has also shown that it can be highly beneficial to be able to classify the subbottom composition using acoustic techniques. Their use for classification is, however, largely unknown and will, therefore, be investigated in this disserta-tion.
2.4
Precision and accuracy
The concepts precision and accuracy will be used often in this dissertation. An explanation is, therefore, required of these concepts and, most notably, of the difference in meaning of these two terms in statistics.
Precision and accuracy describe, respectively, the standard deviation and bias of an estimator. That is, an estimator with the lowest possible standard deviation is called precise and an estimator without bias is called accurate.
Thus, the precision describes the variation between repeated measurements at the same position. The accuracy describes the systematic error, i.e., the error that remains the same for repeated measurements. The accuracy can only be estab-lished when the true value is known, e.g., for the case of simulation experiments or when calibration measurements are available. A graphical example of the two concepts is given in Fig.2.13.
The use and importance of precision and accuracy will be explained using three examples. The first two describe, respectively, the influence of measurement precision and accuracy. The third describes the importance of the measurement question. The first example is taken from literature [29], with small adaptations.
Example 4 The influence of measurement precision
Suppose that a volume of silt has been measured with a precision of 10%, i.e., a
standard deviation of10%. The measurement result is called Vmeas. Also, suppose
2.4. PRECISION AND ACCURACY 21
Precise
Imprecise
Figure 2.13: A dartboard example of precision and accuracy.
99.9% confidence it can be stated that the true silt volume Vtrue is less than,
re-spectively, Vmeas+ 10%, +16.5% and +30%, see Fig.2.14.
Suppose that the silt is polluted and has to be stored in a depot. Also, suppose that
this depot should be large enough with 99.9% confidence. This corresponds to the
worst case of the three ranges given above: Vmeas+ 30%. At the same time, there
is a high probability that the depot will be much too large. In other words, a most unsatisfactory situation.
Now, suppose that an improved measurement Vmeas,2 can reduce the standard
de-viation to 5%. Then, the same confidence can be reached with Vmeas,2 + 15%.
On the average, Vmeas will be equal to Vmeas,2 when both measurements are
accu-rate. Thus, a reduction of 12% in depot volume can be expected (1.3Vmeas down
to1.15Vmeas).
With this knowledge, a decision can be made for more precise measurements when the cost of the increased depot size outweighs the cost of the more precise measure-ments.
Note that this example is strongly dependent on the assumptions, i.e., a
measure-ment precision of 10% and a required confidence of 99.9%. Other values will lead
to different conclusions, see Tab.2.1.
22 CHAPTER 2. MEASUREMENT OF THE SUBBOTTOM -40% -30% -20% -10% Vmeas +10% +20% +30% +40% pr obabi lit y densi ty 84% confidence 95% confidence 99.9% confidence
Figure 2.14: This figure shows how the confidence ofVmeas+ 10%, +16.5% and +30% is
obtained.
required Standard deviation
confidence 2%⇒1% 5%⇒2.5% 10%⇒5% 20%⇒10% 50%⇒25%
84.0% 1% 2% 5% 8% 17%
95.0% 2% 4% 7% 12% 23%
99.9% 3% 7% 12% 19% 30%
Table 2.1: Reduction in depot volume when the standard deviation of the measurements is halved for several required confidence values and a range of values for the standard deviation.
Suppose that a volume estimate is required of the amount of exploitable sand of
an 1 × 1 km2 area. Also, suppose that layer thickness estimates are available for
each 100 × 100 m2 square of this area. Thus, there are Ns= 100 layer thickness
estimates in total. Furthermore, the assumption is made that the layer thickness estimates are independent and have a normal distribution. For simplicity, the precision and accuracy of each estimate is assumed to be the same and they are
equal to, respectively, σl= 5% and bl= +5% (positive bias). Then, the precision
σv and accuracy bv of the volume estimate are given as follows:
precision [141]: σv= σ l √ Ns = 5% √ 100 = 0.5% (2.1) accuracy: bv= bl= +5%. (2.2)
The precision of the volume estimate shows a significant improvement over the layer thickness estimates because the errors of the layer thickness estimates average out. The bias, however, is equal for each layer thickness estimate and remains, therefore, the same for the volume estimate. Worse still, the bias is unknown -it would have been removed otherwise- and cannot be used in a statistical assessment of the volume, as described in the previous example. Accurate measurement of the
2.4. PRECISION AND ACCURACY 23 subbottom is, therefore, crucial for reliable assessment of the subbottom.
Example 6 The influence of the measurement question
Both previous examples have worked with rather different levels of precision for the volume estimates. The second even showed that the precision of the principal measurements, the layer thickness estimates, is relatively unimportant as long as there are sufficient independent measurements. The reason being that the errors of the individual measurements will average out.
