Research On High Precision Joint Inversion Method Of Gravity And Magnetic With Undulating Terrain

The structure subsurface density and magnetic susceptibility is an important basis for resource exploration.As resource exploration gradually in undulating terrain areas such as mountains and hills,the research and development of high precision and strong applicability of gravity and magnetic joint inversion method in undulating terrain is useful.We focus on the discretization method of high-resolution inversion,highprecision solution,high-efficiency and remanence inversion in the undulating terrain,so as to accurately reveal the three-dimensional physical structure in subsurface,thus providing important technical support for the actual exploration in the undulating terrain.The density and magnetic susceptibility of unstructured tetrahedral grids inversion is often used in undulating terrain,which can better fit undulating terrain and geological bodies,but the efficiency is low due to the complexity of forward calculation.Some people use small size structure hexahedron grids to approximate the undulating terrain and geological bodies.This method will be low efficiency due to the large amount of data.Singular value curve reflects the main features of data,and the larger its amplitude is,the more obvious the data features are.The singular value curve analysis of the inversion kernel function matrix can compare the features among different kernel function matrices.Higher resolution inversion results can be obtained for the kernel function matrix with obvious features in inversion.The depth resolution plot makes use of the feature that the right singular matrix contains the depth information of subsurface to compare the energy of different depths,so as to judge the depth resolution in the kernel function matrix.The singular value curves and depth resolution plot are used to analyze the resolution of structural and unstructured grids,and the resolution advantage is taken as the main basis for the selection of inversion method for undulating terrain.It proves that even if we don't consider unstructured grid characteristics of high terrain matching,the resolution of unstructured grid is still better than that of structured grid.The experimental results of model data and actual data show that compared with the structural grid,the unstructured grid can describe the top of the geological body more clearly,the inversion physical property results are more focused,and the resolution of the deep part is improved,especially the resolution of the deep part in the magnetic inversion results is more obvious.In addition,the unstructured grid division with better volume consistency can obtain higher precision results,indicating the research direction of gravity magnetic physical inversion,and the tetrahedral grids can better fit the undulating terrain,and will play a greater role in the inversion of undulating terrain.Based on the advantage of cross-gradient without prior information,it is used to carry out gravity and magnetic joint inversion.In order to solve the problem that the distribution of unstructured grid is complex and the cross-gradient cannot be calculated by the difference form of adjacent elements like that of structured grid,the gravity and magnetic cross-gradient joint inversion method is achieved based on Taylor formula to effectively realize the gravity and magnetic joint inversion of unstructured grid.By making the equation of the tetrahedron unit center coordinates and its physical property,it needs selected multiple adjacent tetrahedron units of the target tetrahedron to make the Taylor formula related equations,and it solves the equations to calculate the target tetrahedron cross-gradient values.The advantage of this method is that the gradient value required to calculate the cross-gradient is the coefficient of the first several terms of Taylor formula.For any order of Taylor formula,the gradient result can be obtained directly by solving equations.By comparing the calculation accuracy of cross-gradient of physical property model under first-order,second-order and third-order Taylor formula,it is found that the calculation accuracy of cross-gradient under the secondorder Taylor formula is much higher than that under the first-order Taylor formula,the accuracy of the third-order Taylor formula is not much improved and more timeconsuming,and the accuracy reaches the best when the number of elements involved in the calculation is slightly more than the number of unknown coefficients of Taylor formula.By comprehensive consideration of computational accuracy and efficiency,the second-order Taylor formula is used to calculate cross-gradient for gravity and magnetic joint inversion.The model test shows that the cross-gradient gravity and magnetic joint inversion based on the second-order Taylor formula can significantly improve the inversion accuracy and resolution,and achieve high-precision gravity and magnetic cross-gradient joint inversion in undulating terrain.The most important factor restricting the practical application of tetrahedral grids cross-gradient inversion is computational efficiency.In order to solve the problem of the efficiency of Taylor formula cross-gradient calculation,we show the error of Taylor formula cross-gradient calculation.The error is mainly positively correlated with the theoretical cross-gradient amplitude.The optimization scheme is proposed based on tilt angle boundary identification method to realize the efficiency of Taylor formula cross gradient joint inversion.The tilt angle method can clearly determine the high-value anomalies range.The second-order Taylor formula is used to calculate the crossgradient within the high-value anomalies range,and the first-order Taylor formula is used at the outside of high-value anomalies to realize the cross-gradient joint inversion of gravity and magnetic based on the mixture of first-order and second-order Taylor formula,which can reduce the computing time.By comparing the model data and the actual data,it is proved that the optimization method can significantly improve the computational efficiency with almost no loss of accuracy.This method is applied to the gravity and magnetic joint inversion with the undulating terrain area of Inner Mongolia to verify the effectiveness of this method in practical application.Due to the natural remanence in the actual magnetic data,the magnetization inclination angle is not equal to the direction of the earth's basic magnetic field,so there will be certain errors in the inversion of magnetic susceptibility in the case of giving magnetization direction.In order to better reveal the characteristics of underground field sources,the unstructured tetrahedron joint inversion method based on secondorder Taylor series is extended and applied to gravity and magnetic joint vector inversion,and the magnetization direction characteristics of geological bodies are obtained effectively,which provides an important technical support for better analysis of the formation background of field sources.The model test shows that the crossgradient joint inversion method can effectively focus the magnetization intensity,and obviously improve the precision of the magnetic vector results.By applying the gravity and magnetic cross-gradient joint vector inversion method to predict the mineral resources in Inner Mongolia,more reliable inversion results can be obtained,and the magnetization vector results can be used to explain the causes of resources more reasonably.To provide more accurate density and susceptibility for mineral exploration,the advantages of unstructured tetrahedral grids inversion of physical properties are systematically analyzed,and the inversion of unstructured tetrahedral grids inversion is proved to be more practical in undulating terrain.A high precision and high efficiency gravity and magnetic joint inversion method with unstructured grids is established,and the magnetic vector inversion problem with remanence condition is effectively solved.It provides higher precision physical property results for geological interpretation and promotes the application of gravity and magnetic exploration in mineral resources exploration in undulating terrain.