PGS Ex. 1120
`
`(Referred to in Dr. Triantafyllou’s August 27, 2015
`deposition transcript as Ex. 1076 in IPR2014-01477)
`
`

`
`EX. PGS 1076
`
`Supplement to Ex. PGS 1041
`
`

`
`LEAST SQUARES FILTERING AND TESTING FOR
`POSITIONING AND QUALITY CONTROL DURING 3D
`MARINE SEISMIC SURVEYS
`
`VASSILIS N GIKAS
`
`Surveying Engineering N.T,U.A.
`
`Thesis submitted for the Degree of
`Doctor of Philosophy
`
`NEWCASTLE UNIVERSITY LIBRARY
`
`"1R'e.:is 1.5433
`
`

`
`ABSTRACT
`
`Three-dimensional seismic exploration has been widely accepted as an integral part of
`
`the development of new oil and gas fields and as a fundamental tool in exploiting
`
`additional reserves in existing fields. Positioning is an important ingredient to the
`
`success of a 3-D seismic survey.
`
`In recent years the problem has become extremely
`
`complex, mainly due to the expansion of the type and quantity of survey data collected.
`
`Moreover it has become increasingly common for clients to require proof in real-time
`
`that the survey ‘quality’ specifications are being met.
`
`This research project has aimed to develop a completely general,
`rigorous and
`integrated methodology which will enable inulti-source surveying observables derived
`during offshore hydrocarbon prospecting,
`to: be. integrated to evaluate the relative
`
`position and quality measures of the seismic sources, hydrophones and associated
`
`hardware in real-time during modern multi-source, multi-streamer operations.
`
`In order to achieve this, a unified algorithm has been developed in which Kalman
`
`filtering adopted as the basic stochastic process. The significant innovation of the
`
`method is centred upon its ability to cope with any geometrical configuration (i.e. any
`
`number of vessels, sources and streamers) while the number of states in the system is
`
`reduced to a minimum. The full system has been programmed and successfiilly tested
`
`using two sets of real marine positioning data. Substantial practical support including
`
`real data and detailed technical discussions on the subject has been offered by the
`
`exploration industry.
`
`Analysis with real data has shown, for the first time, that a completely rigorous solution
`
`to the problem is feasible. More spwifically, analysis showed that single polynomials
`
`can be adopted as a realistic representation of the seismic streamer shape. Source nodes
`
`and hydrophone groups deployed at modern single vessel configurations can be located
`
`with a positional precision of about 2.0-3.0 metre Zdrms and 4.0-5.0 metre Zdnns
`
`respectively. Maximum external reliability at any node in the network varies between
`
`4.0-8.0 metre. Also, analysis showed that the computational cycle time is typically less
`
`

`
`ACKNOWLEDGEMENTS
`
`I wish to thank my supervisor, Prof. Paul Cross, for giving me the opportunity to
`
`undertake the work, having faith in my ability to carry the project through to the end
`
`and for his continuous enthusiasm and advice.
`
`This project has been undertaken in association with QC Tools, Inc., who supplies
`
`software, systems and consultancy to the exploration industry. Therefore, thanks are
`
`due to everyone who has helped over the three years, especially Alex Asiama Akuomoa,
`
`Dave Ridyard and Duncan Griffiths for their sustained efforts in providing the data sets
`
`that have been analysed during the course of this research and the detailed technical
`
`discussions on the current state of the art. I would also like to acknowledge Winnie and
`
`Stanley Herr for showing me the bright lights and warm hospitality of Houston during
`
`my stay in Texas.
`
`I am indebted to all those in the department who have helped over my research period
`
`with ideas and computing related matters, especially Rahmi Celik, Chris Pinel, Paul
`
`Denys and Joel Barnes‘. " Special thanks harejalso due to Noel Zinn of Western Atlas
`International “for his valuable technical comments and suggestions and interest in this
`
`research.
`
`Great appreciation is due to Commission of the European Communities, Athens
`
`Academy, Eugenides Foundation and Onassis Foundation for their generous financial
`
`support of research into streamer modelling at the University of Newcastle upon Tyne.
`
`My thanks also go to all those at my home University in Athens for their support and
`
`advice, especially Ass. Prof. Demitris Paradissis for
`
`listening to my ideas and
`
`encouraging me to pursue such avenues.
`
`Finally,
`
`thanks must go to my family, my parents Nicholas and Paraskevi, and my
`
`

`
`LIST OF CONTENTS
`
`ABSTRACT
`
`ACKNOWLEDGEMENTS
`
`LIST OF CONTENTS
`
`LIST OF FIGURES
`
`LIST OF TABLES
`
`LIST OF ACRONYMS
`
`INTRODUCTION
`
`Overview
`
`Research Objectives and Scientific Results Expected
`
`Research Methodology
`
`Thesis Outline
`
`CHAPTER ONE
`
`3D
`POSITIONING
`AND
`ACQUISITION
`MARINE SEISMIC SURVEYS - AN OVERVIEW
`
`1.1
`
`Introduction
`
`1.2 Acquisition of Marine Seismic and Navigation Data
`
`1.2.1 General
`
`1.2.2 Acquisition Method_s
`
`1.2.2.1 Towed Streamer Technique
`
`1.2.2.2 Ocean Bottom Cable Technique (Transition Zone)
`
`1.2.2.3 Vertical Cable
`
`1 .2.2.4
`
`Cable (4D Seismic Recording)
`
`1.3
`
`The Evolution of Positioning in Marine Seismic Networks
`
`1.3.1
`
`Fixed Offset Period
`
`1.3.2 Vessel Relative and Semi-Integrated Positioning Network Period
`
`1.3.3
`
`Integrated Positioning Network Period
`
`1
`
`ii
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`iii
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`x
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`xv
`
`xvii
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`1
`
`Ulahbé
`
`oo~lO\osu:wN~o\ooooo~l_
`
`ii—l%ljF‘I1‘O—I‘
`
`

