Pajari Instruments Ltd., since 1945




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   Borehole Surveying Accuracy

The accuracy of a borehole survey is dependant on the characteristics of the instrument and the accuracy of the instrument alignment with the axis of the borehole. The instrument alignment in the borehole is controlled by using centralizers in the survey train with the instrument in between. The closer in size the centralizers are to the diameter of the borehole, the more accurate the instrument alignment with the borehole will be (Fig.1a). Some space must be provided between the centralizer and borehole diameters to permit efficient passage of the survey train.

If the borehole is near horizontal, a smaller diameter survey train will lie within the bottom of the hole with sufficient accuracy in many applications without centralization. Even in this case, the difference in the diameters between the survey train and the borehole will control the accuracy (Fig.1b). In addition, the survey train should rest on identical diameters so that tilting of the instrument on a larger diameter element in the survey train cannot occur (Fig.1c).

The matter of centralization is specific to each job and will need to be considered to arrive at a realistic appreciation of the accuracy of a borehole. In the following article, only the instrument accuracy will be considered.

  Instrument Characteristics

The manufacturer of the instrumentation usually provides guidance on the accuracy of the instrument readings. This varies from usually or generally +/- 0.X to precise maximum error expectations dependant on the angular position of the instrument. The variation results from the design of the instrument and the calibration methods used to define the error data. The accuracy will change with time and with some variable effects dependant on frequency and severity of use.

The Pajari Instruments micro-mechanical Tropari Instrument is calibrated as follows:

  • Azimuth (magnetic/compass) is calibrated to read within 0.5 of the instrument orientation in all four quadrants in the earths natural magnetic field at 0.6 gauss. The maintenance of accuracy is dependent on severity of use. The benefit of micro-mechanical instruments is that the accuracy can be determined in the field with simple tests (see - Tropari SDP - Checking Sensitivity).

  • Inclination is determined by a plumb device being locked into protractor teeth spaced at 1 intervals. The maximum error of a reading is therefore +/- . As with azimuth, the accuracy is dependant on the sensitivity of the specific pivots or bearings involved. If these are sensitive to small movements, the error is within Pajari Instruments specified error (see website on sensitivity for more detail).

  • The Tropari is a single-shot instrument using a preset time to activate the locking cycle. The timing mechanism will change with time and eventually this may cause errors when an instrument is being lowered within the 10 minute locking cycle or retrieved before it is fully locked. Timing can be calibrated in the field and therefore does not require servicing for changes in the timing function alone.



The e-SYNC-i or e-SYNC-t instruments are based on electronic sensors of various types. Electronic sensors have characteristics that apply to all electronic instruments. The accuracy of an electronic instrument is dependant on how it is manufactured, how the data is interpreted and how it is calibrated. All electronic sensors change with time and use. Recalibration must be done in a suitably equipped laboratory within a set recalibration frequency.

  • The e-SYNC series of instruments possess thermally and directionally calibrated sensors that are verified directionally once these are incorporated into the instrument. A complete record of this calibration is electronically stored for comparison at each re-calibration. The recalibration frequency is set at 18-24 month intervals and with the e-SYNC series, all corrections are made by inexpensive software methods.

  • Vibration affects the output accuracy of many sensors. The e-SYNC series notifies the user of the severity of vibration at the time the test was made.

  • The standard accuracy for e-SYNC series is +/- 0.5 for inclination. This represents the largest error at any inclination. Most inclinations are more accurate than this figure. If more accurate calibration data is required for a specific inclination interval, consult our technical personnel. The e-SYNC series instruments are extremely rugged and are individually tested to withstand the quoted hydrostatic pressure and normally expected shock conditions. Shock conditions leading to instrument failure will leave interpretable injury on the exterior of the instrument. If higher shock or pressure ratings are required, please contact our technical personnel.

  • The e-SYNC instrument readings can be customized to specific industry practices by referencing the 0 index to any inclination position (i.e. horizontal, up, down etc) and the direction rotation to clock-wise or counter clock-wise for both inclination and tool-facing.

  • The tool-facing accuracy of the e-SYNC-t is +/- 1.




