WO1996002733A1

WO1996002733A1 - Method of correcting for error components in wellbore survey data

Info

Publication number: WO1996002733A1
Application number: PCT/GB1994/001523
Authority: WO
Inventors: Andrew Goodwin Brooks
Original assignee: Baker Hughes Incorporated
Priority date: 1994-07-14
Filing date: 1994-07-14
Publication date: 1996-02-01
Also published as: AU7190294A

Abstract

A method of determining the azimuth of a surveying instrument in a borehole from measurements of components of the earth's magnetic and gravitational fields, wherein the azimuth angles are computed from two or more surveys taken in different borehole orientations. Each pair of surveys may be used to solve a quadratic equation determining the vertical component of the earth's magnetic field. A graphical solution method using three or more surveys is also disclosed. A further method is useful in attitudes close to horizontal east-west, wherein the measured axial component of the earth's magnetic field in one attitude is used to determine the axial component in a second attitude, using the assumption that the axial error component due to drillstring magnetization changes slowly or not at all.

Description

Method of Correcting for Error Components in Wellbore

Survey Data

Technical Field

The present invention relates to a method of determining the azimuth angle of a surveying instrument in a borehole in which the earth's magnetic field may be contaminated by an additional magnetic field due to drillstring magnetization. More particularly, the present invention relates to a method of computing azimuth without requiring accurate prior knowledge of the magnitude or direction of the earth's magnetic field and without requiring computation of the axial component of the earth's field. The present invention further relates to computing azimuth in steeply inclined boreholes which are oriented close to the east-west direction, wherein most prior methods become highly inaccurate.

Background Art

Conventional borehole survey instruments operate by measuring three orthogonal components of the local gravitational and magnetic fields at a location within the drillstring. These six measurements are then used in well-known equations to determine the following six parameters: gravity field strength, magnetic field strength, magnetic dip angle, borehole inclination, borehole azimuth, and instrument tool face angle. However, the instrument is placed within a drillstring of which portions are ferromagnetic, and it is common for drillstring magnetization to corrupt the measurement of the axial component of the local magnetic field. Unless a correction is made, this corrupted axial magnetic component may lead to incorrect computation of magnetic field strength, magnetic dip angle, and borehole azimuth.

In order to understand the present invention, it is important to establish the definitions of terminology utilized in wellbore survey operations. Surveys are used to determine the position of a wellbore within the earth. The orientation of the wellbore is determined at a particular depth by the deviation of the wellbore from a predetermined axis. The deviations may be measured with respect to two reference vectors:

(1) the earth's gravitational field vector "G"; and

(2) the earth's magnetic field vector "B".

In accordance with convention, G is positive in the vertical downward direction, while B is positive in the north direction and is inclined by a dip angle D below the horizon, as is shown in Figure 1.

The position of the wellbore relative to the earth's gravitational field vector G is identified as an inclination "I" angle, which is the angle between the longitudinal axis of the drillstring and the earth's gravitational field vector G. The position of the wellbore relative to the earth's magnetic field vector B and the earth's gravitational field G is identified as a magnetic azimuth "A", which is the angle between the horizontal component of the longitudinal axis of the drillstring and the horizontal component of the earth's magnetic field vector B.

Wellbore survey operations are also frequently utilized to determine the dip angle "D", which is the complement of the angle between the earth's magnetic field vector B and the earth's gravitational field vector G (that is, 90 degrees less the angle between vectors B and G). The dip angle D is available in look-up tables, computer programs, and charts for all latitudes and longitudes on the earth's surface.

In conventional wellbore survey operations, accelerometers are utilized to measure the direction of the earth's gravitational field vector G, and magnetometers are utilized to measure the earth's magnetic field vector B. Each vector, includes x-axis, y-axis, and z-axis components.

