Systems and methods to calibrate individual component measurement

A machine-readable storage device having instructions stored thereon, which, when performed by a machine, cause the machine to perform operations, the operations comprising:

• determining a set of calibration coefficients for each sensor of a plurality of sensors of a ranging tool, wherein each one of the sensors is configured as a single component sensor, and wherein for each one of the individual sensors of the plurality of sensors the operations further comprise:
• conducting magnetic field measurements, using the individual sensor, at four or more different azimuthal angles of the individual sensor with respect to a rotational position of the ranging tool relative to a line extending to a center of an excitation source from a center of the ranging tool, the excitation source having a current of a known value flowing in the excitation source, the ranging tool separated from the excitation source at a known distance from a center of the ranging tool to a center of the excitation source;
• selecting four of the magnetic field measurements corresponding to four azimuthal angles of the four or more different azimuthal angles of the individual sensor;
• generating, using a processor, the set of calibration coefficients for a tool constant matrix for the individual sensor using values determined for the four selected magnetic field measurements and a design matrix, wherein the design matrix is based on the known value of the current, the known distance from the center of the ranging tool to the center of the excitation source, the four azimuthal angles of the four or more different azimuthal angles, and a known orientation of the individual sensor;
• and
• storing, using a storage device, the set of calibration coefficients of the tool constant matrix for the individual sensor in a tool constant matrix library;
• and
• determining a ranging distance comprising:
• conducting second magnetic field measurements at a selected tool azimuth angle, using the plurality of sensors, in response to current flowing in a conductive structure, the ranging tool and the conductive structure disposed below a surface of earth;
• creating a second tool constant matrix using the set of calibration coefficients for each one of the individual sensors of the plurality of sensors from the tool constant matrix library;
• and
• processing values of the second magnetic field measurements, using the processor, to generate the ranging distance from the ranging tool to the conductive structure, the processing including:
• generating an inverse of the second tool constant matrix for the selected tool azimuthal angle;
• generating a second design matrix from a multiplication of a matrix of values from the second magnetic field measurements and the inverse of the second tool constant matrix;
• and
• generating the ranging distance based on a calculated value for a total magnetic field and a calculated value for a gradient magnetic field, including using a first set of two elements of the second design matrix to calculate the total magnetic field and using a second set of two elements of the second design matrix to calculate the gradient magnetic field.

A system comprising:

• a current generator coupled to an excitation source to provide a current to the excitation source, the current having a known value;
• a plurality of sensors disposed on a ranging tool;
• and
• a processor configured to determine a set of calibration coefficients for each one of the plurality of sensors, each one of the plurality of sensors configured as a single component sensor, wherein for each one of the individual sensors of the plurality of sensors the processor is configured to:
• conduct magnetic field measurements, using the individual sensor, at four or more different azimuthal angles of the individual sensor with respect to a rotational position of the ranging tool relative to a line extending to a center of the excitation source from a center of the ranging tool, the ranging tool separated from the excitation source at a known distance from the center of the ranging tool to the center of the excitation source;
• select four of the magnetic field measurements corresponding to four azimuthal angles of the four or more different azimuthal angles of the individual sensor;
• generate the set of calibration coefficients for a tool constant matrix for the individual sensor using values determined for the four selected magnetic field measurements and a design matrix, wherein the design matrix is based on the known value of the current, the known distance from the center of the ranging tool to the center of the excitation source, the four azimuthal_angles of the four or more different azimuthal angles, and a known orientation of the individual sensor;
• and
• store, using a storage device, the set of calibration coefficients of the tool constant matrix for the individual sensor in a tool constant matrix library;
• wherein the processor is arranged, for each of the plurality of sensors, to generate a ranging distance from the ranging tool to a conductive structure, including the processor arranged to:
• receive values of second magnetic field measurements of the plurality of sensors for a selected tool azimuth angle in response to current flowing in the conductive structure, the ranging tool and the conductive structure disposed below a surface of the earth;
• create a second tool constant matrix using the set of calibration coefficients for each one of the individual sensors of the plurality of sensors from the tool constant matrix library;
• generate an inverse of the second tool constant matrix for the selected tool azimuthal angle;
• generate a second design matrix from a multiplication of a matrix of the values from the second magnetic field measurements and the inverse of the tool constant matrix;
• and
• generate the ranging distance based on a calculated value for a total magnetic field and a calculated value for a gradient magnetic field, including by use of a first set of two elements of the second design matrix to calculate the total magnetic field and use of a second set of two elements of the second design matrix to calculate the gradient magnetic field.