Research And Application Of Joint Inversion Based On Multiple Physical Parameters

Geophysical inversion refers to inferring the spatial distribution of underground field sources through geophysical observation data,providing the occurrence state(shape,attitude,spatial location)and rock physical parameters(density,magnetic,electrical,elasticity,and velocity,etc.)of underground target bodies,has become one of the most important quantitative interpretation tools in mineral and oil and gas resources exploration.However,as the exploration targets become deeper and the exploration environment becomes more and more complex,it is difficult to accurately infer the information situation of the underground target body based on a single geophysical method.In view of the limitations of the single physical property inversion method and the multiple solutions of the geophysical inversion method,the comprehensive interpretation of multiple geophysical data is the only way to improve the interpretation of the inversion.Joint inversion is one of the most effective methods for comprehensive interpretation of multiple geophysical data.It is an ideal solution to solve the problems of inconsistent inversion results of multiple exploration methods,low utilization of multiple data,and serious inversion.Aiming at the serious inversion multi-solution,difficult coupling of multiple physical structures,low computational efficiency,and large memory consumption,etc.This paper has carried out research on joint inversion algorithms for various physical parameters.Based on the existing joint inversion methods,an optimized and improved method is proposed to more effectively reduce the inversion multi-solution,improve the inversion stability,accuracy and efficiency,and form a set of effective and comprehensive multi-property multi-constraint joint inversion algorithm to promote the practical process of joint inversion.The cross-gradient joint inversion method does not need to depend on the rock physical property relationship between different physical property parameters,but assumes that the spatial structure distribution of different physical property parameters in the same underground area is completely or partially the same,so it is suitable for comprehensive interpretation of multiple geophysical methods.Based on the cross-gradient coupling method,the paper studies the coupling method of spatial distribution structure in joint inversion of different physical properties.The objective function of joint inversion of two physical properties was constructed,and iteratively solved using the Gauss-Newton method under the constraint that the cross-gradient function is zero.We have implemented a two physical properties and single constrained 2D joint inversion between gravity,magnetic,magnetotelluric,and seismic methods.Based on the above,we add a normalization operator to the traditional cross-gradient function to overcome the effect of the differences between different physical property parameters.We propose a multi-objective multi-constraint joint inversion algorithm based on the normalized cross-gradient constraints.In view of the difficult problems of low efficiency and large memory consumption in the joint inversion of two-dimensional multi-physical parameters,we introduce the data-space method to convert the model calculation from the model-space to the data-space through the identity equation for numerical solution,thereby effectively reducing memory consumption and improving computing efficiency.The model tests show that each inversion method has its own limitations,and the strategy of joint inversion can make up for the single inversion results,effectively reduce the multi-solution of inversion results and improve the structural consistency of different models.With the increase of the number of different physical property methods,the results obtained by the joint inversion are closer to the true model in both the physical value and spatial geometry,which also shows that the increase in the amount of observation data leads to a decrease in the inversion multi-solution.Therefore,the more physical methodsare used to explore the same underground area,the more accurate the joint inversion results obtained.Meanwhile,the model parameters of different orders and different units in the cross-gradient function are converted into the same order of magnitude and dimensionless model parameters,which can effectively eliminate the result deviation caused by the direct coupling of different model parameters in the joint inversion.In addition,the data-space joint inversion method has the advantages of short calculation time and low memory consumption,and shows strong stability and applicability.Regularization technology can effectively reduce inversion multi-solution and improve inversion stability.Different regularization methods show different inversion effects.In this paper,the theories of multiple regularization methods are studied,the model weighting matrix corresponding to its function terms is derived,and the two-dimensional joint inversion algorithm under different regularizations is implemented.A two-dimensional joint inversion algorithm based on elastic network regularization is proposed.The model tests show that the best fit solution using the L2 is overly smooth,while the best fit solution for the L1 norm is too sparse.However,the elastic-net regularization method,a convex combination term of L2 norm and L1 norm,can not only enforce the stability to preserve local smoothness,but can also enforce the sparsity to preserve sharp boundaries.The field example results show that the new method can recover more detailed,clearer boundaries and higher vertical resolution.Compared with the existing inversion methods,the phenomenon of large-area divergence under the anomalous body can be effectively improved,and the sharp areas of the anomalous body have sharp edges.To facilitate the geological interpretation,the model obtained by the joint inversion is integrated into a(red-green-blue)RGB composite map.The RGB composite map is used to quantitatively explain the stratigraphic sequence and fault location of the study area.Aiming at the problems that the storage capacity of the sensitivity matrix is too large in the three-dimensional joint inversion and the traditional conjugate gradientmethod is prone to the problem of small continuous search steps,a three-dimensional joint inversion algorithm combining data-space and an improved conjugate gradient method is proposed.The algorithm does not need to form and store the sensitivity matrix,which effectively reduces the calculation time and memory consumption of the inversion.The algorithm is applied to the three-dimensional joint inversion of gravity and gravity gradient with physical properties and the three-dimensional joint inversion of different physical properties with gravity and gravity gradient and magnetic methods,respectively.The formula derivation process of 3D data-space conjugate gradient inversion is given for the first time.In addition,based on the fast forward algorithm of the gravity geometric frame,the equivalent relationship of the geometric frame is modified,and the geometric frame relationship of the gravity gradient and magnetic method is given.The algorithm can effectively improve the forward calculation.We apply the algorithm to theoretical models and field examples.The model tests show that compared with separate inversions,joint inversion based on cross-gradient constraints can not only obtain more accurate models,but also obtain higher structural consistency.Compared with the traditional model-space joint inversion method,the improved data-space conjugate gradient algorithm has the advantages of shorter calculation time and less memory consumption.The example results show that the algorithm can not only recover models with higher structural consistency,but also quickly obtain underground models under ordinary computers,showing strong stability and applicability.The data-space conjugate gradient joint inversion is the development trend of big data joint inversion in the future.