Research On The Method Of Improving The Efficiency Of 3D Gravity Inversion Based On Model Dimensional Reduction And Krylov Subspace Algorithm

Gravity prospecting has the characteristics of lightness,quickness and low input,which can quickly obtain large area and high precision gravity data,and is widely used to search for concealed ore.With the increasing difficulty in the exploration of concealed ore,twodimensional gravity interpretation and inversion have been difficult to meet the requirements,that is,to determine the distribution of concealed ore in three-dimensional underground half space,so it is urgent to study the three-dimensional gravity inversion interpretation.In general,the physical properties of concealed rock masses are not uniformly distributed or vary greatly,and their shapes are complex.Therefore,the gravity three-dimensional physical property inversion method is used for the study.However,the large dimension of three-dimensional inversion interpretation will lead to low inversion efficiency,so it is necessary to study methods to improve the inversion efficiency.In this paper,a set of methods for improving the efficiency of three-dimensional gravity physical property inversion are studied.The inversion efficiency is improved by model reduction and subspace method.The correctness and efficiency of the strategy for improving the inversion efficiency are verified by model testing and actual data processing.The main results are as follows:(1)Based on the edge recognition method of normalized total horizontal derivative(NVDR-THDR)and normalized resolution signal amplitude vertical derivative(NVDR-ASA),the target optimization level dimension reduction technology is proposed.The inversion is carried out only in the target area,namely the key research area,to ensure that the number of unknowns is reduced and the inversion efficiency is improved under the condition of meeting the inversion accuracy.Target area optimization techniques include obtaining the edge location and the center location of the geologic body respectively.The number of grids affects the size of the kernel matrix and the number of unknowns in the equation.Under the condition of the same grid units size,by comparing the inversion efficiency and efficiency of the inversion of the target area in the region.The grid number is less,the kernel function matrix size smaller accordingly,build kernel function will improve the efficiency,at the same time to speed up the speed of solving equations,integrated in the target area are both only inversion,can effectively improve the efficiency of the inversion.(2)Vertical dimensionality reduction technology of unstructured grid is proposed based on vertical identification ability of data.The underground half space is divided into unstructured grids to reduce the grids and improve the inversion efficiency.With the increase of the buried depth of the geological target body,the recognition ability of gravity data gradually weakens.In other words,when the width of the abnormal body is smaller than the recognition ability,gravity data cannot identify the abnormal body,thus causing computational redundancy in the deep fine mesh.In this paper,the unstructured grid subdivision is based on the vertical recognition ability of gravity data.With the increase of buried depth,the grid cell size gradually increases,to reduce the number of deep grid cells,thus improving the efficiency of constructing the kernel function and accelerating the speed of solving the equation.(3)In this paper,Krylov subspace generalized minimum residual method(GMRES)is used to solve the equation instead of the traditional conjugate gradient method(CG),which can effectively improve the inversion efficiency.In inversion problems,the matrix scale is usually relatively large,which makes it difficult to directly calculate the original function.In some cases,Krylov subspace transforms a larger system into an approximate smaller system,to reduce the difficulty of theoretical analysis of large complex system and reduce the amount of data computation.In this paper,through model testing and actual data processing,the Krylov subspace GMRES method can achieve convergence results with fewer iterations,effectively reduce the operation time and improve the inversion efficiency.(4)Three strategies,namely plane target optimization horizontal dimension reduction technique,unstructured grid vertical dimension reduction technique and Krylov subspace GMRES method,were applied to the actual data processing,which proved that they could effectively improve the inversion efficiency of actual data.The real data are gravity data of Olympic Dam in Australia and gravity data of Laoli Bay in Henan Province respectively.By comparing the inversion results with the known prior information,the strategy to improve inversion efficiency can not only improve inversion efficiency,but also meet the inversion accuracy,which verifies the effectiveness and correctness of the strategy to improve inversion efficiency...