The Study And Application Of 3D Inversion Methods Of Gravity & Magnetic And Their Gradient Tensor Data

Explorations of potential field data(gravity & magnetic)and their tensor gradient data on multi-platform,such as satellite,airborne,ground,and borehole,have rapidly developed and matured.The matched data processing and interpretation technologies are also constantly updated and improved,which expand the application field and improve the detectivity of potential exploration.Three-dimensional inversion is one of the significant technologies in data processing and interpretation.From inversion results,we can obtain not only the geometric information about the boundary and buried depth,but also physical information such as physical parameter value and physical property distribution of anomalous bodies.These informations may provide a reliable and rich reference for subsequent geological interpretation.However,low resolution and nonuniqueness are the main problems of three-dimensional inversion,and many efforts have been made to solve these two problems.In this thesis,I also concentrate to analyze and solve these two problems of potential inversion.Forward modeling is the basis of inversion.By analyzing the forward simulation data,we can summarize the characteristics and detection capabilities of potential data and their tensor gradient data.In this thesis,firstly,the physical significances of potential and their tensor gradient data are analyzed,and the forward formulas of potential data and their tensor data caused by anomalous cuboid are derived,such as gravity,gravity tensor data,magnetic tensor,magnetic gradient,and total magnetic intensity.In addition,to study multi-dimensional and multi-component data sets,I comprehensively listed the frequency domain conversion factors between the potential data and their tensor gradient data of different heights,different magnetization directions and different geomagnetic directions.Based on the regularization inversion method,I studied to improve spatial resolution of the inversion.Firstly,I analyzed the main factors affecting the results of the regularization inversion,including stability function,model weighting function,upper and lower bounds of model parameters.The L2 norm stability function alwaysgenerate the smooth and low resolution inversion results,while the L1 and L0 norm stability functions can result in the focusing and high resolution inversion results.The model weighting function influences the distribution of the physical property by applying the different weights to each cell.Depth weighting function can effectively overcome the "skin effect" of the field data inversion to improve the vertical resolution.The upper and lower bounds of model parameters can improve the resolution and promote the convergence of the inversion.Based on the above analysis,I propose a new model weighting function,which is composed of a horizontal weighting function and an improved depth weighting function.The combined model weighting function can get a higher horizontal resolution and effectively overcome the "skin effect" and "bottom effect" of the inversion.Both the model test and the real data application verify the effectiveness of the combined weighting function.The regularization inversion based on L0 norm has been widely concerned due to its high-resolution,while the derivative of the objective function to the weighted parameters is an approximation.I re-derive the derivative of the objective function to the weighted parameters,and a more reasonable derivative formula is obtained.In this thesis,I also studied and discusssed how to select the focusing factor.Too small the focusing factor may result in an unstable inversion procedure,and too large the focusing factor may result in an unfocused inversion result.By adding the background anomaly,a method is proposed to make the selection of the focusing factor easier and more flexible.Besides,I tried to improve the resolution of the cokriging inversion.Compared with the regularization inversion,the obvious advantage of cokriging inversion is the ease of adding priori informations.For example,by selecting the long axis direction of the range ellipsoid,the information of trend direction and dip angle can be easily utilized in inversion.Thus the cokriging inversion is an ideal method to interpret the areas where the trend direction and dip angle of the structure are known.Firstly,the formula of the covariance matrix based on Gaussian method is updated to extend the applicability,and the influence of the range ellipsoid on inverison is analyzed.Secondly,by analyzing the covariance matrix,the reason for the low resolution of the conventional cokriging inversion is confirmed.Finally,in order to improve the resolution of cokriging inversion,the threshold is set to pruning the parameter covariance matrix.Combined with the iterative inversion technique,high-resolution of inversion results is obtained.The comprehensive utilization of multi-component potential data acquired from airborne,ground and borehole can reduce the nonuniqueness and improve the accuracy of geological interpretation.Firstly,to recover the same physical parameters with the multi-dimensional and multi-component data,I respectively implement the regularization and the cokriging joint inversion.These two joint inversion methods are organized into the forms similar to the separate inversion respectively,so that it is easy to apply theory and analysis techniques of the separate inversion to joint inversion directly,which improves the realizability of joint inversion.The simulation model test verifies the effectiveness of joint multi-dimensional and multi-component potential data for recovering the same physical parameters.Finally,I focus on the joint inversion of gravity and magnetic data to obtain the similar distribution of density and the magnetic susceptibility.Based on the linear correlation constraint of sinusoidal function,a new joint inversion method is proposed.Simulation models are designed to verify the and effectiveness of the new joint inversion method,and the inversion results of the new joint inversion and the cross-gradient joint inversion are compared and analyzed.The joint inversion based on the correlation constraint of sinusoidal function is applied to the real airborne gravity and magnetic data acquired from the Mc Faulds Lake area of Canada,and the results prove that the new method has the ability to improve the inversion resolution and reduce the nonuniqueness.