Ex. PGS 1057
`
`EX. PGS 1057
`
`
`
`
`
`

`
`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
`
`Department of Surveying
`University of Newcastle upon Tyne
`August 1996
`
`Ex. PGS 1057
`
`

`
`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 multi-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 successfully 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 specifically, 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 2drms and 4.0-5.0
`metre 2drms 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 than the shot interval.
`
`
`
`- i -
`
`Ex. PGS 1057
`
`

`
`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 suplies
`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, Paul Denys and
`Chris Pinel. Special thanks are also 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
`brothers Petros and Sotiris for their continued support and encouragement throughout
`my years in Newcastle.
`
`
`
`
`- ii -
`
`Ex. PGS 1057
`
`

`
`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
`
`
`
`Introduction
`1.1
`1.2 Acquisition of Marine Seismic and Navigation Data
` 1.2.1 General
` 1.2.2 Acquisition Methods
`
`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 Buried 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
` 1.3.4 Ocean Bottom Cable Positioning Methods
`1.4 Positioning and Quality Assurance Requirements
`
`
`
`- iii -
`
`i
`ii
`iii
`x
`xv
`xvii
`
`1
`3
`4
`5
`
`7
`8
`8
`9
`9
`12
`13
`15
`16
`16
`17
`18
`20
`21
`
`Ex. PGS 1057
`
`

`
`List of Contents
`
`21
`22
`26
`26
`26
`27
`28
`30
`30
`34
`35
`37
`38
`40
`40
`41
`42
`44
`
`46
`48
`48
`50
`56
`56
`58
`
`65
`
` 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 Observables
`
`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
`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
`
` STREAMER MODELLING
`
`
`
`CHAPTER THREE
`3.1
`Introduction
`
`
` THE KALMAN FILTER
`
`- iv -
`
`Ex. PGS 1057
`
`

`
`List of Contents
`
`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 Polynomial 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-linearites
`3.4 Other Filters And Terminology
` 3.4.1 The Bayes Filter
` 3.4.2 Alternative Forms of Kalman Filters
`
`CHAPTER FOUR QUALITY MEASURES
`POSITIONING
`
`IN OFFSHORE
`
`Introduction
`4.1
` 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
`4.4 Measures of Reliability
` 4.4.1
`Internal Reliability
`
`4.4.1.1 The Marginally Detectable Error
`
`4.4.1.2 Design Parameters that Effect Internal Reliability
` 4.4.2 External Reliability
`
`
`- v -
`
`66
`67
`69
`69
`70
`71
`72
`75
`75
`76
`77
`78
`79
`82
`82
`83
`
`85
`85
`86
`88
`88
`89
`89
`90
`92
`95
`98
`98
`98
`101
`102
`
`Ex. PGS 1057
`
`

`
`
`CHAPTER FIVE
`
`List of Contents
`
`FILTER
`KALMAN
`INTEGRATED
`AN
`ALGORITHM FOR POSITIONING 3D MARINE
`SEISMIC NETWORKS
`
`Introduction
`5.1
`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
`6.1
`Introduction
`6.2 System Configuration
`6.3 The NCL_NET Program Structure
` 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
`6.5 Performance Improvement and Associated Problems
`FOR
`CHAPTER SEVEN TESTING
`THE
`ALGORITHM
`CORRECTNESS AND COMPUTATIONAL
`EFFICIENCY
`
`
`
`7.1
`
`Introduction
`
`
`
`- vi -
`
`
`
`
`
` SOFTWARE IMPLEMENTATION
`
`103
`105
`108
`108
`110
`111
`119
`121
`123
`123
`124
`124
`
`127
`128
`129
`129
`130
`131
`134
`134
`134
`136
`137
`139
`
`142
`
`Ex. PGS 1057
`
`

`
`7.2 Functional and Stochastic Models
`7.3 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
`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
`
`CHAPTER EIGHT THE EFFECT OF FUNCTIONAL AND
`STOCHASTIC MODELS ON POSITIONAND
`PRECISION
`
`
`
`List of Contents
`
`144
`146
`146
`148
`154
`161
`161
`167
`169
`171
`171
`175
`178
`181
`
`183
`185
`185
`185
`195
`
`204
`211
`211
`217
`228
`
`229
`231
`
`Introduction
`8.1
`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
`8.4 Conclusions
`
`CHAPTER NINE
`9.1
`Introduction
`9.2 Streamer Model And Testing Parameters
`
`
`
`RELIABILITY COMPUTATIONS
`
`
`
`- vii -
`
`Ex. PGS 1057
`
`

