Oil companies underscore importance of geodetic positioning

July 6, 1998
Equations [4,478 bytes] Table 1 [5,471 bytes] Table 2 [3,040 bytes] Table 5 [5,386 bytes] Positioning errors can be introduced from a variety of geodetic sources, dramatically influencing the success of a drilling program. An incorrectly spotted well location can result in drilling on the other side of a lease line or lead to a dry hole ( Fig. 1 [36,344 bytes] ).
Martin Rayson
Quality Engineering & Survey Technology Ltd.
Newcastle, U.K.
Positioning errors can be introduced from a variety of geodetic sources, dramatically influencing the success of a drilling program.

An incorrectly spotted well location can result in drilling on the other side of a lease line or lead to a dry hole ( Fig. 1 [36,344 bytes]).

Today, positioning relies heavily on satellite navigation technology. Although satellite-positioning technologies offer significant benefits over terrestrial counterparts, its use introduces additional geodetic parameters that must be correctly integrated into the mapping project.

Geodesy-the science concerned with the precise positioning of points on the Earth's surface along with the determination of its exact size and shape-has long been considered a "black box" science (Fig. 2 [30,838 bytes]). This article addresses some of the myths and pitfalls that surround its practical use.

What follows is a series of recent field examples detailing geodetic problems along with a discussion of the associated theory, accompanied by step-by-step procedures for correcting the problems. All the coordinates given in this article are theoretical and do not actually relate to actual surface locations.

The datum transformation

The datum transformation, or the mathematical conversion of geographic coordinates from one reference ellipsoid to another, is currently the single largest cause of geodetic error. The coordinates used to describe a position must be intrinsically linked to a reference frame, which in turn has a specific reference spheroid ( Fig. 3 [33,266 bytes]).

The two are combined to create a local or global datum. For coordinates to have any physical meaning, the datum must always be listed for precise reference. The datum serves as an anchor for tying cartesian coordinates or latitudes and longitudes to the coordinate system. Excluding this information leaves the user stranded in terms of position.

For instance, if a user is supplied with a longitude and latitude of 02° 42' E and 33° 18' N, but the datum is not given, then the position on the Earth will still remain unknown.

This oversight is often neglected and causes confusion, leading to mis-ties when two or more data sets, of different vintages, are combined. A comparison of an older and newer system shows an example of this. In Trinidad and Tobago, most legacy survey activity is related to the Old Trinidad Datum of 1903 (OTD 1903).

However, in common with all current exploration regions, more recent survey work utilizes GPS (geographic positioning system) for navigation and positioning purposes.

GPS receivers, as a default, derive coordinates on the WGS 84 datum (World Geodetic System 1984). As such, for a typical mapping procedure it becomes necessary to convert coordinates from the WGS 84 datum to the local working datum (OTD 1903 datum). This process utilizes a series of datum transformation parameters.

Trinidad procedure

Using a recent example from Trinidad, a drilling location was identified using a 3D seismic data volume, derived in the WGS 84 datum. However, the local geologists and engineers required coordinates for the location to be converted to the OTD 1903 datum, necessitating a datum transformation from WGS 84.

The geodetic coordinates of the location, as given in WGS 84, were:

60° 35' 26" W
10° 29' 45" N
The OTD 1903 coordinates originally derived by the oil company's geophysicist were:
60° 35' 23.14" W
10° 30' 05.12" N
Note the numeric difference between the two longitudes and latitudes. In reality, they are the same physical location, yet because they are tied into different datums, they produce different values of latitude and longitude, disproving the myth that longitudinal and latitudinal values are always the same.

A survey company was contracted to position the drilling rig at the location using the above given coordinates. Prior to the rig move, the company surveyor had the foresight to recompute the OTD 1903 datum transformation, deriving the following, incongruous location:

60° 35' 28.86" W
10° 29' 31.64" N
His computation resulted in a discrepancy of 1,043 m, or more than 1 km. This difference was even more clearly illustrated when the geodetic coordinates were projected to UTM Zone 20 grid coordinates:
Incorrect point:
1161864 11 m N
763809.47 m E
Correct point:
1160833.65 m N
763643.35 m E
The problem was then handed to an independent auditor for verification, resulting in the confirmation of the second set of parameters. The rig was eventually moved to the correct location and a significant drilling error averted.

