Three-dimensional Forward And Inversion Of Resistivity And Permeability Models For Controlled-source Audio-frequency Magnetotelluric Methods

The Controlled-Source Audio-Frequency Magnetotelluric Methods(CSAMT)is an electromagnetic method based on the Magnetotelluric Methods(MT)and the Audio-Frequency Magnetotelluric Methods(AMT).The method has been developed from the initial qualitative analysis to the more accurate quantification interpretation,The development of forward and inversion algorithms plays an important role in the development of methods.In practical applications,the observed data is not only affected by the conventional resistivity parameters,but also strongly influenced by the magnetic permeability parameters in some areas.In order to obtain a more accurate and reliable quantitative interpretation,it is necessary to develop a corresponding forward and inverse algorithm.The focus of this paper is to introduce magnetic permeability parameters in CSAMT.The equation of electromagnetic field satisfaction during forward modeling does not neglect the influence of magnetic permeability parameters,and the three-dimensional staggered grid finite difference method is used as the forward operator.The total field separation method is used to calculate the secondary field.The measure field values are used by two kinds of interpolation methods and compare them.The advantages and disadvantages of the method are to select the volume-weighted calculation method which is more suitable for the actual situation.And design the one-dimensional,two-dimensional and three-dimensional models to verify the accuracy of the forward algorithm respectively.The design model explores the response law of the permeability parameter and the influence on the observed data.Thus,the conclusion that the influence of the permeability parameter in a partial region is not negligible is explained.After implementing the two physical property parameters forward algorithm,an inversion algorithm considering two parameters is further implemented.The finite memory quasi-Newton method(LBFGS)method is used as the inversion research method.The inversion research focuses on the calculation of the objective function gradient and the processing of the sensitivity difference between different parameters.The gradient of the objective function is calculated by the law of multivariate function derivation.In this paper,the synchronous inversion of two physical parameters is realized firstly,and propose the problems of two physical parameter responses offset in inversion.Therefore,the inversion of two physical parameters based on cross-gradient constraint is introduced to realize the inversion algorithm.For the problem of sensitivity difference of different parameters,the method based on cooperative inversion is adopted,that is,the synchronous inversion of two physical parameters is completed first,and the synchronous inversion results of the high-sensitivity physical parameters are used as the initial model to introduce the synchronous inversion of the cross-gradient constraints,and the final two-parameter inversion results are obtained.The reliability of the inversion algorithm is verified by designing different models.Finally,the theoretical trials of the two physical parameters of this paper prove that ignoring the permeability parameter for single-parameter inversion will bring a lot of false anomalies to the final inversion,which will seriously affect the final interpretation,thus indicating that the two physical parameters are reversed.The necessity of acting.