`
`List of Contents
`
`9.3 Reliability Analysis Computations
` 9.3.1
`Internal Reliability
` 9.3.2 External Reliability
` 9.3.3 The Effect of the Design Parameters on the Reliability Estimates
`9.4 Conclusions
`
`CHAPTER TEN
`
` SUGGESTIONS FOR
`
`
`
`CONCLUSIONS AND
`FUTURE WORK
`10.1 Design and Development of the Mathematical Algorithms
`10.2 Performance 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
`
`
`
`B.1 Detection
`B.2
`Identification
`B.3 Adaptation
`
`APPENDIX C
`
`APPENDIX D
`
`STATISTICAL TESTING OF THE KALMAN
`FILTER
`
`DESIGN MATRIX COMPUTATIONS
`
`AND
`STRUCTURE
`INPUT
`GENERAL
`FUNCTION DESIGN SPECIFICATIONS FOR
`USE BY THE NCL_NET POSITIONING
`ALGORITHM
`DURING MULTI-VESSEL
`SEISMIC OPERATIONS
`
`
`
`D.1 Introduction
`D.2 Structure Definitions
` D.2.1 Control Information
` D.2.2 State Vector Information
` D.2.3 Observations
`D.3 General Input Function Declarations to Initiate NCL_NET
`Mathematical Computations
`
`
`
`- viii -
`
`232
`232
`235
`242
`247
`
`248
`251
`255
`
`257
`
`269
`
`271
`272
`273
`
`274
`
`276
`278
`278
`283
`284
`
`286
`
`Ex. PGS 1057
`
`

`
`List of Contents
`
`
`APPENDIX E
`
`
`
`DESCRIPTION OF THE RAW MARINE
`POSITIONING DATA
`E.1 Gabon 3D Seismic Survey
` E.1.1 General Description
` E.1.2 Navigation Sensors
`
`E.1.2.1 Navigation Sensor Offsets
`
`E.1.2.2 Acoustic and Laser Observables Definition
`
`E.1.2.3 Survey Configuration Diagrams
` E.1.3 Time Series Diagrams of Raw Positioning Data
`
`E.1.3.1 Vessel and Tailbuoy Positioning and Gyro
`
`E.1.3.2 Front-end and Tail-end Acoustic and Laser Networks
`
`E1.3.3 Compass Azimuths
`E.2
`Irish Sea 3D Seismic Survey
` E.2.1 General Description
` E.2.2 Navigation Sensors
`
`E.2.2.1 Navigation Sensor Offsets
`
`E.2.2.2 Acoustic and Laser Observables Definition
`
`E.2.2.3 Survey Configuration Diagrams
` E.2.3 Time Series Diagrams of Raw Positioning Data
`
`E.2.3.1 Vessel and Tailbuoy Positioning and Gyro
`
`E.2.3.2 Acoustic and Laser Networks
`
`E2.3.3 Compass Azimuths
`
`289
`289
`290
`290
`293
`295
`296
`296
`298
`302
`304
`304
`305
`305
`308
`309
`311
`311
`312
`315
`
`
`
`- ix -
`
`Ex. PGS 1057
`
`

`
`
`
`LIST OF FIGURES
`
`
`
`
`
`Figure 1.8
`Figure 1.9
`
`survey
`
`Horizontal Midpoint Position (HMP)
`Figure 1.1
`2D conventional seismic grid (A), and 3D seismic grid (B)
`Figure 1.2
`Figure 1.3 Marine seismic vessel, RV Sea Star (HGS fleet, 1993)
`Figure 1.4 Marine streamer system and related acoustic sources of streamer noise
`Figure 1.5 Marine seismic acquisition
`Figure 1.6
`Common used shooting configurations near production platforms
`Figure 1.7
`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
`symmetric
`streamer
`source, quad
`Figure 1.10 Dual vessel, quad
`configuration. Simplified front-end acoustic network
`Figure 1.11 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)
`Figure 1.12 Vessel crab angle
`Figure 1.13 Main GPS error sources
`Figure 1.14 RGPS target tracking
`
`Figure 2.1: The ‘rolling quadratic’ technique
`Figure 2.2: Geometrical representation of compass observations
`Figure 2.3: Streamer modelling for a single shotpoint based on a least squares
`polynomial approximation, Gabon 1992
`Figure 2.4: Streamer modelling for a single shotpoint based on a least squares
`polynomial approximation, Irish Sea 1993
`Figure 2.5: Differences in the Cartesian coordinates, of thirteen hydrophone groups,
`between 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: The error diamond
`Figure 4.2: Standard error ellipse (one sigma) and 95% error ellipse
`Figure 4.3: The error ellipse and circles of equivalent probability
`Figure 4.4: Probability of type I and II errors under the null H0 and alternative
`hypothesis HA for a normal distribution.
`
`
`
`
`
`- x -
`
`Ex. PGS 1057
`
`