`
`List of Contents
`
`1.4
`
`Positioning and Quality Assurance Requirements
`
`1.4.1
`
`Positioning Requirements
`
`1.4.2 Quality Assurance Requirements
`
`1.5
`
`Exchange Formats and Integrated Processing of Positioning Data
`
`1.5.1 Types of Positioning Data and Standard Exchange Formats
`
`1.5.1.1 Exchange Formats for Raw Marine Positioning Data
`
`1.5.1.2 Exchange Formats for Processed Marine Positioning Data
`
`1.5.2 Geophysical Contractors’ Navigation and Binning Systems
`
`1.6
`
`Positioning Data Types and Systems
`
`1.6.1 Acoustic Systems
`
`1.6.2 Laser Systems
`
`1.6.3 Magnetic Cable Compass
`
`1.6.4 Gyrocompass
`
`1.6.5 Terrestrial Radio Ranging Systems
`
`1.6.6 Satellite Systems
`
`1.6.6.1 Working Principle and Obsewables
`
`1.6.6.2 Differential GPS
`
`1.6.6.3 GPS Error Sources
`
`1.6.6.4 DGPS in Offshore 3-D Seismic Surveying
`
`CHAPTER TWO
`
`STREAMER MODELLING
`
`2.1
`
`Introduction
`
`2.2
`
`Streamer Modelling
`
`2.2.1 A Hydrodynamic Approach to Streamer Modelling
`
`2.2.2 Curve Fitting Procedures
`
`2.3
`
`Polynomial Approximation
`
`2.3.1 Calculation of Cable Positions Using a Polynomial Function
`
`2.3.2 Testing the Method with Real Data
`
`21
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`21
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`22
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`26
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`48
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`50
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`56
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`58
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`

`
`List of Contents
`
`CHAPTER THREE THE KALMAN FILTER
`
`3.1
`
`Introduction
`
`3.1.1 Predicting, Filtering and Smoothing
`
`3.1.2 Kalman filtering versus Simple Least Squares
`
`3 .2 The Kalman Filter Mathematical Models
`
`3.2.1 The Measurement Model
`
`3.2.2 The Dynamic Model
`
`3.2.2.1 The Polyhoniial Dynamic Model
`
`3.2.3 The Stochastic Models
`
`3.3
`
`The Kalman Filter Algorithms
`
`3.3.1 The Kalman Filter Principles
`
`3.3.2 The Prediction Equations
`
`3.3.3 The Filtering Equations
`
`3.3.4 The Smoothing Equations
`
`3.3.5 Model Non-lineafites
`
`3.4 Other Filters And Temiinology
`
`3.4.1 The Bayes Filter
`
`3.4.2 Alternative Forms of Kalman Filters
`
`CHAPTER FOUR
`
`QUALITY MEASURES
`POSITIONING
`
`IN
`
`OFFSHORE
`
`4.1
`
`Introduction
`
`4.1.1
`
`Introduction to Quality Assessment
`
`4.1.2 The Kalman Filter Predicted Residuals
`
`4.2 Measures of Precision
`
`4.2.1 Design Parameters that Effect Measures of Precision
`
`4.2.2 Classification of Precision Measures
`
`4.2.2.1 Simple Precision Measures
`
`4.2.2.2 Measures Based on the Covariance Matrix
`
`4.2.2.3 Radial Precision Measures
`
`4.3
`
`Statistical Analysis to Quantify Kalman Filter Estimated Parameters
`
`65
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`66
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`69
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`69
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`70
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`89
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`92
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`95
`
`

`
`List of Contents
`
`4.4.1.1 The Marginally Detectable Error
`
`4.4.1.2 Design Parameters that Effect Internal Reliability
`
`4.4.2 External Reliability
`
`CHAPTER FIVE
`
`FILTER
`KALMAN
`INTEGRATED
`AN
`ALGORITHM FOR POSITIONING 3D MARINE
`
`SEISMIC NETWORKS
`
`5.1
`
`Introduction
`
`5.2 Coordinate Systems
`
`5.3 Kalman Filter Functional Models
`
`5.3.1
`
`State Vector
`
`5.3 .2 Observations
`
`5.3.3 Observation Equations
`
`5.3.4 Kalman Filter Transition Equations
`
`5.4
`
`Stochastic Models
`
`5.5
`
`Seismic Sources and Hydrophones Positioning and Quality Measures
`
`5.5.1
`
`Positioning the Seismic Sources and Hydrophones
`
`5.5.2 Measures of Precision
`
`5.5.3 Measures of Reliability
`
`CHAPTER SIX‘
`
`"
`
`SOFTWARE IMPLEMENTATION
`
`6.1
`
`Introduction
`
`6.2
`
`6.3
`
`System Configuration
`
`The NCL_NET Program Stmcture
`
`6.3. 1 Overview
`
`6.3.2 Main Computational Sections
`
`6.3.3 Working Principle and Mathematical Processes of NCL_NET
`
`6.4
`
`Functional Overview
`
`6.4.1 Main Function
`
`6.4.2
`
`Input/Output Functions
`
`6.4.3 Model Computational Functions
`
`6.4.4 General Functions and Header Files
`
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`11]
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`1 19
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`134
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`134
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`136
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`137
`
`

