- "Geographic Coordinate Systems" and "Projected Coordinate Systems" in ArcGIS and ArcMap
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- Coordinate Systems and Map Projections
- What are Map Projections?
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- What are projected coordinate systems?
- Coordinate Systems
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- Map Projections and Coordinate Systems
"Geographic Coordinate Systems" and "Projected Coordinate Systems" in ArcGIS and ArcMap
Accurately describing locations on Earth is essential to exploration geophysics. The interpretation of fault zones, the surface and bottom locations of a well, and the position and orientation of seismic ground control points and receivers are all dependent on being able to accurately describe where they are.
Unfortunately the latitude and longitude of a location and the height are not enough to describe where on Earth it is. There are numerous datums and projections to which the coordinates are referenced, and using the correct one can make the difference between successful exploration and expensive legal fees. There are also numerous applications for analyzing and interpreting spatial data, all of which have different methods for representing a three-dimensional position in two-dimensional space.
Assumptions are dangerous, and not all spatial data is acquired and delivered in the same way. The location of a coordinate in one datum will be different for the same coordinate in another datum.
Understanding the spatial data acquisition methods and the idiosyncrasies of individual applications will allow users to take the correct action to make decisions that ensure positional integrity and accuracy in exploration geophysics. This article describes the theory behind datums, projections and coordinate systems, and highlights the importance of using the correct one for a given purpose.
The terms datum, projection and coordinate system are often misinterpreted and misunderstood.
A datum is simply a foundation and reference for spatial measurements. A system of coordinates is then used to describe those measurements relative to the datum, and a projection is the visual representation of those measurements on a different surface. There are many datums and coordinate systems, each representing a different level of accuracy in different regions around the globe.
A coordinate system and its datum are therefore required to determine accurate locations, and unless a perfect scale model of the Earth is used, it will be necessary to use a projection to visually represent those locations on a different surface.
The following sections describe datums and projections in more detail. A datum is a reference frame that enables a system of coordinates to describe positions in three-dimensional space. The sphere has a known mathematical model that can describe the position of any point at height h above its surface, as shown in Figure 1. Now consider an ellipsoid as a reference frame, which also has a known mathematical model that can describe the position of any point at height h above its surface, as shown in Figure 2.
A more accurate representation — based on the approximate mean sea level — is called the geoid, but requires gravity measurements and the determination of the gravity potential, the theory for which will not be covered in this article. For example, rather than aligning the center of the reference frame with the center of mass of the Earth, the reference frame can be shifted such that its surface coincides with the surface of the geoid in a regional area. This enables positions in the regional area to be described with greater accuracy.
Figure 3 and 4 show the differences between a geocentric reference frame and a regional reference frame. While the geocentric reference frame is a good approximation of the entire geoid, the regional reference frame is usually a better approximation in a regional area Anzlic Committee on Surveying and Mapping ICSM , Two horizontal datums are often used in Canada today.
NAD27 is a regional datum based on a reference ellipsoid that was determined in Clarke NAD83 is a geocentric datum based on a reference ellipsoid that was determined in Geodetic Reference System , over one hundred years later Statistics Canada, Thanks to improved satellite gravity measurements, the differences in height between the geoid and the reference ellipsoid geoidal undulation can be used to provide a more accurate vertical datum, which is important for determining three-dimensional positions e.
Coordinate Systems and Map Projections
Making a similar error during or after drilling could result in failure to reach an intended mineral target, or produce from a zone outside a mineral lease, possibly resulting in a dry well or mineral trespass, respectively.
In addition to the penalty, compensation may be owed to the Crown for the value of any minerals obtained during trespass Alberta Energy Regulator, Figure 5 is a contour plot showing the approximate transformation shift in meters between a coordinate in NAD27 and the same coordinate in NAD83 across the province of Alberta. The magnitude of the transformation shift increases in the North-West direction, continuing into British Columbia, Yukon, and Alaska.
A projection is a two-dimensional representation of a three-dimensional surface.
What are Map Projections?
Paper maps, web maps and mapping applications represent the Earth in two dimensions and therefore require spatial features on its surface to be projected. However, projecting these spatial features will always induce distortion either by area, shape, scale or angle.
A perfect three-dimensional scale model of the Earth is the only way to eliminate all four distortion types. There are many different projections available, and using an appropriate projection depends entirely on the purpose and function of the map. Some projections maintain accurate geographic areas, while others maintain accurate shapes and angles, such as the Transverse Mercator used for nautical navigation.
