P.G.Killeen, G.R.Bernius and C.J.Mwenifumbo, Surveying the Path of Boreholes: A Review of Orientation Methods and Experiences; in Proceedings of the 6th International MGLS Symposium on Borehole Geophysics for Minerals, Geotechnical and Groundwater Applications; Santa Fe, New Mexico, October 22-25, 1995.
Boreholes are designed to obtain information in the third dimension, ie. at depth, below the two-dimensions of the earth's surface. Today it is relatively easy to determine position on the surface, but not so at depth. Unfortunately, all too often, the path of the hole is erroneously assumed to follow the original dip (or inclination) and azimuth (or direction) established at the collar, at the top of the hole. Numerous borehole surveying devices have been developed, none of which are perfect, however quite accurate results are possible by using the right tool in the right hole.
Surveying a borehole is usually accomplished by moving a probe along the hole and sensing the movement of the probe relative to one or more frames of reference which may include the earth's gravitational field, magnetic field or other inertial reference, and/or by sensing the distortion or bending of the housing of the probe itself. The different methods each have their own advantages and limitations such as ability/inability to operate inside steel casing, speed and complexity of operation, accuracy, cost, distance between measurements, ruggedness and reliability.
The Borehole Geophysics Section of the Geological Survey of Canada has reviewed and compared many of the available methods, and has experience surveying a borehole with five different commercially available systems. There is no 'winner', but a review of the above-mentioned is useful in selecting the appropriate borehole surveying methodology.
Only under ideal conditions will the path of a drilled hole follow the original dip (or inclination) and azimuth (or direction) established at the top of the hole. It is more usual that the borehole will deflect away from the original direction as a result of layering in the rock, the variation in the hardness of the layers, and the angle of the drill bit relative to these layers as illustrated in Figure 1. The drill bit will be able to penetrate the softer layers easier than the harder layers, resulting in a preferential direction of drill bit deviation. In some areas experienced drillers have been able to predict the deviation somewhat, and adjust the dip and azimuth of the collar of the hole such that when the drill reaches the desired depth, it will be travelling in the desired azimuth and dip. Deviation of the borehole is encountered in both 'soft-rock' and 'hard-rock' drilling. In base metal exploration for example, the strata being drilled are usually geologic units in a volcanic pile, often dipping very steeply. Drilling perpendicular to a steep dip is almost impossible and the drill bit will definitely penetrate the layers at a more shallow angle than 90 degrees.
Because the purpose of a borehole is to obtain information in the third dimension, i.e. at depth, the location is just as important as the information itself. Most often the information consists of the geology of the drill core, or assays of the core at selected depths. If the hole has deviated significantly, then that information can not be properly assigned to a location in 3-dimensional space beneath the earth's surface. Conclusions about geological structure or models of the size, shape, tonnage and average grade of ore-bodies based on the 'mis-placed' information may be erroneous.
Numerous borehole surveying devices have been developed, none of which are perfect. However, quite accurate results are possible by properly using the right tool in the right hole. Surveying the path of a borehole is referred to as a borehole 'orientation' survey or a 'deviation' survey, and 'dip' at any point refers to the angle between the horizontal and the path of the hole. 'Inclination' is used by some workers to refer to the angle between the vertical and the hole, although in some literature inclination is used (incorrectly) as a synonym for dip. Another confusion is created by the logging tool called the 'dipmeter' which does not survey the path of a hole but measures the dip of strata relative to the hole. This is usually acomplished with an array of multiple electrodes which touch the wall of the hole and sense the dip of the beds intersected by the hole.
Surveying a borehole is usually accomplished by moving a probe along the hole and sensing the movement of the probe relative to one or more frames of reference which may include the earth's gravitational field, magnetic field or other inertial reference, and/or by sensing the distortion or bending of the housing of the probe itself. Different methods have their own advantages and limitations. Some have the ability to operate inside steel casing, and others cannot. Some methods are time consuming and others are fast. Some are relatively simple to use and others are complex to operate. Other considerations are accuracy, cost, distance between measurements, ruggedness and reliability.
