Research On Forward And Inversion Of 3D Electromagnetic Detection In Downhole Time-Domain Based On Finite Volume Method

The study of pure anomalous response(secondary field)in borehole time-domain electromagnetics has the advantages of large detection depth and high resolution,which is a research hotspot in the logging field at home and abroad.In view of the borehole time-domain electromagnetic problem,the conductivity and permeability of borehole and formation non-uniform medium will change dramatically in small-scale(casing,mud,etc).In the Cartesian coordinate system,the mesh element needs to be divided very closely,which will lead to the change of magnitude of the number of unknowns in the equation solving process.Although computer technology has been developed and improved,it is still difficult to meet the actual calculation needs without improving the modeling method.The cylindrical coordinate system can better model the small-scale problem,effectively reduce the number of meshing and improve the computational efficiency.However,the cylindrical grid is inconvenient to establish a complex model and is limited to use in inversion.The hexahedral grid in the form of octree encryption can make up for the deficiency of cylindrical grid in this regard.Therefore,in this paper,the cylindrical mesh generation method is used in the forward modeling and the hexahedral mesh generation method with octree encryption is used in the inversion to carry out the three-dimensional forward and inversion research of borehole time-domain electromagnetic detection.Firstly,this paper introduces the three-dimensional finite volume forward modeling theory of time-domain electromagnetic.Starting from the time-domain Maxwell equations,we use unstructured grids to complete the spatial discretization of finite volume,and then use backward Euler technology for time discretization.Through the spatial and temporal discretization of the equations,the matrix representation of the equation is obtained.Secondly,before the numerical simulation,the response results of the numerical solution and the analytical solution are compared to verify the correctness and accuracy of the algorithm.Then,the characteristics of the magnetic field diffusion field in the uniform half-space are analyzed.The influence of the parameters such as the conductivity of the casing,the relative permeability,the thickness and the inner diameter on the forward response is discussed.The response characteristics of different emission waveforms and different boundary distances are studied.Finally,based on forward response data,the three-dimensional inversion of downhole time domain is completed by using Inexact Gauss Newton method.The research results show that the above research can lay the foundation for correcting the influence of metal casing,and provide technical support for the data processing of time-domain electromagnetic logging,so as to better carry out the three-dimensional forward and inversion research of time-domain electromagnetic logging.