GB2086055A

GB2086055A - Borehole Survey System

Info

Publication number: GB2086055A
Application number: GB8129597A
Authority: GB
Original assignee: Sundstrand Data Control Inc
Current assignee: Sundstrand Data Control Inc
Priority date: 1980-10-23
Filing date: 1981-10-01
Publication date: 1982-05-06
Also published as: IT1142908B; AU533909B2; ZA817068B; SE8105959L; MX150339A; JPS57100308A; GB2086055B; NL8104801A; IT8149530A0; NO813568L; DE3135743C2; JPS6015883B2; FR2492882A1; DE3135743A1; AU7427381A; CA1166843A; FR2492882B1

Abstract

A system for surveying a borehole or mine shaft to determine its trajectory uses a sensing probe with two spaced sets of accelerometers in sections 22, 23 measuring the components of the gravity vector along orthogonal axes at successive positions along the borehole 20. The two sets of accelerometers are connected by a pipe or cable 24 which is flexible to bend but torsionally stiff. The angular orientation of the two accelerometer sets relative to each other about the borehole axis is fixed by the pipe or cable 24 so that any difference in orientation of the two sets is a function of the local trajectory of the borehole. Two sets of accelerometer output signals representing gravity vector components at positions spaced apart along the axis of the borehole are utilized to derive the borehole inclination at each position as well as the change in borehole azimuth angle between the positions of the accelerometer sets. The accelerometer signals and a signal representing the position of the probe along the length of the borehole, are combined to provide a three dimensional representation of the borehole trajectory, relative to a reference point, e.g. the termination of the borehole at the surface. <IMAGE>

Description

SPECIFICATION Borehole Survey Apparatus and Method This invention relates to an apparatus and method for surveying a borehole or the like with measurements of gravity components to provide a representation of the borehole trajectory with respect to a known ground reference point, such as ground O where the borehole starts.

Surveying of a borehole or the like is often accomplished by an instrument or probe which moves through the borehole and measures inclination and azimuth angles at successive points. Inclination, the angle by which the borehole tangent deviates from the vertical, may be measured with a pendulum or accelerometer. Azimuth, the angle of the borehole with respect to a reference direction, such as north, is typically measured with a magnetic or gyroscopic compass. These angles, together with the distance along the borehole, are used to determine coordinates of points along the borehole with respect to the reference, ground 0.

A pendulum for measuring inclination may take the form of a linear servoed accelerometer which responds to the acceleration of gravity. Servoed accelerometers are available which are small, rugged and accurate. The measurement of azimuth is not so simple. Magnetic compasses or other devices for measuring the earth's magnetic field are subject to errors caused by magnetic anomalies in the ground.

Gyroscopic compasses have several drawbacks including large size, bearing wear, sensitivity to shock, drift and precession errors and the requirement for a long settling period for stabilization when a measurement is made.

In accordance with the present invention, an apparatus and method are provided with which the borehole trajectory may be determined from gravity component measurements, as made with the linear servoed accelerometers mentioned above, and from distance along the borehole. The survey measurements are made as the probe is moved through the borehole providing a data output from which the borehole trajectory is determined. The speed and accuracy of a survey based on servoed accelerometer measurements far surpasses that which is achieved with other instruments. In addition, the probe utilizing accelerometers and not requiring a compass for azimuth measurement may be contained in a smaller diameter housing is more rugged.

The invention provides a borehole survey apparatus, comprising: a first set of at least two accelerometers having sensitive axes defining a first plane; a second set of at least two accelerometers having sensitive axes defining a second plane; means mounting both pairs of accelerometers to pass through said bore hole with the planes of the accelerometers spaced apart and with the angular alignment of the accelerometer pairs about the borehole axis fixed with respect to each other; and means for deriving from each accelerometer an accelerometer signal representing the component of gravity along the sensitive axis of the accelerometer.The invention also provides a method of surveying a borehole which comprises: measuring the acceleration of gravity along different axes at successive pairs of points along said borehole, the axes at each point of a pair of points having a known relation; generating signals representing said accelerations; providing a measure of distance of said points along the borehole; and deriving from said acceleration signals and the measure of distance a representation of the borehole trajectory.