`
`List of Figures
`
`Figure 5.1: Coordinate systems involved in positioning marine seismic networks
`Figure 5.2: Relation between the state and geometry of the system components
`Figure 5.3: Compass azimuth observations
`
`Figure 6.1: NCL_NET system communications
`Figure 6.2: NCL_NET program main computational sections
`Figure 6.3: Computational flowchart of NCL_NET software
`
`Figure 7.1: Vessel velocity and crab angle, Gabon 1992 (left) and Irish Sea 1993
`(right)
`Figure 7.2: Raw gyro measurements and streamer orientation angle, Gabon 1992
`Figure 7.3: Raw gyro measurements and streamer orientation angle, Irish Sea 1993
`Figure 7.4: Streamer reference point location, Gabon 1992
`Figure 7.5: Streamer reference point location, Irish Sea 1993
`Figure 7.6: Velocity components of the starboard streamer reference point, Gabon
`1992 (top), and Irish Sea 1993 (bottom)
`Figure 7.7: Location and velocity components of the source points, Gabon 1992
`Figure 7.8: Location and velocity components of the port outer source point, Irish Sea
`1993
`Figure 7.9: Location and velocity components of the starboard towfish point, Irish
`Sea 1993
`Figure 7.10: Along-track location components for three hydrophone groups, Gabon
`1992 (left), and Irish Sea 1993 (right)
`Figure 7.11: Cross-track location components for three hydrophone groups located on
`the starboard streamer, Gabon 1992
`Figure 7.12: Cross-track location components for three hydrophone groups located on
`the starboard streamer, Irish Sea 1993
`Figure 7.13: Statistics of the predicted residuals - front end acoustic and laser
`networks, Gabon 1992
`Figure 7.14: Statistics of the predicted residuals - tail end acoustic network, Gabon
`1992 (left) and front end laser network, Irish Sea 1993 (right)
`Figure 7.15: Statistics of the predicted residuals - Sonardyne and MultiTRAK acoustic
`networks, Irish Sea 1993
`Figure 7.16: Statistics of the predicted residuals - compass azimuths, Gabon 1992
`Figure 7.17: Statistics of the predicted residuals - compass azimuths, Irish Sea 1993
`Figure 7.18: Statistics of the predicted residuals - vessel and tailbuoys Syledis
`observations, Gabon 1992 (left) and Irish Sea 1993 (right)
`Figure 7.19: Differences between Syledis (observed) and filter derived tailbuoy
`location (not including tailbuoy Syledis observations), Gabon 1992
`Figure 7.20: Differences between Syledis (observed) and filter derived tailbuoy
`location (not including tailbuoy Syledis observations), Irish Sea 1993
`Figure 7.21: Differences between starboard tailbuoy Syledis (observed) and filter
`derived tailbuoy location (not including tailbuoy Syledis observations) for
`shotpoints between 300 and 400, Gabon 1992
`Figure 7.22: Differences between starboard tailbuoy Syledis (observed) and filter
`derived tailbuoy location (including tailbuoy Syledis observations),
`Gabon 1992 (top) and Irish Sea 1993 (bottom)
`
`
`
`- xi -
`
`Ex. PGS 1057
`
`

