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REVISION 10 (2026)
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At all times, ownership of the contents of this publication remains with Copyright © 2026 SPE Wellbore Positioning Technical Section (WPTS) and Industry Steering Committee on Wellbore Survey Accuracy (ISCWSA), Education Sub-Committee
Citation
SPE WPTS and ISCWSA eBook Revision 10 (2026) at https://www.iscwsa.net/ebooks/
Revisions
The authors of this publication are fully aware the nature of the subject matter covered will develop over time as new techniques arise or current practices and technologies are updated. It is, therefore, the intension of the authors to regularly revise this eBook to reflect these changes and keep this publication current and as complete as possible.
Anyone who has expertise, techniques or updates they wish to submit to the author for assessment for inclusion in the next revision should email the data in the first instance to:
Angus.Jamieson@hpinc.com and MElGizawy@slb.com
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Acknowledgements
Chapter contributors
Although Professor Angus Jamieson is the main author of this publication with overall responsibility for its content, thanks are given to the following people who contributed to certain chapters;
• Andy McGregor who contributed the write up of the ‘Error model’ chapters • Jonathan Stigant who contributed the f s ch p on ‘Geodesy’ • John Weston of Gyrodata chapter 10 – ‘Basic Gyro Theory’ • Steve Grindrod who con bu d o h ch p on ‘M gn c sp c ng’ • David McRobbie who contributed on ‘Gy o su y ng’
This book was compiled by members of the Industry Steering Committee for Wellbore Survey Accuracy (ISCWSA), a Society of Petroleum Engineers (SPE) Technical Section for Wellbore Positioning.
The main author Angus Jamieson.
Technical Editors
Mahmoud ElGizawy and Rick Von Flatten
Sponsors
Thanks go to the sponsors of this publication, who contributed funding to the project to bring all this knowledge together into one publication, with the aim of creating a guidebook for the industry without restriction;
All comments on this eBOOK, submissions or amendments should be directed to: Angus Jamieson Angus.Jamieson@hpinc.com and Mahmoud ElGizawy MElGizawy@slb.com
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Introduction to Wellbore Positioning
Summary Contents
Subjects
Page
Acknowledgements
2 4 5
List of Figures Introduction
1. 2. 3. 4. 5. 6. 7. 8. 9.
Coordinate Systems and Geodesy
7
Changing from One Map System to Another True North, Grid North and Convergence
21 23 27 31 35 39 42 44 52 61 62 64 67 72 74 76 82 88
Th E h’sM gn cF ld
Principles of MWD and Magnetic Spacing
In-Field Referencing
Survey Calculation Methods
Survey Frequency Gyro Surveying Basic Gyro Theory When to Run Gyros Correcting for Sag
10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27.
Correcting for Magnetic Interference
Multi Station Analysis
Correcting for Pipe and Wireline Stretch Human Error v Measurement Uncertainty
Understanding Error Models
The ISCWSA Error Models: Introduction
The ISCWSA Error Models: Explanation and Synthesis
Anti-collision Techniques Planning for Minimum Risk
109 121 123 124 126 129 135 138
Basic Data QC
Advanced Data QC
Tortuosity
Some Guidelines for Best Practice
Relief Well Drilling Subsea Positioning
Appendices FULL INDEX
142 159
(Turn on navigation for easy section skipping – view/show/navigation – full index at the end of this publication)
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s offgu s mgs, bls ndd g ms All images, tables and diagrams have been created for this publication unless otherwise credited on the figure.
1. The three reference surfaces in geodesy 2. Mathematical Properties of an ellipse 3. The Relationship between Surfaces 4. Geographic Coordinate System
61. Straight plot of sensor readings 62. Adding a mathematical sine wave to the sensor readings 63. Diagram of the axial correction formula 64.‘ ogozon ’fo x lco c on 65. Establishing the unit vectors for each sensor axis 66. Extending the calculation for the unit vectors for each sensor axis 67. Correcting magnetic station observations 68. Forces acting on a finite element of drillpipe 69. Measuring thermal expansion of a typical drillpipe 70. Modelling deviation graphically 71. Plotting the normal distribution curves for two parameters 72. Normal distribution graph describing probabilities 73. Applying normal distribution modelling to a section of wellbore 74. Trajectory error calculations 75. Plotting the uncertainty 76. Calculating positional error
5. Ellipsoid Coordinate Reference Systems 6. Establishing an Astro-geodetic Datum 7. The World's Major Datum Blocks 8. Astro-geodetic datums in the Indonesian Archipelago 9a. The geoid and an outline of the geoid 9b. Ellipsoid attached to the Earth in two different places 9c.'Glob l’ ll pso d ched at the E h’s c n of m ss 9d. All three datums ellipsoids attached to the Earth 10. The application of the geocentric transformation 11. Increase in offset correction with depth and offset distance
12. Lat/long locations on different geodetic datums 13. Datum transformation parameters in China 14. The hierarchy of mapping.
