Research On Quality Evaluation And Error Source Identification For The Aeromagnetic Gradient Tensor Field Measurements

Aeromagnetic gradient tensor field(AGTF)detection has been widely used in mineral resources exploration,geoscientific research,high exploration efficiency,and is not affected by the geomagnetic field.However,quality of the AGTF measurements is subject to strong uncertainty because of the limitation of the instruments’ accuracy,the inevitable interference from the carrying platform,and the unexpected environmental impacts.High-quality measurements serve as an important basis to obtain reliable data for subsequent data interpretations and to promote the development of fine subsurface detection capabilities.Currently,domestic research related to detection of the AGTF has achieved some notable results,including the forward calculation and inverse interpretation of the magnetic gradient tensor,as well as the development,calibration,and verification of the magnetic gradient tensor.However,the research on the quality evaluation and error identification of the AGTF measurements is still in a gap.The existing methods for quality evaluation of geomagnetic field detection data mainly focus on the total field strength(scalar)or vector field,including two types of methods for calculating the inner and outer conformal accuracy of the detection data,which rely on repetitive line or cross-line measurements,or exogenous data as a reference for quality evaluation.In addition to their own limitations,these methods cannot meet the multicomponent and directional characteristics of the AGTF,and cannot be used to evaluate its data quality.In addition,among the few studies on geomagnetic field measurements error identification,the proposed methods have the problems of either only identifying a single type of error source,relying on a special detection method,or failing to identify the actual measurements.Therefore,this paper focuses on the quality of the AGTF measurements and carries out the following research work:(1)Constructing the deviation tensor of the AGTF measurements based on tensor representation.The AGTF measurements exhibit high-order and spatial correlation,and the tensor-as a natural representation of high-order data-can effectively preserve the intrinsic structural properties of the data.Therefore,in order to fully reveal the mechanism of the quality degradation of the measurements and to explore the intrinsic physical connection between the components of the magnetic gradient tensor,this paper expresses the AGTF measurements as a fourth-order tensor.By analyzing the composition and structure of a typical AGTF measurement system,as well as the error sources and error mechanisms affecting the data quality,a measurement model with different representations on a single observation point and the whole observation area is established with tensor algebra.Besides,the mutual expressions between the components of the magnetic gradient tensor are derived by the generalized Hilbert transform based on the Laplace equation constraints satisfied by the magnetic gradient tensor field data,and the deviation tensor is constructed to reflect the quality and error characteristics of the AGTF measurements.(2)Formulating the data generation methods applicable to the quality research of AGTF measurements.A reasonable and correct method for generating AGTF data is the basis for the quality research of the measurements.Therefore,this paper firstly proposes a magnetic data generation method for arbitrarily shaped ferromagnetic object based on 3D printing,whose core idea is to approximate the ferromagnetic object by a collection of magnetic dipoles whose placement is identified with the tool path information generated by 3D printing software and calculate the magnetic signature of the ferromagnetic object using the superposition principle.This paper also extends the traditional magnetic field-based near-field analysis method to the magnetic gradient tensor field and proposes a magnetic moment test method for magnetic sources,which proves the correctness of the proposed data generation method and its superiority in dealing with multiple moving magnetic sources with different magnetic properties.In addition,since the research idea of this paper is to analyze a large amount of data to draw laws and conclusions related to data quality research,a fast magnetic data generation method based on multiple magnetic dipoles is also proposed.By analyzing the frequency distribution characteristics of the generated AGTF data and comparing them with those of the data generated by typical magnets,the rationality of the is demonstrated.(3)Proposing a data quality evaluation method based on the deviation tensor.Since the comprehensive quality of detection data including completeness,spatial consistency and accuracy will make the ideal mutual expression relationship no longer satisfied,and the deviation tensor quantifies the damage of detection data to the ideal mutual expression relationship,this paper firstly proposes a method to qualitatively evaluate the comprehensive quality of detection data based on the deviation tensor.In addition,this paper also establishes the correspondence between the deviation tensor and the normalized relative error of the detection data based on extensive simulation analysis,and then forms a method to quantitatively evaluate the data’s accuracy.To verify the correctness and rationality of the proposed evaluation method,this paper compares the accuracy evaluation results of the AGTF measurements with different qualities with the inversion accuracy obtained by Tensor Euler deconvolution and actual field flight experiments are also designed.The results of the simulation experiments show that the evaluation results obtained according to the proposed method are consistent with the inversion accuracy of the Tensor Euler deconvolution,i.e.,the worse the evaluation result,the lower the inversion accuracy,which proves the rationality of the evaluation method.The field flight experiments prove the correctness of the proposed method by comparing the normalized relative error obtained from the prediction of the proposed evaluation method and the normalized relative error calculated by using external high-precision data as reference.(4)Proposing an error source identification method based on the deviation tensor.On the basis of the deviation tensor,an observation area deviation tensor and an observation area normalized error tensor,which can be used to graphically analyze the different characteristics of various error factors,are constructed,taking into account the spatial correlation of the AGTF measurements.In addition,to provide a basis for theoretical interpretation,an error model of the AGTF measurements is derived.By analyzing the characteristic distinguishability of the observation area deviation tensor and the observation area normalized error tensor under the influence of different error sources and the mathematical model expressions of each error factor,the main error sources of the AGTF measurements are classified into three categories: attitude control errors,magnetic interference of the carrying platform and instrument errors of the tensor measurement system.The proposed error identification process includes the observation area normalized error tensor prediction based on the full convolutional neural network,the attitude control error discrimination based on the spatial autocorrelation index,the magnetic interference and instrumentation error discrimination based on the support tensor machine classification model,and the curvilinear leveling and upward extension.In order to verify the correctness of the proposed error identification method,field flight experiments are designed,and the results show that the error identification results are consistent with those obtained based on a priori knowledge,which proves the correctness and engineering practicality of the proposed method.