Abstract: A method and system for tracking a borehole by means of a probe and an externally produced magnetic field. The magnetic field is produced by a current configuration which facilitates the calculation of the magnitude and direction of the magnetic field at any point in space. In order to locate the probe, magnetometers within the probe are used to measure the magnetic field. Accelerometers within the probe allow the determination of the probe's orientation which enables the measured field vector to be compared to the calculated field vector and the probe's location thereby ascertained.

Abstract: A pipeline survey pig includes an elongated hollow pig body having an enclosure for supporting a generally cylindrical tubular instrument chassis which, in turn, supports an inertial reference unit and associated signal processing and recording devices. A plurality of resilient cup members support the pig body for traversal through a pipeline section under the urging of pressure fluid. The cup members are spaced apart and secured to the pig body by spacer members which may be selectively provided to predetermine the axial spacing of the cup members so that the center of stiffness of the pig is in a predetermined position. The instrument chassis is secured in the pig body by a cam mechanism which is actuatable from one end of the chassis after insertion into the pig body to wedge opposed chassis door members into engagement with the pig body to enhance heat transfer between the chassis and the pig body.

Abstract: A land vehicle navigation apparatus incorporates an inertial angular rate sensor on the vehicle and having a sensitive axis, and an inertial acceleration or tilt sensor having at least two sensitive axes; the latter two sensitive axes are typically located at the vehicle in a plane parallel to the Earth's surface; and a rotary drive is operatively connected to the sensors to rotate them about an axis extending generally at the vehicle in a plane parallel to the Earth's surface; and, circuitry is operatively connected with the sensors to determine three vehicle orientation angles, roll, pitch, and azimuth, with respect to an Earth-fixed coordinate set at a first location, and also to determine the three vehicle orientation angles as the land vehicle travels over the Earth surface; and changes to the azimuth angle during travel are determined by integration of the output of the rate sensor; also, the sensor, drive and circuitry are typically carried by the vehicle.

Abstract: A method and apparatus for stabilizing a communication sensor in a borehole is described. The principle embodiment described includes a pair of centralizers at opposite ends of the housing for the communication sensor to maintain each of such respective ends at a constant lateral displacement from the borehole casing. A pair of flexible joints are provided to isolate the communication sensor to decouple the component to be protected from any motion and/or forces secured to the same urging it from the centralized position.

Abstract: For the purposes of determining the orientation of a surveying instrument in a borehole, while compensating for the effects of perturbing magnetic fields associated with magnetized sections of the drill string both above and below the instrument, the inclination angle .theta. and the highside angle .phi. of the instrument are determined, together with two transverse components Bx and By of the local magnetic field as measured at the instrument in the borehole. Additionally either a single component of, or the magnetide of, the true earth's magnetic field at the location of the borehole is ascertained from a look-up table or directly by measurement away from the influence of the drill string. A value .PSI.a for the azimuth angle of the instrument is then determined from the inclination and highside angles, the measured component(s) of the local magnetic field, and only the single component of, or the magnitude of, the true earth's magnetic field.

Abstract: A system and method for precisely and continuously estimating the path length between the entrance of a borehole and a probe (10) which is supported by an elastic cable (14) and carries a gyrocluster (42) and accelerometer cluster (40). The precise estimate of borehole path length is used to aid the inertial navigation performed within the survey system and is selectively determined by integration of either the rate at which the probe (10) moves along the borehole or a compensated cable feed rate that is based on the rate at which the cable (14) passes into or out of the borehole with correction being made for changes in temperature and gravity induced cable stretch. Selection of the rate to be integrated at any given time being determined by whether the rate at which probe (10) moves along the borehole exceeds the compensated cable feed rate by a predetermined amount.

Abstract: A method of locating, from a relief well, a target borehole of a deep well at a substantial distance below the earth's surface, while approaching the target borehole at a large angle of intersection. A homing tool incorporating a magnetic field sensor having its axis of maximum sensitivity parallel to the axis of the relief well detects an A.C. magnetic field produced by alternating current in the target borehole to provide the data required for directing further drilling of the relief well.

