GeodeticsCan we measure the true distances between us
[email protected]
Schlumberger Public
Schlumberger Private
Geodetic Positioning
Maps used in directional drilling are flat, but the earth is an
oblate spheroid.
How to represent the position of a physical point on or in the
spherical earth on a flat piece of paper.
There must be compromises to obtain an acceptable solution,
AND:
There will always be some error
[email protected]
Universal Studios in collaboration with MGM and Columbia Pictures
present
[email protected]
Geodesy
Geodesy is the study of the shape of the earth. It provides
Concept of latitude and longitude
A grid of imaginary lines on the surface of the earth providing a
reference system
The ellipsoid
The ellipsoid is the definition of the earth's “spherical”
shape.
Geodetic Datum
Mathematical surface that closely fits the mean sea level surface
throughout the area of interest
[email protected]
Geographic Latitude and Longitude
Parallel of Latitudes are circles drawn equally spaced, from the
Equator to each pole.
Longitude are imaginary lines intersecting at North and South pole,
striking latitude at right angle.
[email protected]
The concept of latitudes and longitudes was originated by Greek and
Egyptian scientists.
Grid of lines laid out on the surface of the earth.
Parallels of latitude
Meridians of longitude
Parallels of latitude
Small circles in planes parallel with that of the Equator
Defined in degrees, minutes, and seconds
Defined as
Meridians of longitude
Defined in degrees, minutes, and seconds
Prime meridian is defined to be 0 degrees.
West is 0 to -180 degrees
East is 0 to +180 degrees
Lengths of degrees of longitude vary with the latitude.
Azimuth can not be measured directly.
Distance can not be measured directly.
*
Small circles in planes parallel with that of the Equator
Defined in degrees, minutes, and seconds
Defined as
[email protected]
The concept of latitudes and longitudes was originated by Greek and
Egyptian scientists.
Grid of lines laid out on the surface of the earth.
Parallels of latitude
Meridians of longitude
Parallels of latitude
Small circles in planes parallel with that of the Equator
Defined in degrees, minutes, and seconds
Defined as
Meridians of longitude
Defined in degrees, minutes, and seconds
Prime meridian is defined to be 0 degrees.
West is 0 to -180 degrees
East is 0 to +180 degrees
Lengths of degrees of longitude vary with the latitude.
Azimuth can not be measured directly.
Distance can not be measured directly.
*
Defined in degrees, minutes, and seconds (format 200 11’ 10”)
Prime meridian is defined to be 0 degrees.
West is 0 to -180 degrees
East is 0 to +180 degrees
Lengths of degrees of longitude vary with the latitude.
[email protected]
The concept of latitudes and longitudes was originated by Greek and
Egyptian scientists.
Grid of lines laid out on the surface of the earth.
Parallels of latitude
Meridians of longitude
Parallels of latitude
Small circles in planes parallel with that of the Equator
Defined in degrees, minutes, and seconds
Defined as
Meridians of longitude
Defined in degrees, minutes, and seconds
Prime meridian is defined to be 0 degrees.
West is 0 to -180 degrees
East is 0 to +180 degrees
Lengths of degrees of longitude vary with the latitude.
Azimuth can not be measured directly.
Distance can not be measured directly.
*
Schlumberger Public
Schlumberger Private
The Ellipsoid
The oblate spheroid (squashed sphere!) is the principal shape used
in modeling the surface of the earth .
The flattening is only about one in three hundred but it makes
significant difference in calculations for the scale of maps used
in the oilfield.
[email protected]
With Geographic Latitude and Longitude, we can define the position
of a point on earth surface, but we can not measure distance of two
interest point. We need a model to simulate the shape of the earth,
thus be able to measure distance.
An ellipsoid is the general name of the volume obtained when an
ellipse is rotated about one of its axes.
Specifically, an oblate ellipsoid of revolution (oblate spheroid)
is an ellipse rotated about the shorter (semi-minor) axis.