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Geological Survey, Figure 7 shows an example of four different projections using Tissot's indicatrix, and how the distortion characteristics differ between them.
While a geographic coordinate system is a spherical representation of positions described using angles from central lines of latitude and longitude, a projected coordinate system is a planar representation of positions described using x and y coordinates from a central x and y axis.
The UTM projection uses its own central meridian from which to derive positions within its zone. The central meridian is given a false Easting of m with values increasing from West to East, therefore eliminating negative numbers for the entire width of the zone.
Scale factors are ratios of the scale along meridians and parallels compared to a standard line of true scale.
These scale factors determine the scale distortions for measurements on a projected surface. The central meridian in each UTM zone is given a constant scale factor of 0.
Since the scale factor increases with distance in the East and West directions, two vertical lines of true scale 1. The maximum variation in each zone reaches 1 part per 1 ppt from true scale at the Equator U.
Reducing the longitudinal width of a single UTM zone is necessary for reducing scale distortions, but presents a problem when describing spatial features that span more than one UTM zone.
As you can see from the contour plot, the scale factor dramatically increases in magnitude for points that are located outside the zone in which they were projected. Analyzing spatial data using an appropriate projection is therefore critical to minimizing scale factor errors.
The term coordinate system refers literally to a system of coordinates, which in the context of this article is a unit of measure for determining locations relative to a reference frame.
This should not be confused with the term coordinate reference system CRS , which is used to describe a coordinate system, a datum, and optionally a projection, collectively. Many software applications allow users to specify a CRS geographic or projected rather than having to define a coordinate system, a datum, and a projection individually.
The following sections identify some of the key factors when using coordinate systems, datums and projections in various applications.
The area of interest is defined by the extent and coverage of spatial data, and each area of interest should be treated differently, whether global, regional, or local. Many different datasets covering many different areas of interest are often used collectively in a single geophysics project. Separating a large project into smaller areas of interest that can be defined by a specific CRS may improve the accuracy of results.
Transformations are required whenever there is a datum difference between the data source and destination. As mentioned earlier, the differences between NAD27 and NAD83 datums can lead to significant positioning errors, so a method is required to transform the CRS parameters of the source to match the CRS parameters of the destination.
Using the appropriate transformation method ensures positional integrity, but — like the CRS — there are many transformation methods to choose from. Many software applications will try to perform the transformation automatically, but using the default method can be dangerous. In some cases a transformation must be applied to spatial data before it can be used, especially when the transformation method is either obscured or not possible within the software application itself Berls, n.
If a custom CRS is used in an application, then a custom transformation may also be required in order to transform the data appropriately. There are no explicit rules regarding the collection, analysis and interpretation of spatial data for geophysical exploration, but understanding the theory behind datums and projections provides an awareness of the limitations and impacts that occur from decisions surrounding location accuracy.
Uninformed decisions can lead to inaccurate interpretation and undesired results, potentially leading to financial, legal, regulatory, and environmental implications.
What are projected coordinate systems?
I would like to thank Brady Troyer, P. Steve Jensen, P. Alberta Energy Regulator. Petroleum and Natural Gas Tenure in Alberta. Edmonton: Alberta Government. Albrecht, J. Map Projections and Distortion. Fundamentals of Mapping. Berls, N. Natural Resources Canada.
Sanz Subirana, J. I: Fundamentals and Algorithms.
Noordwijk: European Space Agency Communications. Statistics Canada. Surveyor General Branch. National Standards for the Survey of Canada Lands.
Edmonton: Natural Resources Canada. Geological Survey. Map Projections — A Working Manual. Washington: U. Weisstein, E.
About the book
Spherical Coordinates. Etris, Nick J. Crabtree and Jan Dewar Errors and Omissions A large volume of data is being converted to make this online archive. If you notice any problems with an article examples: incorrect or missing figures, issue with rendering of formulas etc.
The CSEG does not endorse or warrant the information printed. Methodology The terms datum, projection and coordinate system are often misinterpreted and misunderstood. Datums A datum is a reference frame that enables a system of coordinates to describe positions in three-dimensional space.
Figure 1. A mathematical model to determine Cartesian coordinates relative to a spherical frame Weisstein, Figure 2.
Map Projections and Coordinate Systems
Figure 3. An example of a geocentric reference frame relative to the geoid — not to scale. Figure 4.