Geodesy and Cartography

Geodesy and CartographyByNorm Berls

Location in the Petroleum IndustryOn the earth: Latitude & LongitudeOn maps: X & Y coordinatesExample:Latitude: 30.0 N Longitude: 93.0 WX: 500,000 meters Y: 3,318,785 meters

CartoLab DemoComputation of XY from LatLonTransforms TabSet CRS 1 Geodetic Datum only: WGS84Set CRS 2 Geodetic Datum: WGS84 Mode UTM: Zone 16 NorthSusped Geodetic TransformsTransform PointLatitude 30.0 Longitude -93.0 to XY

The Earth is not a SphereMountains and Ocean basins.Mascons make the gravity field irregular.Rotation makes the equator bulge and the poles flatten.

Shape of the EarthEllipsoidMathematical ModelAn approximation

EllipseSemi Major AxisSemi Minor AxisFlatteningInverse FlatteningEccentricity

CartoLab DemoView an Ellipsoid on the DBDatabases TabEllipsoid DatabaseInspect WGS84 semi-major axis in meters semi-minor axis in meters inverse flattening is a unitless ratio

Some common Ellipsoids

NameSemi-MajorSemi-MinorWGS846378137.06356752.3 International 19246378388.06356911.9 Clarke 18666378206.4 6356583.8 Krassovsky 1940 6378245.06356863.0

Size of the Earth

Latitude and LongitudeLongitude: an east-west measurement relative to a prime meridian.Latitude: a north-south measurement relative to the equator.

Latitude on an Ellipsoid

Sign conventionsSouthern Hemisphere Latitudes are handled as negative numbers.-35.0 and 35.0S mean the same thing 35.0 and 35.0N mean the same thingWestern Hemisphere Longitudes are handled as negative numbers.-35.0 and 35.0W mean the same thing. 35.0 and 35.0E mean the same thing.

CartoLab DemoPresentation Modes and UnitsTransforms TabDefine CRS 2Switch to Informal ModeSet ParmsCentral Meridian switch to DMSH modeOrigin Latitude switch to DMSH modeFalse Easting switch to ftUSFalse Northing switch to ftUS

LatLon PrecisionHow many decimal places are enough?+- 1.0 meter is sufficient for Oil Industry purposes.90.0 / 10000000 = 0.0000091 meter = 0.000009 degreesLatitudes range between -90.0 and +90.0 degrees.Longitudes range between -180.0 and +180.0 degrees.

Naming ConventionsA line of constant Latitude on a map is called a Parallel.A line of constant Longitude on a map is called a Meridian.Both sets of lines together are called a Graticle.

Measuring Latitude and LongitudeIn the old days:Pick an arbitrary point on the earthEstimate Latitude and Longitude using astronomical means.Survey other points with transit and chain.Reconcile other points via triangulation.Compute Latitude and Longitude of triangulated network points (bench marks).Result is a Horizontal Datum.Arbitrary locations within the network can be surveyed relative to bench marks.

Horizontal DatumsContain math errors.Patchworks of discontinuous networks.Mapping over discontinuous areas requires measurements in one area be shifted to align correctly with the other (conflation).Limited geographic extent.No one covers the whole world.Mapping on boundaries a problem.Measurements on one datum must be shifted to align correctly with the other (conflation).Only measure horizontal locations; Vertical locations measured on a separate (unrelated) Vertical Datum.

Measuring Latitude & LongitudeTodayExact orbit of satellites known.Difference between time signal sent and time signal received yields distance.GPSDistances yield Latitude, Longitude and Height of receiver.Special receivers and techniques yield precision of centimeters.Measurement system called a Geodetic Datum

Horizontal vs. GeodeticEllipsoid for Horizontal Datum offset and rotated relative to center of earth.Ellipsoid for Geodetic Datum centered on gravitational center of earth and axis centered on polar axis (geocentric).In practice, Horizontal Datums and Geodetic Datums are both referred to as Geodetic Datums.The same LatLon values expressed on two different Geodetic Datums may be as much as 1 kilometer apart on the real earth.Any earth location will have different LatLon coordinates depending upon which Geodetic Datum those values are measured.Mapping of LatLons from different Geodetic Datums requires that locations be conflated.