The oblate spheroid is the principal shape used in modeling the
surface of the earth .
The flattening is only about one in three hundred but it makes
significant difference in calculations for the scale of maps used
in the oil field.
Radius at the north pole is 13 miles less than at the
equator.
*
The Earth is not an exact ellipsoid
For map projections, a constant ellipsoidal shape and size is used
for different region
Different reference ellipsoids are used for different regions of
the Earth
Over 50 ellipsoids in use today.
Approximately 15 ellipsoids cover 98% of the “oil country” areas of
interest
[email protected]
Earth is not an exact ellipsoid
Different dimensions of ellipsoids result from
varying accuracy in the geodetic measurements
*
[email protected]
Point out that ellipsoid is usually above and close to geoid over
the ocean.
Point out that ellipsoid is way under geoid in mountain area.
Emphasize that the earth’s surface shape is the main reason for
multiple ellipsoids. An attempt to get “best” fits for many shapes
has generated many ellipsoids.
169.bin
Schlumberger Public
Schlumberger Private
Geodetic Datum
A geodetic datum is a mathematical surface that closely fits the
mean sea level surface throughout the area of interest. It consists
of :
Ellipsoid
This is a significant political concept.
*
Schlumberger Public
Schlumberger Private
Map Projection
A mathematical formula that convert the latitude-longitude position
on the surface of a sphere into another method of positioning which
can be plotted onto a flat map with some degree of controlled error
and known accuracy.
The most common map positioning methods is X-Y Cartesian
coordinates.
[email protected]
Lambert Conformal Conic Projection
Schlumberger Public
Schlumberger Private
Lambert Projection
Projection of the earth on to a cone. The cone axis coincides with
the geographic poles axis of the earth.
Introduced by Johann Heinrich Lambert 1772
[email protected]
Lambert Map Projection
Greatest similarity that any plane figure can have with one drawn
on the surface of a sphere.
Meridians are equally-spaced radii of the concentric circular arcs
representing parallels of latitude.
Straight lines between points approximate great circle arcs for
maps of moderate coverage.
Most accurate for predominantly east-west regions
[email protected]
*
Lambert Map Projection
Two parallels may be made standard or true to scale. In the State
Plane Coordinate System (SPCS) for States, the choice of standard
parallels has the effect of reducing the scale of the central
parallel by an amount which cannot be expressed simply in exact
form
[email protected]
Two parallels may be made standard or true to scale. In the State
Plane Coordinate
System (SPCS) for States using the Lambert projection, the choice
of standard parallels
has the effect of reducing the scale of the central parallel by an
amount which cannot be
expressed simply in exact form, while the scale for the central
meridien of a map using
*
Universal Transverse Mercator (UTM) is the worldwide specification
of Transverse Mercator Projection
[email protected]
Universal Transverse Mercator (UTM)
World is divided up into 60 equal zones (each, therefore, 6° wide)
between 84° North and 80° South.
Polar regions are covered by other special projections.
[email protected]
Each zone has its own origin at the intersection of its central
meridian and the equator.
Each zone is flattened and a square imposed on it. Thus, its outer
edges are curved when
drawn on a flat map since they follow the meridian lines on the
globe. Each of the 60
zones is numbered, starting with zone 1 at the 180th meridian. The
areas East and West
*
Universal Transverse Mercator (UTM)
Zones are numbered 0 to 60 with zone 31 having the 0 degree
meridian (Greenwich) on the left and 6 degree E on the right
Each zone is further divided into grid sectors each covering 8
degrees of latitude, identified by a letter from C to X (I and O
excluded) but it is seldom used
[email protected]
Universal Transverse Mercator (UTM)
UTM GRID SECTOR ORIGINS
In longitude the origin (zero value) is a line 500,000m West of the
center meridian of the relevant grid sector (eg 3o E for zone
31).
In latitude the origin is at the equator.