In order to understand the techniques of the present invention for compensating for the magnetic field biasing error "e", it is important first to understand the coordinate systems utilized in surveying operations. Figure 2 provides a view of the Cartesian coordinate system which is established relative to the bottomhole assembly of a drillstring. The z-axis of the coordinate system is in alignment with longitudinal axis of the bottom hole assembly. The x-axis and y-axis are perpendicular to the z-axis, and are fixed in position with respect to the bottom hole assembly. Therefore, rotation of the bottomhole assembly about the z-axis also rotates the x-axis and the y-axis by an amount measured in terms of tool face angle "T". Note that the inclination angle I provides a measure of the position of the bottomhole assembly of a drillstring relative to the gravity field vector G, and the tool face angle T provides a measure of the angle in the xy-plane between the y-axis and the highside HS of the tool. The three measured components of each field are subscripted x, y, and z. The tool coordinate axes are shown in Figure 2.

The tool "orientation" is usually expressed in terms of the following three drilling angles: inclination I which is the angle between the z-direction and vertical; azimuth A which is the angle between the horizontal projections of the z-axis and the macfnetic north vector; and gravity tool face T which is the angle in the xy-plane between the high side HS of the tool and the y-axis. Figure 3 shows these drilling angles. A further useful drilling angle is the magnetic tool face angle M, defined here as the angle in the xy-plane between magnetic north N and the y-axis.

During survey operations, magnetometer readings are taken along the three axes to determine the magnetic field vector B components: these measurements are identified as B_x, B_y, and B_z. Accelerometer readings are taken along the three axes to determine the gravitational field vector G components: these measurements are identified as G_x, G_y, and G_z. Since these vectors have both a direction and a magnitude, these tri-axial measurements will have to be scaled, or calibrated, to accurately reflect the magnitude of the vector they represent.

Survey tools utilize these x-y-z arrays of accelerometers and magnetometers to determine the directions and magnitudes of the B and G vectors in the x-y-z frame of reference. This information is used to determine the tool's "attitude", expressed by the inclination angle I, and the azimuth angle A and the tool face angle T.

Once a set of values for B_x, B_y, B_z, G_x, G_y, and G_z are determined for a specific wellbore depth, the azimuth A, inclination I, and tool face angle T of the wellbore at that depth can be determined. Also, the value of the magnetic dip angle D can be calculated. The three accelerometers are normally used to find I, T and G, the magnetometers are used to find B, and a combination of measurements from all sensors are required to calculate A and D. An expected magnetic field strength B and dip angle D can be looked up in reference tables, computer programs, or charts based on the wellsite's longitude and latitude.

Once the azimuth A and inclination I are determined for the wellbore at a number of specific depths, a directional map of the wellbore can be plotted. This directional map shows how far, and in what direction, the wellbore is deviated from the vertical and magnetic north, and ultimately where the well is bottomed.

In order to provide the greatest accuracy in magnetic field measurements, the wellbore surveying tool is typically housed in a non-magnetic subassembly. Additionally, surrounding subassemblies may also be constructed of a non-magnetic material. However, the drillstring can nonetheless become magnetized during drilling operations, to such an extent that the accuracy of the magnetic field measurements is severely impaired. Any magnetization of the bottomhole assembly in the vicinity of the surveying equipment will introduce a biasing error "e", which is an undesired error component contained in magnetometer readings due to the magnetization of the drillstring. The biasing error includes the following two types of error components:

(1) an axial biasing error e_z; and

(2) a transverse (or "cross-axial") biasing error e_xy.

Many methods have been developed to correct for the effects of drillstring magnetization, including those described in U. S. Patent Nos. 3,791,043 to Russell, 4,163,324 to Russell, 4,345,454 to Brown, 4,433,491 to Ott, 4,510,696 to Roesler, 4,682,421 to van Dongen, 4,709,486 to Walters, 4,761,889 to Cobern, 4,819,336 to Russell, 4,956,921 to Coles, 4,999,920 to Russell, 5,103,177 to Russell, and 5,155,916 to Engbretson. With the exception of the methods described in ϋ. S. Patents 4,345,454, 4,709,486, and 5,103,177, all of these methods require accurate prior knowledge or external measurement of at least one component of the earth's magnetic field. Accuracy of the computed azimuth angle is then highly dependent on the accuracy with which these components are provided. In certain borehole attitudes, particularly those close to the horizontal east-west vector, accuracy of azimuth angles computed by these methods may be very poor.