`
`List of Contents
`
`THE
`CHAPTER SEVEN TESTING
`CORRECTNESS
`EFFICIENCY
`
`FOR
`ALGORITHM
`AND
`COMPUTATIONAL
`
`7.1
`
`7.2
`
`7.3
`
`Introduction
`
`Functional and Stochastic Models
`
`Locating.‘ the Seismic "Spread Elements
`
`7.3.1 Vessel Positioning and Heading
`
`7.3.2 Streamer Base Line Orientation and Reference Point Location
`7.3.3 Float Nodes and Hydrophone Groups Positioning A
`i
`
`7.4 Assessment of the Predicted Residuals of the Observations
`
`7.4.1 Acoustic and Laser Range and Bearing Observations
`
`7.4.2 Compass Azimuths
`
`7.4.3 Vessel and Tailbuoy Absolute Positions
`
`7.5
`
`Independent Checks
`
`7.5.1 Tailbuoy Location - A Control Point
`
`7.5.2 Computation of Acoustically' Observed Ranges
`
`7.5.3 Computation of Compass Observed Azimuths
`
`7.6 Conclusions
`
`AND
`FUNCTIONAL
`EFFECT OF
`CHAPTER EIGHT THE
`STOCHASTIC MODELS ON POSITIONAND
`PRECISION
`
`8.1
`
`Introduction '
`
`8.2 The Functional Model
`
`8.2.1 The Streamer Model
`
`8.2.1.1 Polynomial Functions of a Different Order
`
`,
`
`8.2.1.2 Harmonic Function
`
`8.2.2 The Effect of Measurement Geometry and an Allusion to the
`Design of Seismic Networks
`
`8.3
`
`The Stochastic Models
`
`8.3.1 The Stochastic Model of the Observation Model
`
`8.3.2 The Stochastic Model of the Dynamic Model
`
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`211
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`217
`
`

`
`List of Contents
`
`CHAPTER NINE
`
`RELIABILITY COMPUTATIONS
`
`9. 1
`
`Introduction
`
`9.2
`
`Streamer Model And Testing Parameters
`
`9.3 Reliability Analysis Computations
`
`9.3.1
`
`Internal Reliability
`
`9.3.2 Extemal Reliability
`
`9.3.3 The Effect of the Design Parameters‘ on the Reliability Estimates
`
`9.4 Conclusions
`
`CHAPTER TEN
`
`CONCLUSIONS AND
`FUTURE WORK
`
`SUGGESTIONS FOR
`
`10.1 Design and Development of the Mathematical Algoiithms
`
`10.2 Perfonnance of the Integrated Model with Real Marine Positioning Data
`
`10.3 Suggestions for Future Work
`
`REFERENCES AND BIBLIOGRAPHY
`
`APPENDIX A
`
`KALMAN
`CONVENTIONS
`
`FILTER
`
`NOTATIONAL
`
`APPENDIX B
`
`STATISTICAL TESTING OF THE KALMAN
`FILTER
`
`'
`
`B.l Detection
`
`B.2
`
`Identification
`
`B3 Adaptation
`
`APPENDIX C
`
`DESIGN MATRIX COMPUTATIONS
`
`APPENDIX D
`
`AND
`STRUCTURE
`INPUT
`GENERAL
`FUNCTION DESIGN SPECIFICATIONS FOR
`USE
`BY
`THE NCL_NET
`POSITIONING
`ALGORITHM
`DURING
`MULTI-VESSEL
`
`SEISMIC OPERATIONS
`
`229
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`27]
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`274
`
`

`
`List of Contents
`
`D.2 Structure Definitions
`
`D.2.1 Control Information
`
`D.2.2 State Vector Information
`
`D.2.3 Observations
`
`Input Function Declarations
`D3 General
`Mathematical Computations
`
`to Initiate NC-L__NET
`
`APPENDIX E
`..
`
`DESCRIPTION OF THE RAW MARINE
`POSITIONING DATA
`
`E.l Gabon 3D Seismic Survey
`
`E.1.l General Description
`
`E. 1.2 Navigation Sensors
`
`E.l.2.l Navigation Sensor Offsets
`
`E. 1.2.2 Acoustic and Laser Observables Definition
`
`E‘. I .23 survey 'C’o‘fifii;u'rati'on Diagrams
`
`E. 1.3 Time Series Diagrams of Raw Positioning‘ Data
`
`E.l.3.I Vessel and Tailbuoy Positioning and Gyro
`
`E. 1 .3 .2 Front-end and Tail-end Acoustic and Laser Networks
`
`El .3.3 Compass Azimuths
`
`E.2
`
`Irish Sea 3D Seismic Survey
`
`13.2.1 General Description
`
`E.2.2 Navig'ation'*Sens’ors
`
`13.2.2.1 Navigation Sensor Offsets
`
`E.2.2.2 Acoustic and Laser Observables Definition
`
`13.2.2.3 Survey Configuration Diagrams
`
`E.2.3 Time Series Diagrams of Raw Positioning Data
`
`E.2.3.l Vessel and Tailbuoy Positioning and Gyro
`
`I-3.2.3.2 Acoustic and Laser Networks
`
`E2.3.3 Compass Azimuths
`
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`