Abstract: Disclosed is an inertial navigation borehole survey system wherein the signals supplied by accelerometers (40) that are contained within the borehole survey system probe (10) are corrected for gravitational gradients encountered as the probe (10) travels through a borehole (12). The gravity correction is effected in the survey system signal processor (24) and is based on a gravity gradient signal that mathematically corresponds to: ##EQU1## where f represents the specific force due to gravity; f.sub.o represents the specific force of gravity at wellhead (20) of borehole (12); R.sub.o represents the average radius of the earth; .rho.(H) represents the local density of the geological formation penetrated by the borehole as a function of depth H; and .rho..sub.ave represents the means density of the earth. In utilizing the gravitational gradient to generate a gravity correction signal, the signal processor (24) effects a summation process that mathematically corresponds to: ##EQU2## where (.DELTA.H).sub.

Abstract: A pipeline pig device comprises a longitudinal housing of given length, having adjacent each end a substantially centralizing packer or seal by which pipeline fluids may be used to propel the device. Intermediate the longitudinal housing are a plurality of outwardly extending feeler arms which ride against the pipeline interior. Movement of the feeler arms caused by the pig traversing bends, miters or other deviations from straight, round pipe are transmitted to a recording system which, in combination with odometers, will provide information and/or changes in such bends.

Abstract: Apparatus and method for the surveying of bore holes, for example, oil wells and the like, to permit accurate three-dimensional mapping thereof, using a single rate gyroscope and an accelerometer package in an instrumentation pod which is lowered into the bore hole. Signals from the accelerometers and the rate gyroscope plus the increments by which the pod is lowered into the well permit continual calculation of pod attitude and updated of pod position at all depths in the hole.

Abstract: A pipeline survey pig including an onboard inertial reference unit and signal processing units for receiving acceleration and angular velocity signals generated by the inertial reference unit, calculating resultant values of angular velocity and accelerations and averaging the calculated values to provide recordable signals related to the position of the pig and changes in curvature of the pipe. The pig is supported by a plurality of resilient cup shaped support members which have a stiffness characteristic whereby the natural frequency of vibration which may cause lateral excursions of the pig is less than the signal generating rate yet greater than the frequency of the signal to be measured. The center of stiffness and the center of gravity of the pig are disposed along the central axis of the pig and the pipeline section being measured and are preferably coincident with each other.

Abstract: A fiber-optic rotation sensor particularly adapted to be placed adjacent a drill head to measure the orientation of a drill string with respect to the axis of rotation of the earth during or after drilling for minerals such as oil and gas. The analog sensor is based on a Sagnac interferometer and uses light beams counterrotating in one or more oblong circular shaped coils of optical fiber in which dual phase modulators are used to generate an AC signal to enable detection of a rotation rate output. The sensor also includes means to mechanically or electrically flip the sensitive axis of the rotation sensor to null out bias drift. If one coil is used, the flipping is in 90.degree. segments. When two coils at 90.degree. to each other are used, they are flipped 180.degree..

Abstract: A method of determining the orientation of a surveying instrument in a borehole from measurements of the earth's gravitational and magnetic fields wherein the azimuth angle is calculated directly without correcting an apparent azimuth. Those measurements are used to calculate the borehole axial magnetic component at each orientation of the surveying instrument in the borehole, and the borehole axial magnetic component is used, along with those measurements, to directly calculate the proper azimuth angle. In a preferred embodiment, measurements are taken at a plurality of orientations in the borehole and the borehole axial magnetic component is calculated in simultaneous equations and then compared to insure the accuracy of the azimuth computation at each orientation. The orientations are preferably non-colinear.

Abstract: A borehole survey apparatus includes an angular rate sensor, a tilt sensor, a rotary drive to rotate the sensors about an axis extending in the direction of the borehole, circuitry connected with said sensors to determine the azimuthal direction of tilt of the borehole at a first location therein, drive control circuitry and a switch operatively connected with the sensors whereby they may be connected in feedback relation with the rotary drive so that an axis defined by a support for the rate sensor is maintained at predetermined orientation relative to horizontal during travel of the apparatus in a borehole relative to the first location, and integration circuitry connected with the rate sensor whereby changes in borehole alignment during travel may be determined.

Abstract: Logging apparatus for measuring alternating magnetic fields generated by electric current flow on a subterranean target near a borehole is disclosed. Electric current of a predetermined temporal form is made to flow on the target; the resulting magnetic field is measured by magnetometers in a downhole sonde. The orientation of the sonde is fixed by various combinations of gyroscope, accelerometer, magnetometer measurements, and borehole survey data.