77. Plotting the ellipse uncertainty 78. Plotting a matrix of covariances
15. Types of projection for various plane/orientation of surfaces 16. Transverse Mercator/Lambert Conformal Conic projection 17. The plane surface to the ellipsoid 18.M c o s s ‘Homolosn ’p oj c on 19. Example projection zones 20. Earths elliptical cross section 21. Map projection surface for parallel map North 22 . h ‘ on g nc ’Angl 22b. The three north references 22c. Combining all three 23. Worked examples of calculating grid direction and bearings. 24. Extended direction/bearing examples 25. Basic Earth internal layers 26. Elements of the magnetic field vector
79. Measured depth error - effect on North, East and TVD. 80. Effect of azimuth error on North and East elements 81. Variance Covariance matrix 82. Calculating and plotting the collision risk
83. The ellipse of uncertainty in 3D 84: ISCWSA error model schematic. 85: Error model axes definition. 86a/b/c: Axis Errors. 87. Definition of Separation Factor 88. Calculating separation factor – Separation Vector Method 89. Calculating separation factor – Pedal Curve Method 90. Scalar (expansion) method 91. Comparing the uncertainty envelopes for two calculation methods 92. Collision probability table 93. Example of a deep, close approach report 94. Fine scan interval graphic 95. Typical scanning interval report 96. Traveling Cylinder Plot - basic 97. Traveling Cylinder Plot – with marker points 98. Traveling Cylinder Plot – marker points and uncertainty area 99. High side referenced Traveling Cylinder Plot 100. Azimuth referenced Traveling Cylinder Plot 101. TVD Crop diagrams 102. Basic ladder plot 103. Ladder plot with uncertainty added 104. Ladder plot using inter-boundary separation only 105. Minimum risk planning wheel 106. Measured depth error effect on North, East and TVD 107. Smooth curve through the observed points to show North, East and TVD 108. Spotting inconsistencies in the survey from the plot 109. Plotting the dogleg severity against measured depth 110. Example well plan graph 111. Actual inclination against measured depth graph
27. Tracking Magnetic North Pole 28. Main field declination Jan 2010 29. Magnetic observatories 30. Magnetic Observatory locations 31. Diurnal field variation
32. Magnetic storm as seen from space 33. Example of a non-magnetic drill collar 34. Graphical representation of two types of toolface 35. Examples of pulser equipment 36. Typical toolface display 37. Example NMDC length selection chart
38. Magnetic field survey methods 39. Examples of IFR survey results 40. Typical software display of an IFR survey
41. Calibrating a marine observation frame on land 42. Tangential method to derive a shift in coordinates 43. Balanced Tangential Method 44. Methods of dealing with curvature 45. Minimum curvature method 46. Example drilling trajectories 47. Typical slide sheet 48. Representation of a basic gyrocompass 49. Schematic representation of a two axis gyroscope 50. Illustration of gyroscopic precession 51. Dynamically tuned gyroscope 52. lcul ng h E h’s of o on 53. Measuring azimuth 54. Instrument configuration with accelerometers 55. Calibration stand 56. Sag correction schematic 57. Typical sag correction software output 58. Typical sag sheet 59. Drillstring magnetisation 60. Examples of axis components of magnetometers
112. Unwanted curvature accumulation graph 113. ‘ g ng’ fo coll s on o d nc pl nn ng 114. Graphic of separation factor calculation 115. Estimating the range from a magnetic source 116. How the uncertainty forms on the ranging shot
117. Ranging on crowded platforms 118. Relief well penetration point 119. Satellite positioning 120. GPS considerations on vessels
121. Baseline Acoustic Array 122. Networked Acoustic Array 123. Reading a permanent seabed AT by vessel 124. Wellhead and Platform coordinates
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n oduc on
The subject of Borehole Surveying has frequently been dealt with in best practice manuals, guidelines and check sheets but this book will attempt to capture in one document the main points of interest for public access through the UHI and SPE websites. The author would like to thank the sponsors for their generous support in the compilation of this book and their willingness to release all restrictions on the intellectual property so that the industry at large can have free access and copying rights. After matters of health and spirit, Borehole Surveying is, of course, the single most important subject of human interest. We live on a planet of limited resources supporting a growing population. At the time of writing, the efficient extraction of fossil fuels is crucial to the sustainable supply of the energy and materials we need. Whilst renewable energies are an exciting emerging market, we will still be dependent on our oil and gas reserves for many years to come. As an industry we have not given the accuracy and management of survey data the attention it deserves. Much better data quality and survey accuracy has been available at very little additional cost but the industry has frequently regarded accuracy as an expensive luxury. Simple corrections to our surveys such as correcting for the stretch of the d llpp o ns gco c on nd F (s l )h b ns n sb longng o h ‘hgh ch’ ndofthemarket ndw h ,unlk n ly llo h su ydscpln s, h owngoodd w y,wh n‘b ’d b com s l bl . The advent of the ISCWSA, The Industry Steering Committee for Wellbore Survey Accuracy, brought in a new era in survey practice. Not only was work done on improving the realism of error models, but a bi-annual forum was provided to allow industry experts to share ideas and experiences. This project has emerged out of a recognised need for better educational materials to support the understanding of borehole surveying issues. The contents of this e-book are free to use and distribute. Any additional chapters will be welcome for assessment and potential inclusion in the book so this is the first draft of a work in progress. My thanks also go to the many participants in this effort who have contributed from their knowledge in specialist areas. In particular to Andy McGregor who contributed the write up of the error model, Jonathan Stigant who contributed the first chapter on geodesy and John Weston, Steve Grindrod and David McRobbie who contributed other chapters on gyro surveying and magnetic spacing.
Prof Angus Jamieson BSc FRICS Technical Consultant to Helmerich and Payne UK Inverness Scotland
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Introduction to Wellbore Surveying
Compiled and co-written by
Angus Jamieson
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1.
oodn ys ms ndG od sy
1.1 The Origin – Reference Surfaces and Elevations in Mapping
T here are three basic surfaces that are pertinent to good mapping, shown here, these are:
Terrain : The topographic surface of the ground or seabed
Geoid : An equipotential surface that is irregular and approximates to Mean Sea Level (MSL)
Ellipsoid : A regular model surface that approximates the geoid, created by rotating an ellipse about the polar axis. Used to simplify the computational complexity of the Geoid
Figure 1: The three reference surfaces in geodesy.
