Two Dimensional Inversion Of Airborne Transient Electromagnetic Data In Axial Anisotropic Medium

Airborne transient electromagnetic method(ATEM)is an electromagnetic exploration method developed from ground electromagnetic method.The purpose of developing ATEM is to carry out rapid general survey in large areas and areas unfavorable to ground exploration methods,such as rivers,glaciers and deserts.As for the research of forward and inversion of ATEM,the current research focuses on isotropic medium,among which the research on one-dimensional forward and inversion of ATEM is relatively mature,and the research on two-dimensional and three-dimensional forward and inversion is also gradually mature.For anisotropic media,there are only a few reports on the research of ATEM anisotropy forward and inversion.The one-dimensional anisotropic forward and inverse modeling of ATEM has high efficiency,but the one-dimensional case does not conform to the actual underground medium distribution,however,the computation of anisotropic three-dimensional forward and inversion of ATEM is very large,so it is particularly necessary to carry out the research of anisotropic two-dimensional forward and inversion of ATEM.This paper mainly studies the two-dimensional inversion of principal axial anisotropy by ATEM.Forward modeling is the basis of inversion,and the second field of wave number domain is solved by two-dimensional finite element method,and then converted to the space domain.The total field in frequency domain is obtained by the sum of the secondary field and the primary field solved by one-dimensional numerical simulation,and then the time domain is inversely transformed to realize the two-dimensional forward modeling of principal axial anisotropy of ATEM.Then,the theoretical model is designed to verify the correctness of the two-dimensional forward code.In the aspect of inversion,the objective function for the two-dimensional inversion of principal axial anisotropy of airborne transient electromagnetic method is established,and the adjoint equation method is used to solve the sensitivity matrix to further realize the gradient calculation of the objective function.The open source Limited-memory Broyden-Fletcher-Goldfarb-Shanno(LBFGS)inversion theory and algorithm process are studied and applied to optimize the above objective function and update the parameters of the iterative principal axial anisotropy model,so as to realize the two-dimensional inversion of principal axial anisotropy of airborne transient electromagnetic method.Fortran language is used to write the code,and the two-dimensional inversion program of principal axial anisotropy of airborne transient electromagnetic method is obtained.The results of synthetic data and measured data verify the reliability and stability of the program.In order to reduce the multiplicity of solutions and improve the stability of the inversion,the anisotropic constraint term is introduced into the objective function to realize the constrained two-dimensional inversion of principal axial anisotropy in airborne transient electromagnetic method.The inversion results of the synthetic data of the theoretical model show that the resistivity values and positions of the abnormal bodies in X-axis and Y-axis directions can be recovered relatively well,and the inversion results of the resistivity in Z-axis direction are poor when the anisotropic constraints are not added;However,when the anisotropy constraint is added,the recovery of Z-axis resistivity is improved,but the inversion results is still not as good as X-axis and Y-axis resistivity.In order to improve the computational efficiency of the two-dimensional inversion program of the principal axial anisotropy of ATEM,the footprint method is added to calculate the sensitivity.The inversion results of the synthetic data of the theoretical model show that,compared with the two-dimensional inversion of the principal axial anisotropy of ATEM without footprint method,the efficiency of the two-dimensional inversion with footprint method is improved.