`
`List of Figures
`
`Figure 7.23: Differences for two acoustic ranges between the observed values and
`those derived from the Kalman filter (not including the observation),
`Gabon
`Figure 7.24: 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: Differences for three compass azimuths between the observed compass
`azimuths and those that derived from the Kalman filter (not including the
`observations), Gabon 1992
`Figure 7.26: Differences for three compass azimuths between the observed directions
`and those derived from the Kalman filter (not including the observations),
`Irish Sea 1993
`
`
`Figure 8.1: Cross-track tailbuoy coordinates computed for three different polynomial
`orders, Gabon 1992 (top) and Irish Sea 1993 (bottom)
`Figure 8.2: Cross-track coordinates of a hydrophone group located midway along the
`cable computed for three different polynomial orders, Gabon 1992 (top)
`and Irish Sea 1993 (bottom)
`Figure 8.3: Statistics of the predicted residuals computed for a fourth order
`polynomial model - compass azimuths, Irish Sea 1993
`Figure 8.4: Along-track coordinates of a hydrophone group located midway along the
`cable computed for three different polynomial orders, Gabon 1992 (top)
`and Irish Sea 1993 (bottom)
`Figure 8.5: Statistics of the predicted residuals of the compass azimuths computed for
`a harmonic streamer model, Gabon 1992
`Figure 8.6: Statistics of the predicted residuals of the compass azimuths computed for
`a harmonic streamer model, Irish Sea 1993
`Figure 8.7: Streamer orientation angle time series computed for a harmonic function
`streamer model, Gabon 1992
`Figure 8.8: Cross-track tailbuoy coordinates computed for a fifth polynomial (order
`five) and a harmonic function streamer model, Gabon 1992 (top) and Irish
`Sea 1993 (bottom)
`Figure 8.9: Along and cross-track hydrophone and tailbuoy coordinates computed for
`a polynomial (order five) and a harmonic function streamer model, Irish
`Sea 1993
`Figure 8.10: Cross-track tailbuoy coordinates computed for three different geometry
`configurations, elimination of the stbd tailbuoy location (a), elimination of
`the stbd tailbuoy location and tail acoustics from/to stbd streamer (b), and
`elimination of the stbd tailbuoy location, tail acoustics from/to the stbd
`streamer and the stbd tail-end compasses 12 and 13 (c), Gabon 1992
`Figure 8.11: Streamer orientation angle computed assuming a priori standard
`deviations of 1.0 and 1.5 metre for the acoustic and laser ranges
`respectively, Gabon 1992
`Figure 8.12: Statistics of the predicted residuals of the compass azimuths. These
`estimates were computed assuming a priori standard deviations of 1.0 and
`1.5 metre for the acoustic and laser ranges respectively, Gabon 1992
`Figure 8.13: Statistics of the predicted residuals of the vessel and tailbuoy Syledis
`derived locations. These estimates were computed assuming 1.0 and 5.0
`
`
`
`- xii -
`
`Ex. PGS 1057
`
`

`
`List of Figures
`
`metre a priori standard deviations for the tailbuoy observations for the
`surveys in Gabon 1993 (left) and Irish Sea 1993 (right) respectively
`Figure 8.14: Vessel crab angle time series computed assuming a drift rate of 0.04
`degrees/sec for the vessel crab angle, Irish Sea 1993
`Figure 8.15: Streamer orientation angle time series computed assuming a standard
`deviation of 0.1 degrees/sec for the streamer orientation angle driving
`noise, Gabon 1992
`Figure 8.16: Streamer orientation angle computed for the stochastic model ‘model II’
`shown in Table 8.17, Irish Sea 1993
`Figure 8.17: Cross-track tailbuoy coordinates computed for three different stochastic
`models of the polynomial coefficients dynamic model: curves 1 and 3
`correspond to models “model I” and “model II” respectively shown in
`Figure 7.17, and curve 2 corresponds to the “standard solution” - Table
`7.2, Gabon 1992 (top) and Irish Sea 1993 (bottom)
`Figure 8.18: Along-track tailbuoy coordinates computed for three different stochastic
`models of the polynomial coefficients dynamic model: curve 1 and 3
`correspond to models “model I” and “model II” respectively shown in
`Figure 8.17, and curve 2 corresponds to the “standard solution” - Table
`7.2, Gabon 1992 (top) and Irish Sea 1993 (bottom)
`
`
`Figure 9.1: Internal reliability measures for all observations in the network, Gabon
`1992
`Figure 9.2: Internal reliability measures for all observations in the network, Irish Sea
`1993
`Figure 9.3: External reliability values computed for the source nodes and a sample of
`receiver groups caused by an outlier of the size of MDE for three
`observations: an outlier of 7.5 meters in the acoustic observed range
`between the devices fixed on the port source and the front end of the port
`streamer - range 22 (top), an outlier of 2.0 degrees in the tenth compass of
`the starboard streamer (middle), and an outlier of 11.0 meters in the
`latitude component of the centre tailbuoy observation (bottom), Gabon
`1992
`Figure 9.4: Maximum external reliability (maximum horizontal shift) computed at
`any node in the network, Gabon 1992
`Figure 9.5: Maximum external reliability (maximum horizontal shift) computed at
`any node in the network, Irish Sea 1993
`Figure 9.6: Maximum external reliability (maximum horizontal shift) computed for
`any node and for any observation in the network, Gabon 1992
`Figure 9.7: 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 is eliminated, Gabon 1992
`Figure 9.8: 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 from/to the starboard streamer are
`eliminated, Gabon 1992
`Figure 9.9: Internal reliability computed for the vessel gyro and all compass units
`deployed in the network, and external reliability (maximum horizontal
`- xiii -
`
`
`
`Ex. PGS 1057
`
`

