Two Dimensional LBFGS Inversion Of Transient Elecctromagnetic Data In Spindle Anisotropic Medium

Transient electromagnetic method(TEM)was first proposed by geophysicists in the United States.After that,scholars in various countries have carried out a lot of related forward and inverse research work.This method has many advantages,such as high sensitivity,penetrating high resistivity layer,strong ability to distinguish low resistivity layer,large detection depth,convenient construction,flexibility and so on.It is widely used in finding mineral resources,solving hydrological problems,engineering exploration and geothermal exploration.With the continuous development of TEM,the processing and interpretation of actual field exploration data put forward higher requirements for TEM.Most of the previous TEM studies are based on the assumption that the underground media are isotropic,but in fact,the underground media mostly show anisotropic characteristics,and the research of anisotropy has been relatively mature in some electromagnetic exploration fields,Some research results have been applied in practice,but there are few related research results in TEM.However,based on the rapid development of TEM in recent years,the research on TEM anisotropy is increasing gradually.In this paper,two-dimensional inversion of TEM anisotropy is studied.Forward modeling is the basis of inversion.In the two-dimensional forward modeling,the primary field plus the secondary field is used to obtain the total field,and six electromagnetic components are solved by the finite element method.In the calculation process,the nonlinear conjugate gradient method is used to solve the forward equation,and the field value in the frequency wavenumber domain is obtained.After two times of Fourier inverse transformation,the field value is converted to the time domain,and finally the response in the time domain is obtained.A two-dimensional theoretical model is established to verify the correctness of anisotropic two-dimensional forward modeling.In inversion,the finite memory quasi Newton method(lbfgs)is selected as the inversion method,which has the advantages of high efficiency and high speed.Firstly,the calculation formulas of the objective function and the gradient of the objective function in the case of anisotropy are derived,and then the calculation formula of the Jacobian matrix in the case of transient electromagnetic spindle anisotropy is derived by the adjoint equation method.The finite memory quasi Newton method(lbfgs)is used to update and iterate the parameters of the anisotropic model.The FORTRAN language is used to write the inversion code to realize the two-dimensional inversion of TEM spindle anisotropy.The inversion results of the synthetic data of the theoretical model verify the reliability of the two-dimensional anisotropic inversion program.In this study,the two-dimensional inversion results of the theoretical model synthetic data show that: the transient electromagnetic method has a significant effect on the exploration of low-resistance anomalous bodies;On the whole,of the three spindle inversion resistivity inversion effects,the X-axis direction resistivity recovery effect is the best,followed by the Y-axis direction,and the Z-axis direction recovery effect is poor.