This example will show that both levels of precision can be relevant and that they depend on the measurement question. To demonstrate this, the following three questions will be investigated:
A. A volume estimate is required of sand. The material is not environmentally sensitive and the estimate is required to calculate the economic value of the sand
deposit. The volume estimate should have a precision of at least5%.
B I. A volume estimate is required of polluted silt to size a silt depot. The material
is environmentally sensitive and at least97.5% of the surface area should be clean
after dredging. This means that after dredging a new measurement should have at
most a 2.5% probability of finding polluted silt. The volume estimate should have
a precision of at least 5%.
B II. A volume estimate is required of polluted silt to size a silt depot. The
material is environmentally sensitive and at least97.5% of the volume of polluted
silt should be removed after dredging. The volume estimate should have a precision
of at least 5%.
For all three questions, the situation of an1 × 1 km2 area will be investigated with
layer thickness estimates for each As = 100 × 100 m2 square. Thus, a total of
Ns= 100 layer thickness estimates is available.
For question A, the volume estimate is simply a summation of all layer thickness
estimates times the area As. Equation 2.1 describes the precision σvof this volume
estimate. Thus, to obtain a precision of5% for the volume estimate, a precision of
the layer thickness estimates of σl= σv√Ns= 5% ×
√
100 = 50% already suffices.
For question B I, the volume is estimated by summation of the layer thickness
estimates that include the 97.5% requirement. This results in the layer thickness
estimate ˆln being corrected by two times its standard deviation:
ˆ
Vdepot,97.5% area=
Ns
n=1Asˆln(1 + 2σl) . (2.3)
This volume estimate is the 97.5% clean area estimate and not an accurate
es-timate of the true volume. The precision of this eses-timate is the same as for the unbiased estimate and will, in most cases, be much smaller than the bias. The
97.5% estimate will, on average, be 2σl% larger than the true volume of polluted
silt. The relevant precision is, therefore, the precision of the layer thickness
esti-mate σl. This precision should be equal to the halve of the required precision for
the volume: σl= 2.5%.
For questionB II, the translation from the requirement to a measurement question
24 CHAPTER 2. MEASUREMENT OF THE SUBBOTTOM 0 100 200 300 400 500 600 700 800 900 1000 0.2 0.4 0.6 0.8 1.0 distance x (m) la yer th ickness ( m ) cumulative error estimate true
Figure 2.15: The cumulative error of dredging insufficient material.
required Dredging Correction
confidence 1% 2% 5% 10%
97.5% 6.3% 6.6% 7.7% 10.1%
99.9% 0.7% 1.1% 2.3% 4.2%
Table 2.2: Precision of the layer thickness estimate σl as a function of the dredging
correctionlxand the confidence that all material is removed.
layer thickness estimates do not average out. Namely, dredging too much material has no benefit, while removing insufficient material leaves polluted silt behind, see also Fig.2.15. The expectation value of the remaining volume can be expressed as follows: E[Vremaining] = Ns n=1As ∞ −∞ 1 √ 2πσl exp −12 l − ln σl 2 × ln− (l + lx) if l + lx< ln 0 if l + lx≥ ln dl
where ln is the true depth, l is a parameter that represents the estimator for the
depth ln and lxis the dredging correction. Table 2.2 shows the precision of the layer
thickness estimate σl as a function of the dredging correction and the confidence
level that all material is removed. The silt volume estimate is given as follows: ˆ
Vdepot,97.5% vol=
Ns
n=1As(ˆln+ lx). (2.4)
This volume estimate is the97.5% volume estimate and not an accurate estimate
of the true volume. The precision of this estimate is the same as for the unbiased estimate and will, in most cases, be much smaller than the bias. The dredging
correction lx, therefore, determines the relevant precision. The measurement
2.4. PRECISION AND ACCURACY 25
have a precision of 5% and at least 97.5% of the volume of polluted silt should be
removed. This leads to a measurement precision of7.7%.
This example has shown that different measurement questions can lead to large dif-ferences in the required measurement precision, even though the required precision of the volume estimate is equal.
These three examples show the importance of having knowledge on the preci-sion and accuracy of the subbottom observations. Without it, a correct interpre-tation of the measurement results is impossible. The leads to the question if there is sufficient knowledge on the precision and accuracy of geometry and composition estimates? The following list identifies several issues with respect to subbottom samples and acoustic observations.