Considering first the bore hole survey apparatus or sensing probe of the invention, the two measurement planes defined by the respective pairs of accelerometers are perpendicular to their respective borehole tangent and to the borehole axis. The accelerometers of each set are preferably two in number and mutually perpendicular, but the provision of a third or further accelerometers in each set provides an improvement in accuracy and enables operation if one of the first two-mentioned accelerometers malfunctions.

The two sets of accelerometers are preferably joined by a longitudinally flexible, torsionally stiff connector, to follow the borehole trajectory while maintaining a fixed angular relationship between the accelerometer pairs, about the borehole axis. The apparatus further preferably includes means for deriving from the accelerometer signals a representation of the borehole trajectory.

Advantageously the probe has first and second sections with one set of accelerometers mounted in eachsection. The sections are joined by a connector which is torsionally stiff and inextensible about its longitudinal axis and flexible about axes at right angles thereto as a cable or pipe. This connector insures that the distance along the borehole between probe sections remains fixed; that the joint between the two sections is stiff in torsion; and that each set of accelerometers follows the local borehole axis and is free to rotate about the borehole axis. More particularly, the two probe sections are joined by a cable or pipe which is resilient to bend along the borehole axis but is rigid with respect to torsional stresses about its axis.Alternatively, the two sets of accelerometers may have a common housing which is flexible to follow bends in the borehole, but torsionally stiff to resist twisting.

A further feature of the invention is the method of surveying the angles of inclination and azimuth along a borehole, including measuring the acceleration of gravity (along orthogonal axes) in planes transverse to the borehole axis at successive points along the borehole, generating signals representing the acceleration, and deriving from the acceleration signals a representation of the borehole trajectory.

The inclination of the borehole at each measurement plane can be found from the vector sum of the two components of earth's gravity measured by the corresponding accelerometer pair. This has been known in the prior art. A principal feature of the invention is that the incremental change in azimuth of the borehole between the two measurement planes may be determined from the four output signals of the two accelerometer pairs and the distance along the borehole between measurement planes. The borehole trajectory may be determined in terms of inclination, azimuth and borehole length.

More particularly, as the probe is moved along the borehole, gravity measurements from the two accelerometer pairs and a correlated measurement of distance along the trajectory of the hole are made, from which the course of the borehole in three dimensions is determined.

Further features and advantages of the invention will readily be apparent from the following specification and from the drawings, in which: Figure 1 is a broken diagram of an apparatus embodying the invention, including sections through a borehole showing the sensing probe; Figure 2 is a block diagram of the accelerometers and a circuit for transmitting acceleration signals to the surface; Figures 3-12 are geometric diagrams which illustrate derivation of the inclination and incremental azimuth angles and the borehole position coordinates from the acceleration and borehole distance measurements; Figure 13 is a development tree showing in chart form the derivation illustrated geometrically in Figures 3-12;; and Figures 14 and 1 5 are block diagrams illustrating a system and method for deriving the borehole trajectory from the accelerometer signals with measurements taken at positions spaced apart a distance equal to the spacing of the accelerometer pairs.

The invention is described herein in connection with a borehole as for an oil or gas well. It can be used for other mining or civil engineering applications such as surveying subterranean structures as a mine shaft, for example. Reference to a borehole in the claims shall be broadly construed unless the context requires a different interpretation. Derivation of a representation of the borehole trajectory may be accomplished, for example, in the form of three dimensional coordinates or of a plot of an existing borehole to determine its physical location. The trajectory representation may also be derived as the borehole is drilled to monitor the drilling operation and to enable an operator or drill controller to direct the drill along a desired path. The invention is not limited to a particular trajectory representation.

In Figure 1, a borehole 20 extends downwardly from the point 20a at the ground surface and is lined with a casing 21. The sensing probe has a first section 22 and a second section 23 spaced therefrom, the two sections being joined by a cable or pipe 24. The sensing probe is lowered into the borehole on a hoisting cable 25 which also includes conductors for supplying electrical power to the probe and for directing signals from the probe to circuitry above ground at the well head.

