Three-dimensional Controlled-source Audio-frequency Magnetotelluric Inversion For Resistivity And Magnetic Susceptibility Using Cross-gradient And Magnetic Data Constraints

Generally,the forward and inverse algorithms and data interpretation of CSAMT only consider the difference of resistivity,and ignore the influence of other electrical parameters(such as permeability).However,in some cases,for example,in ferromagnetic deposits or basic ultrabasic igneous rock areas,there are not only differences in electrical conductivity but also obvious differences in magnetic conductivity between geological targets and surrounding rocks.When CSAMT is carried out in such a work area,the observed electromagnetic field data will inevitably be affected by permeability parameters,and the contribution of permeability parameters to CSAMT response can not be ignored.In order to improve the reliability of CSAMT inversion results,it is urgent to carry out three-dimensional forward and inversion research considering the influence of resistivity and permeability.Based on the integral form of Maxwell's equations considering the influence of permeability parameters,the CSAMT three-dimensional numerical simulation algorithm considering the influence of resistivity and permeability parameters is realized.Two dimensional and threedimensional theoretical models are established to verify the accuracy of the developed CSAMT three-dimensional forward algorithm.The response of three-dimensional theoretical models of low resistance magnetization and high resistance magnetization is calculated,and the influence of permeability parameters on the response of CSAMT is analyzed.On the basis of CSAMT resistivity and permeability dual parameter three-dimensional forward algorithm,the inversion objective function with smooth constraints is defined,and the finite memory quasi Newton method(lbfgs)is used to realize the CSAMT resistivity and permeability dual parameter synchronous inversion algorithm.Six theoretical models are designed for synthetic data inversion,and the effectiveness of the inversion algorithm is verified.The results show that,due to the influence of permeability parameters,the shape and position of permeability can not be well recovered for low resistance magnetized body,but also affect the shape and position of resistivity;the recovery effect of high resistance magnetized body is better than that of low resistance magnetized body.In order to solve the problem of poor inversion results of CSAMT algorithm,the cross gradient constraints of resistivity and permeability are added to the objective function,and the CSAMT two parameter synchronous inversion algorithm based on cross gradient constraints is realized.The results show that the shape and position of the permeability can be recovered for the low resistance magnetized body under the cross gradient constraint,but the permeability value is smaller than the true value;similarly,the recovery effect of the high resistance magnetized body is better than that of the low resistance magnetized body,but the recovery of the permeability value is not ideal.In order to further improve the inversion effect of CSAMT,the magnetic data constraint is added to the objective function to realize the synchronous inversion algorithm of CSAMT resistivity and permeability based on cross gradient and magnetic data constraint.The results of numerical examples show that the shape and position of resistivity and permeability can be well restored for both low resistance and high resistance magnetizers,and the recovery of permeability is close to the true value.The inversion test of the measured data verifies the practicability of the inversion algorithm,and the inversion results of the measured data are in good agreement with the actual geological conditions.