Full magnetic gradient tensor from triaxial aeromagnetic gradient measurements:Calculation and application

The full magnetic gradient tensor （MGT） refers to the spatial change rate of the three field components of the geomagnetic field vector along three mutually orthogonal axes. The tensor is of use to geological mapping, resources exploration, magnetic navigation, and others. However, it is very difficult to measure the full magnetic tensor gradient using existing engineering technology. We present a method to use triaxial aeromagnetic gradient measurements for deriving the full MGT. The method uses the triaxial gradient data and makes full use of the variation of the magnetic anomaly modulus in three dimensions to obtain a self-consistent magnetic tensor gradient. Numerical simulations show that the full MGT data obtained with the proposed method are of high precision and satisfy the requirements of data processing. We selected triaxial aeromagnetic gradient data from the Hebei Province for calculating the full MGT. Data processing shows that using triaxial tensor gradient data allows to take advantage of the spatial rate of change of the total field in three dimensions and suppresses part of the independent noise in the aeromagnetic gradient. The calculated tensor components have improved resolution, and the transformed full tensor gradient satisfies the requirement of geological mapping and interpretation.

Calculation and correction of magnetic object positioning error caused by magnetic field gradient tensor measurement

Magnetic field gradient tensor measurement is an important technique to obtain position information of magnetic objects. When using magnetic field sensors to measure magnetic field gradient as the coefficients of tensor, field differentiation is generally approximated by field difference. As a result, magnetic objects positioning by magnetic field gradient tensor measurement always involves an inherent error caused by sensor sizes, leading to a reduction in detectable distance and detectable angle. In this paper, the inherent positioning error caused by magnetic field gradient tensor measurement is calculated and corrected by iterations based on the systematic position error distribution patterns. The results show that, the detectable distance range and the angle range of an ac magnetic object（2.44 Am^2@1 kHz） can be increased from（0.45 m, 0.75 m）,（0？, 25？） to（0.30 m, 0.80 m）,（0？,80？）, respectively.

Three direction analytical signal analysis method of magnetic gradient tensor and application in the interpretation

Compared to conventional magnetic data,magnetic gradient tensor data contain more high-frequency signal components,which can better describe the features of geological bodies.The directional analytic signal of the magnetic gradient tensor is not easily interfered from the tilting magnetization,but it can infer the range of the fi eld source more accurately.However,the analytic signal strength decays faster with depth,making it diffi cult to identify deep fi eld sources.Balanced-boundary recognition can eff ectively overcome this disadvantage.We present here a balanced-boundary identifi cation technique based on the normalization of three-directional analytic signals from aeromagnetic gradient tensor data.This method can eff ectively prevent the fast attenuation of analytic signals.We also derive an Euler inversion algorithm of three-directional analytic signal derivative.By combining magnetic-anomaly model testing with the traditional magnetic anomaly interpretation method,we show that the boundary-recognition technology based on a magnetic gradient tensor analytic signal has a greater advantage in identifying the boundaries of the geological body and can better refl ect shallow anomalies.The characteristics of the Euler equation based on the magnetic anomaly direction to resolve the signal derivative have better convergence,and the obtained solution is more concentrated,which can obtain the depth and horizontal range information of the geological body more accurately.Applying the above method to the measured magneticanomaly gradient data from Baoding area,more accurate fi eld source information is obtained,which shows the feasibility of applying this method to geological interpretations.

Magnetic susceptibility inversion method with full tensor gradient data using low-temperature SQUIDs

Full tensor magnetic gradient measurements are available nowadays. These are essential for determining magnetization parameters in deep layers. Using full or partial tensor magnetic gradient measurements to determine the subsurface properties, e.g., magnetic susceptibility, is an inverse problem. Inversion using total magnetic intensity data is a traditional way.Because of di culty in obtaining the practical full tensor magnetic gradient data, the corresponding inversion results are not so widely reported. With the development of superconducting quantum interference devices(SQUIDs), we can acquire the full tensor magnetic gradient data through field measurements. In this paper, we study the inverse problem of retrieving magnetic susceptibility with the field data using our designed low-temperature SQUIDs. The solving methodology based on sparse regularization and an alternating directions method of multipliers is established. Numerical and field data experiments are performed to show the feasibility of our algorithm.