`
`LIST OF FIGURES
`
`Figure 1.1
`Figure 1.2
`Figure 1.3
`Figure 1.4
`Figure 1.5
`Figure 1.6
`Figure 1.7
`
`Figure 1.8
`Figure 1.9
`
`Figure 1.10
`
`Figure 1.11
`
`Figure 1=.12
`Figure 1.13
`Figure 1.14
`
`Figure 2.1:
`Figure 2.2;
`Figure 2.3:
`
`Figure 2.4:
`
`Figure 2.5:
`
`Horizontal Midpoint Position (HMP)
`2D conventional seismic grid (A), and 3D seismic grid (B)
`Marine seismic vessel, RV Sea Star (HGS fleet, 1993)
`Marine streamer system and related acoustic sources of streamer noise
`Marine seismic acquisition
`Common used shooting configurations near production platfonns
`Ocean bottom cable shooting configuration.
`3D H-spread technique
`(Syntron, Inc.)
`One vessel, dual source, triple streamer survey configuration
`Quality management policy scheme for positioning marine seismic
`surveys
`,
`Dual vessel, quad source, quad streamer symmetric survey configuration.
`Simplified fiont-end acoustic network
`Time series of.-raw acoustic distance measurements between two acoustic
`nodes fixed on the frond-end of the same streamer. Due to the physical
`connection between these sensors the observed range should be more or
`less fixed (in this case approx. 77 metre).
`It is clearly visible that these
`signals are strongly affected by (combined sea bottom and/or surface)
`reflections, Irish Sea 1993 (see Appendix E2)
`Vessel crab angle
`Main GPS error sources
`
`RGPS target -tracking
`
`Thefrolling quadratic’ technique
`Geometrical’ representation of compass observations
`Streamer modelling for a single {shotpoint based on a least squares
`polynomial approximation, Gabon 1992
`Streamer ‘modelling for a single‘ shotpoint based on a least squares
`polynomial approximation, Irish Sea 1993
`1
`‘Differences in the Cartesian coordinates, of thirteen hydrophone groups,
`those derived using a linear up -to eight ==*order polynomial fitting
`model and those derived using a ‘rolling quadratic’ algorithm for the
`compass data shown in Figure 2.3, Gabon 1992
`
`Figure 3.1:
`
`Predicting, filtering and smoothing
`
`Figure 4.1:
`Figure 4.2:
`Figure 4.3:
`
`The error diamond
`Standard erroriellipse (one sigma) and 95% error ellipse
`The error ellipse and circles of equivalent probability
`Probability of type 1 and II errors under the null Ho and alternative
`
`

`
`List ofFigures
`
`Figure 5.1:
`Figure 5.2:
`Figure 5.3:
`
`Coordinate systems involved in positioning marine seismic networks
`Relation between the state and geometry of the system components
`Compass azimuth observations
`
`Figure 6.1:
`Figure 6.2:
`Figure 6.3:
`
`NCL_NET system communications
`NCL_NE'l‘ program main computational sections
`Computational flowchart ofNCL_NET sofiware
`
`Figure 7.1:
`
`Figure 7.2:
`Figure 7.3:
`Figure 7.4:
`Figure 7.5:
`Figure 7.6:
`
`Figure 7.7:
`Figure 7.8:
`
`Figure 7.9:
`
`Figure 7.10:
`
`Figure 7.11:
`
`Figure 7.12:
`
`Figure 7.13:
`
`Figure 7.14:
`
`Figure 7.15:
`
`Figure 7.16:
`Figure 7.17:
`Figure 7.18:
`
`Figure 7.19;:
`
`Figure 7.20:
`
`Figure 7.21:
`
`Figure 7.22:
`
`Vessel velocity and crab angle; Gabon 1992 (left) and Irish Sea 1993
`(right)
`Raw gyro measurements and streamer orientation angle. Gabon 1992
`Ra_w..g'yro measurements and streamer orientation angle, Irish Sea 1993
`:St'r‘ea‘mer referencepoint location, Gabon 1992
`Streamer reference point location, Irish Sea 1993
`Velocity components of the starboard streamer reference point, Gabon
`1992 (top'),‘and Irish Sea 1993 (bottom)
`Location and velocity components of the source points, Gabon 1992
`Location and velocity components of the port outer source point, Irish Sea
`1993
`
`Location and velocity components of the starboard towfish point, Irish Sea
`1993
`Along’-track location components for three hydrophone groups, Gabon
`1992 (lefi), and Irish Sea 1993 (right)
`Cross-track location components for three hydrophone groups located on
`the starboard strearner, Gabon 1992
`Cross-track location components for three hydrophone groups located on
`the starboard streamer, Irish Sea 1993
`Statistics of the predicted residuals — front end acoustic and laser networks,
`Gabon 1992
`Statistics of the predicted residuals - tail end acoustic network, Gabon
`1992 (lefi)_and.front
`laser network, Irish Sea f19_93 (right)
`Statistics. of theipredicted residuals - Sonardyne and Mu_ltiTRAI( acoustic
`networks, Irish Sea 1993
`Statist_ic_s.of the ._predicted residuals - compass (azimuths, Gabon l9___9_2
`Statistics ofthe predicted residuals - compass azimuths, Irish Sea 1993
`Statistics of the .,predic_ted residuals
`- vessel and tailbuoys Syledis
`
`Differences between Syledis__V(observed) and filter derived tailbuoy location
`(not including tailbuoy Syledis.obseryat_i_o_ns), Cr_ab9_n .1992
`Differences between Syledis (observed) and filter derived tailbuoy location
`(not including tailbuoy Syledis observations), Irish Sea 1993
`Differences between starboard tailbuoy Syledis (observed) and filter
`derived tailbuoy location (not including tailbuoy Syledis observations) for
`shotpoints between 300 and 400, Gabon 1992
`(observed) and filter
`Differences between starboard tailbuoy Syledis
`derived tailbuoy location (including tailbuoy Syledis observations). Gabon
`
`