Two accelerometers (not shown in Figure 1) are located in the first probe section 22 and preferably have their sensitive axes X, Y at right angles to each other defining a measurement plane at right angles to the longitudinal axis of the probe section. The probe axis corresponds with the axis of the borehole. Similarly, two accelerometers (not shown in Figure 1 ) in the second section 23 have their sensitive axes X; Y' at right angles to each other defining a measurement plane at right angles to the longitudinal axis of the probe section 23 and the borehole axis.

As will be explained below, the borehole position coordinates are determined from the inclination angle with respect to the gravity vector and an angular measure of the zenith of each measurement plane. These angles are readily and accurately determined from measurement of the gravity vector with orthogonally positioned accelerometers in a measurement plane at right angles to the borehole axis.

However, measurement of the gravity vector with any pair of accelerometers whose axes are sensitive to independent vectors in a plane having a known attitude in the borehole (i.e., the sensitive axes are neither colinear nor parallel) may be transformed geometrically to the inclination and zenith angle measurements.

In a typical probe the diameter of the section housings is of the order of 2-3 inches and two servoed accelerometers cannot be mounted side-by-side. Accordingly, the accelerometers in a pair are physically spaced apart axially of sections 22, 23, but are sufficiently close together as compared with the spacing between the accelerometer pairs to be considered coplanar.

A third acceleromater could be added to each set with its sensitive axis at right angles to the axes of the other accelerometers of the pair as indicated by Z, Z'. The third accelerometers afford an improvement in accuracy, and enable operation if an X orY accelerometer malfunctions.

Cable or pipe 24 is fixed at each end to the probe sections 22, 23 and serves to space the sections apart a predetermined distance in borehole 20. The cable 24 is flexible to follow bends in the borehole but resists torsional stresses to prevent rotation of one section with respect to the other. This maintains a preestablished relationship between the accelerometer axes X, X' and Y, Y'. Preferably, with the probe sections 22, 23 axially aligned, axes X, X' are parallel with each other and define a plane through the longitudinal axis of the probe. Similarly, axes Y, Y' are parallel and define a second plane through the probe axis, at right angles to the first. It is not essential that the corresponding axes be parallel, only that they have a fixed relationship.However, processing of the signals developed by the accelerometers is simplified if the sensitive axes are nominaliy parallel.

Each of the accelerometers is preferably a linear, servoed accelerometer with an associated electronic circuit (not shown) which generates an analog signal having an amplitude representing the component of gravity acceleration along the sensitive axis of the accelerometer. Jacobs U.S. patent 3,702,073 shows such an accelerometer. An electronic circuit in the probe, to be described in more detail below, multipiexes the analog signals, converts them to digital form and couples them through conductors in hoisting cable 25 with circuitry at the well head. The acceleration signals are connected with the data input of data storage unit 26. The output of data storage unit 26 is connected with a processor 27 which, as will appear, derives a representation of the borehole trajectory.A transducer 28 associated with hoisting cable 25 provides a signal ALto the processor 27 indicating the position of the sensing probe in the borehole.

Keyboard and display 30 is connected with data processor 27. A representation of the borehole trajectory may be displayed as in terms of coordinate dimensions in a three axis system. The keyboard provides for operator input and control. The representation of the borehole trajectory may be printed or recorded for future use. Means for performing these functions are known and are not illustrated in the drawings.

The sections 22, 23 of the sensing probe have cylindrical pressure housings. Resilient centralizers 31 on the outside of the housings engage the inner wall of borehole liner 21, positioning the housings so that their longitudinal axes coincide substantially with that of the borehole. Lower section 23 of the probe has a housing divided into two parts, 32, 33. Cable 24 is connected with the upper end of housing part 32. Accelerometers X', Y' are located in housing part 32. The second housing part 33 of the second probe section 23 has the centralizers 31 thereon and is long enough to maintain proper alignment with the borehole. The housing parts 32, 33 are joined by a swivel connector (not shown) so that housing part 32 can rotate freely with respect to part 33 to maintain the desired alignment with the upper probe section 22.

