Research On Magnetotelluric Constrained Inversion Method

The existence of non-uniqueness and instability in magnetotelluric inversion results in low resolution of the inversion in the deep.At present,the main method to solve the problem of non-uniqueness of magnetotelluric is constrained inversion.Therefore,the study of MT constrained inversion method is of great significance for improving the accuracy of MT inversion,reducing non-uniqueness and selecting the optimal inversion parameters.The MT constraining methods are generally divided into hard constraints and soft constraints.The hard constraints directly changes the model parameters that need to be constrained,and the model is modified in inversion iterations to finally achieve constraint inversion.The advantage of hard constraints is that the theory is simple,and it is convenient for local control and human-computer interaction.The disadvantage is that it needs to manually determine the constrained parameters and spatial position,which is difficult to select.The inversion result of hard constraints excessively rely on the prior information.Soft constraints mainly have the following four methods:(1)Regularization Constraint: The regularization factor plays a role of the balance function and the stability function in the least squares inversion.The size of the regularization factor can be adjusted in the inversion.(2)Weighted constraints: Using weight matrix to act on the model parameters;or add constraints to the Jacobian matrix,the essence of which is to solve the constrained equation and conventional inversion equation simultaneously.(3)Boundary Constraints: Using the idea that the logarithm of the resistivity is always positive,the model parameters with upper and lower bounds are used instead of the original logarithmically model parameters for inversion to improve the stability of inversion and reduce inversion non-uniqueness.(4)Prior model constraints: Based on existing prior information,specific prior models and weighted matrices are set to achieve the purpose of improving the inversion resolution in local areas.The advantage of soft constraints is easy to control the model parameter as a whole,and the inversion result is stable and efficient.Combining soft constraints with hard constraints and implementing human-computer interaction in magnetotelluric data processing is the main development trend of the MT constrained inversion method.Efficiency and resolution of magnetotelluric 2D inversion are far lower than 1D inversion,which has more flexible constraint methods.1D inversion is prone to produce false anomalies,so the use of 1D inversion is restricted.The inversion interpretation of field MT data still relies on the primary 1D and 2D inversion,the actual application of 3D inversion is not yet mature.How to make full use of the advantages of 2D and 1D inversion are questions that deserve special attention.Based on the above discussion,this paper first studies the basic theory of 1D magnetotelluric constraint inversion(including the Marquette method and the conjugate gradient method),and then focuses on the various methods of hard constraints and soft constraints and compares their advantages and disadvantages and applicability.After that the basic principle and implementation process of 2D finite element forward modeling of magnetotelluric are introduced.The 2D conjugate gradient inversion study of magnetotelluric is carried out,and the three methods including regularization constraint,weighted constraint and initial model constraint are studied.Besides,the 2D inversion algorithm is used to modify the results of 1D constraint inversion,and based on 1D constraint inversion,2D inversion iterations are performed to remove one-dimensional false anomalies and improve resolution.