`
`List ofFigures
`
`Figure 7.23:
`
`Figure 7.24:
`
`Differences for two acoustic ranges between the observed values and those
`derived from the Kalman filter (not including the observation), Gabon
`Differences for two acoustic ranges between the observed values and those
`that derived from the Kalman filter (not including the observation), Irish
`Sea 1993
`
`Figure 7.25:
`
`Difierences for three compass azimuths between the observed compass
`azimuths and those that derived from the Kalman filter (not including the
`observations), Gabon 1992
`,
`.
`Differences_ «for t-hree compass azimuths between theiobserved directions
`Figure 7.26:.
`and those d.c‘,r}ived from the‘ K..a1m'an=;filter-=~(not including. the observations),
`Irish :-;Sea 1993
`
`Figure 8.1:
`
`.
`
`Figure 8.2-:
`
`'Gros's:trackv:tailbuoyeacoordinates computed for three different polynomial
`orders, Gabon 19,92(;to'P)1and.:.Iri,sh Sea:'1L993 (bottom)
`Cr_o.ss-traj.0k ¢0.0.Idinates of a éhydrophone group ..-located midway along the
`cable _compu_t'ed for ;_rlifi‘erent polynomial orders, :_-Gabon 1992 (top)
`
`Figure 8.3:
`
`Figure 8.4:
`
`Figure 8.5:
`
`Figure 8.6:
`
`Figure -8.7:
`
`Figure 8.8:
`
`Figure 8.9:
`
`Statistics of the predicted residuals computed for a fourth order polynomial
`model - compass azimuths, -Irish Sea 1993
`-
`2
`.-
`Along-track coordinates of a hydrophone group locate'<'l..-.-midway along the
`cable ;co_mputed .for.»-three diflerent polynomial orders, Gabon 1992 (top)
`and Irish Sea 1993 (bottom)
`.. Statistics o£_the;_predicted.:resi_duals of..the compass azimuths computed for
`a harmonic. :strearnt.3|T%IIl0de|;;.Gal>.Ot1s-—-1:992
`Statistics of the .-predicted =residuals,"of.___the compass azimuths computed for
`a harriionic streamer model,-I Irish-=:S_e_a 1.993
`.
`-'
`Streamer orientation angle time series computed for a harmonic function
`streamervmodel. Gabon 1992-.
`.
`-
`:
`Cross-._traclc-tailbuoyacoordinates computed for a fifih polynomial (order
`five) and a harmonic fiinction streamer model, Gabon‘ 1992 (top) and Irish
`S€.3._._.;1”3t(b_ottom)
`'
`=
`._
`_.
`_-
`1
`-_v
`..
`Along and cross-track hydrophone. =3n_d:tailb.U.0y;.coordinates computed for
`a polynomial (order ,-five) and -a harmonic function streamer model. Irish
`Sea I993
`.1
`geometry
`for
`Figure 8.10;-.Cr..0SS~traclc tai_lbuo,y. coordinates
`configurations, elimination of the stbd;::.tailbuoy;=location-(a), elimination of
`tl)q§t_l?dtai1_bU0Y 109..%t.i9n and; tai,l.ao0u.stic$efi.on1/I9 asgbed strearner (1_>__)__. and
`elimination of the stbd .tailbuoy location,
`tail acoustics from/to the stbd
`streamer. and the stbd tail-end compasses I2 and.=..I3.(c), Gabon 1992
`Streamer orientation angle computed assuming-ft": prioiti standard deviations
`of 1.0, and 1...5.._ metre for the acoustic and laser ranges respectively, Gabon
`1992
`These
`Statistics: of the -predicted residuals of the compass azimuths.
`estimates were computed ass'umin'g’-a prion‘ standard deviations of 1.0 and
`1.5 metre for the acoustic and laser ranges respectively, Gabon 1992
`Statistics of the predicted residuals of the vessel and tailbuoy Syledis
`
`Figure 8.11:
`
`Figure 8.12:
`
`Figure 8.13:
`
`