The borehole survey is carried out by causing the probe to move through the borehole from one end to the other in either direction while data is collected and processed. The survey may be conducted as the probe is lowered into the borehole or as it is raised from the bottom. For increased accuracy, data may be collected as the probe moves in each direction and the survey results averaged.

The borehole azimuth is referenced to the outside world by establishing an initial azimuth condition of the probe at the surface. For example, the probe may be physically aligned with a fixed benchmark and the alignment verified with a surveying instrument 35.

Figure 2 illustrates diagrammatically the accelerometers and signal handling circuitry in the probe. Upper probe section 22 contains the X, Y and Z accelerometers which have analog signal outputs ax, ay, az. The lower probe section 23 has X', Y', Z' accelerometers with analog outputs ax" a,,,, azva Power from a surface source 37 is connected through the hoisting cable 25 with a power supply 38 in the probe. The analog acceleromater signals are connected with sample and hold circuits 39, 39' and are multiplexed through analog to digital converters 40, 40' to a signal control 41 through which they are transmitted to the surface.Signal control 41 provides timing for the sample and hold circuits 39, 39' and the A/D converters 40, 40'. Signals from cable length transducer 28 are correlated with the acceleromater signals to identify the point along the borehole at which each set of signals is taken.

A source of error in the survey may be minimized by providing temperature sensors 42, 42' in each probe section together with temperature controls 43, 43' to maintain the temperature of temperature sensitive elements within desired limits. Analog temperature signals t, t' are sampled and transmitted to the surface with the acceleration signals. The temperature signals are utilized in a temperature compensation circuit 26 to minimize further any temperature error.

The probe sections 22, 23 must be long enough to maintain alignment between the section axes and the borehole axis. The maximum length is limited by the minimum radius of bend in the borehole liner. Within these limits a typical probe section is between 2 and 20 feet long. The distance between accelerometer pairs should be at least 10-1 5 feet. The maximum spacing is dictated by handling problems. A typical probe is between 50 and 1 50 feet long.

Figures 3-12 illustrate the geometric relationships which underlie the derivation of the borehole trajectory from the gravity component signals provided by the two pairs of accelerometers. Figure 1 3 shows in chart form some of the relationships. Following is a tabulation of notations and terminologies used in the drawings and in the subsequent discussion.

0 ground reference NEG unit direction vectors North, East, Downward (gravity) coordinates of the center n of circle Cn with respect to NEG coordinate system C borehole curve C upward projection of borehole unit circle at the nth cross section of the borehole Cn' or unit circle at the n+1 cross Cn+1 section of the borehole On center of Cn On upward projection of On I distance from Cn to Cn' along the borehole curve C XnYn two orthogonal accelerometers at On Xn'Yn' two orthogonal accelerometers at On' such that when the curve C is a straight line, the sensitive axes of Xn and Xn' point at the same direction.

Similarly, the sensitive axes of Yn and Yn' point in the same direction axn ayn acceleration signals from axn' ayn' XnYnXn'Yn' Zn zenith on Cn' the point on Cn closest to the surface unit vector from On to Zn in unit horizontal vector 900 clockwise from in looking down the borehole kn, knl local unit vector tangent to the borehole axis at On, n in the plane defined by QOnOn' 0 n the point on Cn marked by Zn or in 90 n the point on Cn pointed by jn Q center of the borehole curve with radius rn between n and On' Ahln azimuth and inclination of borehole axis at n relative to ground 0 using NEG coordinate system Inin' inclination of circles Cn C OnOn' the vector from On to On' OOn' the vector OnOn' in NEG coordinate system angle from zenith Zn to Xn accelerometer axis a bearing angle of the direction of bending from Zn to On' ss bending angle af the borehole from On to On' r radius of the borehole curve from On to On', equal to 1/2ss0 γ #n-#n'=α-ss a a quantity used in the geometric analysis g gravity constant Mn transformation matrix between (i, j, k)nl and (i, j, k)n Mn+1 transformation matrix between (ij, k)n' and (N, E, G); note that (i,j,k)n'=(i,j,k)r+1 Figure 3 is a three dimensional diagram with a rectangular coordinate system NEG having an origin at ground reference 0. Borehole curve C extends downwardly under the northeast quadrant.

