The Study On High-precision Imaging And Density Inversion Methods Of Gravity And Its Gradient Tensor Data

To reveal the accurate position of the geological body and the distribution of physical properties(density)using gravity and its gradient data,the density inversion of the gravity tensor data and the imaging technology of the spatial distribution of the geological body are studied.This paper focused on solving the data integration,resolution discussions,and also analyzed the application effects of airborne and ground-based gravity exploration technology,thus improving the precision of imaging and density inversion results.In addition,we analyzed the application effects of the combined technologies of airborne and ground-based co-gravity data to enhance the exploration capabilities of deep geological bodies.It promoted the development of airborne gravity gradiometry technology and the establishment of aviation and ground cooperative exploration technology systems.We mainly carried out:1)The relationship between gravity data and its gradient tensor data was quantitatively analyzed in the spatial domain and the frequency domain,and the advantages of the measured gradient tensor data relative to the those calculated from gravity data were analyzed.Gravity data contains relatively more low frequency information and have good reflection of the relatively deep(long wavelength)anomalies.Gradient data,on the other hand,is energetically high in the high frequency region and rather sensitive to relatively shallow(short wavelength)anomalies.The fractal relationship between gravity gradient tensor data and geological body is analyzed,which lays the foundation for data selection of subsequent processing and interpretation work.2)Based on the features and advantages of gradient tensor data,a new fast method of horizontal imaging with higher accuracy is studied.Emphasis is placed on the comprehensive utilization of tensor components and the optimized combination of tensor components,making it more effective to fuse the included information and improve the accuracy of interpretation accuracy and precision.Imaging method based on equalized tensor invariants and eigenvalues are proposed,which can balance the anomalies of deep and shallow geological bodies with different amplitudes and improve the imaging resolution.In order to reduce the interference and transmission of noise,the derivation of the method including tensor data is based on the stability of Laplace equation.The results of model and actural data test show that the new method can balance the amplitude anomaly more accurately and clearly,and reflect the details of field sources.Compared with the conventional method,the imaging resolution is higher and has a certain noise resistance.3)We developed the correlation imaging technology of gravity gradient tensor data.On the basis of shielding the anomalous interference of the deep background,the multi-parameters of gravity gradient data are integrated into the imaging and constrained to each other,which avoids the larger influence of single component measurement error or less data volume on the result.The theoretical noise-contaminated model test and the measured data processing results show that the joint imaging method can effectively locate the depth of geological body more accurately,eliminate the false boundary and have higher resolution,indicating the applicability and reliability of the method.4)Based on the features of multi-component and large amount of information of gradient tensor data,3D density inversion of multi-component data was used to further improve the resolution compared with gravity data or single-component results of gradient tensor.Optimal density inversion algorithms were proposed for the joint inversion of large volume gravity gradient tensor data.One way is to reduce the computational time of the inversion process by introducing the Lanczos bidiagonalization(LB)method to reduce the kernel function matrix used in the inversion and avoid the product operation of large kernel function matrix in the conjugate gradient method.The weighted generalized cross-validation method was used in the LB algorithm to discuss the optimal regularization parameter selection.Synthetic model tests show that this method obviously increases the computational speed.As the number of iterations increases,the residual error is smaller and the better the fit between the predicted data and the actual observed data.The most suitable number of iterations is selected by statistical fitting difference root mean square error and calculation time.Another optimization method was to introduce the preconditioned conjugate gradient method(PCG)into the density inversion,reducing the number of equations and accelerating the convergence rate.We improved the parallel algorithm based on GPU to reduce the extra time and memory of the preprocessing,and discussed the accelerating ability of different preprocessing operators through model tests.The results show that the parallel PCG method can reduce the number of iterations compared with the conventional conjugate gradient algorithm,and weigh out the extra time required for the preprocessing decomposition calculation to improve the computational efficiency.In addition,an improved ICCG algorithm is proposed to overcome the shortcomings of the unfilled Cholesky factorization,which is unfilled,and its applicability is reduced when the coefficient matrix is weakly diagonally dominant,so as to ensure the stability of the algorithm and improve the computational efficiency.The results of the synthetic model test show that the improved algorithm has its own convergence with higher resolution,and the computational efficiency of 3D density inversion is higher.The two optimization algorithms are applied to 3D density inversion of the measured FTG data in the salt dome of the Gulf of Mexico.The spatial morphology of the cap rock in the study area coincides with the geological data.The buried depth of the center is similar to that of the predecessors.Compared with the traditional density inversion algorithm,the speed is improved,and the effectiveness and applicability of the method are proved.5)For aviation,ground-based collaborative gravity processing and interpretation technology,we developed joint correlation imaging and density inversion techniques of different height data.The singular value decomposition(SVD)method was used to analyze the singular value spectrum of several combinations of different height data.It is found that the singular value decay rate is slower with the increase of the number of observation surfaces at different heights,thus indicating more large eigenvalues are involved in the imaging or inversion process which improve the resolution of the result.Observed data from multiple height observation surfaces were constructed for processing,which is equivalent to the information reflecting different depths of underground field sources.They increase the amount of information involved in imaging and inversion,reducing the multiplicity of imaging or inversion,and also no additional depth-weighted and prior information is required in imaging and density inversion process.The noisy synthetic model test thowed that compared with the traditional ground data results,the joint imaging and density inversion methods of multiple height planes can effectively improve the vertical resolution of the result and have good noise immunity.In addition,the combination analysis can provide some reference for the collection and processing of actual airborne gravity/gravity gradient tensor data.The new high-precision interpretation methods proposed in this paper are not only suitable for fast processing of gravity gradient tensor data,but also generally applicable to gravity data.Both the theoretical model and the actual data test show that the improved imaging and inversion methods can quickly interpret the horizontal distribution range,the depth information and the density distribution range of the field source body,respectively,to obtain high-precision results,providing ideas for the processing and interpretation of large-scale and high-precision gravity exploration data.