Research On Electromagnetic Exploration Data Inversion Based On Sparse Regularization

In recent years,the shortage of resources and problems with environmental and natural disasters caused by national economic development have brought severe challenges to China's geophysical exploration technology.The realization of near-surface geophysical exploration is the basis for the development of mineral resources,prediction of geological disasters and construction of smart city.It is closely related to human security and sustainable development of national economy.Airborne electromagnetic(AEM)method is a moving platform geophysical detection technology.It is suitable for exploration of mineral,oil and gas,engineering and environmental exploration in areas with complex terrain or harsh environment.It has the advantages of high efficiency,environmental protection and low cost.It has gradually become an important technical tool for near-surface structural detection.For the complex underground and resistivity structures,the traditional one-dimensional(1D)data inversion and interpretation technology cannot meet the needs of fine AEM near-surface detection.On the other hand,most of the current three-dimensional(3D)AEM inversions are based on smooth regularization constraints,which cannot realize the fine inversion of complex underground structures.AEM exploration has large survey areas and collects large amount of data,so 3D EM data inversion will consume a lot of time.Therefore,it is very important to carry out researches on high-precision and efficient 3D AEM data inversion for fine near-surface structural detection.Facing the dilemma that the inversion and interpretation of AEM data is difficult to develop in practice due to the dual constraints of resolution and computational efficiency,this paper realizes the framework of constructing the generalized model constraints for regularization inversion based on iterative weighted least squares(IRLS).To improve the inversion resolution of EM data,this paper applies the sparse transform in the field of image processing to the construction of regularization term in the objective functional of the inversion,and carries out the research on regularization inversion method based on sparse transform.For the time-consuming problem of 3D inversion for large-scale AEM data,based on sparse regularization inversion,this paper applies compressed sensing method to 3D AEM data reconstruction,and carries out the research on inverse algorithm based on large-scale compressed sensing data reconstruction.To realize the high-precision and efficient 3D inversion of AEM data,in this paper we first use the finite-difference algorithm based on staggered grids to discretize the controlling equation of the secondary field in the frequency-domain,then we use the quasi minimum residual(QMR)method to solve the large-scale linear equations,and realize the 3D AEM forward simulation in the frequency-domain by adding the primary and secondary field.Based on the IRLS inversion framework,this paper flexibly changes the form of model constraints by introducing the generalized model constraint,realizes the regularization inversion method based on generalized model constraints.Flexibly selecting the form of model constraints can easily obtain inversion results with different characteristics.Using L₂ norm constraint will produce smooth inversion results,while using L₁ norm constraint will produce inversion results with obvious block structures,while the constructed focusing operator can obtain more focusing inversion results.To obtain high-precision inversion results,based on the generalized model constraints for inversion algorithm,by combining with the sparse transform recently developed in the field of information technology,this paper realizes the regularized inversion method based on sparse transform.Based on the multi-scale and multi-directional characteristics of sparse transforms(such as wavelet transform,curvelet transform and shearlet transform),this paper transforms the electrical underground model in space-domain into sparse coefficients in sparse domain,to realize the feature extraction of the model at different scales.The sparse coefficient contains much of model information,such as the overall overview of the model and the boundary details of the abnormal structure.Thus,in the inversion process,by constantly updating the sparse coefficients,the key coefficients that can describe the main characteristics of the model can be recovered and the inversion convergence standard is satisfied,to obtain higher precision results than the constrained inversion of the traditional space-domain model.The wavelet transform can realize the optimal sparse expression of 1D signal.Compared with the wavelet transform,the curvelet transform has more directionality,which can approximate the optimal sparse expression of two-dimensional(2D)model and can extract the detailed features of the boundary in the model.Compared with the curvelet transform,the shearlet transform has more flexible direction selection and more rigorous mathematical method,Therefore,it is suitable for feature extraction of 3D model.To verify the effectiveness of the regularization inversion method based on the generalized model constraints and sparse regularization inversion method in this paper,according to the applicability of different sparse transform methods,taking 1D time-domain AEM inversion as an example,the sparse regularization inversion based on wavelet transform is studied,and the restoration ability of different regularization inversion methods for 1D layered media is discussed.Taking the inversion of 2D magnetotelluric(MT)data as an example,the sparse regularization inversion based on the curvelet transform is studied,and the recovery ability of different regularization inversion methods for the boundary of complex abnormal body is analyzed.Furthermore,the 3D shearlet transform is used to realize the 3D frequency-domain AEM sparse regularization inversion.By designing a complex underground resistivity model,the constrained inversion with space-domain L₂ norm and L₁ norm and sparse regularization inversion results are compared.Both generalized model constrained inversion and sparse regularization inversion can accurately restore the overall shape of abnormal body,but the sparse regularization inversion has better ability to describe the boundary of complex abnormal body.Finally,the effectiveness of the inversion algorithm is verified by the inversion of a survey dataset.For the problem of low computational efficiency in the case of large-scale and large amount 3D AEM data inversion.In this paper,the compressed sensing data reconstruction technology is used to“compress”and sparsely express the observed data of random sampling points by using sparse transform,and then the forward modeling data of complete sampling points in the whole survey area are reconstructed by using the projection algorithm onto convex sets,that is,the 3D forward calculation of sampling points is carried out through Poisson disk random sampling by using the sparse characteristics of AEM data,The forward response of all data points are reconstructed to replace the traditional method of calculating all measuring points in the target area,which can greatly improve the forward modeling efficiency on the premise of ensuring the reconstruction accuracy.In the inversion,the missing sensitivity matrix is obtained by using the EM field and interpolation function calculated at random sampling points,and then the gradient is obtained.During each inversion iteration,measuring points are randomly selected again to calculate the gradient,to ensure that there will be no large error in the result due to the bias of a certain sampling.In this paper,the sparse regularization inversion algorithm based on shearlet transform and compressed sensing reconstruction technology are combined to realize the high-precision and high-efficiency inversion of large-scale AEM data.Through synthetic examples,the accuracy of forward data reconstruction when wavelet and curvelet transforms are used to realize data“compression”and different sampling rates are analyzed.Further we compare the impact of these two situations on the sparse regularization inversion results of compressed sensing reconstruction.Compared with the sparse regularization inversion of full data sampling,it is proved that the inversion method of compressed sensing reconstruction can significantly improve the inversion efficiency.Finally,taking the frequency-domain AEM data in Byneset,Norway,as example,this paper carries out large-scale AEM 3D inversion.The results are consistent with the actual geological data,and the computational efficiency is nearly twice of that for conventional sparse regularization inversion algorithm,which further verifies the effectiveness of the sparse regularization inversion of compressed sensing reconstruction.In this paper,the sparse regularization inversion method based on compressed sensing reconstruction can not only improve the inversion resolution of 3D AEM data,but can also significantly improve the inversion efficiency,which provides a solid technical support to the practical 3D AEM inversion technology.The research results of this paper will play an improtant role in promoting the application of geophysical EM data inversion and interpretation.