Abstract: A bore hole navigator utilizing a two axis directional gyro on the inner frame of the navigator and a single axis accelerometer on the outer frame is disclosed. This allows the inner frame of the navigator and thus the entire navigator to be smaller in diameter, both because of the removal of the acceleration axis to the outer gimbal and because the electrolytic level sensor, if used, is much smaller than a single axis accelerometer. The overall smaller diameter is maintained by using a belted design wherein the gyro/electrolytic level sensor, the inner frame torquer/gear and the inner frame resolver are connected in series along the length of the navigator, with a high gear reduction ratio on the inner frame torquer providing a positive drive within a smaller diameter. This configuration, together with unique calculation algorithms allows smaller diameter and deeper holes to be surveyed.

Abstract: A method of, and apparatus for, determining the position of an unknown fixed location, e.g. the end of an underground passage inaccessible to human beings, involves establishing a chain of measuring station of known station spacing between a base and a position at the unknown fixed location. Each station (except, optionally, the foremost one) of the chain is provided with light sources and photodetectors as well as a goniometer for measuring in at least one plane the angle of inclination of the station immediately ahead of it. The stations of the chain are spaced apart by a known distance and arranged so that each station is within the operative range of the immediately preceding station. By transmitting the measurement results from each station to the base, and processing the data, the position of the fixed location from the measurement results.

Abstract: A control system guides a boring tool in a borehole. The tool has a longitudinal tool axis and includes a driver for advancing the tool axially through the earth and steering mechanism for directing the motion of the tool relative to the tool axis in response to control signals. The control system includes an axial electromagnetic source for generating an axial alternating magnetic field directed along an axial source axis. A sensing assembly remote from the source means includes first and second pickup coils for sensing the alternating magnetic field. Each of the first and second pickup coils has a respective coil axis and is rigidly mounted in respect to the other with their respective axes at a substantial angle with respect to each other, defining a sensing assembly axis substantially normal to both coil axes. Each coil generates a respective null electrical signal when the lines of magnetic flux at the respective coil are normal to the respective coil axis.

Abstract: A universal measuring gauge for geological structures is disclosed, having an application part including an arm and a gib, which is normally attached to it on one side, the arm being, on the other side, shaped into a universal bearing journal (pin), which passes through the bearing bush; two opposite axes equipped, on their ends, with normally fixed inclination indicators, radiate from the bush center; a suspension part including two vertical discs with a protractor scale, pivoted on the mentioned axes and firmly connected with the suspension, the lower suspension part being equipped with a transparent horizontal protractor scale and in the center of the lower suspension part, the upper half-bush of the bearing is formed, the bearing being passed by a hollow pin, carrying the transparent horizontal disc with indices, the hollow pin being axially and radially guided (glided) in the upper and lower half-bushes of the bearing; and an orientation part containing the mentioned lower half-bush, where the lower need

Abstract: A borehole survey apparatus including(a) angular rate sensor means having a sensitive axis,(b) tilt sensor means,(c) a rotary drive operatively connected to said (a) and (b) sensor means to rotate same about an axis extending generally in the direction of the borehole,(d) and circuitry operatively connected with said (a) and (b) sensor means to determine the azimuthal direction of tilt of the borehole at a first location therein, said (a) sensor means also connected in feedback relation with the drive whereby the sensitive axis of the (a) sensor means is maintained at a predetermined orientation relative to horizontal during travel of said apparatus in the borehole relative to said first location, and whereby changes in borehole alignment during said travel may be determined.

Abstract: A borehole mapping apparatus which employs a ring laser gyroscope. The path of the laser is defined by looping paths of laser beam travel having long and short stretches of travel. The ratio of the stretches being substantially greater than two.

Abstract: The inclinometer comprises a single module for measuring the inclination and azimuth of a bore, such as that of an oil well. The single module contains a removable cassette with an inclination measurement means disposed on one side thereof and an azimuth measurement means on the opposite side so as to provide a measurement recording on the substrate of the recording means. An optical assembly is provided within said module for the inclination and azimuth measurement means. Further, a power source is disposed within said module. The module has an inner and outer housing means being provided within said inner housing for providing a rotational movement thereto.In accordance with another embodiment, the inclinometer comprises a first module being a power module for supplying power to the components of the second module.