U.S. Patent No. 4,345,454 to Brown describes a method and apparatus for measuring inclination and azimuth in a plurality of toolface attitudes. While this technique can effectively reduce the influence of small transverse magnetic anomalies associated with the drillstring, it cannot eliminate the effects of the axial anomalies which are generally much more significant and which are the subject of this invention. U.S. Patent No. 4,709,486 to Walters describes a method for determining azimuth by taking measurements in a plurality of attitudes and using a pair of such measurements to solve for the uncontaminated axial magnetic component B_z in each attitude. This method suffers from the drawback that it can be difficult to select the correct one of the two possible roots for B_z; although the patent states that such ambiguity can be removed by comparing B_z at a plurality of locations, there is no reason to believe that B_z should be the same at each location and therefore some ambiguity remains. U.S. Patent 5,103,177 to Russell describes a method and apparatus for determining azimuth by making a plurality of measurements of B_z at different locations within the drillstring; such a method is not feasible using the equipment commonly provided with measurement-while- drilling tools which contain a single axial magnetometer at a fixed position within the drillstring. Disclosure of Invention

Applicant has discovered that it is possible directly to calculate the vertical component B_v of the earth's magnetic field from surveys made in a plurality of borehole attitudes. While this method requires the solution of a quadratic equation for each pair of surveys and therefore gives two possible results, it is reasonable to assume that B_v is approximately constant and it is usually a simple matter to select the proper root by comparison with an approximate estimated value of B_v. In contrast with prior art techniques, the estimate of B_v is not utilized in calculating borehole orientation, the estimate of B_v is used only for identifying the correct one of the two possible roots. The value of B_v thus obtained through direct calculation from survey measurements can be substituted into further equations which solve for the horizontal component B_h of the earth's field and for the various azimuth angles A. It is therefore an objective of the present invention to provide a method of determining B_v the vertical component of the earth's magnetic field, B_h the horizontal component of the earth's magnetic field and azimuth A from a plurality of surveys without the need for computing or comparing values of B_z.

It is another objective of the present invention to provide a technique whereby possible values of the vertical component of the earth's magnetic field B_v and the horizontal component of the earth's magnetic field B_h from a plurality of surveys may be represented in the form of curves, and the most probable true values may then be considered to lie close to the intersection of the various such curves. This represents a generalization of the above method since the quadratic solution for B_v is equivalent to determining the point of intersection of one pair of such curves. In this case, no external estimate is required of B_v or of any other component of the earth's magnetic field.

Applicant has further discovered that most existing methods for determining azimuth corrected for drillstring magnetization lose accuracy as the borehole attitude approaches the horizontal east-west vector. This is unfortunate because the azimuth error due to drillstring magnetization tends to reach a maximum in such attitudes, thus accurate correction procedures are most urgently needed. It is therefore a further objective of the present invention to provide a method for determining azimuth with improved accuracy in attitudes approaching horizontal east-west.

These objectives and advantages are accomplished through the present invention by providing a method for determining the azimuth angle of a surveying instrument in a borehole, which includes the steps of: (1) measuring components of the earth's gravitational and magnetic fields at a plurality of non-parallel orientations within the borehole, (2) calculating the vertical component of the earth's magnetic field directly from such measurements, and (3) computing an azimuth angle for each orientation from the gravitational and magnetic field measurements and the calculated vertical component of the earth's field. A further method is provided which is particularly advantageous in borehole attitudes close to the horizontal east-west vector, comprising computing the azimuth angle in a first orientation which is not close to horizontal east-west, computing the axial magnetic error component due to drillstring magnetization, applying a similar axial error component to the measured field in a second orientation, and computing azimuth in the second orientation. Additional objectives, features and advantages will be apparent in the written description which follows.