`
`List of Figures
`
`shift) at any node caused by these MDEs. In this trial the starboard
`tailbuoy, all tail acoustics from/to the starboard steamer and the compass
`units 12, 13 of the same streamer are eliminated, Gabon 1992
`Figure 9.10: Internal reliability computed for the vessel and tailbuoy geodetic derived
`positions, and external reliability (maximum horizontal shift) at any node
`caused by these MDEs. These results computed for three different
`geometry configurations, elimination of the starboard tailbuoy location
`(a), elimination of the starboard tailbuoy location and tail acoustics
`from/to the starboard streamer (b), and elimination of the starboard
`tailbuoy location, tail acoustics from/to the starboard tailbuoy and the
`starboard streamer tail compasses 12 and 13 (c), Gabon 1992
`
`
`Figure E.1 Geometry configuration sketch, Gabon (1992)
`Figure E.2 Seismic network “body-fixed” coordinate systems
`Figure E.3 Front-end and tail-end SONARDYNE acoustic network, and front-end
`laser network, Gabon 1992
`Figure E.4 Geometry configuration sketch, Irish Sea (1993)
`Figure E.5 MultiTRAK acoustic network, Irish Sea 1993
`Figure E.6 Front-end SONARDYNE acoustic network, Irish Sea 1993
`
`
`
`
`
`- xiv -
`
`Ex. PGS 1057
`
`

`
`LIST OF TABLES
`
`
`
`
`
`
`
`Table 1.1 Contractors’ navigation and binning/processing systems
`Table 1.2 Radio positioning systems
`Table 1.3 The effect of DGPS on the main error sources of the GPS system
`
`Table 5.1: Unknown parameters - state vector- for one vessel, m1 floats and m2
`streamers configuration
`Table 5.2: Driving noise uncertainties for the three basic elements of a marine
`seismic network
`
`
`Table 7.1: Stochastic model of the observations, data I - Gabon 1992, and data II -
`Irish Sea 1993
`Table 7.2: Stochastic model of the dynamic model, data I - Gabon 1992, and data II -
`Irish Sea 1993
`
`
`Table 8.1: 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)
`Table 8.2: Measures of precision computed for a fifth order polynomial streamer
`model, Gabon 1992
`Table 8.3: Measures of precision computed for a fifth order polynomial streamer
`model, Irish Sea 1993
`Table 8.4: 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: Stochastic model of the dynamic model of the parameters of a harmonic
`streamer model, Gabon 1992 (left) and Irish Sea 1993 (right).
`Table 8.7: Measures of precision computed for a harmonic function streamer model,
`Gabon 1992
`Table 8.8: Measures of precision computed for a harmonic function streamer model,
`Irish Sea 1993
`three different geometry
`for
`Table 8.9: Measures of precision computed
`configurations, elimination of the stbd tailbuoy location (a), elimination of
`the stbd tailbuoy location and tail acoustics from/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
`
`
`
`- xv -
`
`Ex. PGS 1057
`
`