The Borehole Geophysics Section of the Geological Survey of Canada has reviewed and compared many of the available methods, and has experience surveying boreholes with several different systems. A review of methods for surveying a borehole follows, based roughly on the chronological evolution of the technology. Experience with five different commercially available systems is illustrated with a comparison of survey results from a single borehole in the Val d'Or area of Quebec. A review of the above-mentioned experience is useful in selecting the appropriate borehole surveying methodology.
A survey of a borehole should provide an accurate plot of the path of the hole in 3-dimensional space, i.e. the (x,y,z) coordinates (northing, easting, true depth) of every point along the path is known. In practice, the coordinates of a finite number of points are determined, and the path between these points is calculated by extrapolation. From this, it should be obvious that: the greater the number of known data points, the less extrapolation required, and the more accurate the survey. The coordinates of points are not measured directly, but are computed from measurements of the dip, azimuth and length-along-the-hole (usually called 'depth'), as shown in Figure 2. These are the three components of the 'hole vector', The first data set are the dip, azimuth, and depth (which is zero) at the collar of the hole. The (x,y,z) coordinates of the top of the hole are based on the surface survey grid being used in the area, and of course do not have to be computed from the dip and azimuth data. However, along the length of the hole the dip and azimuth will change from that at the collar.
Measuring length along the hole is relatively easy, although not a trivial problem. The calibration of the pulley or sheave wheel and the depth encoder attached to it is subject to error, since it relies on an accurate determination of the number of pulses from the encoder for each metre of cable that passes over the pulley. In addition, the cable used for the depth measurement may stretch, or it may effectively increase in diameter due to icing conditions in winter, or the pulley may effectively increase in diameter for the same reason, or decrease diameter due to wear. A one percent error in depth measurement, for example, may mean a 5 metre depth error at a depth of 500 metres, and this could be larger than the error caused by precision dip and azimuth measurements. This review, however, is primarily concerned with dip and azimuth measurements.
The Acid Etch Clinometer: One of the earliest and simplest surveying devices is based on a measurement inside the drill rod with an acid bottle (Figure 3). A 4% hydrofluoric acid solution etches the wall of the glass etch tube leaving a permanent record of the dip of the hole, which can be read upon retrieval of the probe (Urban and Diment, 1989). Etching time is a minimum of 20 minutes, but as soon as the etching time has elapsed, the drilling can begin again. Further etching is slight and does not erase the etch line made while stationary. In a deep hole, etching time (stationary) must be increased to equal the time required to lower the device to the measurement depth, which may be up to 2 hours. In about 4 hours the acid will have neutralized. The acid etch device will fit inside the smallest diameter drill rods (size E). The method is still in use today usually for a single measurement at the bottom of a hole when drilling has stopped. This gives a 'quick and dirty' indication of hole deviation, but it provides dip information only.
The path of the hole could be in any direction on a cone of equal dip as shown in Figure 4, until the azimuth with respect to North is also measured. Even if the dip of the hole were known at numerous points along the hole, the true path could be virtually anywhere as illustrated in Figure 5. Here, three dip measurements are made along the path of a borehole, and the three cones of equal dip angle are shown. The azimuth of the hole is also included on each cone to illustrate three straight-line segments of the hole. It is easy to see that without the azimuth information, there is an infinite number of possibilities for the true path of the hole based on dip measurements alone.
The Tropari (and its successor the Pajari): In this instrument, a compass and clockwork mechanism are mounted on gimbals with the bottom side weighted to maintain the gravitational vertical reference (i.e. as an inclinometer) as it moves freely in its housing (Figure 6a, 6b, and 6c). It is lowered in the hole to the measurement depth, and at a preset time the clock locks all the moving parts and the tropari is retrieved from the hole to read the dip and magnetic azimuth value at that measurement depth. The dip is measured to within 1 degree and the azimuth is read to the nearest half degree. Two versions are available with a maximum time period of 90 or 150 minutes. The clockwork locking takes place in the last 10 minutes of the set time period, during which time the instrument should be stationary in the hole. Measurements are usually made at 50 or 100 m intervals in the hole, depending on the depth of the hole and the desired accuracy. The device will fit inside an EX (46 mm) hole. It is available with pressure rating to 1675 metres depth and with thermal housing for temperatures over 100 degrees celsius. It can be run in an open hole on a wireline, or at the end of a drill string by raising the drill-rod string 6 or 7 metres and allowing the tropari to pass through the drill bit to a position about 5 m away from it. The tropari, a Canadian invention, is still widely used in mineral exploration in Canada and throughout the world.
