3D MT Inversion Based On Model Space Compression

At present,the three-dimensional inversion technology of magnetotelluric(MT)data has been basically mature,and has been widely used in the processing and interpretation of various measured data.This technology can overcome the limitations of traditional one-dimensional and two-dimensional inversion and obtain a more accurate geoelectric model,so it has broad development and application space in scientific research and industrial production.The regularization term in the current mainstream magnetotelluric three-dimensional inversion mainly uses the L2 norm-based smooth constraint technique in the model space.This technique can guarantee the inversion of the convex function of the objective function,so that the inversion has better stability and convergence rate.However,the 3D inversion results of the magnetotelluric inversion based on the smooth constrained inversion of the L2 norm have poor boundary recognition ability,resulting in a low resolution of the obtained 3D geoelectric model,which cannot provide accurate geological information.In order to overcome this problem,this paper proposes a magnetotelluric three-dimensional inversion method based on model space compression technology.The basic principle of the proposed method is to transform the spatial domain model into wavelet domain by wavelet transform in the 3D inversion process,and then replace the traditional smooth regularization by the sparse regularization of the wavelet domain model.Since the wavelet transform has multi-scale features,the inversion model can be restored from coarse to fine by setting corresponding thresholds in the inversion to ensure stable convergence of the inversion.In the definition of the inversion objective function,in order to ensure the sparse property of updating the wavelet coefficients in the inversion,we use the L1 norm to construct the regularization term of the wavelet domain,and the data fitting term still uses the L2 norm to ensure the inversion has Better convergence rate.In the implementation of the inversion algorithm,we transform the data sensitivity information by the mapping relationship between the spatial domain model and the wavelet domain model,and use the implicit method to calculate the correlation between the wavelet domain sensitivity matrix and the vector,and then use the Gauss-Newton method.The model update quantity in the wavelet domain is obtained.Finally,the wavelet domain model update quantity is mapped back to the spatial domain by wavelet inverse transform and the spatial domain updated model is further obtained.Since the regularization term uses the L1 norm to cause the condition number of the inversion equation to be large,the iterative solution converges slowly.To solve this problem,we propose a preprocessing technique for conjugate gradient solving,which effectively improves the speed of solving inversion equations.Through the inversion test of theoretical model and measured data,the method is comparable in speed to the traditional Gauss-Newton method,but the resolution of the model is greatly improved,especially for the description of deep anomalies and the boundary recognition of anomalous bodies.The method proposed in this paper is helpful for improving the imaging resolution of magnetotelluric three-dimensional detection,and can be further improved and popularized in subsequent research.