Geometry
• The position of the survey vessel is determined with GPS or DGPS. The precision and accuracy of these positioning systems are well known. The location of the bottom samples and acoustic measurement equipment can be derived relatively straightforwardly when the equipment is mounted on the survey vessel, i.e., in a fixed position with respect to the GPS antenna. The precision will decrease significantly when the position is variable, e.g., when equipment is towed behind the survey vessel.
• The subbottom samples may become inaccurate due to compaction of uncon-solidated sediment layers. Also, it may be difficult to determine the depth of the water bottom. The latter problem can be solved by combining acoustic (multibeam) observations with the bottom samples.
• The most important source of inaccuracy for acoustic observations is the time to depth conversion. Bottom samples or in-situ measurements are required to obtain the sound speed in the subbottom layers. The obtained sound speeds are then used to perform the time to depth conversion.
The precision of the acoustic observations is determined by the frequency bandwidth and the signal to noise ratio. This will be investigated in chapter 5 of this dissertation for simple step transitions and more complex gradual transitions.
Composition
• The composition estimates from bottom samples have, in most cases, a preci-sion that is more than sufficient. Inaccuracies can, however, arise for certain properties that change during the extraction of the bottom samples. For example, the gas content of a sample can change when the ambient pressure changes, i.e., when the sample is brought to the surface.
26 CHAPTER 2. MEASUREMENT OF THE SUBBOTTOM
Survey preparation & collection of historical data Acoustic observations Geostatistical Interpolation Geometry of objects Geometry & Composition of objects Variogram Sufficiently precise? Additional cross-lines no
Determine position of bottom samples Take bottom samples Calibrate geometry estimate & determine composition of objects Calibrate geometry & compostion estimate yes Geostatistical interpolation Determine geometry and composition of objects
Layer detection Layer classification
Figure 2.16: Measurement strategy for the combination of acoustic techniques and bot-tom samples.
• The precision of composition estimates from acoustic observations is, basi-cally, unknown. In most cases, it is not even known if a specific property of the subbottom composition can be determined using acoustic techniques. These questions will be investigated in chapter 5 of this dissertation. In short, more knowledge is required of the precision and accuracy of acoustic, subbottom classification.
2.5
Strategy
In section 2.3, the combination of acoustic techniques with bottom samples has been discussed. The primary goal of the combination of both techniques is to reduce the cost of surveys. In this section, the strategy will be described to achieve this goal.
2.5. STRATEGY 27 The strategy is shown in Fig.2.16. The most important aspect of the strategy is that first a survey is performed using acoustic techniques, followed by a survey that takes bottom samples.
The first step in Fig.2.16 is survey preparation and collection of historical data. In this step, the decision is made on the required information and the equipment that is required to obtain this information, the "What-question" and "How-question". The decision on the equipment also includes what purpose the acoustic techniques will serve. In section 2.3, three purposes where listed for the acoustic techniques: estimation of the geometry, composition and the variogram. The information required of the subbottom determines which purpose is relevant. The following list summarizes when a specific purpose is relevant:
Geometry The acoustic technique can detect the relevant layer transitions. Composition The acoustic technique can classify the subbottom layers and
de-tect the layer transitions.
Variogram The acoustic technique cannot detect the relevant layer transitions, but can detect other layer transitions that have the same geo-statistical be-havior as the relevant layer transitions.
The second step in Fig.2.16 is the acoustic survey. This survey consists of the collection of acoustic observations, followed by layer detection and layer clas-sification if possible. The results from the detection and clasclas-sification step are interpolated to obtain an area covering estimate. This estimate is judged on its precision and additional cross-lines are sailed when necessary. Note that the pro-posed strategy requires that layer detection and classification are performed during the acoustic survey, in other words, in (near) real-time.
Thus, the result of the acoustic survey is either the geometry of objects, the geometry and composition of objects or the variogram. The next step is to use these results to determine the number and position of bottom samples in order to obtain the required precision:
Geometry In principle, one or more bottom samples are required of each object. In most cases, however, objects can be grouped together based on their mor-phology. Grouping is also possible when (limited) classification is possible with the acoustic observations.
Composition Bottom samples are only required to calibrate the composition estimate. These samples should be positioned such that they optimally cover the range of estimated values.
Variogram Knowledge of the variogram means that the distance between bottom samples can be determined that is required to obtain a certain precision of the area covering interpolation [50].