The Magnetic Single Shot: Using basically the same principle as the tropari, the magnetic single-shot replaces the clockwork locking mechanism with a camera that takes a photo (shot) of the dip and compass needle at the measurement depth. The probe is then retrieved to read the film disc. Probably the most widely used version is that developed by Sperry-Sun Drilling Services, Inc. (see Figure 7a, 7b, 7c and 7d) which is available in two diameters: the standard "A" size of 1.75" (44 mm) diameter and the "B" size of 1.38" (35 mm) diameter, and thermal shielding is available for hot holes. The 'shot' is taken at a time based on several possible mechanisms, including a timer, a motion sensor that senses when the probe has stopped moving, or a magnetic sensor that senses when the probe has reached a special nonmagnetic section of the drill rod near the drill bit. The insertion and removal of the film disc is done quickly through a slot in the housing. Development of the film disc takes about five minutes. The disk is placed in a magnifying reader to determine the dip and azimuth measurement.
The Magnetic Multi-shot: Sperry-Sun made a significant advance by installing in the probe, an 8mm film camera (Figure 8) that takes photos of the dip and azimuth readings at several measurement depths in one trip in the hole. Krebs (1964) described such a multiple exposure system as early as 1964. The multishot timer advances the film and turns on the battery-powered lights at each measurement. Normal operation consists of synchronizing a stopwatch with the camera and taking note of the time at each measurement-depth where the probe is stopped for about 45 seconds. Since the standard time interval between shots is 20 seconds, one or two good (stationary) readings will fall within the 45 second stopover. The "A" size tool holds 6 hours (1000 readings) of film at 20 second times and the "B" size tool holds 3 to 14 hours of film depending on a variable clock setting which may be set from 15 seconds to 1 minute. The film is developed on-site in a dark-bag and read in a projector fitted with a time counter/frame counter. The film is advanced to the times (frames) that correspond with the recorded measurement-depth/time data, and the dip and azimuth values are read.
Solid State Devices: Although it has been possible to measure magnetic field directions electronically for about 50 years, the physical size of the components was more suitable to installation inside an aircraft than a borehole probe. However as miniturization of electronic devices evolved, this changed. Holm (1964) utilized a compass and pendulum mechanism which could be recorded electrically and remotely at the surface. In recent years, new hardware was adapted from satellite and guided missile technology for use in logging tools. The magnetic compass was replaced by a ring-core fluxgate magnetometer (Figure 9) and the dip measurement was made by solid state tilt-meters or accelerometers with no moving parts.
The solid state tiltmeters are oriented orthogonal to each other in the probe to measure dip, and at the same time compensate for roll of the probe as it moves in the hole. The tiltmeters consist of an electrolyte which half fills the space between two conductors on opposite sides of a disc-shaped glass container. As the container rotates (tilts), the electrolyte moves, changing the resistance between the conductors on opposite sides, which is calibrated in terms of the degree of tilt (Balch and Blohm, 1991). The accelerometers use the principle of sensing the position and movement of a 'pendulous mass', as it tries to move when the probe tilts, and driving it back to a 'zero' position with a servo-motor. The current required to drive the motor is proportional to the degree of tilt.
Dip and azimuth data are transmitted to the surface in real time for recording and display as exemplified by probes developed by OWL Technical Associates Inc., USA and IFG Corp., Canada or stored in solid state memories in the probe (e.g. Boretrak, UK). These three typical examples of the technology use 38 mm (1.5") diameter probes.
