Direct Time-domain Response In The Transient Electromagnetic Field And Its Application

Changing electric field can produce the magnetic field and changing magnetic field canproduce the electric field. Changing electromagnetic field is transmitted throughout space sothat electromagnetic wave is formed. To study the fluctuating rule of electromagnetic wave,wave equation should be considered. The essence of the general electromagnetic waveequation is the homogeneous damping wave equation. The solution problems of pure waveequation and the diffusion equation have been discussed many times. But so far, its solutionhas rarely been involved for the general wave equation. The solution of homogeneousdamping wave equation is studied in detail in this paper. Time-domain near-source transientelectromagnetic field has the merits of strong signal, deep detecting depth and high accuracy.However, dipole approximation in the near-source will cause greater error based on traditionaltransient electromagnetic theory, and these advantages are restricted. Studying the analyticalformula of direct time-domain is one way of solving the problem. On this basis, there isdeeper discussion in this paper.Firstly, electromagnetic wave, its application and its development are described briefly,the characteristics, the development, the research results about theory and application and theprospect of the transient electromagnetic method are introduced, and the background andsignificance of this paper are given.Secondly, three-dimensional homogeneous damping wave equation is solved by adoptingthe method of variable separation. And based on boundary conditions, the solution of thegeneral wave equation is acquired. Then with the initial conditions, the correspondingcoefficients are determined based on the orthogonality of trigonometric function system bytaking two-dimensional case for instance. Therefore the solution of homogeneous dampingwave equation in direct time-domain is obtained.Thirdly, based on the hypothesis of point charge source, the analytical formulae of directtime-domain for transient electromagnetic field are given in homogeneous half space throughproper simplification, and the formulae of indirect time-domain about electric dipoleapproximation are summarized on the x axis and the y axis. On this basis, the expressions ofsquare loop source and circle loop source under the hypotheses of two sources for transientelectric field are gotten in time-domain on the x axis and the y axis in homogeneous halfspace.Finally, in the homogeneous half space, transient electric field in time-domain under thehypotheses of point charge and electric dipole are compared on the x axis and the y axis. Andthere is detailed numerical analysis for transient electric field of square loop source and circleloop source under the hypotheses of two sources on the x axis and the y axis.Transient electric field values generated by square loop source under the hypotheses oftwo sources are similar so that they are equivalent for the far-source zone on the x axis and the y axis in homogeneous half space. However, for the near-source zone, the difference ofresults about square loop source under the hypotheses of point charge and electric dipole isgreater, and the difference between point charge and electric dipole can not be ignored. Forcircle loop source, the conclusion is similar. Therefore, especially in the near-source zone, thetheory about the calculation of large scale real source based on the dipole source can not meetthe needs of detection of high-precision. And based on the hypothesis of point charge source,the analytical formulae of direct time-domain can provide a theoretical basis for the detectionof the whole source zone and high-precision in the transient electromagnetic field.