Tensor Magnetic Gradiometer Research Articles

Error Calibration for Crosstalk of SQUIDs in Full Tensor Magnetic Gradiometer Based on Moore–Penrose Inverse and Helmholtz Coil

In order to calibrate crosstalk error between superconducting quantum interference device (SQUID) magnetometers in a multichannel SQUID system, we propose an innovative error calibration method for crosstalk of SQUID magnetometers based on the Moore–Penrose inverse method and Helmholtz coil in this article and successfully apply it to an eight-channel SQUID magnetometers based full tensor magnetic gradiometer (FTMG). We first analyze the causes of crosstalk through working principle of the SQUID readout circuit and build the crosstalk error model of the eight-channel FTMG. Then, we introduce the solution method of 56 crosstalk coefficients based on the Moore–Penrose inverse method and the construction method of matrix needed for solution based on Helmholtz coil. The effect of nonuniformity of Helmholtz coil on the calibration of crosstalk is analyzed and calculated. The effectiveness of the proposed method is proved by repetitive simulation and comparative experiments. Compared with the traditional direct measurement method, this method has the advantage of high efficiency, and the more the channels of SQUID, the more obvious is the superiority.

Error Calibration for Full Tensor Magnetic Gradiometer Probe Based on Coordinate Transformation Method

In order to calibrate the zero offset error and triaxial non-orthogonal error of full tensor magnetic gradiometer (FTMG) probe composed of superconducting quantum interference device (SQUID) magnetometers, we propose a new calibration method in this article. With the help of the triaxial Helmholtz coil, we can generate a magnetic field with known parameters. By establishing the objective functions containing the error parameters for the outputs of the SQUIDs and solving them with the least-squares fitting algorithm, the included angle between the SQUID sensor and the Helmholtz coil can be obtained, then all the required error parameters can be calculated by coordinate transformation method. Compared with the traditional method, this method does not need to rotate the SQUID magnetometers-based probe to collect the data set for calibration, thus avoiding the influence of motion induced noise on the calibration results. In order to verify the effectiveness of the proposed method, we adopted the widely used ellipsoid fitting method as a comparison method and conducted field comparison experiments. The results show that the proposed calibration method is better than the traditional ellipsoid fitting calibration method under the same experimental environment. The root mean square errors of five independent magnetic gradient tensor components are reduced to 0.39, 0.35, 0.41, 0.31 and 0.57 nT/m from 1630.55, 756.59, 3097.56, 1051.09 and 1245.64 nT/m by the proposed method.

Multiobject Localization Using Magnetic Tensor Gradiometer Array and Improved iForest

The current magnetic localization technology based on magnetic tensor gradient (MTG) information mostly focuses on single-object localization using a tensor gradiometer, which cannot be applied to more common scenarios where there are multiple objects in the test area and their number changes over time. The difficulty is that magnetic detection is a “blind” experiment. The lack of prior information will lead to poor accuracy, slow inversion speed, or even failure. This letter presents a novel method to estimate the information of multiple objects, including their number, trajectory, and magnetic moment. Specifically, an improved isolation forest algorithm is used to predetermine the best possible number, center coordinates, and magnetic moments of the objects from the rough solution set obtained by the magnetic tensor gradiometer array. Given the above prior conditions, we can safely get the accurate estimation of the objects by formulating a suitable cost function between the measured magnetic data and those theoretically calculated based on the extended multiple magnetic dipole mathematical model. The results of the simulation experiment show that the proposed method provides a useful way for multiobject localization.