OWL (Figure 10) quotes a sensitivity of 0.1 degrees (maximum RMS error of +/- 0.2 degrees) over a range of dip from 90 degrees (vertical) to 10 degrees. The azimuth has a sensitivity of 1 degree (maximum RMS error +/- 2 degrees) over a range from 0 to 359 degrees. A special version is available which extends the range of dip measurements to include a full sphere (i.e. 360 degrees).
IFG (Figure 11) quotes a sensitivity (resolution) of 0.1 degrees (overall accuracy better than 0.5 degrees) over the entire range of dip from 89 degrees (nearly vertical) to 10 degrees, and an uncertainty of +/- 0.3 degrees for the azimuth over a range from 0 to 359 degrees (Balch and Blohm, 1991; Killeen et al, 1996).
The Boretrak (Figure 12) claims a resolution of 0.01 degrees over a range of +/- 30 degrees of dip, and a maximum depth of 300 metres. The azimuth data are not measured and recorded but rather kept constant by means of fixed lightweight rods used to lower the probe in the hole. Early development of systems such as this were described by Roxstrom (1959) and Holz (1961).
Geographic North vs Geomagnetic North: Although the progression of the technology as described above was impressive, the magnetic azimuth must still be converted to geographic azimuth (Figure 13). The desired final computed coordinate positions of the borehole are with respect to the geographical coordinate system in which every point along the path of the hole has a northing, easting and vertical depth. However, the measurements described thus far, are made with respect to the geomagnetic field. The computed azimuth is a magnetic azimuth until it has been converted into a geographic azimuth. Using the declination of the local field, the magnetic coordinates of the borehole can be rotated into the geographical coordinate system. It is usual to obtain the value for the geomagnetic declination from regional geomagnetic declination and inclination maps.
Although these magnetic-based methods are adequate for most holes, surveys based on magnetic azimuth cannot be done inside steel casing, or where there are anomalous magnetic fields (discussed later). All of these considerations led to the development of non-magnetic systems.
Azimuth measurement based on gyroscopic platforms: The inertia of a spinning mass can be used as a stable reference for a series of directional measurements in a borehole. The gyroscope mechanism (Figure 14) replaces the magnetic compass, and its orientation with respect to geographic north must be determined at the collar of the hole. The inertia of the gyro and its stability (freedom from drift) are related to both the mass and its rate of spin. A spin of 40,000 rpm is common, and the jewelled bearings can wear out quickly, adding to the cost. However, surveys can be carried out inside metal pipe and in the presence of magnetic anomalies. Early versions were combined with a camera as in the 'Single-shot' device (see for example the Sperry-Sun gyro-based probe in Figures 15, 16 and 17). Recent versions called 'surface recording gyros' transmit the data to the surface digitally in real time. New optical gyros with virtually no moving parts, such as the ring-laser gyros described by Anderson (1986), may eventually replace the mechanical gyroscopes.
Optical instruments; Light Beam Methods: A completely different borehole surveying technique is based on a light source in one end of a long rigid tube, with the lightbeam focused on a target in the other end of the tube. Bending of the tube as it moves in the borehole causes deflections of the light on the target, and this information is converted into borehole orientation survey data. The technique is not affected by magnetic fields and can be used inside metal pipe or drill rod. For best results, the probe should have only about 1 mm clearance between it and the wall of the hole for maximum sensitivity to the bending effect. This means that surveying inside the drill rod is actually preferable since it is safer than logging in an open hole where the chance of getting the probe stuck is greater.
In the first version, designed in Sweden (the 'Fotobor' (Hood, 1975), by Reflex Instruments AB; Figure 18 ), the illuminated target was a set of concentric rings and a level bubble, used as the vertical reference (Figure 19). A camera recorded the data on film (Figure 20) for processing and correlation with the time and depth data recorded at the surface. Another optical system made by Gyro-log Ltd., Canada; (Figure 21) uses the position of the lightbeam 'spot' on a target (Figure 22) (instead of rings) for measuring the bending of their 'Light-Log' instrument, and calculating the path of the hole. The most recent Swedish version (the 'Maxibor', Figure 23) detects the position of the rings with optical sensors and the data are recorded in a solid state memory in the probe for later processing and display at the surface.