`
`List ofFigures
`
`Figure 8.14:
`
`Figure 8.15:
`
`Figure 8.16:
`
`Figure 8.17:
`
`‘Figure 8.18:
`
`Vessel crab angle time series computed assuming a drift rate of 0.04
`degrees/sec for the vessel crab angle, Irish Sea 1993
`Streamer orientation angle time series computed assuming a standard
`deviation: of 0.1 degrees/sec for the streamer orientation angle driving
`noise, Gabon 1992
`Streamer orientation anglecomputed for the stochastic model ‘model II’
`shown in '1"-.able 8.-17, Irish Sea 31993
`‘
`Cross-track tailbuoy coordinates computed for three different stochastic
`models of the ='polyriomia'l "coefficients dynamic model:
`curves 1? and 3
`correspond ‘to models “model -‘I’ and ‘model II’-yrespectively shown in
`Figure 7.17, and curve 2 corresponds to the ‘standard solution’ - Table
`7.2, Gabon 1992 (top) and Irish Sea 1993 (bottom)
`Along‘-track itailbuoyicodrdinates~—computed1:for ‘three different stochastic
`models =of~Ithe polynomial;-'eo_el’ticierits
`model:
`curve 1 and 3
`‘correspond to models‘ ifinodel I’ and; 5.model 11’ respectively shown in
`Figure 8;'l7;aand‘?=c’urve 2- corresponds :to";the' ’:_‘jstandar"d solution’ - Table
`7.2, Gabon 1992 (top) and Irish Sea 1993 (bo‘tto'm‘)‘* :
`
`Figure 9.1:
`
`Figure 9.2:
`
`Figure 9.3:
`
`Internal reliability measures for all "observations in the network, Gabon
`=]=.._9j92
`;
`..
`~‘
`;
`=
`=
`Intemal -reliability measures for all observationsiin theinetwork, Irish Sea
`1993
`»
`-
`‘Extemal reliability values=computed-‘for the-' source nodes and a sample of
`receiver groups c-aused ¥b'y"-I butlier‘ of””thesize =of'MDE for three
`obseri-vation's:~"an outlier-of "715 ‘meters in the aco'us'ti’c' observed’ range
`between the devices fixedbn"the‘jpdrt'source*and?the =fi'ont end of the port
`streamer - range 22 (top), an ’ou‘t‘lie’r’ of 2:0 degrees-in’the tenth compass of
`the starboard streamer (midd'|e),- andA.an.."oi1tlier of"‘1'l.-0 meters in the
`latitiude componettt of thecentre tailbuoy "observation (bottom')',= Gabon
`
`Figure 9.4:
`
`Figure 9.5:
`
`Figure 9.6:
`
`Figure 9.7:
`
`Figure 9.8:
`
`Figure 9.9:
`
`Maximum external reliability (maximum ‘horizontal shift) computed at any
`node in -the net'iivork';—' Gabon 1992
`5'
`’
`Maiéimum‘ extemalreliability (maximum horizontal shifi) computed at any
`node in the network, Irish Sea 1993
`Maximum external reliability (<niaximum"horizontal shifi) computed forvany
`node‘ ‘and for
`"observation in the network,
`"1992
`Internal. reliability computed for the vessel «g-yrfoiand all compass units
`deployed in the network, and external reliability ‘(maximum horizontal
`shift) at any node caused by these MDEs. *"‘In;‘this't_rial the starboard
`ttailbuoy is -‘eliminated, Gabon‘ 1992
`Internal reliability computed for the vessel gyro and all compass units
`deployed in the network, and external
`reliability (maximum horizontal
`shift) at any node caused by these MDES.
`In this trial
`the starboard
`tailbuoy and all tail acoustics iiomito the starboard streamer are eliminated,
`Gabon 1992
`Internal reliability computed for the vessel gyro and all compass units
`
`

`
`List ofFigures
`
`Figure 9.10:
`
`tailbuoy, all tail acoustics from/to the starboard steamer and the compass
`units 12, 13 of the same streamer are eliminated, Gabon 1992
`Internal reliability computed for the vessel and tailbuoy geodetic derived
`positions,‘ and external reliability (maximum horizontal shifi) at any node
`caused by these MDES.
`These results computed for three different
`geometry configurations, elimination of the starboard tailbuoy location (a),
`eiimination of the starboard tailbuoy location and tail acoustics from/to the
`starboard streamer (b), and elimination of the starboard tajlbuoy location,
`tail acousticsfrom/to, the starboard, t_ai_lbuoy_ and the starboard streamer tail
`compasses 12 and 13 (c), Gabon .l__99._2_i,_
`A
`H
`V
`G
`A
`
`Figure E. 1
`Figure E.2
`Figure E..3
`
`Figure E.4
`Figure E.5
`Figure E,6
`
`Geometry configuration sketoh, Gabon (1992)
`_.
`Seismic network ‘body—fixed‘ coordinate systems
`Front—end and tail~end SONARDYNE acoustic network, and front-end
`laser..network,_,
`.;l_99_2
`Geometry configuration sketch,
`MultiTRAK acoustic network, Irish Sea 1993
`Front-end SONARDYNE acoustic network, Irish Sea 1993
`
`