Accuracy Evaluation of Calibrating Magnetic Tensor Gradiometers From Total-Field Gradient Measurements in Aeromagnetic Survey

The magnetic gradient tensor is the spatial rate of change of the magnetic vector along the three axes of the Cartesian coordinate system. It is particularly suitable for aeromagnetic surveys because it is relatively insensitive to temporal changes and regional variations of the geomagnetic field. However, the complexity of the flight environment and defects in the existing calibration methods for airborne magnetic tensor gradiometers cannot guarantee the measurement accuracy of tensor data. Research shows that the generalized Hilbert transform can convert total-field gradients, measured over an extensive survey area, into the magnetic gradient tensor components, so a high-precision total-field gradiometer can be employed to calibrate a magnetic tensor gradiometer, using a generalized Hilbert transform calibration method (GHTCM). However, practical survey conditions cannot meet the requirements of the generalized Hilbert transform, which degrades the accuracy of GHTCM. Based on the theory of the generalized Hilbert transform, we first analyze the error sources and error mechanisms of the GHTCM according to the differences between real and ideal survey conditions and then build models to design an appropriate evaluation algorithm for the accuracy of the GHTCM. Simulation experiments based on the open-source flight simulator, FlightGear, and a practical flight experiment are designed. The results indicate that the proposed method can correctly evaluate the accuracy of the GHTCM. This evaluation algorithm is the basis of obtaining the high-precision calibration data for practical airborne magnetic gradient tensor in the survey.

Analysis and Correction of the Magnetometer's Position Error in a Cross-Shaped Magnetic Tensor Gradiometer.

When using the technique of magnetic gradient tensor measurements to obtain the position of magnetic objects, calibration of the magnetic tensor gradiometer plays a pivotal role in precisely locating the target, and extensive research has been carried out on this up to now. However, previous studies have always lacked sufficient discussion on the position error of magnetometers in magnetic tensor gradiometers caused by inaccurate installment of magnetometers. In this paper, we analyze and correct this position error based on a magnetic dipole source. The result of the simulation exemplifies that the magnetometer’s position error will affect the locating accuracy and, therefore, it is worth correcting this error. The relationship between position error and magnetic gradient tensor components is established, followed by an error correction method based on this relationship. Simulations illustrate that this method can effectively decrease the effect caused by the position error of magnetometers and improve the locating performance with locating error and magnetic moment errors dropping from 2 to 0.2 m and to , respectively.

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.

Modelling tensor magnetic gradient responses in marine CSEM

Conventional marine CSEM and tensor magnetic gradiometer measurements were compared over numerical models of idealised exploration targets in 1 km water columns. It was found that because of their low amplitudes, tensor gradiometer measurements present challenges. When background-normalised data were compared, it was found that tensor magnetic gradient data showed comparable amplitudes. It was also found that one tensor component showed little variation with the underlying model. This suggests that it might be used to estimate a background when seafloor topography or dipping strata are present.

Underwater operation of a full tensor SQUID gradiometer system

For the first time a mobile underwater full tensor magnetic gradiometer (FTMG) system based on low-Tc superconducting quantum interference devices (SQUIDs) has been deployed in order to scan the sea floor for magnetized targets. The application is mainly focused on waste deposits and unexploded ordnance (UXO), but could also include shallow geological features as well as archaeological remains. The main methods for detection and localisation of underwater UXO and waste deposits are side sonar scanning and magnetic mapping. While modern sonar scanners can achieve a very high spatial resolution and long detection range, they still have problems detecting targets under cover—for magnetic sensors a layer of non-magnetic sand or ooze does usually not have an effect on the signal apart from an increased distance. In this paper we discuss the setup of the mobile underwater FTMG SQUID system, its challenges and main performance features. It also illustrates its detection and localization capabilities in tests on known magnetic targets.

Compensation for aircraft effects of magnetic tensor gradiometer with nonlinear least square method

Abstract Based on the detailed analysis of magnetic interference fields, mathematical model of compensation coefficients is constructed and nonlinear compensation method is proposed for magnetic tensor gradiometer in this paper. Firstly, a mathematical model containing compensation coefficients of magnetic tensor gradiometer is deduced by extending the Leliak method from the magnetic interference vector field compensation model. Secondly, four different types of constraint conditions, which are independent of the attitude of the magnetic tensor gradiometer and invariant with maneuvers, and a class of vector constraints are used to establish proper vector and tensor constraint equations. Then the compensation coefficients are solved using the nonlinear least square algorithm. Effectiveness and convergence of the proposed method are proved by simulation experiment, and the magnetic interference signals of aircraft effects are decreased remarkably.