How can such a difference occur and how can it be prevented? To understand this, it becomes necessary to discern the theory behind datum transformation and its parameterization.

The seven basic parameters

The datum transformation is a mechanism whereby coordinates expressed in one datum are converted to coordinates expressed in another datum, such as WGS 84 to OTD 1903.

The conversion process requires a mathematical model, consisting of seven basic parameters, which define the difference between the two datums ( Fig. 4 [8,621 bytes]).

The seven parameters consist of:

  • Three translation parameters-The difference between the spheroidal centers, expressed by dX, dY, and dZ (all in meters) within the Cartesian coordinate frame. The translation parameters are sign dependent. For example, to go from WGS 84 to OTD 1903, the parameters may be:
    dX = 61.00 m
    dY = 2285.00 m
    dZ = -471.00 m
    Whereas, to go from OTD 1903 to WGS 84, the magnitude of the translation parameters are the same but their signs are reversed.
  • Three rotation parameters-Rotations about the X, Y, and Z axes which align the axes of the spheroids (seconds of arc). Two principle rotation conventions are used. The first is the position vector rotation (Bursa-Wolfe model), which has a positive clockwise convention. The second is the coordinate frame rotation, which has a positive anti-clockwise convention.
  • One scale parameter-Matches the size of the two spheroids (parts per million).
Using the example for Trinidad and Tobago, a correct four-step procedure for the datum transformation is as follows:

First, on the WGS 84 datum, convert the geodetic coordinates to Cartesian coordinates using the WGS 84 reference ellipsoid parameters ( Fig. 5 [13,313 bytes], semi major-axis and inverse flattening).

Second, enter the Cartesian coordinates (Datum 1) along with the given transformation parameters into datum transformation Equation 1, assuming the positive clockwise convention (see Equation 1 in Equations box).

Third, compute the Cartesian coordinates (Datum 2) of the position in the OTD 1903 datum. Finally, convert the Cartesian coordinates to geodetic coordinates using the OTD 1903 reference ellipsoid parameters.

Often the datum transformation is simply expressed by the three translation parameters as provided in Defence Mapping Agency publications. In such cases, the datum transformation equation can be simplified (see Equation 2 in Equations box).

In the Trinidad example, a three-parameter transformation was used. However, in the first computation, an error occurred when the incorrect signs were applied to the translation parameters. For instance, OTD 1903 to WGS 84 was used rather than the opposite.

This is a common a problem and care should be taken to ensure the correct direction is applied.

Sign conventions

In Peru, a land-drilling location was defined in the WGS 84 datum, requiring the datum to be converted to the local Provisional South American datum of 1969 (PSAD 69). The WGS 84 coordinates were converted using a seven-parameter transformation model with government sources providing the parameters.

The results of the transformation were considered uncertain as a result of mis-ties with an existing data set. The transformation was recomputed by an independent source with comparisons provided in Tables 1 and 2.

The computations resulted in a radial separation of 890 m. Applying the wrong sign convention to the rotation parameters produced a crucial error. The rotation parameters supplied by the Peruvian authorities used a positive anticlockwise convention. Conversely, the software program used to perform the initial transformation applied a positive clockwise convention.

This necessitated altering the signs on the rotation parameters to fit with the software format. Fortunately, the error was corrected prior to the rig arriving on location. Computer software conversion programs must be used with care.

Mis-spotted well heads

A well head survey was performed on behalf of an oil company to determine the new surface position for three wells drilled during the late 1970s. A conversion was needed to integrate well logs with a recently acquired 3D seismic volume using coordinates in a UTM map projection referenced to the WGS 84 datum.

A survey contractor was requested to provide the well head coordinates. Unfortunately, large discrepancies between the previous known coordinates (first survey) and the new coordinates (second survey) were found, coinciding with a radial difference equal to that between the local datum and WGS 84 datum.

The contractor was asked to confirm the well head coordinates. The contractor replied, as before, that all well head positions were correctly referenced to the WGS 84 datum. The company therefore assumed that a labeling error occurred when the wells were originally drilled.