Abstract: A scriber arm mounted to two synchronized cranks, one of which defines the minor axis of the ellipse while the other defines the major axis.

Abstract: An apparatus and method for preventing damage to the mechanical components of a borehole inclinometer is disclosed. The inclinometer uses a freely suspended pendulum to align with the vertical at a selected position in the borehole. A compass connected to the pendulum rotates to an orientation defined by the earth's magnetic field. To protect the components which suspend the pendulum, the pendulum is clamped between a timer and a lens as the inclinometer is lowered into the borehole. At a selected time, the pendulum is unclamped and is permitted to reach an equilibrium, measuring position. After a selected interval, the timer urges the pendulum against the lens to clamp the pendulum. The inclinometer is raised from the wellbore, and the orientation of the pendulum relative to the lens is observed to determine the azimuth and inclination of the borehole.

Abstract: An improved ellipsograph capable of drawing dotted or dashed lines comprising a drawing unit with a small motor which drives a pen holder and two pull discs causing them to turn synchronously to draw ellipses in any shape from real circle to horizontal line by adjusting the radius of circumambulation of the pen and of the puller carriers, and a drawing control unit for controlling and selecting a dotted or a dashed line.

Abstract: This invention relates to mapping or survey apparatus and methods, and more particularly concerns derivation of the azimuth output indications for such apparatus in a borehole from the outputs or output indications of either an inertial angular rate vector sensor (or sensors) and an acceleration vector sensor (or sensors), or a magnetic field vector sensor (or sensors), and from the outputs of an acceleration vector sensor (or sensors). At least one of such sensors in any instrument may be canted relative to the borehole axis. Borehole tilt is also derived.

Abstract: In order to improve the accuracy of borehole survey systems utilizing probes with inertial components including inclinometers, two ring laser gyro units are included to provide rotation information to the system. When the probe is moving in a borehole, inclinometer iformation is used to produce a synthetic rotation signal to take the piece of a third gyro and the earth's rotation is used for a similar purpose in combination with signals from the two ring laser gyros when the probe is stopped. Wire line velocity is used in combination with the inclinometer and gyro information to provide signals representing the probe velocity and position. Coordinate transformations are provided in the probe to transform the inertial signals and wire line velocity signals into earth reference coordinate system. Kalman filtering incorporates noninertial velocity data to reduce the effect of errors inherent in the generation of various input signals to the system.

Abstract: Bore hole instrument and methods of manufacturing and using the same. The instrument includes an elongated flexible probe which is inserted into a bore hole and can travel freely around bends of relatively short radius in the hole. The probe includes a plurality of sensors, explosive charges or the like which are spaced apart and embedded in a flexible body comprising a mass of cushioning material, with a flexible outer casing of fabric having a high tensile strength. The probe is driven into a bore hole in piston-like fashion, and the flexible body enables the probe to travel freely around bends of relatively short radius. Instrumentation for processing signals from the probe is located at the surface of the earth, and a flexible cable interconnects the instrumentation with the probe.

Abstract: When surveying a borehole using an instrument responsive to the earth's magnetic field, a length of non-magnetic drill collar is necessary to house means for measuring the magnetic field in the borehole perpendicular to the direction of the borehole axis. The instrument determines the inclination angle and the highside angle from the gravitation measurements, with these measurements and the magnetic measurements, the azimuth angle is determined. Using the method of this invention a minimum length of non-magnetic material necessary for an accurate measurement may be calculated and used.

Abstract: A borehole is surveyed by positioning at the mouth of the borehole a survey instrument having a casing and a three-axis rate gyroscope unit mounted within the casing, and sensing at least two components of gravity in at least two mutually transverse directions with respect to the survey instrument by means of a gravity sensor unit. The survey instrument is then moved along the borehole with the start and finish of the run being at the mouth of the borehole or at some known reference along the path of the borehole. During the run the rates of rotation about three non-coplanar axes are sensed at a series of locations along the length of the borehole by means of the rate gyroscope unit.

Abstract: A measurement system detects a downhole drilling variable in relation to the rotational orientation of a drill string during drilling. The system includes a downhole reference signal generator and a downhole variable signal generator. The reference signal generator is coupled downhole to the drill string for generating a downhole reference (DR) signal indicative of the angular relationship between the angular orientation of a lower portion of the drill string about its axis and a directional reference, such as gravity or the earth's magnetic field. The downhole variable signal generator detects downhole parameters and generates a downhole variable (DV) signal representative of a downhole parameter of interest during drilling, such as the bending moment applied to the lower portion of the drill string.