Terrain: The terrain is the surface we walk on or the seabed. This surface is irregular. It is the surface we have to set upou su ym su ngd c s,such s ‘o ls on’o G c . h n u of h su f c wlldc h d c onofg y po n . n moun nous n, h c lwlld fl c n ow ds h m n‘centreofm ss’of the mountains. The Geoid: The equipotential surface of the Earth's gravity field which best fits, in a least squares sense, global mean sea level (MSL). An equipotential surface is a one where gravity is an equal force everywhere, acting normal to the surface.The geoid is an irregular surface that is too complex for calculation of coordinates. The Ellipsoid: The ll pso d s ‘mod l’ of h Earth that permits relatively simple calculations of survey observations into coordinates. The ellipsoid provides h m h m c l b s s of g od sy. o h h G o d s n ‘ c u l phys c l surfaceliketheterrain,but h llpsod s ‘ h o c l’su f c h sd sgn d o‘m ch’ h g od sclos ly s possbl n h ofop ons. o lso h h nom l o h g od(whch s‘ c l’) sno h s m s h normal to the ellipsoid.
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An ellipsoid is created when an ellipse is rotated around its polar axis. h ‘m h m c l’pop sof n llps shown nfgu 2. ‘ ’ s assigned to represent the semi-m jo x s o qu o l d us nd ‘b’ the semi-minor or polar axis. The fl n ng, ‘f’, qu ls h o of h dff nc n‘ ’ nd‘b’o ‘ ’. 1.1.1 MSL, Elevation and Height Mean Sea Level is established by measuring the rise and fall of the tides. hs s noh ‘nxc’sc nc. h d s ff c d by h jux pos on of ‘c l s l’ obj c s, mos no bly h moon bu lso h planets to varying degrees. A well-established MSL reference datum is one where tidal movement has been observed for over 18 years at what s c ll d ‘ m y po ’. h m jo y of countries with a coastline today have established these primary ports along that coastline and the predicted level of tides is reported by the US National Oceanographic and Atmospheric Administration (NOAA) and the UK Hydrographic Office tide tables.
LINKS
NOAA tide tables UKHO tide tables
In order to tie MSL to both onshore elevations and offshore depths, these observations are tied to a physical benchmark usually in a nearby
Figure 2: Mathematical properties of an ellipse.
building wall or some other place unlikely to be inundated by the sea. This benchmark is quoted as a certain height above mean sea level. Sometimes MSL is used also as chart datum for the reduction of depth measurements to a common reference. Sometimes chart datum is established as the lowest level of low water, in order to provide mariners with the least possible depth at a point (i.e. the worst case). Onshore selected benchmarks represent an origin or starting point that can be used to provide the starting point for levelling across the whole country and continent.
h f ncsfo ohAm c h‘
l umof1929’-l n m d o h ‘ on lG od cV c l
um’( GV 29)- nd c nly djus d‘ o hAm c nV c l
um of 1988’ ( AV 88).
Figure 1 shows the difference between heights (h) above the reference ellipsoid and the height above the geoid (H) also known s ‘o hom c' h gh . A more general picture of this relationship with the definitions is in figure 3. The caution is that the GPS sys mpo d s‘h gh’ bo h llpsod,no M elevation. These heights have to be adjusted to make sure they match elevations from other datasets. 1.1.2 Coordinate Systems There are three fundamental types of coordinate systems that are used to define locations on the Earth: ‘G oc n c’ coo d n s m su ng X, Y, Z f om h centre of n ll pso d, ‘G og ph c l’ - latitude and longitude and height (figure 4) nd ‘ oj c on’ - easting and northing and elevation. Various subsets of h s c n lsob us d s‘2 ’conss ngofonly latitude and longitude or easting and northing.
Figure 3: Shows the relationship between surfaces.
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1.1.3 Geographical coordinates These are derived from an ellipsoid and the origin of the coordinates is the centre of the ellipsoid.
h y usu lly f nc d o h ‘G nw ch’ meridian that runs through the Greenwich observatory just east of London in the UK. Meridians increase from 0° at Greenwich to 180° east and west of Greenwich. The ‘n n onl n ’ uns h ough h Pacific and is nominally at 180° east or west of Greenwich. However, different island groups in the Pacific decide to be one side or the other of the Date Line, and the line is drawn at various longitudes to defer to national boundaries. On older maps h ‘0’° m d n s no lw ys Greenwich. There are several other reference meridians, mainly in Europe. A list of these can be found in the EPSG parameter database. In order to facilitate loading of data in some software applications, the convention is that o h nd E s ‘pos ’ nd ouh nd West are negative. However the reader should beware that local applications that do not apply ou s d h ‘qu d n ’, m y not obey this convention.
Figure 4: Geographic coordinate system.
oj c on coo d n s f d o s ‘x’ nd ‘y’. However, h s c n b confus ng s n bou 50% of h wo ld, s ng s p s n d by ‘y’ nd no h ng by ‘x’. Caution is advised! usu lly c ll d s ngs nd no h ngs. om m s h y
More information about how these two types of coordinate system relate will be discussed in the following chapters.
CONTENTS
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1.2 Principles of Geodesy – The forgotten Earth science!