Description of the Drawings

The novel features believed characteristic of the invention are set forth in the appended claims. The invention itself, however, as well as a preferred mode of use, further objectives and advantages thereof, will best be understood by reference to the following detailed description of an illustrative embodiment when read in conjunction with the accompanying drawings, wherein:

Figure 1 is a simplified graphical depiction of the earth's field vectors;

Figure 2 provides a view of the Cartesian coordinate system which is established with reference to the longitudinal axis of a drillstring disposed within a wellbore;

Figure 3 provides a graphical view of the azimuth, inclination, and tool face angles relative to the coordinate system;

Figure 4 is a depiction of a survey instrument located within a drillstring and subject to the influence of drillstring magnetization;

Figure 5 is a graph illustrating the relationship between those possible values of the squared horizontal component and the vertical component of the earth's magnetic field which are consistent with a set of gravitational and transverse magnetic measurements;

Figure 6 is a graph illustrating the relationship between those possible values of the horizontal and vertical components of the earth's magnetic field which are consistent with a set of gravitational and transverse magnetic measurements; Figure 7 is a graph illustrating the two possible values of the horizontal and vertical components of the earth's magnetic field which are consistent with two sets of gravitational and transverse magnetic measurements; and

Figure 8 is a graph illustrating the possible relationships between the horizontal and vertical components of the earth's magnetic field which are consistent with a plurality of sets of gravitational and transverse magnetic measurements.

Description of Invention

Borehole directional surveying is normally accomplished by means of instruments which measure three orthogonal components of the earth's gravitational field G and the earth's magnetic field B at a plurality of survey stations spaced along the borehole. These six measurements are made with respect to an instrument- fixed set of axes in which the z-axis is parallel to the drillstring and the x-axis and y-axis make up a right- handed triad. The six measured quantities G_x, G_y, G_z, B_x, B_y and B_z are related to the local gravitational field G, the horizontal component B_h and the vertical component B_v of the local geomagnetic field, and to the inclination I, azimuth A, and toolface attitude T of the instrument by the following equations:

(1) G_x = G*sinI*sinT (2) G_y = G*sinI*cosT

(3) G_z = G*cosI

(4) B_x = B_h*cosI*cosA*sinT + B_h*sinA*cosT - B_v*sinI*sinT (5) B_y = B_h*cosI*cosA*cosT - B_h*sinA*sinT - B_v*sinI*cosT

(6) B_z = B_h*sinI*cosA + B_v*cosI These may be solved as follows for the six unknowns

G, B_v, B_h, I, T, and A :

(7) G = (G_x ² + G_y ² + G_z ²)^.5 (8) I = cos^-1(G_z/G)

(9) T = tan^-1(G_x/G_y)

(10) B_v = (B_z*G_z - B_x*G_x - B_y*G_y)/G

(11) B_h = [B_x ² + B_y ² + B_z ² - B_v ²]^.5

(12) A = tan^-1 [G* (B_x*G_y - B_y*G_x)/{G_z*(B_x*G_x + B_y*G_y) + B_z*(G_x ² + G_y ²)}]

The surveying instrument is typically housed in a non-magnetic subassembly within the ferromagnetic drillstring. Magnetization of the drillstring at each end of the subassembly may introduce an axial magnetic error component e_z in addition to the axial component B_z of the earth's field, as shown in Figure 4. While equations (7) through (9) may still be used to derive G, I and T from the accelerometer measurements, the computed values of B_v, B_h, and A may be corrupted by the error component e_z if they are determined using equations (10) through (12).

It is assumed that the magnetization error field is wholly in the z-direction, and therefore the measurements of B_x and B_y are uncontaminated. These uncontaminated measurements may be used to determine a relationship between possible values of B_v and B_h. Equations (1), (2), (4) and (5), defining the transverse components of the gravitational and magnetic fields, may be combined as follows :

(13) B_x*G_x + B_y*G_y = G*sinI*(B_h*cosI*cosA - B_v*sinl)

(14) B_x*G_y - B_y*G_x = G*sinI(B_h*sinA)

If B_v is known, equations (13) and (14) can be used to determine the azimuth A :

(15) A = tan^-1[(B_x*G_y - B_y*G_x)/{(B_x*G_x + B_y*G_y + B_v*G*sin²I)/cosI}]