Abstract: A well mapping apparatus comprises:(a) a magnetic field sensing device whose output is proportional to a local magnetic field vector,(b) an acceleration sensing device whose output is proportional to a local gravity vector,(c) the devices supported for rotation about a common axis, in a borehole,(d) the outputs being usable in the determination of azimuth and inclination of the borehole.

Abstract: A borehole survey method employs a first sensor for measuring angular rate, and a second sensor or sensors for sensing tilt, and a rotary drive for the first and second sensors, and includes the steps:(a) operating the drive and the first and second sensors at a first location in the borehole to determine the azimuthal direction of tilt of the borehole at such location,(b) then traveling the first and second sensors and the drive lengthwise of the borehole away from the location, and operating the drive and at least one of the first and second sensors during such traveling to determine changes in borehole alignment during such traveling.

Abstract: Inclination measurement apparatus having a housing, a reference pendulum mounted for swinging about one axis of the housing to respond to deviation of the housing means about such axis, an inclination indicator responsive to the inclination of such housing about another axis, and connected to such reference pendulum, whereby to adopt a predetermined reference position relative to such first axis, a movable locking device operable to restrain movement of such inclination indicator about such transverse axis and being releaseable to permit such movement, the locking device being movable into and out of engagement with the indicator device to secure such indicator device against movement about such transverse axis.

Abstract: A borehole mapping and/or navigational instrument includes a carrier movable lengthwise in the borehole; structure on the carrier defining an axis of rotation; and a tilt sensitive device rotatable about the axis of rotation, that device having a tilt sensitive axis with components along the axis of rotation and along perpendiculars to that axis. One or more angular rate sensors may be provided to be rotatable about the axis of rotation.

Abstract: A transducer for sensing the angular position or rate of change of displacement of a housing of a borehole survey instrument with respect to a reference position includes a rotor magnetically suspended within a stator which is in turn secured to the housing. The rotor is constrained by the magnetic suspension to rotate about a single axis relative to the stator. A frame of reference is established for the transducer, against which subsequent measurements are compared. Optical sensing means are included for sensing the movement of the rotor about the axis of motion to develop an indication of the angular position or rate of change of position of the housing.

Abstract: An apparatus and its use for measuring the differences in gravity at spaced locations in a wellbore. The apparatus includes first and second gravity measuring devices mounted at spaced vertical positions from each other and encapsulated for movement through a wellbore. A first electrical control current, proportional to the force of gravity acting upon the first gravity measuring device, is provided as a bias current to a second electrical control current. The second electrical control current is indicative of differences in gravity forces detected by the first and second gravity measuring devices, thereby providing a gravitational gradient reading.

Abstract: An instrument including a gyroscopic rotor mounted to precess about a predetermined axis in response to pivotal movement of the rotor about a sensing axis, with the rate of precession being measured and being utilized to determine the amount of said pivotal movement above the sensing axis. Two or more such rotors precessing about different axes can respond to different components of the earth's rotational movement, or to other component movements or torques. Differences in the rates of precession of the two rotors indicate the relative strengths of the corresponding components of the earth's movement, and afford a basis for deriving an indication of azimuth.

Abstract: A borehole survey instrument has a probe with a polarized light system for transmitting a signal representing the angular orientation of the probe to the surface. Light from a source in the probe is directed through a polarizing filter with an axis of polarization orthogonal to the longitudinal axis of the probe. The polarized light beam is transmitted to the surface through an optical fiber light conduit. The angle of polarization is detected with a rotating polarizing filter and provides a measure of the probe orientation. In surveying a borehole, azimuth is determined from inclinometer measurements. The probe orientation in vertical sections of the borehole is measured by the polarized light system. Two measures of borehole azimuth are combined, providing an improved measure of azimuth in boreholes near vertical and near horizontal.

Abstract: This invention relates to mapping or survey apparatus and methods, and more particularly concerns derivation of the azimuth output indications for such apparatus in a borehole from the outputs or output indications of either an inertial angular rate vector sensor (or sensors) and an acceleration vector sensor (or sensors), or a magnetic field vector sensor (or sensors), and from the outputs of an acceleration vector sensor (or sensors). Borehole tilt is also derived.