Why“ h Fogo nE h c nc ”? c us h s p dng gno nc of hssc nc ,bu n lluson h s inherently understood! (Daniel Boorstin)
1.2.1 Geodesy Geophysics and Geology – is a study of the Earth. We use models as the other two disciplines do, and make adjustments for distortion and errors in those models. G od syp o d s h ‘f m of f nc ’fo llgoodm ps. s h m nsbywhchw c npu og h llso sof different data attributes and ensure that they are correctly juxtaposed. So while we are interested in the relative position of one piec of d o no h , h m ns by wh ch h s s ch d s houghpo dng n‘ bsolu ’ framework or set of rules that ensures that we can do this correctly. Geodesy is rightly then to be considered the underlying and immutable doctrine required to nsu h m ps ( h c og ph s ‘ ’) p op ly p s n h l world they are designed to portray.
Geodesy is defined as the study of:
the exact size and shape of the Earth
•
• the science of exact positioning of points on the Earth (geometrical geodesy) • the impact of gravity on the measurements used in the science (physical geodesy) • Satellite geodesy, a unique combination of both geometrical and physical geodesy, which uses satellite data to determine the shape of the E h’s g o d nd h pos on ng of po n s.
Let us return to the ellipsoid that we studied in the p ous s c on (fgu 5). hs m , h ‘cu w y’ qu d n of h llpsodsow c ns h centre. On this diagram we can see two coordinate systems. One is the Latitude, Longitude and Height of pon ‘ ’ nsp c bo h llpsodsuf c ( could just as well be below). The other is a three dimensional Cartesian coordinate system where X is in the direction of the Greenwich meridian in the equatorial plane, Y is orthogonal to the Greenwich meridian and Z is parallel to the polar axis (orthogonal to the other two axes). The Cartesian system is directly referenced to the ellipsoid centre, the geographic system is directly referenced to the ellipsoid surface and indirectly to the ellipsoid centre. However, both systems are valid and both describe in dff n ‘numb s’ h coo dn sof h pon ‘ ’.
The relationship between the two systems is per the following algorithms:
Figure 5: Ellipsoid coordinate reference systems.
X = (ν + h) * cos φ * cos λ Y = (ν + h) * cos φ * s n λ Z = [(b2 * ν/ 2 ) + h] * s n φ
(wh ‘ν’ s h dusof h llpsod
).
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1.2.2 Geodetic Datum One of the most important lessons in geodesy is the next step. How do we tie the ellipsoid to the real world? Now h h modlss up,w h o ch o h lwo ld.H s h d fn onof ‘G od c f nc um’: A Geodetic Datum is an ellipsoid of revolution attached to the Earth at some point. There are two types: • Astro-Geodetic (Regional usage) • Global (Global application) W mo f omsmply n llpsod,‘flo ng’ nsp c o ‘g od c f nc d um’. h wo ldw ys odo this, the historic, astro-geodetic (regional), pre-navigation satellite days method and the global method using satellite orbits.
Figure 6 shows how an astro-geodetic datum is established. Astro-geodetic means the geodetic system is set up by direct observation of the stars using very specialized survey instruments. The surface origin is the place where the survey instrument is set up.
The ellipsoid is attached at the observation point and several ‘alignments’ have to take place mathematically:
The equatorial plane of the ellipsoid has to align with the physical equatorial plane
The Polar Axis of the ellipsoid has to be parallel to the physical polar axis of the Earth
The ellipsoid surface has to be positioned so that it matches as closely as possible to the Geoid over the area of interest
Figure 6: Establishing an Astro-geodetic Datum.
In figure 6, note three significant issues: 1. Astro-geodetic (geoid referenced) latitudes are not quite the same as geodetic (ellipsoid referenced) latitudes. hsdu o h slgh dff nc n h nom l o h sp c suf c s. hs s h mod l‘dso on’du o using an ellipsoid. If the region covered is a continent like the USA or Russia, then as the datum network s sp d c oss h l nd h n l s squ s co c ons c ll d ‘ pl c ’ co c ons h o b m d o minimize the distortion. 2. They take much time to observe under demanding accuracy conditions which can be affected by the weather. 3. They are subject to the observation idiosyncrasies of the observer. Relative accuracy between datums established in the same place by different observers can be several hundred meters. The drawback of the astro-geodetic method is that it is only useful over a specified region, and in general cannot be carried across large expanses of impenetrable terrain or water, since inter-visibility is required. Thus in archipelagos, like Indonesia, this can result in a large number of small regional datums none of which quite match with the others. Political boundaries can also mean a multiplicity of datums even in contiguous land masses; West Africa is a good example, where each country has its own unique astro-geodetic datum. Figure 7 shows a global view of continental gon ld um‘blocks’. Egh d ums oco h wo lddo sno s msodffcul,bu nf c h w ll o 100 unique astro-geodetic datums. Figure 8 shows the proliferation of datums in SE Asia.
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Figure 7: The World's Major Datum Blocks.
Figure 8: Shows the multiplicity of Astro-geodetic datums in the Indonesian Archipelago.
A global datum is a datum that is established to model the entire global geoid as closely as possible; something an astro- geodetic datum cannot do. A global is datum is established by observing the orbit of navigation satellites, calculating the E h’s centre of mass based on the orbits and then adjusting the ellipsoid by harmonic analysis to fit the global geoid. There have been several variants, but the two primary ones are WGS 72 and WGS 84. WGS stands for World Geodetic System. The WGS 72 datum was establ sh d fo h ‘ ns oppl ’ s ll sys m, WG 84 w s s bl sh d fo h G sys m. h ‘conn c on’ po n o o g n for the global datums is the E h’s centre of mass. Due to iterative improvement of the gravitational analysis, the centre of mass is slightly different for WGS 72 and WGS 84.