`
`LIST OF TABLES
`
`Table 1.1
`
`Table 1.2
`
`Table 1.3
`
`Contrai':tors* navigation
`’
`Radio positioning systems
`The effect of DGPS on the main error sources of the GPS system
`
`biniriing/processing systems‘
`
`Table 5.1:
`
`Table 5.2:
`
`parameters - ‘state ‘vector- for one vessel, ml
`configuration
`'
`_
`_
`Driving noise uncertainties for the three ‘basic elements of a marine seismic
`network
`1
`‘
`
`floats ‘and’ m2
`
`Table 7.1:
`
`Table 7.2:
`
`Stochastic model of the observations, data I - Gabon 1'992,*and data II -
`Irish Sea 1993
`Stochastic model of the dynamic model, data I - Gabon 1992, and data II -
`Irish Sea 1993
`
`Table 8.1:
`
`Table 8.2:
`
`Table 8.3:
`
`Table 8.4:
`
`Stochastic model for the dynamic model of the polynomial coefficients for
`models of order four and six, Gabon 1992 (left) and Irish Sea 1993 (right)
`Measures of precision computed for a fifth order polynomial streamer
`model, Gabon 1992
`Measures of precision computed for a fifth order polynomial streamer
`model, Irish Sea 1993
`Measures of precision computed for polynomial streamer model of order
`four (top) and six (bottom), Gabon 1992
`
`Table 8.5:
`
`Measures of precision computed for a polynomial streamer model of order
`four and six, Irish Sea 1993
`
`Table 8.6:
`
`Table 8.7:
`
`Table 8.8:
`
`Table 8.9:
`
`Table 8.10:
`
`Stochastic model of the dynamic model of the parameters of a harmonic
`streamer model, Gabon 1992 (left) and Irish Sea 1993 (right).
`Measures of precision computed for a harmonic fimction streamer model,
`Gabon 1992
`Measures of precision computed for a harmonic fiinction streamer model,
`Irish Sea 1993
`geometry
`different
`three
`for
`computed
`precision
`Measures of
`configurations, elimination of the stbd tailbuoy location (a), elimination of
`the stbd tailbuoy location and tail acoustics fiom/to the stbd streamer (b),
`and elimination of the stbd tailbuoy location, tail acoustics from/to the stbd
`tailbuoy and the stbd streamer tail compasses 12 and 13 (c), Gabon 1992
`Measures of precision for a sample of hydrophones computed for two
`
`

`
`List of Tables
`
`Table 8.11:
`
`Table 8.12.:
`
`Table 8.13:
`
`Table 8.14:
`
`Table 8.15:
`
`Table 8.16:
`
`Table 8.17:
`
`Table 8.18:
`
`Table 8.19:
`
`Measures of precision computed assuming a priori standard deviations of
`1.0 and 1.5 metre for the acoustic and laser ranges respectively, Irish Sea
`1993
`
`Measures of precision computed assuming a prion’ standard deviations of
`1.0 degree for the compass azimuths, Gabon 1992
`Measures of precision computed assuming 1.0 metre a priori standard
`deviation for the Syledis derived tailbuoy locations, Gabon 1993
`Measures of precision computed assuming 5.0 metre a priori standard
`deviation for the Syledis derived tailbuoy locations, Irish Sea 1992
`Measures of precision of the vessel NRP "and float nodes computed
`assuming a ; standard deviation of 0.1 m/sec’
`for
`the float nodes
`acceleration, Irish Sea 1993
`,
`Measures of precision for a sample of hydrophone groups computed
`assuming a standard deviation of 0.1 degrees/sec for
`the streamer
`orientation angle driving noise, Gabon 1992
`Testing of the stochastic __mo__del for the dynamic model of the polynomial
`coefiicients, Gabon 1992 (left) and Irish Sea l_9_9_3 (right)
`Measures of precision for a sample of hydrophone groups computed for
`the stochastic models ‘model 1’ (top) and ‘model II’ (bottom) shown in
`Table 8.17, Gabon 1-992
`'~
`Measures of precision for a sample of hydrophoneugroups computed for
`the stochastic models ‘model 1’ (top) and ‘model H’ (bottom) shown in
`Table 3.’ 17, Irish Sea 1993
`
`Table C 1 :
`
`Generalized structure of the design matrix
`
`Table E1:
`
`Table E2:
`
`Table E3:
`Table E4:
`Table E5:
`
`Table E6:
`
`Table E7:
`
`Table E8:
`Table E9:
`
`Table E10:
`
`Table El 1:
`
`Table E12:
`Table E13:
`
`Vessel and tailbuoy positioning sensors, Gabon 1992
`Front__-end SONARDYNIZ
`acoustic network sensors. Gabon
`1992
`Tail-end SONARDYNE TRINAV acoustic network sensors, Gabon 1992
`Front-end laser network sensors, Gabon 1992
`Compass Birds - starboard streamer, {Gabon 1992:
`Compass Birds - centre streamer, Gabon 1992
`Compass Birds - port streamer, Gabon 1922
`Front-end acoustic and laser ranges network, Gabon 1992
`Front-end bearings network, Gabon 1992
`Tail-end acoustic range§,.,n§t)V0fl§.
`Vessel and tailbuoy positioning sensors
`Front-end SONARDYNE acoustic network sensors
`Mu1ti'I‘RAK acoustic network sensors
`
`1,992
`
`Table 1314:
`
`Front-end laser network sensors
`
`Table E15:
`
`Table E16:
`
`Table E17:
`
`Compass Birds - starboard streamer
`Compass Birds - port streamer
`SONARDYNE and MultiTRA1( acoustic networks
`
`