However, if B_v is unknown, equations (13) and (14) can instead be combined in the following manner to eliminate A :

(16) (B_x*G_x + B_y*G_y + B_v*Gsin²I)² + (B_x*G_y - B_y*G_x) ²*cos²I = (B_h*GsinI*cosI)²

Equation (16) represents B_h ² as a quadratic function of B_v, which is graphed in Figure 5. The parabolic curve results from the single degree of freedom introduced by discarding equation (6), and it represents all combinations of B_v and B_h ² which are consistent with the measured values of B_x, B_y, G_x, G_y and G_z, and with equations (1) through (5). It is apparent from the form of this curve that the relationship between possible values of B_h and B_v can be represented by another curve which is of somewhat similar shape, as depicted in Figure 6; Figure 5 plots the square of the horizontal component of the magnetic field (B_h ²) while Figure 6 plots B_h versus B_v.

Many prior methods of compensating for axial magnetization require the provision of an accurate value for one or more components of the earth's macfnetic field. As can be seen from equation (16) and from Figures 5 and 6, if an estimate can be provided for B_v there is a unique solution for B_h, while A may be determined using equation (15). If an estimate is provided for B_h, for the total magnetic field B = (B_v ² + B_h ²)^-5, or for the magnetic dip angle D = tan^-1(B_v/B_h), then up to two solutions may be obtained, such solutions consisting of the intersections of the curve in Figure 6 with the appropriate straight line or circular arc representing the estimated value of the magnetic component. If estimates are provided for both B_v and B_h, the most likely true values of B_y and B_h can be defined as the closest approach of the curve in Figure 6 to the point representing the estimated values.

Applicant has discovered that these methods of compensation for axial magnetization are sensitive to the accuracy of the estimates of B_v and B_h, which are typically obtained from computer programs, charts, or look-up tables, and which can be an order of magnitude less accurate than measurements taken by the instrument. Accordingly, this invention provides a means for determining B_v, B_h and A without the need for accurate external estimates of B_v, B_h, B or D.

The shapes of the curves in Figures 5 and 6 depend on the local magnetic dip angle and on the instrument attitude. Two measurements taken with the sensor in different attitudes (that is, with a different inclination I and/or azimuth A, and which is also described as "non-parallel" locations) will produce two curves of different shapes, as shown in Figure 7. In each case, a curve represents all combinations of B_v and B_h which are consistent with the uncontaminated measurements. Hence, the true values of B_v and B_h must lie at an intersection of the two curves.

The intersections can be found algebraically by simultaneously solving the following equations

(17) B_x1 = B_h*cosI₁*cosA₁*sinT₁ + B_h*sinA₁*cosT₁ - B_v*sinI₁*sinT₁

(18) B_y1 = B_h*cosI₁*cosA₁*sinT₁ - B_h*sinA₁*sinT₁ - B_v*sinI₁*cosT₁

(19) B_x2 = B_h*cosI₂*cosA₂*sinT₂ + B_h*sinA₂*cosT₂ - B_v*sinI₂*sinT₂

(20) B_y2 — B_h*cosI₂*cosA₂*cosT₂ - B_h*sinA₂*sinT₂ - B_v*sinI₂*cosT₂ for the four unknowns B_v, B_h, A₁, and A₂. Assuming that G₁, I₁, I₂, T₁, and T₂ have been obtained from the accelerometer equations (7) through (9), this can be accomplished by (21) t(B_χ1*G_x1 + B_y1*G_y1 + B_v*G*sin²I₁)²/cos²I₁ + (B_x1*G_y1 -

B_y1G_xl)²]/sin²l₁ = [(B_x2*G_x2 + B_y2*G_y2 + B_y*G*sin²I₂)²/COS²I₂ + (B_x2*G_y2 - B_y2*G_x2)²]/sin²I₂

This is a quadratic equation in B_v. Of the two possible roots, it is usually possible to select the proper one, since approximate knowledge of B_v is available from the aforementioned computer programs, charts, or look-up tables. This contrasts with the prior art method of Walters in which the value of B_z is used to discriminate between roots, since B_z is a function of azimuth which can neither be assumed to be constant nor to be known in advance.