Raw data consists of a series of dip and azimuth values measured at numerous depth points ranging from 100 m apart to less than 0.1 m apart depending on the method. The examples shown in Figure 24 are the data from five surveys of a 950m deep borehole in the Val d'Or mining area of Quebec. Remember that the figures do not show the path of the hole, but rather the variation in the measured azimuth and dip plotted versus 'depth' which for raw data is actually 'length along the borehole'. The results include data from Tropari, Sperry multi-shot, OWL, IFG, and Maxibor surveys. All, except the Maxibor, rely on the earth's magnetic field for the azimuth determination. In figure 24a, the measured azimuth values are plotted versus depth. The azimuth varies from 150 degrees (i.e.south-southeast) at the top of the hole, to an azimuth at the bottom of the hole of 170 degrees (almost due south), according to the magnetic-based methods, and 135 degrees for the optical method (Maxibor).
In summary, the magnetic methods indicate that the hole direction swung southward by about 20 degrees as it deepened but the optical method indicated the hole swung northward by 15 degrees. The magnetic methods produce absolute measurements at each depth and results of the survey are not dependent on previous measurements. Thus, even though the casing obviously affected the results of the OWL, IFG and Tropari tools near the surface, the survey data for the rest of the hole is unaffected. Note also the OWL and IFG tools 'saw' the two steel wedges in the hole at 350 and 450 metres, but make a 'recovery' as they leave the anomalous areas. It is interesting that the Maxibor also 'saw' the two wedges as indicated by slight jogs in the azimuth log shown in Figure 24a. This is consistent with the fact that the wedges are placed in the hole to produce a correction factor (change the dip and/or azimuth) of a deviating borehole during drilling. The Sperry Multi-shot data points are about 30 or 40 m apart, and the Tropari data are 100 m apart and they did not detect the wedges. The dip data from all five tools plotted in Figure 24b seem to be in agreement. One Multi-shot data point at about 750 m appears to be anomalous and would not influence the survey results. However if we look at the results closely, the dip at the bottom of the hole is measured as 22 degrees by OWL and IFG, 26 degrees by Sperry and Maxibor, and 21 degrees by Tropari.
The raw dip and azimuth data must be converted into a plot of the path of the hole in 3 dimensional space by interpolating between measurement points as shown in Figure 25. Called 'desurveying' (Howson and Sides, 1986), a number of different algorithms can be used for the interpolation. After desurveying, the visual output is a display of the path of the hole projected on planes in an east-west or north-south direction, or in plan view one scheme of which is illustrated by Figure 26.
The selection of the desurveying algorithm is especially important if the data points are sparse and can be a large source of error if the wrong method is used. This is the case when only a few points in the hole have been measured with some of the slow borehole surveying devices. For example, a straight-line interpolation between measured points would be one desurveying method which could be used. However the true path of the hole doesn't usually follow straight line segments. Various computation methods involving curve-fitting between points have also been proposed. Reviews of the various methods of computing borehole position, and their possible errors have been presented by several authors including Walstrom et al., (1969), Walstrom et al., (1972), Harvey et al., (1971), Truex (1971) and Wolff and deWardt (1981). These methods include the Angle Averaging Method, Balanced Tangential Method, Radius of Curvature Method, and Minimum Curvature Method, details of which are beyond the scope of this paper.
Most modern orientation probes make measurements continuously, and these are sampled as often as every half-second. Measurements of dip and azimuth can be made every 5 cm along the path of the hole at a logging speed of 6 metres per minute for example. This data interval is much smaller than the length of the orientation probe itself. Because the interval between readings is so small, the borehole desurveying method used to compute the position coordinates of the hole will have very little effect on the results. Therefore, in that case, the simplest method which assumes a straight path between measurements may be chosen.