Curve C is a projection of the borehole curve on the ground. The coordinates NE define a horizontal plane at the ground surface. G extends downwardly at right angles thereto and represents gravity direction. The circles Cn and Cn' represent unit circles with centers on the borehole curve at On and On' The planes of the circles are normal to the borehole curve and the circles are spaced apart along the borehole a distance I, equal to the spacing between accelerometer pairs in the sensing probe. It is assumed that the borehole curve between 0n and 0n' is a circular arc of radius rn about a center Qn, Figure 4.

The sensing probe is moved through the borehole and readings are taken from the two pairs of accelerometers at successive sensor positions spaced apart a distance I, equal to the spacing between the sensor pairs. As will be explained below, the inclination of the borehole at each accelerometer position and the change in azimuth angle between accelerometer positions can be determined from the accelerometer readings. If the measurements start at ground reference 0 and the azimuth is known at that point, the azimuth may be determined for any point along the borehole by summing the incremental azimuth figures. Measurement may start at ground reference 0 and proceed to the bottom of the borehole or may start at the bottom of the borehole and continue up to ground reference.In the latter case, the determination of the actual borehole azimuth at the various positions is not known until the survey is completed and the cumulative incremental azimuth measurement is summed with the azimuth at ground reference.

The inclination and azimuth angles and the distance along borehole curve C for points on the curve may be used to derive an identification of the location of each borehole point in the rectangular coordinate system NEG.

The acceleration signals ax and a, from a pair of orthogonal accelerometers determine the inclination I of the plane of the accelerometers and the orientation angle w between the zenith or point on the unit circle closest to the ground and the sensitive axis of the X accelerometer. In Figure 6 unit circle CH is horizontal and Cn is tilted with respect thereto about a diameter jn' jn. Figure 7 is a further detail of Figure 6 looking perpendicularly at the vector Xn.It will be seen that, the X-accelerometer signal axn=g coswn sin In the Y-accelerometer has reading ayn=gcos(#n+#/2)sin ln =-g sin Wn sin In and -ay tan #n= ax As the accelerometer signals aXn and avn are known, both c9n and In can be determined. These determinations are made for the unit circles Cn and Cn'. From this information and the assumption that the borehole follows the arc of a circle between positions n and n', the change in azimuth from n to n' may also be determined.

More particularly, aXn2+ayn2=g2(cos2s)n+sin2cl)n) sin2 In Thus (axn+avn)1/2=g sin In or (axn+avn)1/2 ln=Arc sin[ g This gives inclination of the borehole at On. That of On' is calculated similarly. This is represented at step 43, Figure 13.

In Figure 8, three concentric circles are shown: the circle CH is horizontal, or parallel to the ground, the circle Cn is perpendicular to the borehole at On with zenith Zn and is tilted with respect to CH about an axis defined by j, and in The circle Cn' is perpendicular to the borehole at n' with zenith Zn', and obtained by turning the circle Cn about Vn and Vn at an angle 2p. Circle Cn' intersects the circle CH at jn' and -jn'. The turning point Tn on Cn is 900 apart from Vn and on Corresponding to the 2ss angle turning, the point Tn on Cn is moved to Un on Cn'.Thus, both Tn and Un are 900 from Vn In Figure 8, a is the angle between Zn and Tn and 8 is the angle between Zn' and Unl.

Figure 10 shows the circles Cn and Cn' superimposed, looking along the axis of the borehole.

