Research On Suppression Method Of Magnetic Gradient Tensor Conversion Boundary Effect Based On Minimum Curvature

The magnetic gradient tensor is the spatial rate of change of the magnetic field vector along the three axes of the Cartesian coordinate system,it contains rich magnetic field information and is less affected by the earth's magnetic dip and magnetic declination,and is an important research object in the current field of magnetic exploration.When processing the magnetic gradient tensor data,if the conversion accuracy between the magnetic gradient tensor components is high,the conversion results can be used to perform mutual inspection of the data of each component,so as to evaluate the quality of the magnetic gradient tensor measurement data.Among the existing magnetic anomaly data conversion processing methods,the frequency domain conversion method using Fourier transform for processing has the advantages of simple conversion formula and fast conversion speed.However,due to the existence of the approximation of the binary integral of the discrete Fourier transform in the conversion process,this method will lead to a large conversion error at the boundary position,which is called the boundary effect.At present,in order to suppress the boundary effect of the potential field extension and derivative conversion of the gravitational potential field data using the frequency domain conversion method,the method of expanding the original potential field data is mostly used.However,in the field of magnetic potential field,especially There are relatively few related studies in the magnetic gradient tensor field.The minimum curvature method is mostly used in the interpolation calculation of data in the field of earth science,and it is a common mathematical analysis method.The minimum curvature edge expansion method can better respect the distribution law of the original data and meet the requirements of smooth interpolation as much as possible when expanding the magnetic gradient tensor field data.In this paper,the research on the boundary effect suppression method based on the minimum curvature of magnetic gradient tensor transformation is carried out.The main contents are as follows:1)Analyze the principle and related calculation of the conversion between the nine components of the magnetic gradient tensor using the frequency domain conversion method.A spherical magnetic anomaly model is established to simulate the conversion process,and the boundary effect problem caused by the conversion process is analyzed.A boundary effect suppression scheme based on the minimum curvature edge expansion method is proposed to improve the conversion accuracy between the magnetic gradient tensor components.2)Starting from the mathematical model of minimum curvature,the iterative format required for edge expansion is deduced,the overall process of edge expansion with minimum curvature and the given method of relevant parameters are designed,and the calculation amount of edge expansion is estimated.The minimum curvature edge expansion software suitable for magnetic gradient tensor data is designed with the idea of structure,and tested,and the model verification of boundary effect suppression is carried out with the model simulation data,and the corresponding empirical parameters are given.3)Use the instrument system developed by the research group to carry out field measurement experiments,and perform edge expansion processing on the measured magnetic gradient tensor data.The results show that the proposed minimum curvature edge expansion method can suppress the boundary effect caused by the transformation of the magnetic gradient tensor components in the frequency domain,which provides a reference for the practical application of the transformation between the magnetic gradient tensor components.