The shift in position of one particular well meant a serious reconsideration of the field's reservoir potential. After experiencing difficulty in matching the well logs to the seismic volume, a third, one-well survey was conducted to reconfirm the new well position.

The third survey used the WGS 84 datum with similar survey tools incorporated in the first survey. The third survey revealed that the new well coordinates from survey two were wrong, and that the coordinates from survey two placed the well very close to the original position.

The first contractor was again asked to examine the navigation data from its survey, in particular, the Integrated Navigation System parameters. It became apparent that the first contractor had applied a series of datum-shift parameters throughout the whole survey that had not been removed. Therefore, all positions had been automatically transformed from the WGS 84 datum to the local datum.

As a result the well was moved back to its central reservoir location. Mis-spotted well heads, if integrated with seismic interpretation, can dramatically alter the interpretation of a reservoir's characteristics. Old well locations must be carefully checked to ensure they are integrated into the interpretation.

Converting map projections

An example that involves problems associated with map projections-the conversion of longitude/latitude to planar grid coordinates and vice-versa-came about recently when an oil company instructed a survey contractor to convert a well location from UTM Zone 31 North cartesian grid coordinates (ED 50 datum) to a WGS 84 datum.

The ED 50 datum is as follows:

6493700.00 m N
413200.00 m E
The rig locality was computed using a GPS surveying tool, and the rig position was initially described in the following geodetic coordinates referenced to the WGS 84 datum:
58° 34' 23.123" N
01° 30' 21.342" E
Next, the survey contractors transformed the coordinates to UTM Zone 31 cartesian coordinates, referenced to the ED 50 datum, in two steps:
  1. Convert the geographical coordinates from WGS 84 datum to ED50 datum using a three-parameter shift:

    58° 34' 25.324" N
    01° 30' 27.262" E
  2. Convert the ED50 geographical coordinates to UTM Zone 31 grid coordinates using the standard parameters and software package:

    6493698.50 m N
    413199.33 m E
The final coordinates were sufficiently close to those requested by the oil company, thus the survey contractor considered its work complete and submitted a report to the oil company.

Unfortunately, the report erroneously labeled the final position as being referenced to WGS 84 datum rather than ED50 datum, although the rig had actually been positioned correctly.

The drilling department took this as an oversight on the contractor's behalf and initiated an unneeded coordinate conversion from the WGS 84 datum to the UTM Zone 31, ED50 datum. The final coordinates generated the following:

6493913.28 m N
413291.15 m E
This introduced an apparent error of 234 m and caused the company to take immediate steps to suspend drilling operations and relocate the rig.

Grids

A grid is the most convenient way of representing positions on a map, consisting of a series of intersecting lines that represent Northing and Easting departures from some point of origin. All map projections follow the same grid convention.

Although the parameters used to describe the map projection differ between projections, there remains one underlying constant, the associated datum. This is because all coordinates expressed on a grid are projected from geographical coordinates, and these coordinates are tied to the Earth through the datum origin.

Just because coordinates have been converted to a plane grid, does not mean they became disassociated from the datum. Therefore, when grid coordinates are listed, it is imperative that the associated datum also be listed (UTM Zone 42 North, Indian datum 1830).

Without knowledge of the datum, grid coordinates cannot be confidently converted back to geographical coordinates, unless an assumption is made.

Universal Transverse Mercator

The most widely used grid system is the Universal Transverse Mercator (UTM) grid. This internationally accepted grid uses simple transformation formulae to convert between geographical and grid coordinates and involves simpler division of map sheets.

It is important to understand the theory behind UTM grid conversions with other systems in international work, especially for those companies that work in China and Russia.

The UTM grid consists of 60 x 6-degree TM zones, resembling segments on an orange. Zone 1 begins at 180° west and extends to 174° west. Zone 60 begins at 174° east and extends to 180° east.

East of Greenwich (0°) is Zone 31 (0 to 6° east) and west is Zone 30 (0 to 6° west). The origin of the grid system is expressed by an origin of longitude, called the Central Meridian (CM) and an origin of latitude.

The CM represents the central longitude of the zone. For Zone 31, it is 3° east and for Zone 30 it is 3° west. The origin of latitude is always 0° (equator).