In Figures 8 and 10, it will be seen that α=#ZnOTn=#jnOVn and #=#ZnOUn=#jn'OVn Thus, the zenith shift γ=#n-#n'=#ZnOX-#Zn'OX' =#ZnOZn' =#jnOjn' (after turning the right angle #ZnOjn clockwise by angle γ) The spherical triangle of Figure 9 lies at the right hand side of the circles of Figure 8.In this triangle: Let A=#-ln' a=α B=ln b=# C=2ss By spherical sine iaw: sin a sin b sinA sinB or sin a sin 8 sin (#-ln') sin In Since γ=α-# sin α sin(α-γ) sin Inl sin In sin a sin In= inl (sin a cos y-cos a sin y) sin a (sin In-sin In cos y)=-cos a sin y sin ln' Thus: sin y sin ln' tanα= cos y sin ln'-sin In As γ=#n-#n' all of the quantities on the right hand side of the equation are known from the four accelerometer signals and tan α and α may be determined.

Also with reference to the spherical triangle of Figure 9, the bending angle ss may be determined as follows using a spherical triangle law: C cot 2 sin 1/2 (a+b) tan 1/2 (A-B) sin 1/2 (a-b) Since C=2p we have

sin (α-γ/2) 1 = cot (ln+ln') sin y/2 2 (sin a cos y/2-cos a sin y/2) cot (ln+ln') sinγ/2 2 γ 1 =cos α(tan α . cot -- 1) cot - (ln+ln') 2 2 Since all of the quantities on the right hand side of the equation are known, the angle ss can be calculated.

The three quantities #, a and ss, step 44, Figure 13, are known. The geometric significance of a, the bearing angle of the lower probe center On' looking straight down along the borehole tangent at upper probe center On' is illustrated in Figure 5. The bending angle 2ss is illustrated in Figures 3 and 4 showing how much the borehole cross section Cn' has turned relative to the cross section Cn The position of vectors i, j and k, Figures 3 and 8, may be related for successive circles by coordinate transformation matrices as follows: O On On' Mn Mn NEG (i,j,k)n (i,j,k)n' Mn+1 so that Mn+1=Mn . Mn The matrix Mn has already been obtained in a previous measurement and calculation.It is necessary only to derive the matrix Mnl. Based on Figure 8, the three circle picture, the expression of vectors (Un, Vn, kn') in terms of (in', jn', kn) is: Un=in(cos an cos 2ssn) +jn(sin αn cos 2ssn) +kn(-sin 2ssn) Vn=in(-sin αn) +jn(cos αn) +kn(O) kn=in(cos an sin 2ssn) -jn(sin αn sin 2ssn) +kn(cos 2ssn) The coordinate transformation Mn which releates the two vectors (in,jn, kn) and (in',jn', kn') in Figure 8 is obtained via the (Un, Vn' kn) symbols.

in'=cos #nUn-sin#nVn =in(cos #n cos αn cos 2ss0n+sin #n sin αn) +jn (cos #n sin αn cos 2ssn-sin#n cos αn) +kn (-cos#n sin 2ssn) jn'=sin #nUn+cos#nVn =in(sin #ncos αncos2ssn-cos#2sinαn) +jn(sin#nsinαncos2ssn +cos#ncosαn) +kn(-sin#nsin2ssn) kn'=in(cosαnsin2ssn) +jn(sinα;nsin2ssn) +kn(cos2ssn) This means the coordinate transformation matrix Mn (step 45, Figure 13) can be constructed

in' a11 a12 a13 in in # jn' # = # a21 a22 a23 # # jn # =Mn # jn # kn a31 a32 a33 kn kn where a11=cos S cos a cos 2p+sin a sin a a12=cos S sin a cos sin S cos a In practice, the processor will store the coordinate transformation matrix from previous local coordinates (i, j, k) in the ground zero global coordinate system (NEG).That means the computer already knows the matrix Mn where

in b11 b12 b13 N N # jn # = # b21 b22 b23 # # E # =Mn # E # kn b31 b32 b33 G G In order to update transformation matrix M to M which transforms the coordinates kn') into the global coordinate system (NEG) determine the matrix product Mn+1=Mn . Mn See Figure 13, step 46.