Equation (16) may then be used to determine B_h uniquely, since B_h is always positive, while the two azimuth angles can be found from equation (15).

Under circumstances where the estimated value for B_v is not available, an alternate method for discriminating between the two possible roots consists of calculating the axial magnetization error field "e_z" in each of the two orientations and selecting whichever root indicates the smallest change in magnetization error field. One means of computing these axial magnetization error fields requires first computing the apparent values of the vertical component of the earth's magnetic field :

(22) B_v1 = (B_z1*G_z1 - B_x1*G_x1 - B_y1*G_y1)/(G_xl ² + G_y1 ² + G_z1 ²)^.5

(23) B_v2 = (B_z2*G_z2 - _Bx2*G_x2 - B_y2*G_y2)/(G_x2 ² + G_y2 ² + G_z2 ²) .⁵

If the two roots of equation (21) are designated B_va and B_vb, then the corresponding axial magnetization error fields are given by: (24) e_z1a = (B_v1 - B_va)/cosI₁ in the first orientation using root B_va,

(25) e_z2a = (B_v2 - B_va)/cosI₂ in the second orientation using root B_va,

(26) e_z1b = (B_v1 - B_vb)/cosI₁ in the first orientation using root B^,

(27) e_z2b = (B_v2 - B_vb)/cosI₂ in the second orientation using root B_vb. The apparent change in magnetization error field between the two orientations is then

(28) δ_eza - e_z2a - e_z1a if root B_va is selected, or

(29) δ_ezb - e_z2b - e_z1b if root B_vb is selected.

If |δ_eza| is smaller than |δ_ezb|, then root B_va may be assumed to be the correct root, otherwise root B_vb is used.

In the event that more than two surveys are available in different borehole attitudes, more than two curves can be plotted, as shown in Figure 8. The most likely values for B_v and B_h may then be found graphically as the point closest to the cluster of intersecting curves, and the azimuth angles can be determined as before using equation (15) or using other known methods.

When the borehole attitude approaches the horizontal east-west vector, all of the above techniques lose accuracy as the computed azimuth becomes highly sensitive to the accuracy of the B_x and B_y measurements. Indeed, inspection of equations (4) through (6) clearly shows that in the limiting case of a horizontal borehole only B_z contains information indicating whether the borehole is headed northward or southward, since only B_z then is sensitive to the cosine of the azimuth angle. Hence any method for determining azimuth which ignores the B_z measurements cannot be certain of locating the proper quadrant in a near-horizontal hole. This is particularly unfortunate because the influence of axial magnetization errors on the computed azimuth tends to reach a maximum in horizontal east-west attitudes, so procedures to correct for such magnetization errors would be particularly valuable in such attitudes. Applicant has discovered that because the horizontal east-west attitude is normal to the earth's magnetic field, axial drillstring magnetization may be assumed to be constant or to change only at a slow rate in such attitudes. Changes in drillstring magnetization are generally believed to result from repeated strains in the ferromagnetic material while influenced by the earth's field; but when the earth's field has little or no axial component then little or no axial magnetization will be created. Accordingly, this invention uses the components of the earth's field and the measured value of B_z in a first attitude relatively remote from horizontal east-west, said components and attitude being found by the methods described above or by other methods, then determines the axial magnetization error field by the equation:

(30) e_z - B_z1 - B_h*sinI₁*cosA₁ - B_v*cosI₁ This equation representing the difference between the axial component of the measured magnetic field and the expected value of the axial component of the earth's field as determined by equation (6). Alternatively, e_z may be found as described in equations (22) through (27).

With the assumption that the magnetization error does not change between orientations, this same magnetization error can be used to determine a corrected axial field strength in a second attitude which may be close to horizontal east-west, as follows :

(31) B_z2(corr) * B_z2 - e_z And this value can be substituted into equation (12), to compute borehole azimuth without ambiguity. Applicant has discovered that this technique can provide a more accurate measurement of azimuth than methods which fail to make use of the measured values of B_z, particularly in borehole orientations approaching horizontal east-west.

