| The magnetic gradient tensor(MGT)is the spatial rate of change of the magnetic vector along the three axes of Cartesian coordinate system.MGT measurement has many advantages compared with traditional magnetic measurement,so its measurement technology has raised the attention of domestic and foreign research units in the recent two decades and becomes mature gradually.However,the defects in the existing calibration methods of magnetic tensor measurement systems(MTMSs)lead to residual errors in the tensor measurements and the difficulties in improving the measurement accuracy,which seriously constrains its applications.The resources of calibration errors of MTMSs are various,the first comes from the correction method.The correction method is a necessary priory process before the calibration and it can be divided into two aspects,the first one is correcting the imbalance of each tensor components and the defects in current methods cause residual imbalance errors which are difficult to be eliminated.The second one is the correction of construction of multiple gradient components,expression of the error mechanisms of gradient components is complex and we still lack researches on it.Besides the correction method,another problem is the complexity of the survey environment and defects in the existing calibration methods for MTMSs cannot guarantee the measurement accuracy of tensor data.There are two main types of calibration methods for the MTMSs.One is giving priority to the calibration environment,that is first producing uniform magnetic gradients with a triaxial Maxwell coil,then calibrating three diagonal components of the magnetic gradient tensor in a magnetic shielding environment.However,the survey environment has serious effects on the MTMSs,the ground calibration method is highly different from the practical survey environment.The other is giving priority to the measurement environment,which is calibrating the MTMSs where the geomagnetic gradients are nearly equal to zero.However,the zero output of a magnetic tensor gradiometer in a uniform magnetic field is a necessary condition rather than a necessary and sufficient condition for the calibration.Aiming at the existing problems in the current correcting and calibration methods for the MTMSs,the researches and contents of this paper are as follows:(1)Research on the correction method of the MTMSs.For the correction of the construction of multiple gradient components,although it is difficult to uniformly express the error mechanisms of gradient components obtained by different measurement principles,the errors are similar when constructing the tensor gradiometer.So this paper focuses on the firstorder Taylor series expansion MTMSs,builds the error model of construction of multiple gradient components,then the optimal correction parameters are obtained by using the two independent rotation invariants of the magnetic gradient tensor.The simulation results show that the proposed method can correct the MTMSs to a certain extent.For the residual imbalance errors,this paper analyses the former tensor measurement data,designs the noise eliminator based on the array self-adaptive filter according to that the residual imbalance errors are highly related to the attitudes and the magnetic vector,the result of the experiment confirms that the method can eliminate the residual imbalance errors efficiently.(2)Research on the calibration method of the airborne MTMSs.The problem of the current calibration method for the MTMSs is the lack of nonzero reference values in the survey environment.So this paper proposes carrying out the magnetic survey with the MTMS and total-field gradiometer,measuring the total-field gradient then calculate the MGT data through the generalized Hilbert transform calibration method(GHTCM).However,the flight environment is very complex,in order to obtain the accurate calibration values,we first analyze the error sources and error mechanisms of the GHTCM according to the differences between real and ideal survey conditions,then build models to design an appropriate evaluation algorithm for the accuracy of the GHTCM.The results of the simulation based on the opensource flight simulator Flight Gear indicate that the proposed method can correctly evaluate the accuracy of the GHTCM.In order to verify the proposed calibration method for the airborne MTMSs,this paper designs the validation method based on the result of the inversion,comparing the inversion results using the measurement data and the data after correcting and calibration to reflect the effect of the method.Simulation and practical experiments indicate that the correction and calibration method can improve the inversion accuracy of the location and the structure index of the magnetic source,which verifies the correctness of our methods.(3)Research on the calibration method of the downhole MTMSs.We measure the magnetic vector,then calculate the three tensor components on the z-axis and calibrate the three components,then using the invariants to calculate the calibration parameters for the rest two components.The simulation result shows that the methods can improve the measurement accuracy of the MTMSs.Similarly,the same validation method is applied to the downhole MTMSs.This paper proposes a method to determine the information of the magnetic sheet from downhole MGT data.We give expressions for the magnetic gradient tensor on the axis of a vertical borehole within a tilted sheet.We use an invariant of the tensor to determine the location and thickness of the sheet and tensor components to obtain the direction of magnetization and orientation of the sheet.An iterative procedure can improve the accuracy of the estimated parameters.The simulation results indicate that the invariant correction method can greatly improve the determination accuracy of the geometrical information of the sheet,and the calibration method can improve the determination accuracy of the rest information.Finally,Experiments using an artificial magnetic sheet verify the correctness of the proposed method. |
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