In Figure 11, looking along the borehole in the direction of the vector +kn, Figures 3, 4 and 5, assume that the borehole from On to On' has a bearing clockwise αn degrees from zenith Zn; and that borehole bends along a circular path through an arc 2ssn.

If I is the borehole length from On to On', the local position vector OnOn' from On to On' (step 47, Figure 13) may be expressed, (OnOn')=in(ssn cos αn sinssn) +jn(l/ssn sin αn sinssn) +kn(l/ssn' sin αn sinssn) To write the column vector OnOn' in the NEG coordinate system: OnOn'=Mn (OnOn') (step 48, Figure 13) As seen in Figure 12, OOn+1=OOn'=OOn+OnOn' where 00n is stored from previous calculations. The location of nl relative to the ground reference O is thus determined.

With the vector OOn' pointing to the position On', the azimuth Anl (see Figure 3) may be expressed: En' tan Nn' (Nn'2+En'2)1,2 tan ln'= Gnl where (Nn', Enl, Gn') are the coordinates of the vector OOn' in NEG system with ground O as reference (step 49, Figure 13).

The derivation of the borehole trajectory from gravity vector signals is preferably performed by a programmed digital processor. Figures 14 and 15 are diagrammatic charts illustrating derivation of a representation or the trajectory in NEG coordinates. The illustration and description assume the use of accelerometer signals from positions spaced apart at distance I in the borehole.

The scalar inputs to Figure 14 are the digital gravity vector signals ax, a, and ax', ay'. Each of the blocks of the diagram indicates algebraically or in words the function performed thereby. The program will be described in general terms and related to certain of the geometric explanations given above.

At step 50, ax and a, are combined with gravity g and an arc sin function is utilized at step 51 to obtain the inclination angle I for one position in the borehole. Similarly, at steps 52, 53, ax' and a,' are utilized to derive 1', the inclination at the second point of the borehole. At step 54, the ratio of ax to a, is taken; and at step 55, the arc tangent further gives a measure of the angle o, see Figures 3, 6 and 8.

Similarly, ax' and a,' are combined at steps 56, 57 to provide a signal representing the angle ego'. At step 58, the difference o--o provides the angle y, the shift in zenith between successive positions along the borehole, see Figure 10. The inclination angles I, I' and zenith shift angle y are combined at steps 60, 61 to determine the angle a representing the bearing of the borehole between successive positions. At steps 62, 63 a is combined with the inclination angles I, I' and shift angle y to derive the bending angle ,5.

The scalar quantities a, P, y and I provide inputs for the matrix/vector program illustrated diagrammatically in Figure 1 5. In the notation used in Figure 15, M represents a borehole local coordinate transformation matrix from (i, j, k)nl to (i, j, k)n and Mnl is the global coordinate transformation matrix from (i, j, k)nl to (N, E, G).

Theinitial azimuth Ao for the probe is determined as by the surveying instrument 35 and this information is provided as an input to the system through keyboard 30'. At step 70 a global matrix Mo(Ao, lo) defines the starting position for the probe. The form of the matrix Mo is indicated in the footnote * to Figure 15. For the first measurement position or n=O, the matrix M0from 70 is connected through gate 71 with matrix multiplier 72.

The angles a and y are subtracted at step 73 to provide the angle a which is further combined with a and ss at step 74 to provide the matrix Mn which has the form indicated in the footnote ** to, Figure 1 5. The matrix Mn is multiplied by the matrix Mn at 75 to provide a transformed global matrix Mn+1 for the next position along the borehole. This matrix is delayed at step 76 and is coupled through gate 77 to matrix multiplier 72 when n is 1 or greater, becoming Mn for the succeeding measurement.

p and a are combined at step 78 to provide the vector 0n0n' which is multiplied by matrix Mn at step 72, see Figures 11 and 12. The output of this multiplication, 0n0n' is connected with a vector adder 80 where it is summed with the NEG coordinates for the point 0n At the first measurement location (the borehole at the surface), these coordinates are 000. The result of the vector addition is the set of NEG coordinates representing a point on the borehole. This result is also connected through a unit delayor step 81 as an input to the vector adder 80 for the next measurement position. The successive sets of NEG coordinates developed from successive accelerometer measurements provide a representation of the borehole trajectory.