The grid origin is assigned false Easting and false Northing values. This prevents any value within that Zone from becoming negative. False Eastings of 500,000 m and false Northings of 0 are assigned to UTM Zones in the Northern Hemisphere; while a Northing of 10,000,000 m is applied to the Southern Hemisphere. All survey units are quoted in International meters.

The UTM projection suffers distortion as the cylinder is projected onto a plane. As such, a scale factor is used at the CM to limit distortion over the expanse of the UTM Zone. The scale factor on the CM is always 0.9996, meaning the TM cylinder is made slightly smaller than the sphere (secant).

Because the UTM coordinate system is identical in each Zone, different positions on the earth's surface can have identical coordinates. To avoid confusion, the Zone number must always accompany UTM grid coordinates.

One restriction of the UTM grid is that it only extends from 80° south to 84° north. Geographical areas outside these limits must not be mapped using a UTM map projection.

China grid system

In China, there are several national and local map projections that can be utilized, although the China grid system is most common. For example, in a recent well head survey performed by a Chinese survey company, final well head coordinates were supplied to an oil company in the China grid system.

The China grid system operates in 6-degree bands from Zone 12 through Zone 23 ( Table 3 [4,014 bytes]). The latitude origin is 0°, the false Easting origin is 500,000 m, while the false Northing is 0 m. The scale factor is 1.0, as compared to 0.9996 for the UTM Grid System, and all coordinates are described in international meters.

The China grid system is similar to the Universal Transverse Mercator (UTM) projection in most respects, with the exception of scale factor ( Table 4 [7,374 bytes]).

A foreign oil company new to China performed a geodetic survey to redetermine surface coordinates for a series of well heads scattered throughout its concession block. The contract was awarded to a local Chinese survey company, and the final geographical and grid coordinates for the well heads were supplied in the Beijing 1954 Datum.

However, the datum and map projection of data was not clearly labeled except for some projection parameters. Because of the nature of the parameters and inexperience, the grid coordinates were interpreted by the company as belonging to a UTM projection.

Subsequently, a drilling location was selected in the U.S. office and the well location coordinates were transmitted back to China. Because the company assumed the previous grid coordinates were provided in the UTM projection system, the new drilling location was labeled as a UTM grid (Beijing 1954 datum).

Upon receiving the coordinates, the Chinese survey company converted the grid coordinates from the UTM grid system to its own China grid system, then began plans to construct a temporary road to that location.

The Chinese authorities noticed the new location appeared wrong on their maps, and the confusion was corrected, preventing a radial error of about 1,374 m from being introduced to the drilling location.

When operating within a new region for the first time, it is essential that all geodetic and mapping parameters be identified and checked prior to any commencement of operations.

Height discrepancies

A 2D land seismic survey, completed in the 1970s, was positioned using traditional terrestrial survey tools. All height information for the survey was derived relative to mean sea level (orthometric heights), but not clearly documented.

Some years later, a drilling location was selected using seismic data, followed up with the spotting of a rig using GPS. Although the horizontal surface location was deemed satisfactory, there was a major discrepancy between the height derived from the original survey and the GPS survey.

This caused great concern, especially because a drilling target's true vertical depth is calculated from this information.

The height elevations, determined from GPS surveys, were related to the reference spheroid (WGS 84 spheroid) instead of Mean Sea Level. All height information must be reduced to a common vertical datum before elevations from different sources can be correctly integrated. Typically, Lowest Astronomical Tide is used as the vertical datum.

These examples illustrate only a few of the internal and external positioning and surface mapping problems that companies must overcome and avoid in the search for hydrocarbons. Bidirectional geodetic datum shifts and map projection conversions are commonly performed in international work, but handling of the data, and treatment of the calculations, should never be considered a routine affair.

The Author

Martin Rayson is a geodesist and a director of Quality Engineering & Survey Technology Ltd. (Quest). He holds a BS in applied sciences from the University of Kingston (1984), an MS in geophysics and planetary physics from the University of Newcastle (1985), and a PhD in geodesy and geophysics from the University of Newcastle (1989). From 1989 to 1994, Rayson worked for Geoteam U.K. and Halliburton Energy Services. He has been with Quest for the past 4 years, providing advanced geodetic and geophysical solutions to the hydrographic and land survey industries.

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