DefinitionA Geodetic Datum is a system of measurement wherein locations on the earth are specified in terms of Latitude, Longitude and Height measured on an ellipsoid.

Datum ExamplesWGS84NAD27ED50Pulkovo 42SA69Minna

ECEFEarth Centered Earth FixedLatitude Longitude and Height can be converted to ECEF by means of a Helmert Transform.

ConflationHow do we conflate locations from two different Geodetic Datums?Latitude, Longitude & Height ECEFShift, Rotate and Scale ECEF VectorECEF Latitude, Longitude & HeightMolodensky Transform: XYZ Shifts onlyBursa Wolfe Transform: All operations

CartoLab DemoConflation of LatLonTransforms TabDefine CRS 1 Geodetic: 4267 NAD27Define CRS 2 Informal Geodetic: 4322 WGS72Pick Geodetic Transforms1170 for NAD27; 1237 for WGS72Transform point NAD27 Lat: 35.000000 Lon: -91.000000 H: 0.0 WGS84 Lat: 35.000072 Lon: -91.000060 H: -19.989 WGS72 Lat: 35.000037 Lon: -91.000214 H: -22.079

Other Conflation MethodsGrid Interpolation of Shifts (NADCON & NTV2)PolynomialMultiple RegressionSimple LatLon Shifts

HeightHeight is vertical distance above or below ellipsoid.We get it from GPS.If the ellipsoid is an imaginary surface, what good is height?

The GeoidAn imaginary surface where the force of gravity is 1 G.Covers the whole earth.a.k.a. Mean Sea Level.Defined under mountains.Irregular due to mascons.

Geoid vs. EllipsoidHeight = Elevation + Separation.Elevation is the vertical measurement used by the Oil Industry.Elevation determined from older vertical datums and by adjusting GPS height with separation.Separation models cover the whole earth.Separation known better in some places than others but, models improving.

Map ProjectionThe process of creating XY coordinates from Latitude and Longitude is called Map Projection.Light source at center of earth.Slide is the surface of the earth.Projection screen is a piece of paper.

The Orientation of Projection SurfacesCylindersCylindrical ProjectionsAxis Cylinder parallel to axis earth: NormalAxis Cylinder Perpendicular to axis earth: Transverse.Axis Cylinder at other odd angle: Oblique Normal Transverse Oblique

The Orientation of Projection SurfacesConesConic ProjectionsAxis of cone parallel to axis of earth: NormalAxis of cone at some other angle to axis of earth: Oblique Normal Oblique

The Orientation of Projection SurfacesPlanesAzimuthal ProjectionsPlane tangent at pole: PolarPlane tangent at equator: EquatorialPlane tangent at some other point: Oblique Polar Equatorial Oblique

The Positioning of Projection SurfacesTangentSecant

The Consequences of Map ProjectionWhen the 3D Earth is represented in a flat map projection, some kind of distortion must take place.Compression and Stretch (Variable Scale)

The Consequences of Map ProjectionDirectionality VariesWhich Way is North?Grids cannot be exactly transformed between map projections.How can you map a deviated well into a distorted system like a map projection?

CartoLab DemoAnalyze South Louisiana ZoneSet mode to NAD27 State Plane.Select Louisiana South ZoneAnalyze over:Lat 30.0 to 20.0Lon -100 to -80

Map Projection TerminologyMap projections are classified according to which earth attributes they preserve.Shape, Area, Distance & Direction.Conformal projections preserve the shape of objects. Or, angles between intersecting lines are preserved.Equal Area projections preserve the area of objects.Azimuthal projections preserve distance and direction.A map projection may do fairly well in terms of one or two attributes but, will always do poorly in the third.The Oil Industry uses Conformal projections almost exclusively.

Fundamental Map Projection ParametersEvery map projection has a Natural Origin.Usually is a user-specified point on the earth.It corresponds to another point in the system of projected coordinates. Typically users specify:A Latitude often called an origin latitude or base parallel. Sometimes equator is understood.A Longitude often called an origin longitude or central meridian.An X coordinate always called a False Easting.A Y coordinate always called a False Northing.Almost every map projection will have these four parameters. Sometimes a default is understood.