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Figures 9a through 9d show, in cartoon form, the juxtaposition of two astro- geodetic datums with the geoid and a global datum. In figure 9a we see the geoid. There is an outline for representation in the other figures. In figure 9b red and green astro-geodetic datums are shown connected to the surface at two different points. The differences are exaggerated for effect. Figure 9c shows the geoid and the global datum. Figure 9d shows all three ellipsoids juxtaposed with the center of the ellipsoids clearly shown in three different places (again exaggerated for effect). Since latitude and longitude are referenced to the centre of the respective ellipsoid, it is clear that a latitude and longitude on one datum will not be compatible with a latitude and longitude on another datum unless some sort of transform takes place to adjust the one to match the other.
Reference Datum Transformation: Figure 10 shows a global (blue) and an astro-geodetic or regional datum (green), with the offset of the two centres. In order for a coordinate on the blue datum to be transformed to the green datum, the latitude and longitude have to be converted to x,y,z Cartesian coordinates on the blue datum. The dx, dy, dz have to be applied giving the x,y,z on the green datum. This can then be converted back to latitude and longitude on the green datum.
Figure 10: Showing a global datum (blue) and a regional/astro-geodetic datum (green) and the application of the geocentric transformation. The point P has not moved. It is just described by different coordinates.
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Numerically these two sets of coordinates will be different but they will continue to represent the same physical point in space, as can be seen in figures 10 and 11. The corollary is that coordinates referenced to one datum that are mapped in a different datum will appear in the wrong place! The reader should note that in some of the larger regional datums, there are a variety of 3 parameter datum transformation sets depending on where in the region the operator is working (figure 12).
Figure 11: Shows three latitude and longitude locations referenced to different geodetic datums that all represent the same point. The differences in the right-hand two columns shows the error in mapped location if the datums are confused.
Figure 12: Shows various datum transformation parameters in China as they relate to WGS 84. Datums in China are WGS 84, WGS 72 BE, Beijing 1954 and Xian 1980. Note the difference in the parameters for the Beijing datum in the Ordos and Tarim basin, both three parameter transformations and the difference between the South China Sea and the Yellow Sea seven parameter transformations.
These are captured in the EPSG parameter database. Note also there are more sophisticated methods of calculating the datum transformation which may appear in various applications. These include parameters that not only translate but also allow for rotation and scaling differences between the two datums. The EPSG parameter database also contains many of these. Care should be taken when applying such parameters, and it is best to obtain the services of a specialist when using them or coding them into software. For most applications in the E&P domain, a three parameter shift will provide the necessary accuracy. In some countries more elaborate parameters are required by law.
LINK
EPSG parameter database
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1.2.3 Distortions in the Ellipsoidal Model As the reader will have surmised, the ellipsoidal model is not an exact fit. The larger the area covered by a datum, the more distortion there is. Height and Elevation – the elevation above MSL is not the same generally as the height above the ellipsoid. Corrections musb md oG ooh s ll d d‘h ghs’o djus hmom ns l l.M su mnsmd nd adjusted to mean sea level by the surveyor may be assumed to lie on the ellipsoid as long as the separation between the two surfaces is relatively small. Related to the previous one, the direction of the local vertical is not the same as the normal to the ellipsoid. This dff nc sknown s h ‘d fl c on n h c l’ ndh s ob mnmz d sp c lly cossl g gon l nd continental datums. This is done using Laplace corrections at regular intervals across the area of interest. Since these corrections vary in a non-regular and non-linear manner, the datum transformation between two datums may vary significantly across larger datums. The EPSG database is a means of identifying where a particular set of parameters should be used. Radius of curvature adjustment (Figure 13) – The ellipsoid has a radius of curvature at a point (varies across the ellipsoid). When measuring distances at heights above or below the ellipsoid of more than about 5000 ft, the distances need to be adjusted to allow for the change in radius of curva u , so h h y ‘m p’ co c ly on o h ll pso d. Measurements made above the ellipsoid need to be reduced and measurements made below the ellipsoid need to be increased respectively, so h m p of h (compu d h ‘ u ’ llpsod dus)m pco clyono h m p in relation to other features. The calculation can be made with the following equation:
Ellipsoidal length = d[1 –( h/(R + h))] where d = measured length
h = mean height above mean sea level (negative if below) R = mean radius of curvature along the measured line
Figure 13: Shows the increase in offset correction with depth and offset distance.
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Points to Ponder
The most important lesson from all this is that a latitude and longitude coordinate do not uniquely define a point in space unless the datum name is included as part of the description! Please also note that knowing the name of the ellipsoid is not enough. An ellipsoid is a shape in space and the same ellipsoid can be attached to the Earth at an infinite number of places. Each time an ellipsoid is attached to another place it represents a different datum. Particular examples occur in West Africa, where many countries use the Clarke 1880 ellipsoid but set up as a different astro- geodetic datum in each case, and in Brazil where three datums use the International ellipsoid of 1924.
Ten Things to Remember about Geodesy and References:
1. Latitude and Longitude are not unique unless qualified with a Datum name. 2. Heights/Elevations are not unique unless qualified with an height/elevation reference. 3. Units are not unique unless qualified with unit reference. 4. Orientations are not unique unless qualified with a heading reference. 5. Most field data of all types are acquired in WGS 84 using GPS. 6. Every time data are sent somewhere there is a chance someone will misinterpret the references. 7. Most datasets have an incomplete set of metadata describing the references. 8. All software applications are not created equal with respect to tracking and maintaining metadata. 9. Data can be obtained by anyone from anywhere – h do sn’ m k gh ! 10. Most people do not understand geodesy - if you are in doubt – check with someone who knows!
