Abstract: A method is provided for computing the differential azimuth between two sets of spaced-apart gravity component measurement devices in a borehole, employing multiple rotation angles. The method includes modeling relationships of axes as defined; forming equations relating rotation angles to outputs of gravity measuring devices; solving such equations to derive the values representative of all of the rotation angles, using measured values of the outputs from the first and second sets of gravity component measuring devices, and computing from the values of the rotation angles the differential azimuth angle between the first set and the second set of gravity measuring devices.

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: 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: 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: 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.