Abstract: Apparatus for reducing landing shock for instruments run into earth boreholes through drill string bores and to maintain azimuthal orientation being protected with enclosing structure. An instrument package has a depending spear point for engaging a baffle in the drill string. The spear point encloses a spring and fluid damped shock absorber. The instrument package further includes a second internal fluid damped shock absorber and a spring type rotary shock absorber for the measuring instrument.

Abstract: An improved tilt meter mechanism characterized by a pyramidal pendulum support for a tilt sensor, and means for leveling the support to zero the sensor. A pair of motor driven gibs movable along vertical rails are provided, and a biasing mechanism urges angled faces of the support firmly against the gibs. To zero the tilt sensor, the motors associated with the gibs are individually actuated to move the gibs in directions substantially normal to the X-Y measurement plane of the sensor to bring the X-Y measurement plane into alignment with a gravitationally normal reference plane.

Abstract: A drill core inclinometer is releasably mountable in a core barrel and includes a device for measuring the vertical and transverse inclination of the drill core before the core is detached from the matrix. The device, once it has effected the measurements, is arrested so that the measurements are retained and remain unaffected while the core is brought to the surface.

Abstract: An improved inclinometer and method for simultaneously measuring tilt and relative bearing in remote hostile environments such as oil and gas wells involving a pair of pendulum masses attached to perpendicularly intersecting shafts and individually capable of creating rotational motion through angles characteristic of tilt and relative bearing wherein, by use of a differential gearing system, the rotational motion induced by tilt and rotational motion induced by relative bearing are summed as a single rotational motion parallel to the axis of rotation of the relative bearing induced rotation and collinear to the well bore such that potentiometers responsive to relative bearing and the sum of tilt and relative bearing generate electrical signals that can both be transmitted to the surface without the use of troublesome slipring electrical contacts or the like. In this manner the reliability and durability of instrument is improved.

Abstract: Two tubular elements are connected by a ball-and-socket joint and arrangements are provided for measuring angular displacement which occurs between the longitudinal center axes of the two elements.

Abstract: The invention makes it possible to determine impressions independently of a core cutting machine.A hooking device makes it possible to lower the assembly by a simple cable owing to the provision for an additional mass. The position of the eccentric is ascertained by the penetration of pointed rods into a disc under the pressure of one or more of several feelers which releases the rod carrier.The device may be used for the precise determination of the line of greatest slope relative to the impressions even for inclines varying from the vertical by less than 10.degree..

Abstract: A compass card is provided for use in achieving the angular alignment of a whipstock relative to a whipstock anchor having a keyway therein for subsequent insertion in a packer apparatus for use in a subterranean well. The compass card comprises an annular card having polar coordinates in mirror image reverse relationship on one face thereof and may have a plurality of sheet-like magnetic elements secured to the other face adjacent a central opening therein.

Abstract: A measurement system detects a downhole drilling variable in relation to the rotational orientation of a drill string during drilling. The system includes a downhole reference signal generator and a downhole variable signal generator. The reference signal generator is coupled downhole to the drill string for generating a downhole reference (DR) signal indicative of the angular relationship between the drill string and a directional reference, such as gravity or the earth's magnetic field. The downhole variable signal generator detects downhole parameters and generates a downhole variable (DV) signal representative of a downhole parameter of interest during drilling. The DV signal and the DR signals are thereupon processed, either downhole or uphole depending in part on the telemetry system employed. The system is especially adapted for indicating the resultant lateral force applied to the drill string at the drill bit during drilling which is useful in projecting the probable drilling direction.

Abstract: A method of determining azimuth involves use of an angular accelerometer, and includes:(a) rotating the accelerometer about a first axis while the accelerometer is carried on a body which is itself rotating about a second axis, and(b) detecting the accelerometer output of the accelerometer which is caused by said rotation.The accelerometer may for example be rotated in a bore hole in the earth, with the first axis extending in the direction of the hole.

Abstract: A borehole mapping and navigational instrument which travels up and down in a well. The instrument includes a housing which supports at least a rate gyroscope, accelerometer, and an electric motor to rotate the accelerometer about an axis which is canted about the axis of the housing. Since the accelerometer is rotated, its tilt sensitive axis then effectively has components along the X and Y directions normal to the Z axis, whereby components along all three axis are provided.