Correction and compensation of an airborne fluxgate magnetic tensor gradiometer

An airborne fluxgate magnetic tensor gradiometer is built on fluxgates to measure directional derivatives of the magnetic field. It has been used to carry out many geophysical exploration programs quickly and efficiently. However, two key issues greatly reduce the data quality of a tensor gradiometer. One is that the fluxgate magnetic tensor gradiometer suffers various errors, such as scale drift, non-orthogonality, misalignment, zero offset, dynamic, and nonlinear errors of individual fluxgates, along with differences between characteristics of fluxgates. The other is that manoeuvring an aircraft flying in the geomagnetic field can generate magnetic interference effects on a tensor gradiometer. Regarding the common airborne fluxgate magnetic tensor gradiometer that has a cross-shaped structure, we have proposed the magnetic interference model of the aircraft and the error model of a single fluxgate. Then we have seamlessly combined these two models into the unified calibration model of a tensor gradiometer by a recursive method. Finally, we have simultaneously determined the correction coefficients and the magnetic properties of the aircraft by a calibration flight at high altitude in an area of low magnetic gradient. We have evaluated the performance of the proposed method through simulation and actual flight results using a microlight aircraft. The root-mean-square noise of each component has reached the level of less than 1.5 nT/m, and the improvement ratios are from 4096 to 17444 in terms of the measured field data of tensor components. The proposed method reduces the reliance of the installation on the aircraft and can easily be applied to other tensor gradiometers, such as airborne superconducting magnetic tensor gradiometers.

A ground-based test facility for airborne magnetic gradient tensor instruments simulating calibration flights

Progress is slow in terms of the research and evaluation of calibration algorithms for full tensor magnetic gradient instruments using airborne tests. The main reason is that, based on knowledge gained by actual calibration flights, problems exist regarding high risk, high costs, and long development cycles. In this paper, we describe a ground-based simulation facility for calibration flights which combines the nonlinear aerodynamic model with a magnetic interference model. Environmental magnetic fields can be calculated and produced by tri-axial coils, which are measured by the magnetic tensor gradiometer in calibration flights. Influence from systematic errors and magnetic interference can be extracted from the simulated calibration flight provided by the facility. Compared to system evaluation in airborne operation, this method has the benefit of zero risk, low costs, and short duration of evaluation cycles. In view of ground-based multi-degree of freedom motion platforms, it has the advantages of simple manufacture, good dynamic characteristics, and adaptability to different aircraft types.

Invariant Calibration of Magnetic Tensor Gradiometers

Magnetic tensor gradiometers are based on multiple sensors arranged in a unified coordinate system. Current calibration methods focus on each gradient tensor component separately, rather than the entire tensor system, so the advantages of tensor measurement are not completely realized. In this letter, the nonorthogonal error, misalignment error, scale-factor error, and zero offset in a magnetic tensor gradiometer with multiple elements are modeled. Optimal correction parameters are obtained by using two independent rotation invariants of the magnetic gradient tensor.

Correction of a Towed Airborne Fluxgate Magnetic Tensor Gradiometer

The small impact of the geomagnetic field enables a magnetic tensor gradiometer to be easily installed on the flight platform for airborne geophysical exploration, especially for the detection of shallow buried mines and magnetic moving targets. Using the fluxgates as the core components, the gradiometer has the advantages of wide temperature range, low cost, and high resolution, but has the disadvantage of relatively low accuracy. This is because of the scale factor error, the nonorthogonal error, the misalignment, the zero offset, the dynamic error in a fluxgate, and the inconsistency among the error of fluxgates. In this letter, a correction method for a towed airborne magnetic tensor gradiometer is proposed that is composed of four fluxgates arranged in a cross-shaped structure. The theoretical framework of the proposed method is based on the static error model and the dynamic characteristics of single fluxgate, the feature that the gradient tensor of the geomagnetic field at high altitude is approximately zero, and on the phenomenon that the unchanged tensor rotation as a result of nonuniform magnetic field on the ground can indicate the inconsistency of the scale factors among different tensor components. The actual flight results using a helicopter have demonstrated and validated the performance and effectiveness of the proposed method. The improvement ratios of the field tensor components are from 359.6 to 1765, and the RMS of each component has reached to the level of 1 nT/m.