`
`LIST OF ACRONYMS
`
`Two dimensional
`Three dimensional
`
`Anti spoofing
`American Standard Code for Information Interchange
`
`Baarda method
`Best linear unbiased estimator
`
`computed - observed
`
`Coarse/Acquisition GPS signal
`comm depth ppm
`Circular erroriprobable
`
`Companie Generale du Geophysique
`
`D‘ifi‘eren'tial=GP S‘
`Detection Identification Adaptation (statistical
`
`testing procedure for
`
`geodetic networks)
`
`Dip move-out
`
`Department of Defense
`
`V
`distance root mean square
`European Association of Geoscientists and Engineers
`
`European datum 950
`
`External reliability
`Geometric mean error
`
`Global overall model
`
`Global Positioning System
`
`High frequency
`
`Hal|iburton’s Geophysical Services
`
`Horizontal mid-point
`
`Hertz
`
`Integrated navigation system
`
`Internal reliability
`
`Joint Program Office
`
`Kilo Hertz
`
`kilometre
`
`2-D
`3-D
`
`AS
`ASCII
`
`B—method
`
`c-o
`
`C-/A
`cop
`CEP
`
`CGG
`
`DGPS
`DIA
`
`DMO
`
`DoD
`
`drms
`EAGE
`
`ED50
`
`ER
`GME
`
`GOM
`
`GPS
`
`HF
`
`HGS
`
`HMP
`
`Hz
`
`INS
`
`IR
`
`JPO
`
`KHz
`
`Km
`
`

`
`List ofA cronyms
`
`LBL
`
`LOM
`
`LOP
`
`LORAN
`
`LS
`
`LSM
`
`MDE
`
`MHS
`
`Long baseline (positioning method)
`Local overall model
`
`Line of position
`
`Long Range Navigation System
`
`Local slippage (test statistic)
`
`Least square method
`metre
`
`Marginally detectable error
`
`Maximum horizontal shift
`
`Mega Hertz
`
`NCL_NE'l‘
`NMO
`
`Newcastle Network
`
`Nomial move—out
`
`NTUA
`
`P-code
`
`PMRL
`
`PRN
`
`QA
`
`QC
`
`QI
`
`QUEST
`RG1-‘S
`
`SA
`
`SBL
`
`SEG
`
`SIPS
`
`SSBL
`
`Navigation reference point
`
`National Technical University of Athens
`
`Precision code
`
`Post mission receiver location
`
`Pseudorandom noise
`
`Quality assurance
`
`Quality control
`
`Quality improvement
`Engineering and Survey Technology Ltd.
`
`target t'ra"c‘kin'g GPS
`
`Selective Availability I
`
`Sort baseline (positioning method)
`standard deviation
`
`Society of Exploration Geophysicists
`
`Seismic Integrated Positioning System
`
`Super sort baseline (positioning method)
`
`tailbuoy
`
`TQM
`
`Total qu.a1ity.management
`
`Ultra high frequency
`
`UKOOA
`
`UMPI
`
`USBL
`
`WGS84
`
`Y-code
`
`811115
`
`United Kingdom Offshore Operation Association
`Uniformly most powerful invariant (test statistic)
`
`Ultra sort baseline (positioning method)
`
`World Geodetic System I984
`
`Encrypt P-code
`
`root mean square error
`
`

`
`INTRODUCTION
`
`OVERVIEW
`
`In order to explore the continental shelf seabed and the structures beneath it, seismic
`
`surveys are usually undertaken. These surveys involve large vessels towing seismic
`
`sources (‘guns’) and several long (possibly 6km) ‘streamers’, each carrying (possibly
`
`several hundred) hydrophones that sense the arrival of the reflected and refracted sound
`
`waves. By measuring their amplitudes and travel times it is possible to reconstruct an
`
`image of the sub-surface geology. The displays which result from seismic processing
`
`are used by oil companies to detemiine where to drill future exploration and production
`
`wells.
`
`In order to do this analysis it
`
`is necessary to know the position of each gun and
`
`hydrophone for each measurement. Earlier systems leading just to two-dimensional
`
`profiling did not place great accuracy requirements on the liydrographic surveying
`positioning. During the time of 2-D seismic recording the navigation lines were widely
`spaced (possibly several kilometre) so that prospective hydrocarbon targets could be
`
`identified (to some extent) by correlated geological characteristics.
`
`For such an
`
`acquisition scheme the impact of maririe positioning inaccuracies ‘on the resolution of
`
`the processed seismic data in most cases is minimum.
`
`Over the last decade the situation has dramatically changed. Geophysical and economic
`
`pressures have led to an increasing number