CONTENTS
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1.3 Principles of Cartography – ’s ‘ qu Wo ld’!
s ?
Figure 14: Shows the hierarchy of mapping.
The foundation is the datum. Geographic coordinates (latitude and longitude) describe points in the datum. These are then converted into Projection coordinates.
Without knowledge of the datum, projection coordinates are not unique and can easily be wrongly mapped.
Why is it necessary to project geographic coordinates? We do this for three primary reasons:
Ease of communication Ease of computation Presentation and Planning
• • •
1.3.1 Projection Categories Figure 14 shows the various surfaces and orientation of the surfaces with respect to the ellipsoid axes. The three surfaces for projecting the ellipsoid are a cylinder, a cone and a plane. The main projection types used in E&P are Transverse Mercator and Lambert Conformal Conic . Other projection types that occur less frequently are: Mercator, Oblique Mercator (Alaska) Oblique Stereographic (Syria), Albers Equal Area . The majority of the standard projections in use in E&P are listed with parameters in the EPSG database.
h m ny ‘s nd d’ poj c on parameter definitions, but a project projection can be custom designed for specific purposes if needed. In general, one or two of the following criteria can be preserved when designing a projection:
Shape Area Scale Azimuth
The majority of the projections we use are conformal. This means that scale at a point is the same in all directions, angular relationships are preserved (but not necessarily north reference) and small shapes and areas are preserved.
Figure 15: Shows the various types of projection based on various plane surfaces and the orientation of the surface with respect to the ellipsoid.
They are also generally computational.
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Figure 17 shows that making the plane surface secant to the ellipsoid allows for a greater area to be covered with an equivalent scale distortion.
LINK
EPSG parameter database
1.3.2 Mapping Parameters A projection requires a set of parameters that are used to convert between latitude and longitude and easting and northing. These parameters can be found in the EPSG geodetic parameter database.
Figure 17: The plane surface can be tangent or secant to the ellipsoid. Secant permits the scale distortion to be distributed more evenly and therefore a larger area to be covered per unit distortion.
For a Transverse Mercator projection and a Lambert Conformal Conic projection these are respectively:
The geographic origin is the intersection of the central meridian with the latitude of the origin. The projection origin values at that point are the false easting and false northing. The reason for the high positive values for these parameters where applicable, is to avoid negative values. In both cases above this is for the easting but is not necessary fo h no h ngs wh ch bo h‘0’, s h p oj c on sno n nd dfo us souhof h o gn.
There are several other types of projection, most of which are of more interest to cartographers than having any application in E&P.
1.3.3 Distortions in Mapping We have already seen in the Geodesy section above, that by modelling the Geoid using an ellipsoid, we have already introduced some distortion in the way that the Earth is represented. Without adjustment, that distortion increases as we proceed further from the point of origin where the datum was established. However, with a well-established datum, these distortions can be minimized. When we make calculations from the E h’s su f c o fl (projection) surface, we introduce an additional set of distortions. These are in area, shape, scale and azimuth.
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These distortions: • Can be calculated and understood, but without proper care and well educated workforce, it is easy to make mistakes. • Are non-linear; that is to say, the size of the distortion varies across the projected area are very important component in mapping wellbores. The most important and potentially destructive distortions when projecting geospatial data to a map are scale and orientation, particularly when mapping wellbore positions. Figure 18 shows ‘m c o’ l l x mpl of sc l nd azimuth distortion. This effect happens even at short distances but not so obviously to the eye. The orientation or zmuhch ng swh sc ll dcon g nc . s lu c nb c lcul d nd ppl d o‘ lwold’m su m ns to adjust them to projection north referenced value. Similarly, scale distortion can be applied to survey measurements to represent a scaled distance on the map.
1.3.4 Azimuth Distortion A key point to remember is that the projection central meridian is truly a meridian - there is no azimuth distortion. As one moves away from the central meridian east or west, the other meridians plot on the projection as curved lines that curve towards the nearest pole, whereas grid north lines are parallel to the central meridian. At any given point, the difference in azimuth between the grid north lines and the meridian lines is the convergence angle. On the equator, convergence is generally zero also, and increases as one moves north. Figure 18 shows ‘glob l’ c oon wof h conc p.
Figure 18: The plane surface can be tangent or secant to the ellipsoid. Secant permits the scale distortion to be distributed more evenly and therefore a larger area to be covered per unit distortion.
Figure 19 shows a simple way to verify that the value derived is correct (i.e. that the sign of convergence has been correctly applied). It is important when dealing with convergence to do a coupl of ‘s n y’ ch cks:
Always draw a diagram (Figure 19)
•
• Always check that the software application is applying the correct value, correctly • Always have someone else check that the results agree with supplied results of wellbore location • If you are not sure – find a specialist The formal algorithm is Grid azimuth = True Azimuth – Convergence but many applications do not observe the correct sign. It is better to use True Azimuth = Grid Azimuth ± Convergence α where (per figure 19), α - W s of M, nd α + East of CM in Northern hemisphere and the opposite in Southern hemisphere. In the equation above, use the sign in the diagram, not the sign you get with the software, because some applications use the opposite convention.