The survey instrument described herein utilizing servoed accelerometers provides reliable results so long as the borehole is not within about one degree of true vertical or true horizontal. If these conditions are encountered, the accelerometer measurements should be supplemented with some other measurement of the borehole trajectory.

Claims

1. A borehole survey apparatus, comprising: a first set of at least two accelerometers having sensitive axes defining a first plane; a second set of at least two accelerometers having sensitive axes defining a second plane; means mounting both pairs of accelerometers to pass through said borehole with the planes of the accelerometers spaced apart and with the angular alignment of the accelerometer pairs about the borehole axis fixed with respect to each other; and means for deriving from each accelerometer an accelerometer signal representing the component of gravity along the sensitive axis of the accelerometer.

2. A borehole survey apparatus according to claim 1 , including: means for deriving from said accelerometer signals, at positions spaced along the borehole, angle signals representing the inclination angle of the borehole at each position; and means for deriving from said accelerometer signals an azimuth representing the incremental azimuth angle of the borehole between positions.

3. A borehole survey apparatus according to claim 1 or claim 2 including: means for deriving a distance signal representing the distance from a reference of each position along the borehole; and means for deriving from the accelerometer and distance signals the coordinates of the borehole positions with respect to said reference.

4. A borehole survey apparatus according to any preceding claim, wherein each set comprises two accelerometers with mutually perpendicular axes.

5. A borehole survey apparatus according to any preceding claim, wherein the means mounting the accelerometers comprises a sensing probe to be moved through the borehole, having a first section with an axis extending along the borehole axis, a second section spaced from said first section and having an axis extended along the borehole axis, and means joining said two sections maintaining a fixed spacing between them, said joining means being flexible to bend along the axis of the borehole as said first and second sections change position relative to each other with changes of inclination and azimuth of the borehole, said joining means resisting rotation of one section with respect to the other about the borehole axis to maintain the angular alignment about the borehole axis of the sections with respect to each other;; the first section mounting the first set of accelerometers and the second section mounting the second set of accelerometers.

6. A borehole survey apparatus according to claim 4 in which, with the sensing probe sections aligned, the sensitive axis of each of the first set of accelerometers is coplanar with the sensitive axis of the corresponding accelerometer of the second set.

7. A borehole survey apparatus according to claim 5 or claim 6 having a third accelerometer in each probe section with a sensitive axis along the axis of the section.

8. A borehole survey apparatus according to any of claims 5 to 7, having: a housing for each section; and means for centering the housings in the borehole.

9. A borehole survey apparatus according to claim 8 in which said housings are free to rotate in the borehole.

10. A borehole survey apparatus according to any of claims 5 to 7, having: a housing for each sensor probe section; and in which the means for joining the sections is a connector fixed at each end to one of said housings, said connector having an axis which follows the axis of the borehole, the connector being rigid with respect to twisting about its axis and resilient to bend along the borehole axis as said housings shift with respect to each other at different positions along the borehole.

11. A borehole survey apparatus according to any preceding claim including means for deriving from the accelerometer signals a representation of the borehole trajectory.

12. A borehole survey apparatus substantially as described herein with reference to the drawings.

13. A method of surveying a borehole which comprises: measuring the acceleration of gravity along different axes at successive pairs of points along said borehole, the axes at each point of a pair of points having a known relation; generating signals representing said accelerations; providing a measure of distance of said points along the borehole; and deriving from said acceleration signals and the measure of distance a representation of the borehole trajectory.

14. A method of surveying a borehole according to claim 1 3 in which the orthogonal axes at each point define a plane at right angles to the axis of the borehole.

1 5. A method of surveying a borehole according to claim 13 or claim 14 in which the representation of the borehole trajectory is in terms of coordinates related to a reference point.

1 6. A method of surveying a borehole according to any of claims 13 to 1 5, in which: two sets of spaced apart accelerometers are moved through the borehole; and successive measurements are made by sampling signals from the accelerometers.