`
`
`
`Table 8.10: Measures of precision for a sample of hydrophones computed for two
`different geometry configurations - elimination of mid acoustics (a), and
`elimination of compasses 1, 3 and 9 (b), Irish Sea 1993
`Table 8.11: 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
`Table 8.12: Measures of precision computed assuming a priori standard deviations of
`1.0 degree for the compass azimuths, Gabon 1992
`Table 8.13: Measures of precision computed assuming 1.0 metre a priori standard
`deviation for the Syledis derived tailbuoy locations, Gabon 1993
`Table 8.14: Measures of precision computed assuming 5.0 metre a priori standard
`deviation for the Syledis derived tailbuoy locations, Irish Sea 1992
`Table 8.15: Measures of precision of the vessel NRP and float nodes computed
`assuming a standard deviation of 0.1 m/sec2 for the float nodes
`acceleration, Irish Sea 1993
`Table 8.16: 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
`Table 8.17: Testing of the stochastic model for the dynamic model of the polynomial
`coefficients, Gabon 1992 (left) and Irish Sea 1993 (right)
`Table 8.18: Measures of precision for a sample of hydrophone groups computed for
`the stochastic models ‘model I’ (top) and ‘model II’ (bottom) shown in
`Table 8.17, Gabon 1992
`Table 8.19: Measures of precision for a sample of hydrophone groups computed for
`the stochastic models ‘model I’ (top) and ‘model II’ (bottom) shown in
`Table 8.17, Irish Sea 1993
`
`
`Table C1: Generalized structure of the design matrix
`
`Table E1: Vessel and tailbuoy positioning sensors, Gabon 1992
`Table E2: Front-end SONARDYNE TRINAV acoustic network sensors, Gabon
`1992
`Table E3: Tail-end SONARDYNE TRINAV acoustic network sensors, Gabon 1992
`Table E4: Front-end laser network sensors, Gabon 1992
`Table E5: Compass Birds - starboard streamer, Gabon 1992
`Table E6: Compass Birds - centre streamer, Gabon 1992
`Table E7: Compass Birds - port streamer, Gabon 1992
`Table E8: Front-end acoustic and laser ranges network, Gabon 1992
`Table E9: Front-end bearings network, Gabon 1992
`Table E10: Tail-end acoustic ranges network, Gabon 1992
`Table E11: Vessel and tailbuoy positioning sensors
`Table E12: Front-end SONARDYNE acoustic network sensors
`Table E13: MultiTRAK acoustic network sensors
`Table E14: Front-end laser network sensors
`Table E15: Compass Birds - starboard streamer
`Table E16: Compass Birds - port streamer
`Table E17: SONARDYNE and MultiTRAK acoustic networks
`
`
`
`- xvi -
`
`Ex. PGS 1057
`
`

`
`LIST OF ACRONYMS
`
`
`
`2-D
`3-D
`AS
`ASCII
`B-method
`BLUE
`c-o
`C/A
`CDP
`CEP
`CGG
`DGPS
`DIA
`
`DMO
`DoD
`drms
`EAGE
`ED50
`ER
`GME
`GOM
`GPS
`HF
`HGS
`HMP
`Hz
`INS
`IR
`JPO
`KHz
`Km
`L1
`L2
`
`
`
`Two dimensional
`Three dimensional
`Anti spoofing
`American Standard Code for Information Interchange
`Baarda method
`Best linear unbiased estimator
`computed - observed
`Coarse/Acquisition GPS signal
`Common depth point
`Circular error probable
`Companie Generale du Geophysique
`Differential GPS
`Detection Identification Adaptation (statistical testing procedure for
`geodetic networks)
`Dip move-out
`Department of Defense
`distance root mean square
`European Association of Geoscientists and Engineers
`European datum 1950
`External reliability
`Geometric mean error
`Global overall model
`Global Positioning System
`High frequency
`Halliburton’s Geophysical Services
`Horizontal mid-point
`Hertz
`Integrated navigation system
`Internal reliability
`Joint Program Office
`Kilo Hertz
`kilometre
`GPS L-band signal 1 (1575.42 MHz)
`GPS L-band signal 2 (1227.6 MHz)
`
`- xvii -
`
`Ex. PGS 1057
`
`

`
`List of Acronyms
`
`LBL
`LOM
`LOP
`LORAN
`LS
`LSM
`m
`MDE
`MHS
`MHz
`NCL_NET
`NMO
`NRP
`NTUA
`P-code
`PMRL
`PRN
`QA
`QC
`QI
`QUEST
`RGPS
`SA
`SBL
`sd
`SEG
`SIPS
`SSBL
`t/b
`TQM
`UHF
`UKOOA
`UMPI
`USBL
`WGS84
`Y-code
`rms
`
`
`
`
`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
`Newcastle Network
`Normal move-out
`Navigation reference point
`National Technical University of Athens
`Precision code
`Post mission receiver location
`Pseudorandom noise
`Quality assurance
`Quality control
`Quality improvement
`Quality Engineering and Survey Technology Ltd.
`target tracking GPS
`Selective Availability
`Sort baseline (positioning method)
`standard deviation
`Society of Exploration Geophysicists
`Seismic Integrated