The effect of increasing the interval between measurements was investigated by Balch and Blohm (1991). They presented an example of a survey of a 600 m deep borehole using the IFG orientation probe. By using only part of the measured data, thus simulating measurements at larger intervals, they recomputed the position of the bottom of the hole. In their worst case example with an average sample interval of up to 10 metres, the position of the bottom of the hole varied by about +/- 4 metres. They also compared logging continuously at 9m/minute with logging in an incremental mode, stopping every 5 metres in the hole. They found the error in computing the position of the bottom of the hole was within +/- 2 metres, between the continuous and incremental mode.
Balch and Blohm (1991) also considered possible errors in converting measured magnetic azimuths into geographic azimuths. They repeated the computations using the wrong geomagnetic declination, for the 600 m depth borehole used in their other field tests. By varying the declination up to one degree west (from 346&figs.html#176; to 345&figs.html#176;), the position of the bottom of the hole varied up to +/- 5 metres. They concluded that the error in the position of the bottom of the hole is more sensitive to errors in the value of the geomagnetic declination used in the computations, than the errors that might arise from the orientation probe measurements in the borehole. Killeen et al, (1996) summarized the other sources of possible error in a magnetic-based orientation probe, including errors due to:
1) Zero offset, 2) Gain adjustment, 3) Orthogonality, 4) Linearity, and 5) Temperature drift, all of which can be corrected by post-processing.
Another possible external source of error is the presence of anomalous magnetic fields caused by magnetite or other magnetic minerals nearby or intersected by the hole. Good results may be obtained when using the new magnetic orientation probes in boreholes where strongly magnetic (but relatively thin) units are present. This success is primarily a result of the high sample rate which provides closely spaced measurements making it possible to eliminate the erroneous measurements. In the case where the magnetic anomalies are large and broad in extent, they will effectively swing the apparent azimuth of the hole around in the direction of the source of the anomaly. The possibilities for using this to detect the location of off-hole magnetic bodies was also briefly discussed by Killeen et al (1996).
The five raw data sets were desurveyed using straight-line interpolation as mentioned above, and the resulting five paths of the hole are displayed together for comparison. The geographical path of the Val d'Or borehole is displayed in four different ways: in Figure 27a as the projection of the path of the hole in a North-South vertical section, in Figure 27b as an East-West vertical section, in Figure 27c as a plan view, and in Figure 27d as a combination of all of the above views in a wire grid box showing the path in "3-D".
It is instructive to observe the differences in the computed paths of the hole as shown in their different projections. The North-South section (Figure 27a) shows the true vertical depth to be about 750 m. The Tropari and Maxibor paths are almost identical, but they show the hole bottom to be located about 100m north of the position indicated by the OWL, IFG and Sperry paths. In the East-West section (Figure 27b), the Tropari and Sperry paths agree, the OWL and IFG paths agree but show the hole bottom to be about 40 m further east, and the Maxibor indicates the hole bottom is an additional 150 m further east. The plan view (Figure 27c) shows how the magnetic methods roughly group together. The optical method (Maxibor) indicates a significantly different hole path. The path of the hole shown as a dashed line in the '3-D' view (Figure 27d) is based on the IFG tool alone, since plotting all five paths and their projections (the solid lines) would be too confusing.
It must be remembered that there is no 'right answer' in this case. For example, there may be a magnetic anomaly affecting the results of four of the surveying probes, but not the Maxibor. Even among the magnetic-based methods, there are significant differences in the computed path of the hole. These data should give the reader some qualitative appreciation at least, of the possible errors in surveying boreholes with today's technology. It is unfortunate that a gyro-based method was not included here, but the hole had to be cemented due to mining constraints before a gyro tool became available. It is hoped to be able to find a hole which breaks through into a mine drift, at a future date. In that case, the exact position of the bottom of the hole could be determined with traditional engineering survey methods and this could be used as a basis for a more definitive comparison of the results.