Magnetic tensor gradiometry using Ramsey interferometry of spinor condensates

We have realized a magnetic tensor gradiometer by interferometrically measuring the relative phase between two spatially separated Bose-Einstein condensates (BECs). We perform simultaneous Ramsey interferometry of the proximate $^{87}$Rb spin-1 condensates in freefall and infer their relative Larmor phase -- and thus the differential magnetic field strength -- with a common-mode phase noise suppression exceeding $50\,\mathrm{dB}$. By appropriately biasing the magnetic field and separating the BECs along orthogonal directions, we measure the magnetic field gradient tensor of ambient and applied magnetic fields with a nominal precision of $30\,\mathrm{\mu G\,cm^{-1}}$ and a sensor volume of $2\times10^{-5}\,\mathrm{mm}^3$. We predict a spin-projection noise limited magnetic energy resolution of order $\hbar$ for typical Zeeman coherence times of trapped condensates with this scheme, even with the low measurement duty cycle inherent to BEC experiments.

Analysis and Simulation of Flight Effects on an Airborne Magnetic Gradient Tensor Measurement System

A magnetic tensor gradiometer is used to measure the spatial derivatives of three orthogonal magnetic field components. Being relatively insensitive to the geomagnetic field affords it the capability of being loaded onto flying platforms to conduct an airborne geophysical survey. It is especially suitable for exploring shallow buried mines and moving magnetic targets. The aerodynamic model was provided by the open source flight simulator, FlightGear. Estimations of the magnetic gradient tensor model of the magnetic dipole, the magnetic interference model of the aircraft, and the error model of the measuring device were all used to investigate the effects of flight on the airborne magnetic gradient tensor measurement system (AMGTMS). A thorough analysis of its causes, such as the vibration of the aircraft, the different rotating sequences of the coordinate system, and the reasonable sequence of data processing, was also done. The results can be applied to the guide design, integration, calibration, and data processing of the AMGTMS, thus reducing the research and development risk.

Compact fluxgate magnetic full-tensor gradiometer with spherical feedback coil

The magnetic tensor gradiometer, which is used for measuring the spatial derivatives of three orthogonal magnetic field components, is an important magnetic field characterization tool. Here, the construction of a magnetic full-tensor gradiometer is described, which utilizes four fluxgates arranged on a planar cross structure, and a single, triaxial, spherical feedback coil assembly. In this arrangement, one of the fluxgates is used as a reference, controlling the currents through the feedback coils. Since the fluxgates are working in the near-zero magnetic field environment, the magnetic tensor gradiometer is stable and of an improved accuracy. This design avoids the crosstalk normally caused by individual feedback coils for each fluxgate, and reduces the orthogonality and orientation errors. Moreover, the calibration parameters can be directly inferred using the spherical feedback coil. The measured gradient tensor magnitude can reach 0.52 nT/m/Hz(1/2) @ 1 Hz in unshielded laboratory conditions, while exhibiting good noise immunity. The functionality of the system is verified by locating a small, single, permanent, and dipole magnet in space. The gradiometer is compact, while employing global feedback, and therefore it is especially suitable for deployment on space-constrained moving platforms.

