Fast Forward And Inversion Method For Large-scale Gravity And Magnetic Data In The Fourier Domain And Its Application

With the rapid development of gravity and magnetic instrumentation technology,it has become possible to acquire massive field and gradient tensor data in multi-dimensional space such as satellite,airborne and ground,which brings opportunities for geophysical refinement of exploration.At the same time,it also becomes a challenge for large-scale and refined exploration of gravity and magnetic data.The traditional Fourier domain method has a dramatic increase in computation time and memory requirement as the grid size increase,and the forward modelling is the basis for the inversion,which also leads to problems of large memory requirement and low computational efficiency for large-scale refinement of the inversion.In addition,due to the multi-solution and mathematical ill-condition problems of gravity and magnetic potential field inversion,how to use multi-dimensional and multi-component data information and known constraint information to constrain the inversion and improve the reliability of the inversion results is another challenge faced by gravity and magnetic inversion.In order to effectively improve the speed and accuracy of large-scale gravity and magnetic data inversion imaging,this paper has carried out thoroughtly study on the 3D gravity and magnetic data forward simulation and inversion imaging methods.To address the problem of low accuracy and efficiency of 3D gravity and magnetic forward method in the Fourier domain,this paper developed a fast and highly accurate gravity and magnetic forward algorithm based on 3D fast discrete convolution in the Fourier domain.Aiming at solving the problems of low accuracy and inefficiency of the existing gravity and magnegtic smooth inversion methods,efficient smooth inversion method with L₂norm is investigated based on the fast gravity and magnetic forward method.In order to solve the problems of low resolution and low efficiency of focused inversion of gravity and magnetic data,this paper carried out a study of a reweighted focused inversion method based on an imposed background model.In addition,to further improve the spatial resolution of the gravity and magnetic data,this paper carried out a study on the joint inversion method of multi-dimensional and multi-component data.The main innovations and contents of this reasearch are listed as follows:（1）A fast gravity and magnetic potential field forward modelling method based on 3D discrete convolution technique is proposed.This method makes full use of the Toeplitz property of matrix when the grid is uniformly discretized,and only the first row and column elements need to be calculated and stored to obtain the complete kernel function coefficient matrix.The computation time and storage requirement of the kernel function coefficient matrix are greatly reduced.The 3D fast discrete Fourier transform is used to achieve fast convolution of the kernel function coefficient matrix and physical properties.In addition,a new analytical expression for the prismatic gravity and magnetic anomaly is derived to calculate the kernel function coefficient matrix,which improves the computational efficiency of the kernel function coefficient matrix while ensuring computational accuracy.And,a kernel function coefficient matrix compression storage strategy is used to reduce the computation time of the kernel function coefficient matrix and discrete convolution time without loss of computational accuracy,effectively improving the computation efficiency of the gravity and magnetic potential field forward modeling.The model examples show that the method has high computational accuracy,small memory consumption and high computational efficiency,which provides an effective way to study the response characteristics of large-scale gravity and magnetic anomalies.（2）A study of efficient smooth inversion method based on L₂norm was carried out.To address the low accuracy and low efficiency problem of gravity and magnetic data inversion,smooth inversion based on L₂norm is investigated in this study.The inversion method based on L₂norm is relatively easy to generate smooth results with relatively low resolution.In order to obtain inversion result with higher resolution,a combination of a horizontal weighting function and an improved depth weighting function is introduced into the model parameters,which can not only improve higher resolution,but also effectively overcome the skinning effect of the inversion results.The proposed fast forward algorithm for gravity and magnetic potential fields is applied to the smooth inversion inversion algorithm to further improve the efficiency of the inversion and reduce the memory requirements of the inversion method.（3）A reweighted focused inversion method based on an imposed background model is proposed.In the reweighted focusing inversion method with L₀norm,the reweighted focusing inversion method has been improved by introducing the latest SF minimum support stability function and adding background anomalies and materiality constraints on the upper and lower limits of the model.This method effectively avoids the problems of unstable singularities and inversion solution process due to too small selection of focusing factor,and improves the stability,convergence speed and spatial resolution of the reweighted focusing inversion.（4）A joint inversion method for multi-dimensional and multi-component data is proposed.In order to address the feature that gravity and magnetic data at different locations and with different components usually reflect different aspects of physical properties,we propose a regularized joint inversion method for multi-dimensional spatial and multi-component data.Compared to single component data inversion,multi-dimensional and multi-component joint inversion can make up for the lack of information in single component data inversion and improve the spatial resolution of the inversion results.Therefore,the integrated use of multi-component gravity and magnetic data from multi-dimensional spatial measurements such as airborne and ground-based can effectively improve the resolution of the inversion result.（5）A 3D density imaging study of the San Nicholas sulfide deposit is carried out.Application of the rapid and high-resolution inversion method proposed in this paper to the exploration of the San Nicholas massive sulfide deposit.The smooth inversion method based on L₂norm and the focusing inversion method based on imposed background model were used to perform 3D density inversion imaging on the measured gravity data of the sulphide deposit.Comparison with the real geological information of the mine area and drilling information shows that the inversion result match well with the real boundary of the ore body and can well trap the boundary of the massive sulfide deposit,which proves the validity and applicability of the method of this paper to the real data.