Transverse MercatorThe #1 map projection used by the Oil Industry. 90% of all Oil Industry maps are based on Transverse Mercator.A conformal projection based on a transverse cylinder.Cylinder is said to be tangent at some meridian called the Central Meridian.A scale factor gets multiplied against all XY locations reducing them and causing the cylinder to shift into a secant position.

Transverse Mercator Parameters

Transverse Mercator Graticle

Transverse MercatorNever use Transverse Mercator to map an area larger than 6 degrees of Longitude wide.Use Transverse Mercator on areas that trend basically North-South.

CartoLab DemoTransverse MercatorTransforms TabDefine CRS 2Recommendation Lat: 0, 30 Lon: -120, -115Analyze Lat: 0, 30 Lon: -120, -115 Lat: 0, 30 Lon: -117, -113Convert Lat: 25 Lon: -117

UTMUniversal Transverse MercatorSame projection algorithm as Transverse Mercator.A few special rules have been imposed to govern parameter setting.Origin Latitude is always the equatorFalse Northing is 0.0 for the Northern Hemisphere and 10,000,000 for the Southern Hemisphere.False Easting is always 500,000 metersScale factor is always 0.9996Earth divided into 60 zones each 6 degrees wide. Central Meridian is in middle of zone.Zone 1 has a Central Meridian of -177.0Zone 2 has a Central Meridian 6 degrees east at -171.0 etc.Parameters are only Zone Number and Hemisphere.CartoLab Demo

UTM Zones

Lambert Conformal Conic2 ParallelsThe #2 map projection used by the Oil Industry.A conformal projection based on a normal cone.Cone is secant about the earth at two parallels.

Lambert Conformal ConicParameters

Lambert Conformal Conic

Lambert Conformal ConicUsed to map areas that trend basically East-West.Should not be used to map areas greater than 6 degrees in Latitude extent.Should not be used to map areas that cross the equator.CartoLab Demo

State Plane Coordinate Systems

State Plane Coordinate SystemsNAD27An old Horizontal Datum.An irregular system of measurementStill used by the Oil Industry.XY in units of US Survey FeetBefore 1959: 1 meter = 39.37 inchesAfter 1959: 1 inch = 2.54 centimetersDefinitions differ by 2 PPMIn GeoFrame you must create a new units system wherein the geographical distance is ftUS in order to get correct NAD27 State Plane Coordinates.NAD83A modern Geodetic Datum

CartoLab DemoCompute XY on NAD27Set CRS1 to WGS84 datumSet CRS2 to NAD27 State Plane and select Louisiana South.Suspend WGS84 transformSelect (1170) NAD27 transformTranslate Lat: 30.0 Lon: -90.0X: 2422060.127 ftUSY: 486561.419 ftUS

Azimuthal EquidistantA very important map projection.A conformal projection based on an oblique plane tangent to the earth at a point.True distance and direction can be measured from the natural origin.

Azimuthal Equidistant

Azimuthal Equidistant

Azimuthal EquidistantUsed to map smaller areas.Do not use to map areas larger than 7 degrees of Latitude or Longitude.Azimuth (clockwise from North) shows up accurately when measured at the natural origin.Distance can be measured accurately from the natural origin.A good way to convert deviated well DX/DY offsets into Latitude and Longitude. Set natural origin exactly on top of spud location.

Coordinate Reference SystemsCRSA geodetic datumA prime meridianA map projectionA local coordinate systemA CRS is a fully detailed coordinate system such that a location in the CRS can be traced back to an exact location on the earth.

CartoLab DemoReview CRS 2 from previous demo.

Local Coordinate Systemsa.k.a. Engineering coordinate systems.Shift XY shift applied to projected coordinates. The XY point has projected coordinates and is called an Origin. Origin assumes coordinates of 0,0 after shifting.Scale reduce XY to Row/ColumnRotate Clockwise about the OriginSkew Angle between the X and Y axes is not 90

CartoLab DemoLay out a local CRS Generate graticleFor CRS2 from previous demo:Set rotation to 45Set skew to 75Generate array over:Lat 30.0 to 20.0Lon -100 to -80Set rotation to 0.0 and run again.

Cartography TutorialTutorialCartographic Traps

The EPSG DatabaseDemo

The End