GÖKOVA KÖRFEZİ’NİN HAVADAN MANYETİK İMZASI

The gulf of Gokova, which is located in the Aegean Extensional Zone of Turkey, has been a point of interest for many investigators. This gulf takes place within the regional extensional tectonic regime in NS directions. The extension of Western Aegean in N-S directions has also formed many other grabens which are perpendicular to grabens in E-W directions. The gulf has an approximate length of 100 km’s (in EW) and 25 km’s (in NS). Datca and Bodrum peninsulas take place towards south and north of the gulf, respectively. In recent years, Full Tensor Gradiometer (FTG) potential field methods have widely been used among the gravity and magnetic methods. In the past, vertical component of the magnetic field has been measured as it had been done in the gravitational method. However; this method has turned into total area measurements (x, y and z components) in recent applications. This method was applied to the data of total aeromagnetic field. FTG method was applied by measuring the data of total aeromagnetic field components. The FTG analysis (Full Tensor Magnetic Gradiometer) of the magnetic anomaly existing in the gulf was performed in order to give a different point of view to the geological structure of the gulf of Gokova in which there were intense seismic activities. Field components (Tx, Ty, Tz) of the aeromagnetic anomaly in the gulf of Gokova were estimated. Components obtained at the end of conversion were then applied the derivatives of Txx, Txy, Txz, Tyy, Tyz, Tzz and information about the location of the geological source which causes anomaly were taken. It was observed that the northern boundary of the ultramafic body had continued up to a distance of 9 km’s towards the northern coast of the gulf of Gokova. The anomaly in the gulf showed that ultramafic rocks, peridotites and the ophiolitic melange of Datca peninsula had continued within the sea. The method has been useful in correct mapping of different geological units that have variable magnetic sensitivities and in revealing their locations

Full Tensor SQUID Gradiometer for airborne exploration

IPHT Jena and Supracon AG develop and fabricate full tensor magnetic gradiometer (FTMG) systems, based on low-temperature-superconducting (LTS) planar-type SQUID (Superconducting Quantum Interference Device) gradiometers of first order. The systems are operated by Spectrem Air Ltd., jointly owned by Anglo American and De Beers. This paper describes details of the system setup, data processing and achieved performance parameters. The sensors work at 4.2 K in liquid helium. With a base length of only 3.5 cm a real gradient measurement is possible. With six gradiometer the full magnetic gradient tensor can be measured with redundancy, allowing for high system reliability and the application of enhanced noise reduction techniques. The data of the FTMG system will allow for a 3D inversion for the underlying magnetic sources. Examples of 2D maps of tensor components with high spatial resolution are shown.

A Superconducting Magnetic Tensor Gradiometer for Underwater UXO Detection

Magnetic surveys are routinely used for detection of discrete magnetic targets, such as unexploded ordnance (UXO). Gradient tensor measurements have a number of benefits over measuring total field intensity or its vector gradient: they provide detailed information about a target in a single pass, without necessarily passing directly over the target; they determine the location of the target using a direct method, rather than the indirect inversion method required with other measurements; and they determine directly the magnitude and orientation of the magnetic moment, as well as the location of the target, aiding discrimination between sources and characterization of the munitions. The CSIRO is building a magnetic tensor gradiometer, designed for underwater deployment, based on high temperature superconducting quantum interference devices (SQUIDs). Technical challenges for the project include: designing a high temperature SQUID device that can achieve the required gradient sensitivity in motion; developing a gradiometer housing that can deal with the boil-off gas from the liquid nitrogen cryogen while underwater; identification and removal of wave-induced magnetic noise; compensation for magnetic noise caused by motion and the platform itself; and developing a dipole-tracking algorithm for gradient tensor measurements that is both robust and computationally undemanding. This paper presents the progress to date on this project including an evaluation of gradiometer performance in laboratory conditions, and describes some simple methods for localization and characterization of compact magnetic sources using gradient tensor measurements.

Optimizing a direct string magnetic gradiometer for geophysical exploration

Magnetic gradiometers are tools for geophysical exploration. The magnetic gradient is normally calculated by subtracting the outputs of two total field magnetometers which are separated by a baseline. Here we present a unique device that directly measures magnetic gradients using only a single string as its sensing element. The main advantage of a direct string magnetic gradiometer is that only gradients can induce second harmonic string vibrations. A high common mode rejection ratio is thus naturally achieved without any balancing technique. Performance depends on the ability to dissipate heat while minimizing air damping. By combining high current, an elevated temperature and low pressure, we can easily achieve sensitivity of 0.18 nT/m/square root of Hz. Further increases in sensitivity can be attained by optimizing the sensing element. In this paper we present an in-depth study of the most critical parameters of the magnetic gradiometer. We describe the design for the next generation of sensor, which will reach the required sensitivity of 0.01 nT/m/square root of Hz using only 1 W of power. By combining a few single-axis magnetic gradiometer modules, it will be possible to deploy a full tensor magnetic gradiometer with more than sufficient sensitivity for airborne geophysical applications.