Figure 19: Shows two projection zones with Central Meridians, as well as non-central meridians plotted on the projection (curved lines) that converge towards the nearest pole. Two additional grid north lines are shown to the right and left of the figure. Grid north lines are parallel on the projection, creating a grid. Convergence and scale sign distortion vary in a non-linear fashion across the projection, but can be calculated for any given point.
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1.3.5 Scale Distortion Referring back to figure 18, it is clear from the example that a projection will distort the distance between two points. Clearly the true (Earth surface measured) distance between Anchorage and Washington DC has not changed, but the l nghon h m pc nch ng d p ndngon h poj c on. Mos poj c onsw us h subun y‘c n lsc l f c o ’. n the example above the Mississippi West state plane projection has a central scale factor of 0.99975. This means that on the central meridian a 1,000-meter line measured on the ground will be represented by a line 999.75 meters at the scale of the map. If the map has a scale of 1:10,000, then the line on the map will be represented by a line 9.9975 cms long. If you plotted the same line on the central meridian of a UTM projection with a central scale factor of 0.9996, then the line on the map would be represented by a line 9.996 cms long.
CONTENTS
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2.
h ngngfom n M p ys m oAnoh
2.1 Ellipsoids and datums
This is covered in more detail in the Geodesy section above but here are some basic guidelines.
The Earth is elliptical in cross section due to the fact that the planet is mainly molten rock and the rotation of the E hcuss slgh ‘fl nng’ s h cn fuglfoc throws the mass of liquid away from the centre of spin. A datum by definition is an ellipsoidal model of the Earth and a centre point. Historically we have estimated the dimensions of the ellipsoid and its centre from surface observations and the best fit datum has naturally varied from region to region around the world. For example, in the USA, an elliptical model and centre point was chosen in 1927 and is referred to as the NAD 27 datum. It uses the Clarke 1866 Ellipsoid (named after Alexander Ross Clarke a British Geodesist 1828 - 1914 with dimensions as follows:
Figure 20a: Earths elliptical cross section.
Semi-Major Axis: 6378206.4 metres Semi-Minor Axis: 6356583.8 metres
Whereas in 1983 the datum was updated to NAD 83 which uses a spheroid as follows:
Semi-Major Axis: 6378137 metres Semi-Minor Axis: 6356752.3 metres
Not only did the shape update but the centre point shifted by several hundred feet. In order to correctly convert from one system to another, the latitude and longitude have to be converted to an XYZ coordinate from the estimated centre of the Earth (Geo Centric Coordinates). After that a shift in the coordinates to allow for the shift between the centre estimates is applied. Then the coordinates can be converted back to a vertical angle (latitude) and horizontal angle (longitude) from the new centre on the new ellipsoid. In some cases there may be a scale change and even a small rotation around the three axes so it is not recommended that a home-made calculation is done for such a critical and sensitive conversion.
Figure 20b: Geo Centric XYZ coordinates.
Latitude and Longitude for a point are NOT UNIQUE. They depend on the centre point and spheroid in use.
It is worth checking out the EPSG web site. This is the internet domain of the European Petroleum Survey Group which maintains an accurate database of geodetic parameters and provides on line software for doing such conversions.
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LINK
EPSG website
Here, for example is the conversion of a point at 30 degrees North latitude and 70 degrees West Longitude from NAD 27 to NAD 83.
Latitude
Longitude
NAD 27 datum values: NAD 83 datum values:
30 00 0.00000 30 00 1.15126 1.15126 (secs) 35.450 (meters)
70 00 0.00000 69 59 57.30532 -2.69468(secs) -72.222(meters)
NAD 83 - NAD 27 shift values:
Magnitude of total shift:
80.453(meters)
Points to Ponder
The most important lesson from this is that conversions from one map system to another are complex and require specialist knowledge and accurate input parameters. Mistakes in this area may be undetectable on site and entire databases have been known to be wrongly converted resulting in very expensive consequences. This is certainly not a job for a casual spreadsheet.
The main consideration here is that it is essential that when positioning a well, the geoscientists, the operator and the drilling contractor are all working on the same map system on the same datum as the shift in position can be enormous and frequently far bigger than the well target tolerance.
CONTENTS
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3.
u o h,Gd o h, on gnc umm y&
Ex c s s
3.1 Map projections
Fo ny po n on h E h’s su f c u o h s ow ds the Geographic North Pole (The Earth’s axis of revolution).
This fact is independent of any map system, datum or spheroid. However, when a map projection surface is introduced, it is impossible to maintain a parallel map North that still meets at a single point.
In this example a vertically wrapped cylinder such as those used in Transverse Mercator map projections includes the North Pole but the straight blue line on the globe will become slightly curved on the surface of the cylinder. The black line in the diagram shows the direction of Map North (Grid North) and clearly they are not the same.
Figure 21: Map projection surface exercise showing it is impossible to maintain a parallel map North.
When the cylinder is unwrapped, the two lines look like figure 22a.
Because all True North lines converge to a single point, the angle fom u oGd o hs f do sh ‘on gnc’Angl.
Convergence is the True Direction of Map North.
In the case of the Universal Transverse Mercator Projection, the convergence within one map zone can vary from -3 degrees to + 3 degrees. When correcting a true North Azimuth to Grid, this convergence angle must be subtracted from the original azimuth. It is essential that a North Arrow is drawn in order to correctly visualize the relative references.
Figure 22a: The ‘Convergence’ Angle.
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When magnetic north is included (see next chapter) we have three different North References to contend with.
These can be in any order with several degrees of variation between them so a clear North Arrow is essential on all well plans and spider maps.