Figure 2 shows an inclination reading (heavy line) taken with an instrument at the top of the prism. The maximum error angle (from instrument specifications) inscribes the maximum error circle at depth D. The actual borehole will, therefore, be somewhere within the maximum error circle at depth D. It is obvious from Figure 2 that the area of the circle increases as the depth D increases.

The radius of the maximum error circle is calculated by trigonometry from the distance D and maximum error angle by:

Radius = tan error angle X D

We can look at some examples of this calculation to gain a perspective of the maximum error distance represented by the radius.








10 m/ft

0.017m/ft 0.087 m/ft 0.175 m/ft 0.349 m/ft 0.875 m/ft

50 m/ft

0.087 m/ft 0.436 m/ft 0.87 m/ft 1.75 m/ft 4.37 m/ft

100 m/ft

0.17 m/ft 0.87 m/ft 1.75 m/ft 3.49 m/ft 8.75 m/ft

500 m/ft

0.87 m/ft 4.4 m/ft 8.73 m/ft 17.46 m/ft 43.74 m/ft

1000 m/ft

1.74 m/ft 8.7 m/ft 17.46 m/ft 34.9 m/ft 87.49 m/ft

10,000 m/ft

17.4 m/ft 87.2 m/ft 174.6 m/ft 349 m/ft 874.9 m/ft

Use consistent units

For instruments that provide inclination measurements only, the radius measurement finalizes the error definition.




The rotational orientation of a tool around the axis of the borehole is the tool-facing measurement. Tools that require their facing direction to be measured include cameras, wedges, directional drilling devices, casing cutters, core orientation equipment, x-ray and ultrasonic devices. Tool-facing surveys are procedure specific and require accessories (running gear) that are not required in the directional survey of the borehole heading. At Pajari Instruments we emphasize the fact that directional surveying and tool-facing are separate procedures, each with their specific requirements of accuracy, efficiency, and costs.

Figure 3 illustrates the tool facing measurement system with an e-SYNC-t. The standard instrument will give a 0 reading when the index mark on the instrument is vertical upward in the borehole irrespective of the inclination of the hole. 

The instrument is attached to the applicable tool and secured with the index marks of the instrument and the tool being longitudinally aligned. Alignment can be accomplished by variable thickness washers between two threaded units or by using an alignment coupling.

The +/- error envelope for the tool-facing reading defines the maximum error expected from the instrument. However, instruments which measure tool-facing by plumb devices (gravity sensors/pendulums) cannot give a tool-facing in vertical holes. The accuracy decreases rapidly in the last few degrees approaching vertical and is not measurable at vertical. Instruments which read tool-facing from gyro, gyro-compass or north-seeking gyro instruments will give the tool-facing in vertical holes to the azimuth accuracy of the instrument. If the tool-facing in near vertical holes can be surveyed at least 6 meters (20 ft) away from ferromagnetic metals, tool facing can be done to azimuth accuracy with magnetic compass based instruments.




The azimuth error envelope imposed on the inclination maximum error circle creates a wedge shaped area that contains the borehole location at depth D. Figure 4  illustrates  the relationships between the inclination and azimuth error envelopes.

The maximum azimuth error envelope (+/- X) can be calculated to give distance along the circumference (C) and area for a specific calculated maximum inclination error radius (R) as follows:

C= [2(+/- X)/360] * π2R

And for area (A):         

A= [2(+/- X)/360] * πR

Table 2 provides a perspective of the combined inclination and azimuth error envelopes for a few examples.

TABLE 2 Area of Azimuth Error Envelope

R Azm. +/- 0.5 Azm. +/- 1.0 Azm. +/- 2.0 Azm. +/- 5.0
1 m/ft A= 0.017m/ft A= 0.087m/ft A= 0.174m/ft A= 0.436m/ft
5 m/ft A= 0.436m/ft A= 2.18m/ft A= 4.363m/ft A= 10.91m/ft
10 m/ft A= 1.74m/ft A= 8.73m/ft A= 17.45m/ft A= 43.63m/ft
50 m/ft A=43.6m/ft A= 218.2m/ft A= 436.3m/ft A= 1090m/ft
100 m/ft A= 174.5m/ft A= 872.7/ft A= 1745m/ft A= 4363m/ft


Pajari Instruments Ltd. 2015

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