GRID SECTORS
Grid sectors are divided into squares of 100 x 100 km and then
further divided into squares of 10 x 10 km.
[email protected]
UTM Zone Number
Northing
[email protected]
Coordinates
Easting
To avoid negative values, the CM in any zone is defined as 500,000
m.
At the equator a zone is about 600,000 meters wide, tapering
towards the polar region.
Eastings range in value from approximately 200,000 to
800,000.
Northings
0 meters at the equator and increasing toward the north.
Southern Hemisphere
*
Easting range in value from approximately 200,000 to 800,000.
Northing
0 meters at the equator and increasing toward the north.
Southern Hemisphere
[email protected]
Coordinates
Easting
To avoid negative values, the CM in any zone is defined as 500,000
m.
At the equator a zone is about 600,000 meters wide, tapering
towards the polar region.
Eastings range in value from approximately 200,000 to
800,000.
Northings
0 meters at the equator and increasing toward the north.
Southern Hemisphere
*
Means :
The rig is (500,000-410,250) = 89,750m West of CM of sector 31U and
6,850,000 m of Equator
[email protected]
24.unknown
Convergence
Convergence is the correction applied to convert True North to Grid
North.
At the central meridian, Grid North equals True North.
Convergence will vary with distance away from the central meridian
and with distance away from the equator.
Northern Hemisphere
Southern Hemisphere
Central Meridian has 0.9996 Scale Factor
Lines of True Scale (1 : 1) lie approximately 180 km to either side
of the central meridian.
Northern Hemisphere
Southern Hemisphere
Is applied to each survey
GN
TN
LONGITUDINAL
Schlumberger Public
Schlumberger Private
Grid Convergence
Grid Convergence
Convergence is the correction applied to convert True North to Grid
North
[email protected]
Schlumberger Public
Schlumberger Private
Grid Convergence
Grid Convergence
DEFINITION: The angle between True North and Grid North as measured
from True North
Easterly Convergence (clockwise) is positive
Westerly Convergence (anticlockwise) is negative
Convergence is SUBTRACTED from Corrected Azimuth
GN
TN
WEST
[email protected]
Governmental reporting requires the use of Grid North.
Under no circumstances should Schlumberger employees prepare or use
a well plan based upon a Local Coordinate System which uses
anything but Grid North.
Requests from a customer to do this should be directed to Senior
management and will be evaluated on a case by case basis.
[email protected]
Get across the errors when Grid North is not used.
A lot of people do not realize that most planning is done to grid
because of inheritance of “defining grid properties” of the start
and end points by the well plan.
*
Local Coordinate Systems
DD’s normally use a system of local coordinates for day-to-day
activities.
This local system depends upon and has a direct relationship to all
the concepts presented thus far.
Assumptions are often made in defining local coordinate systems
which are not obvious, but very important.
Care must be used in specifying local coordinate systems so that
all implicit and explicit relationships to “legal” coordinate
systems are preserved.
[email protected]
The local coordinate system concept is the sixth major building
block.
Some relationships are described as “implicit” because most people
are not familiar with them or do not recognize that the concept
applies.
Common implicit relationships to legal systems:
Orientation of axis
Definition of unit
Local Coordinate Systems
Must have its origin (0,0,0) at a point that can be positioned in
the “legal” coordinate system, which consist of :
Reference Point :
Field Reference Point
Vertical Reference Datum :
[email protected]
![%(=3(ý12671Ë /,67 1i]HY SURGXNWX 0U 3(3$ :KLWH .J ......%(=3(ý12671Ë /,67 1i]HY SURGXNWX 0U 3(3$ :KLWH .J SUDQt SUDFt SUiãHN SRGOH S tORK\ ,, 1D t]HQt (YURSVNpKR SDUODPHQWX D](https://static.dokumenty.site/doc/80x56/60da88f9606fe1521818057e/312671-67-1ihy-surgxnwx-0u-33-klwh-j-312671-67.jpg)
