Numerical Simulation On The 2.5-Dimensional FDTD Modeling Of TEM Field With A Loop Source And Application Research

In recent years,the rapid development of transient electromagnetic sounding method(TEM)has became mature in some areas.As a new method of electrical prospecting,transient electromagnetic sounding method(TEM)has been more and more widely used in various fields,such as the mineral resources exploration,hydrological geology,engineering geology and environmental geology.After decades years of development,it has made great progress in the aspect of theoretical research and the level of application,however,with the complexity of the transient electromagnetic theory of multidimensional and the difficulty to achieve which severely restricted the effect of exploration and the scope of its application,so it is necessary to further study and improve the theory of forward and inversion.Due to the forward method is the basis of the inversion theory,therefore,to carry out the theory of multi-dimensional numerical of TEM is one of the frontier researches at present.In the practical work,we almost use rectangular loop,but the theory research can not catch up it.The theory of one dimension and two dimensions has become so mature,but there is a certain deviation between the theory and the actual response.Although the theory of three-dimensional transient electromagnetic response is the most close to the actual situation,it also needs an effective algorithm.Apart that the time that consumed in the process of actual operation is longer and need such high requirements for hardware.So,sometimes still need a more complicated algorithm.So the researchers invent a compromise method: 2.5-D(two-dimensional geoelectric section with three-dimensional source)problem,which greatly reducing the amount of calculation and has important value to practice.But this theory is not very mature.So in this paper,we study the numerical simulation on the 2.5-dimensional FDTD modeling of TEM field with a loop source.Based on the basic knowledge of TEM,this article embarks from the Maxwell's equations,derives the homogeneous diffusion equations of time domain electromagnetic field: for solving the two-dimensional geoelectric response,we first exchange the equations to 2-D with Fourier transform along the geoelectric body.Using the Finite Difference Time Domain Method(FDTD)to realize the numerical simulation in the research space region,spatial discretization and different electrical parameters to simulate the electrical distribution with space grid in two-dimensional geoelectric section;substitute the differential expression with finite difference fractional,acquiring the matrix equation of electric field component.Aiming at the question of dual Bessel function in the formulation of electromagnetic field,use the Hankel transformation,cosine transform as well as G-S transformation will we can get the initial condition.For the edge under the ground,we use Mur boundary conditions;in the ground-surface,the method of boundary spline interpolation used.Then use appropriate time step iteration,calculate the distribution of theinduced electric field and the induced electromotive force in frequency domain;using cubic spline interpolation method to realize inverse Fourier transform,finally get the values of transient electromagnetic response on different time.After solved the problem of theoretical derivation,we use the MATLAB to finish the program.After the analysis of the accuracy and reliability of the proposed algorithm between typical geoelectric model analytical solution and the numerical simulation,using the program to simulate the transient response of the different conditions of geoelectric,summed up response regularity for different explanation theory.Then,this paper study the problem of transmitter coil size and offset.The results of 2.5-D transient electromagnetic inversion method research have important theoretical value and have guiding significance for the practical work of transient electromagnetic data interpretation.