When correcting from one reference to the other it is common practice to set the company reference North straight upwards and plot the others around it. In figure 22a & 22b, Grid North is the preferred company reference, so all quoted azimuths would be referenced to Grid and the North arrow is centred on Grid North.
Figure 22b: The three north references.
In this example (Figure 22c), the well is heading 60 o Grid with magnetic North at 6 o west of True and Grid North 2 o East of True.. Depending on the reference used, the azimuth can be expressed three different ways, so it is easy to see how confusion can occur.
Figure 22c: The Convergence angle calculation.
Worked examples follow on the next pages…..
CONTENTS
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Some simple worked examples:
Example 1
Example 2
Example 3
Example 4
Example 5
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Points to Ponder
The most important lesson from this section is that North must be defined. Whether True, Grid, Magnetic, or Local, it must be referenced in some way to True North. If these numbers are not correct, the well will be drilled in the wrong direction, which may not be detectable on site.
Do not rely on anything other than documented evidence and, if still uncertain, a survey company must be brought in to establish the North Reference relationships.
Because they sometimes do not demand that the reference be included, it is important to be thorough when submitting data to regulators because it can otherwise be impossible to establish, after the event, which North was used.
4 h E h’sM gn cF ld
4.1 Basic Outline
A h h ofh pln s n nomousmgn cco h g sh E h’sn g os usful f nc. h lns of magnetic force run from south to north and these provide a reference for our compasses.
Figure 25: Basic Earth internal layers.
ofullyd fn h E h’sM gn cF ld ng h, usually measured in nano Teslas or micro Teslas, the Declination Angle defined as the True Direction of Magnetic North and the Dip Angle defined as the vertical dip of the Earth vector below horizontal. For computing reasons, this vector is often defined as three orthogonal magnetic field components pointing towards True North, East, and vertical referred to as Bn, Be and Bv. A fundamental law of physics relating magnetic field strength to electric current is known as the Biot-Savart Law and this is our best explanation for why B is used to denote magnetic field strength. If you know better, please contact the author - details at the front of this publication. ny loc on, w n d h compon n s of co. h F ld
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Figure 26: Elements of the magnetic field vector.
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4.2 V ons n h E h’sM gn cF ld
n p obl mw h h E h’sM gn cF ld s h wllno s nds ll. h cou s ofhso y, h m gn cco of the Earth has been turbulent with the result that the magnetic vector is constantly changing. In geological time scales this chang s y pd. s f dosh‘ cul ’ on.
Figure 27: Tracking the magnetic North Pole.
In order to keep track of this movement, several global magnetic models are maintained to provide prediction models. For example, an international organization called INTERMAGNET collates data from observatories scattered throughout the world to model the intensity and attitude of the E h’s m gn c f ld. E y y , h d s s n o the British Geological Survey in Edinburgh where it is distilled to a computer model called the British Global Geomagnetic Model (BGGM). Historically this has been the most commonly used model for magnetic field prediction for the drilling industry but there are others. The United States National Oceanic and Atmospheric Administration (NOAA) also produce a model known as the High Definition Geomagnetic Model from their National Geophysical Data Centre in Boulder Colorado. This takes account of more localized crustal effects by using a higher order function to model the observed variations in the Earth field. In practice, when higher accuracy MWD is required, it is increasingly popular to measure the local field using IFR (see chapter 6) and to map the local anomalies as corrections to one of the global models. In this way, the global model takes care of the secular variation over time and the local effects are not dependent on a mathematical best fit over long wavelengths.
LINKS
BGGM
NOAA
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The model in figure 28 below is a combined effort between NOAA and the BGS called the World Magnetic Model which is updated every 5 years. This is a lower order model, as is the International Geomagnetic Reference Field produced by IAGA but these are freely accessible over the internet whereas the higher order models require an annual license.
The higher order world models (BGGM and HDGM) are considered to be better than 1 degree (99% confidence) at most latitudes. This may be less true at higher latitudes above 60 0 but at these latitudes, IFR techniques are frequently used.
Figure 29: Typical magnetic observatories.
Figure 28: Main field declination Jan 2010.
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4.3 Magnetic Observatory Distribution
It should be noted that the global models such as BGGM and even HDGM, can only measure longer wave length effects of the E h’s magnetic field distribution and cannot be expected to take account of very localised crustal effects caused by magnetic minerals, typically found in deep basement formations in the vicinity of drilling. See chapter 6 for a discussion of In Field Referencing (IFR), a technique for measuring the local field to a higher accuracy.
Figure 30: Magnetic Observatory distribution.
4.4 Diurnal Variation h m u n lsmplym ns‘d ly’ ndfo many centuries it has been noticed that the magnetic field seems to follow a rough sine wave during the course of the day. Here is a graph of field strength observations taken in Colorado over a 2 day period.
It can be seen that the field strength is following a 24 hour period sine wave.
See chapter 7 for a discussion of ‘Interpolated In Field Referencing’, a method of correcting for diurnal variation in the field.
Figure 31: Diurnal field variation.
These variations may be small but for high accuracy MWD work especially at high latitudes, they may need to be corrected for. We now know that this effect is due to the rotation of the Earth and a varying exposure to the solar wind. The sun is constantly emitting ionized plasma in huge quantities across the solar system. These winds intensify during magnetic storms and the material can be seen on a clear night at high or low latitudes, being concentrated at h m gn cpol s ndfo mng h ‘Au o o ls’ nd h ‘Au o Aus ls’. During such storms the measurements taken from magnetometers and compasses are unlikely to be reliable but even in quiet times, the diurnal variation is always present .
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