While the technique described above depends on the assumption that the axial error component e_z does not change, this assumption can be relaxed if the instrument is later returned to the first attitude or to another known attitude and a further measurement is made. If the values of the error field as computed from the two measurements in known attitudes should differ, the most likely value of the error field to be applied to any intermediate measurements may be found by interpolation. The only assumption then required is that the axial error field changes slowly or uniformly.

While the invention has been shown in only one of its forms, it is not thus limited but is susceptible to various changes and modifications without departing from the spirit thereof.

Claims

1. A method of determining the orientation of a surveying instrument in a borehole comprising :

measuring gravitational field strength and at least the transverse components of magnetic field strength at a plurality of non-parallel orientations of a surveying instrument within a borehole;

calculating a vertical component of said magnetic field strength from said gravitational strength and the transverse components of magnetic field strength; and computing an azimuth angle for at least one of said plurality of non-parallel orientations directly from said gravitational field strength and transverse components of said magnetic field and said vertical component of said magnetic field strength.

2. The method of claim 1 wherein said step of calculating includes:

selecting one of two possible roots which possibly define said vertical component of said magnetic field strength by comparing a computed value of at least one component of magnetic field with an estimated value of said at least one component of magnetic field.

3. The method of claim 1 wherein said step of calculating includes:

selecting one of two possible roots which possibly define said vertical component of said magnetic field strength by computing a change in axial error component between said non-parallel orientations.

4. The method of claim 1 wherein said step of calculating includes: plotting curves representing possible combinations of two components of magnetic field which are consistent with each measurement of gravitational field strength and the transverse components of magnetic field.

5. The method of claim 4 additionally comprising:

determining a most likely value of at least one component of magnetic field from coordinates of a point closest to intersections of said curves.

6. The method of claim 5 additionally comprising: computing an azimuth angle of each orientation from measured gravitational and transverse magnetic field measurements and from said most likely value of at least one component of magnetic field.

7. A method of determining the orientation of a survey instrument in a borehole comprising :

measuring the earth's gravitational and apparent magnetic fields at a plurality of non-parallel orientations within the borehole;

determining at least one component of the earth's magnetic field;

determining inclination and azimuth of the survey instrument in at least one of said orientations;

computing an axial component of the earth's magnetic field in said at least one orientation from said inclination and azimuth and from said at least one component of the earth's magnetic field;

computing an axial magnetic error field from said computed axial component of the earth's magnetic field and the measured axial component of the earth's magnetic field;

computing a corrected axial component of the earth's magnetic field in a differing orientation from said axial magnetic error field and the measured axial component of the earth's magnetic field in said differing orientation; and

computing the azimuth of the instrument in said differing orientation from the measured gravitational and transverse magnetic fields and from said corrected axial component of the earth's magnetic field.

8. The method of claim 7 wherein said at least one component of the earth's magnetic field is obtained from measurements in or adjacent to said borehole using an instrument which is substantially free from the influence of drillstring magnetization.

9. The method of claim 7 wherein said at least one component of the earth's magnetic field is obtained from computer programs, charts, or look-up tables based on the geographic location of the borehole.

10. The method of claim 7 wherein the azimuth in said at least one orientation is determined by the use of a survey instrument which is substantially free from the influence of drillstring magnetization.

11. A method of surveying a wellbore utilizing a sensor array located within a drillstring in said wellbore in the presence of a magnetic field biasing error which can be defined in terms of (1) an axial magnetic field biasing error, and (2) a transverse magnetic field biasing error, comprising:

measuring gravitational field strength and at least transverse magnetic field strength at a plurality of borehole attitudes; and

directly calculating magnetic field strength from measurements made during said step of measuring, which is uninfluenced by said axial magnetic field biasing error.

12. A method according to Claim 11, wherein said step of measuring comprises:

measuring gravitational field strength and at least transverse magnetic field strength at a plurality of depths within said borehole.