The authors would like to acknowledge the contributions to this study by Aur Resources, Val d'Or, who provided the hole and the Multi-shot data, and in particular we thank Yves Rougerie and Louis Martin. We also acknowledge the material used in the illustrations of the borehole surveying equipment, much of which originated in company brochures. In particular we thank Steve Balch of IFG Corp. for his constructive comments, Cris Lovett of OWL Technical Associates for probe details, Measurement Devices Limited for the Boretrak information, Reflex Instruments AB, for the Fotobor and Maxibor information and BHP Minerals Canada Ltd., for the loan of their Maxibor, Gyro-Log Ltd. for the Light-Log data, J.K.Smit & Sons International Ltd. for the Acid Etch Clinometer data, Pajari Instruments Ltd. for the Tropari data, Sperry-Sun Drilling Services of Canada for the Single-shot, Multi-Shot and Gyro data, and Steve Birk and Doug Robinson of the GSC, for their contributions to the field tests. We also thank Sue Davis for production of all of the line drawings and Rob Kelly and Gilles Lemieux for the photographs.
Anderson D.Z., 1986. Optical Gyroscopes; Scientific American, Vol. 254, No. 4, p 94-99.
Balch S.J. and Blohm D., 1991. Development of a new borehole orientation probe; in Proceedings of the 4th International MGLS/KEGS Symposium on Borehole Geophysics for Minerals, Geotechnical and Groundwater Applications; Toronto, 18-22 August, p. 9-20.
Harvey, R.P., Walstrom, J.E. and Eddy, H.D., 1971. A mathematical analysis of errors in directional survey calculations; Journal of Petroleum Technology, Nov. 1971, p. 1368-1374.
Holm, A., 1964. An instrument for the determination of drill hole geometry; Geoexploration, Vol. 2, No. 1, p 20-27.
Holz, P., 1961. New electronic instrument to survey boreholes; Canadian Mining Journal, Vol. 82, No. 1, p 45-46.
Hood, P.J., 1975. Mineral Exploration: Trends and developments in 1974; Canadian Mining Journal, Vol. 96, No. 2.
Howson, M. and Sides, E.J., 1986. Borehole desurvey calculations; in Computers and Geosciences, Vol. 12, No. 1, p. 97-104.
Killeen, P.G., Mwenifumbo, C.J. and Bernius, G.R., 1996. Development of a borehole surveying probe using 3-component fluxgate magnetometers; in EXTECH I: A Multidisciplinary Approach to Massive Sulphide Research in the Rusty Lake-Snow Lake Greenstone Belts, Manitoba, (ed.) G.F. Bonham-Carter, A.G. Galley and G.E.M. Hall; Geological Survey of Canada Bulletin 426. (in press).
Krebs, E., 1964. Modern borehole surveying; Mining Magazine, Vol. 3, No. 4, p. 220-233.
Roxstrom, E., 1959. Craelius EM bore-hole dip indicator; Canadian Mining Journal, Vol. 80, No. 11, p. 78-84.
Truex, J.N., 1971. Directional survey problems, east Wilmington Oil Field, California; Bulletin, AAPG, April 1971, Vol. 55, No. 4, p. 621-628.
Urban, T.C., and Diment W.H., 1989. Capillary corrections for acid-etch inclinometry in boreholes for glass tubes ranging in diameter from 6-25 mm and over a temperature range of 4-80 degrees C; in Proceedings of the 3rd International MGLS Symposium on Borehole Geophysics for Minerals, Geotechnical and Groundwater Applications; Las Vegas, 2-5 October, p. 233-260.
Walstrom, J.E., Brown, A.A. and Harvey, R.P., 1969. An analysis of uncertainty in directional surveying; Journal of Petroleum Technology, April 1969, Vol. 21, p. 515-523.
Walstrom, J.E., Harvey, R.P. and Eddy, H.D., 1972. A comparison of various directional survey models and an approach to model error analysis; Journal of Petroleum Technology, August 1972, p. 935-943.
Wolff, C.J.M., deWardt, J.P., 1981. Borehole position uncertainty - analysis of measuring methods and derivation of systematic error model; in Journal of Petroleum Technology, December 1981, p. 2339-2350.