Error Analysis and Correction of a Downhole Rotating Magnetic Full-Tensor Gradiometer

Compared with ground magnetic measurement and aeromagnetic survey, downhole magnetic measurements can provide more abundant and accurate distribution information of ore deposits. Measurement of the full magnetic tensor gradient affords more information than either traditional magnetic total field or three, orthogonal axes, vector field measurements. Gradient field measurements are less influenced by any time and/or spatial changes of the Earth's magnetic field during the measurement period. CSIRO has developed the world first downhole magnetic full tensor gradiometer and carried out field tests. This gradiometer is based on a rotation of two fluxgate vector field sensors to enable frequency separation of the common mode from the gradient signals. Reposition of the gradiometer about three, nominally orthogonal axes, enables measurement of the full gradient tensor with one pair of fluxgate sensors. This paper describes a method to improve the accuracy of this type of gradiometer. System errors have been analyzed and classified according to the effect of the errors on the measurement accuracy. Major errors include scale factor error of the two fluxgates, misalignment and motion errors of these two sensors relative to the model system, and transformation errors when moving from the sensor to the instrument coordinate frame of reference. Minor errors include errors of finite length measurement parameters, errors associated with ignoring high-order tensors, the deviation of the rotation axis from ideal, and the temperature co-efficient of the fluxgates' signals. We have developed the error models for the major errors and calibrated the full-tensor gradiometer by using the two independent tensor rotation invariants. 1000 simulations with random errors show the root mean squares of relative error are less than 8% after calibration. The calibration technique was applied to field trail measurements made using a gradiometer that was re-oriented multiple times around a fixed point while measuring a known gradient. Applying the calibration method resulted in an improvement of the tensor magnitude accuracy by a factor of 3.74. This result validated the calibration method.